I agree with everything you said. I just started a channel to derive and explain concepts and theorems of math. But i really wanted to ask you what the name of those books you talk about are called b/c they sound like the perfect tool i need. As well you say that you are a college professor, Ive though about being a college math professor at one of the upper universities like MIT or cal tech. Hows the salary is what i really want to ask. Please reply thank you.
@themrmexico9 The books are the Everyday Math series. The Singapore math series is a good one also. I don't know the salaries at MIT or Cal Tech. I'm sure they are better than at most universities, but still aren't why anyone does what we do. If you can be a math professor at MIT or Cal Tech you could make much more money doing something else. My guess would be near $100,000. Very expensive towns for both schools.
@mozdonny I'm not sure I follow your question. Listeners? Do you mean students? We are, of course, talking about little kids here. This is a debate about elementary school texts. So, yes, this is presuming they are learning math from the beginning.
But the fact is that 50% of students, when they get to college, still do not know "high school" math (or maths to the British folks). So, yeah, I'd say the level of understanding is pretty low.
@mozdonny As far as I know, listeners equals college students so yeah.
I agree with you anyhow, in terms of the robotic way of mathematics education, it confuses most people later on their lives, (if they get to a Bsc instead of Ba ofc.).
Me personally, had to learn maths the self-taught way, took me about 1 month to understand the basics of arithmetics, algebra, aggregation theory etc. from one book. (went for a mechanical engineer Bsc.)
Maths seems something mysterious for most people.
I have to agree with you. I never got that understanding in grade, mid, or high school & by college, its to late, they are never going back. I struggled in college to even pass algebra. It took me 4 attempts & nearly ended my college career. Geometry was easy, I even enjoyed it because I had, as my dad put it, a feel for it. I eventually became a forensic psych & had a 3.8 GPA in grad school so I am reasonably bright but not truly understanding the math closed many possible career paths.
@jamesblackburnlynch I just stumbled on it. All the basic stuff is no problem but, beyond basic algebra I never got it. I can figure the answer but not the efficient way. My dad was a prof at Air Force Academy and that just made him nuts. I have no desire to go back because any daily math is no prob and more complicated stuff I can find the answer. (call dad) Joke. My career doesn't require advanced math but had I really understood school would have been easier & who knows, I may have loved it
@jamesblackburnlynch I just stumbled on it. All the basic stuff is no problem but, beyond basic algebra I never got it. I can figure the answer but not the efficient way. My dad was a prof at Air Force Academy and that just made him nuts. I have no desire to go back because any daily math is no prob and more complicated stuff I can find the answer. (call dad) Joke. My career doesn't require advanced math but had I really understood school would have been easier & who knows, I may have loved it
@jamesblackburnlynch Cont: Not to mention, if kids are just memorizing formulas, that is all they are doing. They are not learning problem solving skills. It is kind of the difference between remembering something & learning how to think. If you continue into college there are other opportunities to learn how to think but if you don't go beyond HS every opportunity to learn how to think is important. I often see that in younger patients. They're very smart but lack general problem solving skills
@dylanparker72 One of the things I find interesting about her video is that she really does a nice job of explaining the other algorithms. Many people have commented on how much they liked the other ways and I think that's actually a testament to her explanation. I think one of the things that may be causing this disagreement is that she may not realize how few people understand what she clearly does.
I find the traditional methods simpler to understand and to explain to young children. If properly taught they make sense. There is no more intuition or logic to any of the newer methods I’ve seen. The reasons certain people have issues with math are many and complex. I don’t think properly teaching and explaining the traditional algorithms is one of them.
@Eirana9 Have you tried explaining the Partial Products method to them? It must be easier to explain because it IS the standard algorithm, only the carry digit isn't hidden. It's clearly represents the number it actually represents. I wonder...are we talking about the same thing? Are we talking about explaining why it works or how to do it? i can see it might be easier to explain how to do the standard algorithm (but certainly not much since they are essentially the same).
I have advanced degrees in Math and Statistics and have taught at the college level. I do not think anyone is saying you should just teach algorithms in a vacuum with no explanation as to why they work. If explained properly the traditional methods have just as much, if not more, logic than those of the other methods. I have seen this taught properly to my 4th grade son using diagrams and word problems to show their relevance.
@Eirana9 Of course many people are saying you should teach these algorithms in a vacuum. Just look at the comments on this video to see many people talking about how children are not yet capable of understanding and we need to just have them memorize.
Then go to an elementary class and ask the teachers to explain the standard method and what the "carry" is for. Some will be able, some will not.
here's the problem with TERC and Everyday Math that all have to agree to...their studies are terrible. just bad statistical analysis. as far as your point, i think students should be taught the most efficient algorithms, but the algorithms should be explained thoroughly as well. singapore math does a good job of this
@shutuprafa Can you point me to the studies you are referring to? I haven't been too impressed with anyone's attempt to study any of the books' success rates. But it's hard to do a real controlled study since people don't want you experimenting on their children.
I like the Singapore books too. If they are less controversial, I have no complaints in using them.
I am a Chinese student who got very frustrated with my country's education system(with a excessive emphasis on exams scores, and no appreciation of the real understanding of the subject ) , to me what everyone around was doing in math was but turning a bunch of notations into another bunch of notations. If you look at the grades of Chinese students, you discover a shocking low in physics, by virtues of this subjects intrinsic demand for comprehensive and insightful analysis
@poklzhou So I left for US, naively thinking that I could finally explore this fascinating world alone side people that are actually interested in the underlying mechanism of a subjects such as math and physics. I don't know if this was because I entered a inferior school, but everything----from the way the teacher present the material to our very textbooks to the learning attitudes of vast majority of my classmates suggested that they are doing the same thing my Chinese fellow is doing...
@poklzhou The most interesting thing you are saying, to me, is that you thought it would be better in the USA. Over here we are always told how much better math education is. Sounds like you thought the reverse. Perhaps everyone thinks others are doing better.
@poklzhou Students' primary (if not only) concern is to be able to solve the problem, and thus earn a decent score. Actually this should have come with no surprise once we get down to the very incentive and motivation behind students. With the presence of overt emphasis of the glamor associated with physical wealth instilled (through every thing from movies to ads) in mind, it makes sense that little people would orient their efforts towards pure intellectual pursuit.
@poklzhou I agree, but I would say that even if your goal is to be rich, you still need to actually learn. The problem is that, as you say, students are generally only interested in the grades (if that!). Years later they regret not actually focusing on the learning. Students who come back to school after being in the work world are focused on the actual learning. If only we could make it clearer to the younger folks that it is in their best interest, no matter the goal.
you are so right, sir. I find when I just memorize a formula I usually don't do as well....but when I actually understand everything, and can understand where that formula came from, I do so much better and understand!! And even more, if you actually understand what you are doing you can predict how you ca solve other problems in math since you KNOW how math works. If you just memorize formulas, you are never going to be able to make a conclusion on how to solve a problem you never saw before!!
As you pointed out - the woman in the video - firstly was successful in learning what she called the "standard" method - which is not very standard outside the American classroom and secondly wants school to be a set of algorithms that are learnt - if her weather forecasts were algorithms they would be rubbish - she has to interpret the output from the algorithms she uses.
If you think young children have a NEED for learning number tricks to keep things interesting - sure, teach them the lattice method or other number tricks. Read The Adventures of Penrose by Theoni Pappas and other quite engaging books about math. After they have their math facts down cold, get them the Life of Fred curriculum. But they must know their times tables. It's not too much to ask. It's not fun, but neither is eating spinach.
To me, these aren't "number tricks." That you feel that they are suggests to me that you aren't interested in the conceptual learning of math that I value above all the other stuff. As I said in this video, I do think kids should learn their multiplication tables. I just don't think that's priority one. The partial products algorithm, for example, isn't a number trick at all. If anything, it's the standard algorithm that is the trick, with its carry digit.
@jamesblackburnlynch The video about math education that you saw was about the curriculum, Everyday Mathematics. EM is an expensive, difficult-to-implement curriculum that frustrated parents with these alternative algorithms. If it was taught properly, it involved piles of handouts and a web site that may or may not have been helpful to parents - because THAT is who is available to help most kids with homework. This was highly impractical and a lot of schools are dropping it...not ours.
@jamesblackburnlynch Of course conceptual understanding can be taught as well. But, how long does it take to grasp that multiplication is "fast addition", such as three sets of three equals nine? Or using manipulatives to demonstrate regrouping? Kids should grasp that. With the younger kids, memorization of math facts needs to be stressed so that they can move on to higher math. It doesn't take long - five or ten minutes - to review math facts, either at home or school.
@miazagora There are many concepts to understand in the elementary curriculum. And they must be hard indeed because so many kids come to college not understanding them. And not even knowing that there are concepts behind what they've memorized (or often, mis-memorized).
Kids in 5th grade HAVE to be proficient in multiplication tables in order to be ready for fractions. They have to be proficient in doing all operations to fractions and decimals before moving on to algebra and more abstract thinking. Geeze, at least teach kids their math facts in elementary school! I get tired of teenagers behind counters of restaurants that don't know how to count back change, for Pete's sake.
I totally agree with you! I honestly did not know why we moved the second row of number (under the line) over when doing the multiplication algorithm until she showed the partial products method. She missed the point that these books are trying to teac, as you stated.
And I have to say I admire that you reply to a comments on a video you put up 4 years ago. That's pretty cool, sir :)
Try to explain to the horny high school student the usefulness of logarithms or integrals or other concepts... actually i had luck there a good math teacher+girls who are tired of stupid boys :)) perfect...
Nonetheless i am a trainer now and i completely agree with this many times i have to explain computer related stuff to people that don't find it useful and yeah...or when talking to my managers it is overkill and this is the way to explain it very good video i will check part2
@VikingNightmare Hey, im a high school student, and yes, i am pretty horny quite a bit...but i still do understand the usefullness of logarithms, integrals, derivatives, polar coordinates, etc...
@stupidfleshmonkies well i am most happy for you i am a horny computer science graduate/trainer at my company and i also understand it, i was actually talking about the stereotype not a particular person
Interesting.... I'm in college now for a completely unrelated major but I tutored a couple of adult students in college algebra and I discovered how much I love teaching people and teaching them that math can be simple if you think about the patterns, especially people who have math anxiety. The thing is, I wouldn't say I was the strongest math student in high school (how well I did depended on the teacher and how much time I had to teach myself) but I'm thinking about teaching math.
Everyday Mathematics does not teach the traditional algorithm; it also places no emphasis on the concepts. It *replaces* the traditional algorithm with two other algorithms, and drills those algorithms. The conceptual argument--that students should learn both concepts and skills--is something no-one can seriously disagree with. I urge you to look at this particular text to see the problem. (For the record: my son is a 4th grader at the U of Chicago Lab School, where this text was developed.)
@profjasonmerchantm, This is a very old video. I have several up where I detail Everyday Math itself. I have a copy and I go over parts of it. I disagree with your interpretation of the book. I feel it "goes over" all the algorithms, though it drills none of them. It's use of the calculator is also interesting.
And if you check the comments to this video you will find many people who disagree about teaching concepts. They don't believe kids this young can do it at all.
@jamesblackburnlynch I certainly hope that I didn't imply that students couldn't grasp conceptual understanding from a very early age. I know first hand that students grasp Algebraic concepts much better in Kindergarten and 1st grade than students in middle or high school. The reason being is that they have a stronger desire for symmetry and balance when they are younger and they have less fear of Algebra and mathematics. I was only stating that the facts MUST be learned at that age.
@kyop69 Well, older folks are capable of learning facts, of course. But I don't see any reason why we can't teach children to understand the concepts of multiplication and division (for example, so that they understand why 1/0 is undefined without anyone explaining it to them) and at the same time ask them to practice multiplying and dividing.
We bought Singapore math, and an Everyday Mathematics book for home use. I would review the Everyday Mathematics book with my daughter before class, and teach her from the Singapore math book. It worked wonders.
@bjalder26 I'm a big fan of the Singapore books. There is no straw man here either. Both books are excellent, in my opinion. But if you like Singapore better, than by all means you should use it. And try to convince your local schools to use it too. My impression is that parents like it better than Everyday Math. I think Everyday Math is quite a bit more demanding, but I don't think we need to go that far. If students will actually learn the material in Singapore math, they will do fine.
The college students I see are poorly prepared for college, because they enter high school unprepared and spend their high school years struggling with basic math, rather than coming to understandings of how numbers relate to each other. As someone who teaches an MCAT preparation course I can tell you that your kids will be at a significant disadvantage if all they do is Everyday Mathematics and they want to become a doctor.
@bjalder26 Yes indeed...we do agree, I think. "Coming to understandings of how numbers relate to each other" is exactly what I'm talking about. Students who memorize procedures and don't step back and think about their answers (because they've learned not to do that) add 1/2+3/5 and some how come out with something less than 1. This is not a failure in skills. This is a failure in understanding. Everyone makes mistakes. But we can see the mistake and fix it. They don't.
The point for the traditional method is that it builds lifelong skills, and builds on those skills, to help children understand the concepts. Everyday Mathematics tries to force feed concepts to children before they know anything to relate them to. More importantly, is it’s been proven as a less effective method over and over again now and Everyday Mathematics has moved to become more “traditional”.
@bjalder26 I haven't seen that proof. I've asked for it, but I can't seem to find any real studies either way. Perhaps no one is willing to "experiment" on children in this way.
As a college professor, I can tell you that the problem my students have (those that are truly deficient in math) is not that they haven't memorized skills. Many have. It's that they have no expectation of understanding. And, eventually, they get flustered.
This is just my opinion but it comes from my experience
It’s a straw man argument to say you need to choose between learning concepts vs traditional algorithms. My daughter’s school uses Everyday Mathematics, and it’s been close to useless for her. Before 3rd grade my daughter learned the multiplication table backwards and forwards, but they reinforce those skills so little in 3rd grade, that we’re reviewing them again now.
@bjalder26 I certainly don't think it's a straw man argument. One could legitimately take that position. But I do not. I'm disappointed that my video clearly has not laid out my position so that everyone hears it. My conclusion is we should do both concept-teaching and skills teaching. But that conceptual-learning should be first and foremost. But skill learning must be there too.
I believe Everyday Math always goes back, to learn things more deeply.
Why don't we teach student to write essays without teaching them vocabulary? I mean, there are dictionaries, right?
Brain research shows that the primary years are best utilized by learning facts. The brain truncates synapses at age 10 to increase efficieny, which means that facts become much more difficult to learn new facts after age 10.
I am agree with the need to have conceptual understanding while the facts are being learned. The simple truth is, though, that facts are key.
@kyop69 While I'll agree it's true that children learn to memorize facts more easily than adults, I don't agree that the evidence suggests kids cannot learn conceptually as well. There are some types of concepts that need to wait. (I don't advocate teaching algebra to small children. That's a level of abstraction that is neither necessary nor possibly ideal to teach at that age). But many do not. Again, if we teach kids that math is (only) memorization at the earliest age, we will not fix it
I caution that it is not developmentally appropriate to teach big math concepts - that drive upper level math - at a 4th/ 5th grade level. Your talk is being approached from the perspective of a college professor - not a 5th grade teacher. Basic skills in elementary lead to investigation of concepts in middle school, which leads to application in high school: culminating in college readiness. Good teaching uses logic to support skills. It cannot, however, function as the entire curriculum.
@mattybohan4 I'm not sure what level of concepts you believe I am advocating. Many others, in the past, have thought I meant far more than I do. I think what I want is reasonable. I have a five year old and a seven year old that suggest it may be so. I remember struggling with place value myself in the 2nd grade. It isn't easy. It's much harder than just memorizing the times tables, I agree. But it is more worthwhile. The struggle itself is worthwhile. As long as it can lead to success.
@jamesblackburnlynch No worries. I responded only because I HAVE taught out of the Everyday Math program. It's shortcomings are frightening IF (huge IF) the teacher sticks strictly to the curriculum and methods given in the book. Parents are unable to be of help usually because they are unfamiliar even with the way that questions are asked. Students are confused because they are asked to "think deeply" about a topic that they are still being taught.
@jamesblackburnlynch@jamesblackburnlynch Good teaching and learning, rooted in explanation always trumps simple answers. The problem is that I now teach middle school (pre-algebra/algebra) and have students that lack SO much of basic understanding (BOTH the algorithm and the reason behind it) that they get stumped mid-way through a problem. It is difficult to teach the harder concept when there is a need for basic explanation at every step of the process.
@jamesblackburnlynch@jamesblackburnlynch Once again - good math teaching cannot and should not have to teach MULTIPLE skill sets all at once... and students with lack of basic computational skills are in this category. So to reiterate - it is not that I totally disagree with you - I just specifically feel that the Everyday Math program never teaches to mastery and focuses more on the big ideas while forgetting about skill base.
@jamesblackburnlynch Good number sense exists when you are able to make the link between the two worlds. In theory, I believe that is what good math education does in elementary and middle school - it builds and informs, rather than trying to work backwards from ideas that students HAVE NEVER HEARD OF. It makes sense for us. Of course - we have done it for a long time. But Everyday Math places a lot of emphasis on an implicit assumption that students GET the big underlying math concepts and
@jamesblackburnlynch then homework sets work in this reverse method. In my classes, students do a lot of practice problems based on what we are studying - YET, they are continually quizzed on WHY we are doing what we are doing, explain what we are doing. That is to say - it ADDS to what we are doing, rather than replaces it. Everyday Math is too one-sided to truly be effective. I really wanted to share my feelings on the Everyday Math program, as the original video post describes all too
@mattybohan4 I hope it works. What I'm saying in this video, and this comes from my experience with the students that struggle with math in distinction to those that don't, is that many students have managed to succeed in math without understanding what they are doing. They just memorize and plug and chug. And that's enough to survive, it seems. But it's not enough to understand and therefore they just get worse and worse. I'm all for skill mastery. Just after concept understanding.
@jamesblackburnlynch well the difficulties that actual classroom teachers face. She is quite astute as to how the program works in a practical setting. Finally - I applaud you for teaching college - where every level of math skill comes to you - impressive as well to take on the challenge of remedial courses. I see the disparity already in 8th grade and it is a challenge. Best of luck to you!
@mattybohan4 Of course you can and should teach the big concepts at all levels... true it looks different at different levels.
My two-year old loves proto-multiplication games. He groups objects (usually dinosaurs), counts the groups, and counts the objects. He uses a meter stick to measure "how many sticks" long everything is. Unfortunately very few people understand what the "big ideas" are... and they thus have trouble understanding how they express at different levels.
I'm for the most part in agreement with you, I work with 4th and 5th grade exclusively however an in a school district where I feel the kids have great teachers but low support from home (I am an instructional assistant, not a full time teacher). I recently was challenged with creating a curriculum for an after school program. The problem I ran into is that I am trying to teach problem solving skills, but the students can't do basic arithmetic. They lose confidence, give up, and shut off. hmm...
My kids grew up with everyday math (thus, I did everyday math my second time through).
I went back for my certificate in elem. ed and TAUGHT everyday math.
Everyday math teaches THINKING math. And understanding that people THINK math in many DIFFERENT ways. It doesn't matter if it's a fast way or a round about way as long as you get the answer. Give kids the permission to THINK math ON THEIR OWN.
@geniusinthehouse I'm familiar with the math of perspective. Is that fine art? As for tennis, I can only hit right-handed. I see you can hit with both hands. The math of it...only the basic physics.
@geniusinthehouse Seriously? What about physics? And chemistry? And accounting? And engineering? And biology? And psychology? Etc. Math is too universally applicable to restrict it to only one field.
Thank your for taking the time to share your thoughts. It is appreciated. However, you, as most do on this issue, offer a false choice - that one must choose one way over the other. Why must it be reform math or traditional math? Why not a blend? My children (12 and 9) are using Everyday Math. They are not flourishing. Part of the reason is the curriculum - it is counter intuitive to learning - coupled with teachers who are not knowledgeable or enthusiastic about math.
@HorologicalRex, Did you watch the whole video? I tried to say the same thing as you did. There is no reason why we can't have both. I want students to understand, first and foremost, and then practice until mastery of skills is there too.
I do think that much of the counter-intuitiveness of EM is due to it being so different from the past. If we all had learned that way, then it wouldn't seem counter-intuitive. It's tricky to make dramatic changes like this.
@jamesblackburnlynch I'm with on understanding and mastery. Sadly, EM doesn't succeed on either front, in my experience. What is counter intuitive isn't using lattice, partial product, etc., but the utter lack of mastery, or at least a firm grasp, of the subject before moving on, is. Only through repetition is mastery of any subject or task achieved. And, sometimes, such work is laborious but it is necessary if one wants to succeed. EM's spiral method of teaching doesn't allow for this.
@HorologicalRex, But...the "spiral" method is exactly that of repetition. They aren't opposed at all. When you talk of an "utter lack of mastery" I have to wonder: of what? A mastery of addition and multiplication tables? Or of the concept of addition and multiplication? As I've said before, the second is the much more important. With it, we can get the first. But if we only do the first, we will teach students (as they do today) that math is not something to be understood, but memorized.
@jamesblackburnlynch If you are suggesting the "spiral" method is one of repetition, i.e., the material is studied and practiced until a firm grasp of the material is achieved before moving on... you couldn't be more wrong. The spiral method is, "we'll teach a, b, c, and d and we'll do each for a few days, then circle back, touch on them again, and then move onto e, f and g, circle back, etc... . And, to be more accurate, it isn't normally a, b, c and d. It is more like a, f, p, and y
@HorologicalRex, clearly the spiral method is one of repetition by your own explanation. I don't think repetition fairly gets to include "mastery." But your point is still there. If there isn't sufficient repetition until mastery (and I've said in my videos that I think that is the case) there should be. I don't think we have to be slaves to the text. Supplement with practice. Nothing wrong with that. I do it all the time. Sounds to me like you are doing this at home.
@jamesblackburnlynch Clearly, you don't understand me. For me, and as framed by the current "Math Wars," teaching by repetition is not the spiral method, but rather by the traditional "drill and kill" and "teaching by rote" manner. I don't see, however, teaching a skill for a couple of days and then dropping it for a month and revisiting it for a couple of days, as teaching by repetition. It appears, however, this is a point we will agree to disagree.
@jamesblackburnlynch Yes, I do work with both kids in the evening and we have two tutors, math majors from our local university, who help us, too. The biggest problem, more so than the curriculum, is the lack of math mastery from the educators. I suspect a skilled, motivated and enthusiastic instructor can educate and inspire most any class regardless of the textbook and curriculum being employed.
@HorologicalRex, I couldn't agree more. It just kills me that people hate math as much as they do. And see it as useless. When I tell people (doctors, dentists, anyone who is forced to ask) what I do for a living, they usually respond "Oh, I always hated math." It's so sad because when I talk to them for a while usually I find how they learned to hate math. So they weren't born with it. We just torture them in this country.
I wish that elementary schools teachers didn't hate it.
@jamesblackburnlynch Again, you offer a "this or that" choice. I, for one, don't see them as exclusive. One can be taught the tables and told the concept. I was taught that way. I agree a conceptual/theoretical understanding is important, and should be taught, but without the practical skills... you can talk the talk, but can't walk the walk. I restore watches and clocks for a living - I meet loads of people who can talk the theory, but can't sit at my bench and put it into practice.
@HorologicalRex, where do I speak of "this or that?" Perhaps you are reading that too often in other comments, because it is not in mine. I have repeatedly said I want both. I spoke of emphasis. I want the emphasis on conceptual understanding. That is followed by practice until mastery. What I observe as a professor who sees math students of all types is that few think of math that way. It is memorize first. And believe me, that doesn't work. There is simply too much to memorize.
@jamesblackburnlynch You're right. My mistake. You didn't offer a "this or that" choice, but, of the two, you'd take "this" (conceptual) over "that" (practical.) We split the atom and put men on the moon starting with memorizing first, as well unravelling the mysteries of the universe by memorizing first, so to say "it doesn't work" is fallacious. It is true memorizing first isn't fashionable now, but to say it doesn't work... world history differs. Continued.....
Your students have probably suffered through substandard teachers, maybe they don't care for math to begin with, just as some students don't care for literature and see it as something to simply "get through," or.... Society biases young minds to think math is to be feared, not cool, worse than going to the dentist... ugh... Anyway, thanks for your videos, I will continue to view them and comment. I think your students are fortunate to be under your instruction.
@HorologicalRex, Thanks for saying that. I really do care, no matter if I'm wrong or right. And I love math. And was always uncool. (With or without the math.)
I have this very problem with them. I show them every day (even in, say, Calculus II) that there is a great deal of math that they don't understand that is high school and earlier...and I demand that they understand. But it's so hard for them to change 12 years of learning. They really want to, often. But it's still not easy.
@HorologicalRex,I would indeed do just as you say. I don't however agree that that's the way it was taught. Instruction was so much more demanding in the past. Most people didn't go to college. They got much further in high school and that's both conceptually and in rote. But even then (the 40's and so on) we were struggling with these same problems. I have the letter from a professor in the 40's to prove it. Understanding was essential then too.
so you want 1st and 3rd graders to undertstand and see the beauty of math? Good luck with that. Also not everyone hates math, I like it because it is all about rules, 6xs 2 will always be 12 no matter what. How easy is that?
I think word problems should be taught more because that really trips up everyone for some reason. Even if you just write "one minus three" people freak out because its not 1 -3 lol.
@cgravier, I don't know what gave you that impression. I harbor no illusions that the average person sees math the way I do. My whole point is that "the beauty of math" isn't a reason for almost anyone to study it. That's why I advocate applications, such as they focus on in EM. For most people, math without purpose is boring and nearly unlearnable. At the same time, they hate word problems. So, I definitely agree more word problems. Until they understand that is when math is useful to them.
I gad fine teachers in 1-5 and mostly fine teachers 6-12. I slacked off a lot in my teens. Algebra was the Achilles heel for me. That started my "I'll never use this" attitude. But I see now I could use it sometimes in daily life. 90% of what I learned was in 1-5.
@usaruss, So which grade as Algebra? I would've thought that was somewhere in that 6-12 stretch. I also had a rotten experience in algebra, though I don't think the teacher was the main cause of that. She wasn't great, but I was the real problem. I didn't come back until geometry in 9th grade.
I think most people still have most of their problems with the 1st-5th grade material. That's that percents and ratios material I was referring to before.
@usaruss, I'm glad to hear it. Explains why you still understand and value math to this day. I wish everyone had had your experience.
My love and understanding of math came from my father. Without him, I would've been stuck on place value in 2nd grade and epsilon-delta proofs in calculus. I didn't run into many teachers of quality in my first 12 years of education.
The students still do not have multiplication & division down well. Volume can wait until they are better equipped for it. So your students are in the advanced sciences and you think math without formulas is easier for them? The methods I saw on Inconvenient Truth were formulas themselves and much more confusing ones at that. Than too, a couple were just guesswork. I don't claim to be a math genius. I am good in basics & and see my daughter having troubles I did not have.
@usaruss, I don't agree that those "formulas" were more confusing. If you already have a system memorized and mastered, of course, anything less familiar with seem less clear at first. But for the kid who hasn't already mastered the so-called "standard algorithm" the "partial product" method is much clearer. The act of "carrying a digit" is confusing at first. But that's because it's hiding what is really going on. The partial product method is exactly that, but without hiding it.
@usaruss, You see, this is probably where you and I disagree. We agree they should memorize multiplication tables. But I think that is a secondary goal. The first goal to get across is that math is useful and makes sense. I don't want students blindly memorizing how to do math as their early exposure. That's exactly what hurts most of the students I see even in college. They don't ask themselves: "what is this for" and "how does this work?" They just try to memorize it.
That just doesn't work for long. Eventually you can't memorize anymore. There's too much. I much prefer understanding, followed by memorizing what doesn't just come naturally. The purpose of having volume calculations early would be to have a nice, simple use of multiplication. Then students might have a clue how to answer "why do I need to know math?"
In college, kids struggle most with percents and fractions. That's crazy. It's only because they've memorized their way. Not enough.
My daughter has also brought home worksheets with volume calculations, with illustrations that don't give full info on some dimensions, such as depth. Volume calculations have no place until the basics are learned.
What real life math situations do you teach your students to prepare for?
@usaruss, Why shouldn't volume be early? It's just basic multiplication. I don't see how they could do it without all the dimensions, but I haven't seen the assignment either. Volume is a real life situation and it can help build up the uses of multiplication. And, better yet, it can begin a good discussion of units. Dimension is such a basic part of math and is often overlooked.
My students are college students. We do physics, biology, chemistry, agriculture, computer science, etc.
Well, my mother was a math teacher for many years. She agreed with me that new methods of teaching did more to confuse kids than to help them. My daughter, in 4th grade had been doing fair with math, but now is having trouble remembering her addition & subtraction. I'm going to have to make up worksheets she can understand, just to keep her from falling behind. I just found out from her teacher that Every Day Math is the book they use. She is sending a copy home for me to see.
@usaruss, The question is what is important to be able to do in math? Is the most important thing memorizing addition, subtraction, multiplication, division tables? As I've said before, I think it's important for students to memorize. But that isn't the most important part of math.
I don't know what your experience has been, but I don't think people in the past loved or understood math. People in their 40's and up often talk about how much they fear and hate math. Memorization didn't work.
Well, I'm pretty sure these students were taught by the new methods, not the old ones. No one I graduated with had that much trouble on a consistent basis.
BTW, I started giving the test because so many employees could not add up
@usaruss, Remember these are elementary books. They'd have to have encountered them when they were children. 10 years later you'll see the effects. These books are only a few years old. There do exist, of course, kids who have been taught only their last few years with this series, but it doesn't really work if you only have it for a couple of years. It's a system to build on itself.
So..why can't your employees add? Calculators. Social passing. Helicopter parents. And much more.
I was hiring people to work in a mall video arcade. They had to keep up with $100 in a cash box. Took in bags or jars of mixed coins from kids and gave them out quarters or tokens in the right amount. Sometimes helped me do collections from the games. Yes, it was rather important to be able to count change. It may also be important if they buy something and are shortchanged by a clerk. If they can't count change, they won't know they were shortchanged.
@usaruss, As I said, I'm not for it, but if everything is done electronically, they can be guaranteed not to be short-changed. Well...the thing is...if people don't have number sense at all, they won't be able to see huge errors that come from typing mistakes. Back to this book...it's great at building number sense. That is, approximating. Something normal people do all the time, but is rarely taught in school. If the thing was $19.23 and they paid $20, they obviously don't get $5 back.
My nephew worked at a store with a college girl. Someone called that some
appliance had broken down & he needed a new one. Said the space was a yard wide; did they have units that would fit? Girl told him "our's aren't measured in yards, they're measured in inches". Overhearing this, he got to the phone before she could hang up and dealt with the customer. Should a college student be able to think back and forth from yards to inches, etc ? I would hope so.
@usaruss, well, yes, there are idiots everywhere. That one is pretty hysterical, actually. But it has nothing to do with this argument. These books cover all of that in detail. They insist that students think about these things and are able to understand the use of math (such as converting from yards to inches and so on) in a context like the one you described.
And yet, many people learn nothing. The solution isn't to go back to what has failed in the past. The solution is to demand more.
When should a student be able to make change back from a dollar without a calculator? Many clerks out there cannot do that. They are better with computers because they have been raised on them. I know many kids who can do anything with a computer but can't pass a simple math test, have poor reading comprehension & can't write a legible sentence..
@usaruss, What is a simple math test to you? A bunch of addition and multiplication and so on? Perhaps you are testing people today on stuff based one what you were taught. Maybe that's not so relevant anymore. Why should they be able to make change?
Personally, I think they should, as I said in the video. I think we should ask our students to learn to understand math AND to master the skills involved. But many people argue that you and I are trying to keep the slide rule alive.
If your new methods work so well, why are students who used it so weak in math? Why can HS grads not add up values of rolls or bags of coins? Why can so many not read a tape measure? Why are calculators being allowed when we did not even have them available? Why use a longer equation and draw those silly brackets which takes longer to do? The world is pushing people to work ever faster & math is being taught that requires more time than ever to do.
@usaruss, First of all, and this is obvious, as you said these methods are "new." The kids you are talking about learned math the old way. That doesn't mean these "new" ways will solve the serious, endemic problems of math in our society. But it points out the first serious problem with people complaining about these "new" methods.
If students really learned from these books, they'd be able to do all you are talking about. They know the uses of math, like tape measures.
3 minutes into this & he's still babbling without saying anything. I learned multiplication/division very well in 4th grade. We were also told why we needed it, had worksheets that gave common uses. I have worked with HS grads who can't use a tape measure, can't add up a column of figures, etc. He babbles about thinking; the formulas are to help thinking along.
@usaruss Yes, if you think math is a bunch of formulas to be memorized, any
discussion of what math is would sound like "babbling." Your contention that "formulas are to help thinking along" isn't my expierence. Have you taught many students math? My experience indicates most don't use them to help with thinking.
But it's true that HS grads today aren't as good as adding up columns of figures as people in the past have been. But they sure are better with computers.
Apparently the first portion didn't post correctly. Here is a repeat. The second part of the message appears below. I understand what you are saying about teaching them to learn however I do think memorization is a key to that. It is the foundation to build on. The Classical education model is built on this. The Grammar stage up to about 4th grade is heavy in memorization with some explanation, Our ability to memorize is greatest st these ages. The Rhetoric stage begins in 5th grade.
@billingsbg, I don't know. My experience has been that students today have never moved beyond the memorization stage. It could be that when the Classical education model was developed, the culture encouraged memorization which led to greater development. But what I see today suggests that many students who learn to memorize math never do anything but that.
Also, while young kids are great at memorizing, they are pretty clever with understanding too.
@jamesblackburnlynch True, to a point. Memorization without understanding is useless. What I am suggesting is either teachers are not teaching or textbooks are not. It could be a combination of the two. This country has moved away from the classical model of education now for several generations. My suggestion is that if we returned to this model we would product thinkers and learners and not memory robots.
@jamesblackburnlynch What you then have are teachers in class rooms that were not taught how to be thinkers and learners teaching our children. How will they do this? The same way they were taught. The Classical method goes back to ancient Rome and was how the great true thinkers were taught. It was the model used for education in this country as well until Horace Mann and others decided that not everyone should be a thinker. I can send you some interesting links.
@billingsbg, It's certainly true that many of the teachers (especially in the elementary level) are folks who learned only to memorize math. Many of them (we have a class just for them) fear and hate math more than the average (which is saying something).
Several books out there are quite good. But they don't do much good if the teachers and parents don't understand or support them. Would they be happier with the classical model? Personally, I don't care what it is, as long as they think.
As you continue into the Rhetoric stage you build on the introductory explanations that were given with memorization. The Final stage, Logic, which they enter in later middle and high school years is when they should begin to challenge but only if they have been properly educated in the first two stages. If they haven't, they don't know what to challenge. This applies with all subjects.
You are right that teachers should be able to explain the "whys" in any subject. However memorization, especially at early ages is a way to store vast amounts of information for future in depth explanation. If you look at the classical education models you see this in play. In the grammar stage memorization is vital, The Rhetoric stage begins around 5th grade and builds on that memorization with the whys.
Hi James, I'm an elementary teacher who developed a simple math aid that gives concrete visuals to factors, multiples, multiplication and division-Math in Color. For elementary kids, math should be a means to understanding building construction, economics, and cooking. You're right that too many people lose sight of the core concepts. My calculus teacher only taught only formulas and drove me crazy. My Physics teacher allowed me to conduct experiments and actually understand concepts.
I don't believe in teaching multiplication tables. You can show it, and explain it, but teach the standard formulas to give them a base to grow from. As to why they need to learn math, they need to learn it to develop their minds, to sharpen their minds. Because some day they will be in a field where some knowledge of math will be useful to them, such as an accountant, builder, mechanic, or small business owner. I couldn't stand teachers who couldn't answer the question "why."
@tubeview72, I'm confused by your point of view. Your first thoughts about just "teaching" them the standard formulas but then you end talking about how you couldn't stand it when they couldn't answer "why." It seems like these two thoughts are in conflict.
Almost no student is helped by the vague argument that math will be useful some day. And if you think about it, with your example careers it's clear that most students won't ever need math. Mechanic? Really?
My point was I couldn't stand teachers who couldn't explain why we need to learn math. Not the why as to how we got the answer, they taught that. Limited space on letters. Mechanics do math when they review customer bills and count change. Not the toughest math, but they need to know it. I have friends who are mechanics and they are sharp with numbers. I have limited space so my arguement is vague. We don't know what these students will be, but many will end up needing math in some way.
Have you had a chance to look at the regents exams for New York State? That is where I teach. The authors of these exams have tried to address the problem of memorization of formulas and methods by making the problems more application-based. The results, so far, have been horrendous. The curve on the Integrated Algebra 1 exam is so steep that a raw score of 34% is passing. The curriculum itself is too dense and not enough focus is given to mastering basic skills such as solving equations.
@AgaMbadi, if this is so (and it may well be) then we need to fix that. As I'm trying to say in this video we need both of them. Understanding and skill mastery. With understanding, the practicing of the skills can happen outside of the class. But if we only practice the skills, the understanding will not come. More importantly, we need to make students understand that understanding is an expectation by including it in evaluating them. If tests are all memorization, then we fail.
sine, cosine, and tangent are built before they learn that there is a direct relationship between the ratios of the sides of a triangle and the angles that form them? I don't think that such an approach is even logical given that you would have to teach them about infinite series first. I hear where you are coming from. Theory cannot be replaced by facts and algorithms and the two must be blended together seemlessly in order for the students to make connections. However, kids' basic skills
@AgaMbadi, I don't understand your point about sine and infinite series. Why would we have to teach them infinite series to talk about sine? Are you talking about Taylor Series? If so, I have no idea why that is a necessity to talk about the trig functions.
@jamesblackburnlynch I made this point because of the ways in which one can express the ratios as infinite series, (and in many other ways as well) to gain a deeper understanding of why and how the ratios themselves correspond to particular angle measurements. Students are often frustrated by the fact that their calculators "magically" convert the side ratios into angle measurements and vice-versa without understanding the algorithms that the calculator uses to determine such calculations.
@AgaMbadi, So you mean, for example, when we take sin^-1 (3/5) or the like? That's the only way I can understand a calculator "converting" ratio of sides into angles.
Do you really encounter students wondering what algorithm the calculator used to find an approximate answer? Do you find them wondering the same thing about how the calculator came up with the square root of 7?
I would much prefer to just draw a picture and leave the infinite series approximation for Numerical Analysis.
@jamesblackburnlynch Yes, my students are very inquisitive about how the calculator produces such results for the trig functions. I remember learning about square roots as a student first by the method of interpolation, which is left out of our curriculum because, once again, "caculators can do that for you". I insist that my students first learn about roots by this method using the calculator to assist them only for the sake of saving time.
(cont.) This further masks the problems that these new texts have created. There is a point in higher level studies of mathematics where the ability to perform simple calculations quickly and efficiently becomes necessary in order to more readily comprehend certain concepts. Sometimes, I feel, it is better to learn that something is true before you learn why it is true. Trigonometric ratios are another good example of this. Do students really have to learn how the trigonometric functions
@AgaMbadi, Are you talking about this particular text book? Have you worked with it? I have them and they don't use calculators the way you describe. They use them very cleverly to investigate and help understanding of mathematics. There do exist books and teachers who advocate whole-heartedly caculator use. This book isn't one of them. If it were, I would not like it.
No calculators. Until you can do it yourself and just don't feel like it. But you could if you had the time.
(cont.) they must be able to quickly "see" in their head the possible factors of 24. If they must rely on a calculator to come up with a pair of numbers that multiply to be 24 and combine to be 5. They are going to have a much more difficult time factoring the expression. As a result of this dilemma, the new textbooks teach students to use a graphing calculator to simply look at the parabolic graph's roots, (which can be spotted only because they are real and rational),
@AgaMbadi, It's not clear to me if you have missed my point of view or not. Are you clear that in the end of these videos I advocate memorization of times tables? I'm not for calculator use. I'm trying to make the point that we need both conceptual understanding and skill mastery. But we must have conceptual understanding as the first and foremost goal. Otherwise we get students who have memorized their way (badly) through math education. With not expectation of math making sense.
@jamesblackburnlynch Great to hear that. Students definitely need to understand why arithmetic operations produce the answers that they do, I just feel that rote methods of learning times tables and pure mental math have become so villified, that primary school teachers refuse to give students the time to master these basic concepts at their own pace. There is a fear prevalent amongst educators at the K-12 level that all students must remain on the same "track" because of Inclusion.
@AgaMbadi, I actually haven't really had that experience. The elementary school teachers I've encountered (through my children and my experiences investigating this stuff) are often rote learners themselves. And the biggest problem with these books is that most of the teachers neither understand it nor believe in it. They want to teach rotely. And they do. They just teach this stuff rotely.
It may be they've been told not to do it, but I've found many who undermind all of this work.
I have taught at both levels, and I can tell you that the greatest difficulties arise when students begin to enter high school. A great example that I like to use to illustrate the flaws inherent in allowing students to become dependent upon calculators for basic arithmetic is the topic of solving quadratic equations. When teaching introductory algebra, the memorization of basic multiplication tables becomes indispensable. When I ask students to factor an expression such as x^2 + 5x - 24
As a college professor, I must first ask you if you have ever had the task put before you of teaching introductory algebra, geometry, or trigonometry to middle school and high school students. Without this perspective, it may be difficult for you to appreciate the frustrations inherent in trying to teach these subjects to increasingly diverse groups of students, many of whom have become hopelessly dependent on calculators for the simplest of arithmetic tasks.
@AgaMbadi, Nope. This sabbatical I'm going to go into the HS and middle-schools to at least observe it. My mother-in-law is a high school math teacher and I've hired many of them. They tell me all sorts of scary stories. (Particularly about "social passing.") I would like to see for myself.
I agree with you that the underlying ideas are key to understanding math. Investigations does that. However, the next step has to be efficient application of those ideas. Investigations doesn't get there. I draw an analogy to learning derivatives in college. We learned the concept. We spent a few weeks computing derivatives by taking the limit. After a few weeks, the teacher introduced "the short cuts", e.g., f(x) = x^n then df(x)/dx = n*x^(n-1), and so on. These programs never get to...
@EvansBurgess, Is there more to your comment? Or was the ellipsis all you needed? I agree after conceptual understanding is worked on applications must be done as well. Or, better yet, they are done in tandem. Those books do exactly that. She complained about the section of the book that did this. It's the "atlas" which is full of good applications of all sorts of math (multiplication, division, fractions, statistics).
By the way, the short cuts are fun, but really...what is the point?
Her video was biased. I learned my times tables through 15s but i was STILL horrible at math. She needs to talk about the REASON these alternative books were developed.
True, parents don't know what these books are asking by "clusters" and for many kids, these alternate methods are a waste of time, as these kids may get it the traditional way.
And understanding calculators is ABSOLUTELY ESSENTIAL for college math. I went on, out of sheer refusal to admit defeat, to take college calc and phys,
PLEASE REPLY: The way you explained 1/0 was excellent. I have had worst maths teachers all my life. I am in college, but my basics are very weak. Could you please tell me some good books? Thank you.
@youngnewtonian, I'm not sure what to offer. What kind of books? What level math are you talking about? What do you want to learn? What do you want to do with it?
hi james, i totally agree with you on this topic but just fyi, multiplication is NOT repeated addition (negative numbers, fractions, and irrational numbers do not follow the idea of repeated addition) and i dont think you should be telling your students that. When i tell my college students that they go nuts, good video though.
@yomrcheng , you can watch my video on why 2^0=1 to see that I understand the idea of generalizing a common-sense definition (exponentiation is repeated multiplication) by abstract rules (b^xb^y=b^(x+y) as a defining rule). But it remains that for natural numbers, multiplication is repeated addition. And we are talking about elementary students (3rd graders and lower). We don't really need to introduce them to irrational numbers yet.
@jamesblackburnlynch , i am not questioning your math knowledge, the comment was not meant to be offensive. But if you tell elementary students that "multiplication is repeated addition" when they are introduced to fraction/negative number multiplication they will apply that same idea and will find that it doesnt hold. So, are you going to tell the students that those are exceptions to "multiplication is repeated addition?"
@yomrcheng, no offense taken. No problem. I would actually take it as a great opportunity to discuss the idea of what a fraction is. Same with negative numbers. Both sets of numbers confuse students even in college. They need to understand early on that their confusion is honest. These ideas are generalizations of common sense ideas but are themselves significantly more abstract. Yet they are still physical. Of course, I wouldn't say it like that!
....The thing is, these new algorithm "tricks," to me, only seem to distance themselves from the concept and focus on getting a right answer. Forget the tricks, use something concrete like base 10 blocks, and make the numbers and systems MEANINGFUL.
@KomodoRogue, I am all for manipulatives. Absolutely. The more concrete the better. But about the lattice method...this book, as I think I mentioned in the video, uses other methods that are MORE intuitive than the standard algorithm. These methods don't hide the methodology in the mysterious "carry" digit.
The lattice method is even more mysterious than the standard method. But...here's how the book uses it. After they've worked with the other, more intuitive methods, they are given a problem where a student uses the lattice method. Then they make them figure out what the student is doing! Now that would make them think deeply about the concept.
Your heart is in the right place and I can see why you might have misgivings with the video but I can't help but feel like you're missing the point. The lattice method, for example, only serves to make place value increasingly abstract, which is one of the most difficult concepts to grasp when learning multiplication. I agree that it's not about the process but about gaining a better understanding of mathematical concepts.... continued
A year later...and i have to say that McDermott is still the smartest voice in this discussion. I wish everyone in US would take 15 minutes and watch "An Inconvenient Truth."
I agree with everything you said. I just started a channel to derive and explain concepts and theorems of math. But i really wanted to ask you what the name of those books you talk about are called b/c they sound like the perfect tool i need. As well you say that you are a college professor, Ive though about being a college math professor at one of the upper universities like MIT or cal tech. Hows the salary is what i really want to ask. Please reply thank you.
themrmexico9 2 months ago
@themrmexico9 The books are the Everyday Math series. The Singapore math series is a good one also. I don't know the salaries at MIT or Cal Tech. I'm sure they are better than at most universities, but still aren't why anyone does what we do. If you can be a math professor at MIT or Cal Tech you could make much more money doing something else. My guess would be near $100,000. Very expensive towns for both schools.
jamesblackburnlynch 2 months ago
1 divided by 0 is 10
success465 3 months ago
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mrstevenos 4 months ago in playlist More videos from jamesblackburnlynch
Is this the level of the understanding of yankee maths listeners at such a low level?
mozdonny 5 months ago
@mozdonny I'm not sure I follow your question. Listeners? Do you mean students? We are, of course, talking about little kids here. This is a debate about elementary school texts. So, yes, this is presuming they are learning math from the beginning.
But the fact is that 50% of students, when they get to college, still do not know "high school" math (or maths to the British folks). So, yeah, I'd say the level of understanding is pretty low.
jamesblackburnlynch 5 months ago
@mozdonny As far as I know, listeners equals college students so yeah.
I agree with you anyhow, in terms of the robotic way of mathematics education, it confuses most people later on their lives, (if they get to a Bsc instead of Ba ofc.).
Me personally, had to learn maths the self-taught way, took me about 1 month to understand the basics of arithmetics, algebra, aggregation theory etc. from one book. (went for a mechanical engineer Bsc.)
Maths seems something mysterious for most people.
mozdonny 5 months ago
I have to agree with you. I never got that understanding in grade, mid, or high school & by college, its to late, they are never going back. I struggled in college to even pass algebra. It took me 4 attempts & nearly ended my college career. Geometry was easy, I even enjoyed it because I had, as my dad put it, a feel for it. I eventually became a forensic psych & had a 3.8 GPA in grad school so I am reasonably bright but not truly understanding the math closed many possible career paths.
shananagans5 5 months ago
@shananagans5 Interesting...what made you watch these videos about math education?
(By the way, it's not too late for you. If you want.)
jamesblackburnlynch 5 months ago
@jamesblackburnlynch I just stumbled on it. All the basic stuff is no problem but, beyond basic algebra I never got it. I can figure the answer but not the efficient way. My dad was a prof at Air Force Academy and that just made him nuts. I have no desire to go back because any daily math is no prob and more complicated stuff I can find the answer. (call dad) Joke. My career doesn't require advanced math but had I really understood school would have been easier & who knows, I may have loved it
shananagans5 5 months ago
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@jamesblackburnlynch I just stumbled on it. All the basic stuff is no problem but, beyond basic algebra I never got it. I can figure the answer but not the efficient way. My dad was a prof at Air Force Academy and that just made him nuts. I have no desire to go back because any daily math is no prob and more complicated stuff I can find the answer. (call dad) Joke. My career doesn't require advanced math but had I really understood school would have been easier & who knows, I may have loved it
shananagans5 5 months ago
@jamesblackburnlynch Cont: Not to mention, if kids are just memorizing formulas, that is all they are doing. They are not learning problem solving skills. It is kind of the difference between remembering something & learning how to think. If you continue into college there are other opportunities to learn how to think but if you don't go beyond HS every opportunity to learn how to think is important. I often see that in younger patients. They're very smart but lack general problem solving skills
shananagans5 5 months ago
@dylanparker72 Thanks for the kind words. I'm still here. I still love youtube.
jamesblackburnlynch 5 months ago
@dylanparker72 One of the things I find interesting about her video is that she really does a nice job of explaining the other algorithms. Many people have commented on how much they liked the other ways and I think that's actually a testament to her explanation. I think one of the things that may be causing this disagreement is that she may not realize how few people understand what she clearly does.
jamesblackburnlynch 5 months ago
I find the traditional methods simpler to understand and to explain to young children. If properly taught they make sense. There is no more intuition or logic to any of the newer methods I’ve seen. The reasons certain people have issues with math are many and complex. I don’t think properly teaching and explaining the traditional algorithms is one of them.
Eirana9 5 months ago
@Eirana9 Have you tried explaining the Partial Products method to them? It must be easier to explain because it IS the standard algorithm, only the carry digit isn't hidden. It's clearly represents the number it actually represents. I wonder...are we talking about the same thing? Are we talking about explaining why it works or how to do it? i can see it might be easier to explain how to do the standard algorithm (but certainly not much since they are essentially the same).
jamesblackburnlynch 5 months ago
I have advanced degrees in Math and Statistics and have taught at the college level. I do not think anyone is saying you should just teach algorithms in a vacuum with no explanation as to why they work. If explained properly the traditional methods have just as much, if not more, logic than those of the other methods. I have seen this taught properly to my 4th grade son using diagrams and word problems to show their relevance.
Eirana9 5 months ago in playlist More videos from jamesblackburnlynch
@Eirana9 Of course many people are saying you should teach these algorithms in a vacuum. Just look at the comments on this video to see many people talking about how children are not yet capable of understanding and we need to just have them memorize.
Then go to an elementary class and ask the teachers to explain the standard method and what the "carry" is for. Some will be able, some will not.
jamesblackburnlynch 5 months ago
here's the problem with TERC and Everyday Math that all have to agree to...their studies are terrible. just bad statistical analysis. as far as your point, i think students should be taught the most efficient algorithms, but the algorithms should be explained thoroughly as well. singapore math does a good job of this
shutuprafa 7 months ago
@shutuprafa Can you point me to the studies you are referring to? I haven't been too impressed with anyone's attempt to study any of the books' success rates. But it's hard to do a real controlled study since people don't want you experimenting on their children.
I like the Singapore books too. If they are less controversial, I have no complaints in using them.
jamesblackburnlynch 7 months ago
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bluelaurie32 9 months ago
I sure wish I'd seen your video response before I crafted my response to her video. Thanks for your efforts :)
bluelaurie32 9 months ago
I am a Chinese student who got very frustrated with my country's education system(with a excessive emphasis on exams scores, and no appreciation of the real understanding of the subject ) , to me what everyone around was doing in math was but turning a bunch of notations into another bunch of notations. If you look at the grades of Chinese students, you discover a shocking low in physics, by virtues of this subjects intrinsic demand for comprehensive and insightful analysis
poklzhou 9 months ago
@poklzhou So I left for US, naively thinking that I could finally explore this fascinating world alone side people that are actually interested in the underlying mechanism of a subjects such as math and physics. I don't know if this was because I entered a inferior school, but everything----from the way the teacher present the material to our very textbooks to the learning attitudes of vast majority of my classmates suggested that they are doing the same thing my Chinese fellow is doing...
poklzhou 9 months ago
@poklzhou The most interesting thing you are saying, to me, is that you thought it would be better in the USA. Over here we are always told how much better math education is. Sounds like you thought the reverse. Perhaps everyone thinks others are doing better.
jamesblackburnlynch 9 months ago
@poklzhou Students' primary (if not only) concern is to be able to solve the problem, and thus earn a decent score. Actually this should have come with no surprise once we get down to the very incentive and motivation behind students. With the presence of overt emphasis of the glamor associated with physical wealth instilled (through every thing from movies to ads) in mind, it makes sense that little people would orient their efforts towards pure intellectual pursuit.
poklzhou 9 months ago
@poklzhou I agree, but I would say that even if your goal is to be rich, you still need to actually learn. The problem is that, as you say, students are generally only interested in the grades (if that!). Years later they regret not actually focusing on the learning. Students who come back to school after being in the work world are focused on the actual learning. If only we could make it clearer to the younger folks that it is in their best interest, no matter the goal.
jamesblackburnlynch 9 months ago
you are so right, sir. I find when I just memorize a formula I usually don't do as well....but when I actually understand everything, and can understand where that formula came from, I do so much better and understand!! And even more, if you actually understand what you are doing you can predict how you ca solve other problems in math since you KNOW how math works. If you just memorize formulas, you are never going to be able to make a conclusion on how to solve a problem you never saw before!!
andreasox23 1 year ago
As you pointed out - the woman in the video - firstly was successful in learning what she called the "standard" method - which is not very standard outside the American classroom and secondly wants school to be a set of algorithms that are learnt - if her weather forecasts were algorithms they would be rubbish - she has to interpret the output from the algorithms she uses.
johncrwarner 1 year ago
If you think young children have a NEED for learning number tricks to keep things interesting - sure, teach them the lattice method or other number tricks. Read The Adventures of Penrose by Theoni Pappas and other quite engaging books about math. After they have their math facts down cold, get them the Life of Fred curriculum. But they must know their times tables. It's not too much to ask. It's not fun, but neither is eating spinach.
miazagora 1 year ago
To me, these aren't "number tricks." That you feel that they are suggests to me that you aren't interested in the conceptual learning of math that I value above all the other stuff. As I said in this video, I do think kids should learn their multiplication tables. I just don't think that's priority one. The partial products algorithm, for example, isn't a number trick at all. If anything, it's the standard algorithm that is the trick, with its carry digit.
jamesblackburnlynch 1 year ago
@jamesblackburnlynch The video about math education that you saw was about the curriculum, Everyday Mathematics. EM is an expensive, difficult-to-implement curriculum that frustrated parents with these alternative algorithms. If it was taught properly, it involved piles of handouts and a web site that may or may not have been helpful to parents - because THAT is who is available to help most kids with homework. This was highly impractical and a lot of schools are dropping it...not ours.
miazagora 1 year ago
@jamesblackburnlynch Of course conceptual understanding can be taught as well. But, how long does it take to grasp that multiplication is "fast addition", such as three sets of three equals nine? Or using manipulatives to demonstrate regrouping? Kids should grasp that. With the younger kids, memorization of math facts needs to be stressed so that they can move on to higher math. It doesn't take long - five or ten minutes - to review math facts, either at home or school.
miazagora 1 year ago
@miazagora There are many concepts to understand in the elementary curriculum. And they must be hard indeed because so many kids come to college not understanding them. And not even knowing that there are concepts behind what they've memorized (or often, mis-memorized).
jamesblackburnlynch 1 year ago
Kids in 5th grade HAVE to be proficient in multiplication tables in order to be ready for fractions. They have to be proficient in doing all operations to fractions and decimals before moving on to algebra and more abstract thinking. Geeze, at least teach kids their math facts in elementary school! I get tired of teenagers behind counters of restaurants that don't know how to count back change, for Pete's sake.
miazagora 1 year ago
I totally agree with you! I honestly did not know why we moved the second row of number (under the line) over when doing the multiplication algorithm until she showed the partial products method. She missed the point that these books are trying to teac, as you stated.
And I have to say I admire that you reply to a comments on a video you put up 4 years ago. That's pretty cool, sir :)
lifemakesmelaf 1 year ago
Try to explain to the horny high school student the usefulness of logarithms or integrals or other concepts... actually i had luck there a good math teacher+girls who are tired of stupid boys :)) perfect...
Nonetheless i am a trainer now and i completely agree with this many times i have to explain computer related stuff to people that don't find it useful and yeah...or when talking to my managers it is overkill and this is the way to explain it very good video i will check part2
Best Regards
VikingNightmare 1 year ago
@VikingNightmare Hey, im a high school student, and yes, i am pretty horny quite a bit...but i still do understand the usefullness of logarithms, integrals, derivatives, polar coordinates, etc...
stupidfleshmonkies 11 months ago
@stupidfleshmonkies well i am most happy for you i am a horny computer science graduate/trainer at my company and i also understand it, i was actually talking about the stereotype not a particular person
VikingNightmare 10 months ago
@VikingNightmare lol yeah i understand, even in my class, there are kids that ask when these things will ever be useful....
stupidfleshmonkies 10 months ago
Interesting.... I'm in college now for a completely unrelated major but I tutored a couple of adult students in college algebra and I discovered how much I love teaching people and teaching them that math can be simple if you think about the patterns, especially people who have math anxiety. The thing is, I wouldn't say I was the strongest math student in high school (how well I did depended on the teacher and how much time I had to teach myself) but I'm thinking about teaching math.
c0cc0 1 year ago
@c0cc0 Math Education majors (teaching in HS) are in HUGE demand. If you want to do that, the world will welcome you.
jamesblackburnlynch 1 year ago
Everyday Mathematics does not teach the traditional algorithm; it also places no emphasis on the concepts. It *replaces* the traditional algorithm with two other algorithms, and drills those algorithms. The conceptual argument--that students should learn both concepts and skills--is something no-one can seriously disagree with. I urge you to look at this particular text to see the problem. (For the record: my son is a 4th grader at the U of Chicago Lab School, where this text was developed.)
profjasonmerchant 1 year ago
@profjasonmerchantm, This is a very old video. I have several up where I detail Everyday Math itself. I have a copy and I go over parts of it. I disagree with your interpretation of the book. I feel it "goes over" all the algorithms, though it drills none of them. It's use of the calculator is also interesting.
And if you check the comments to this video you will find many people who disagree about teaching concepts. They don't believe kids this young can do it at all.
jamesblackburnlynch 1 year ago
@jamesblackburnlynch I certainly hope that I didn't imply that students couldn't grasp conceptual understanding from a very early age. I know first hand that students grasp Algebraic concepts much better in Kindergarten and 1st grade than students in middle or high school. The reason being is that they have a stronger desire for symmetry and balance when they are younger and they have less fear of Algebra and mathematics. I was only stating that the facts MUST be learned at that age.
kyop69 1 year ago
@kyop69 Well, older folks are capable of learning facts, of course. But I don't see any reason why we can't teach children to understand the concepts of multiplication and division (for example, so that they understand why 1/0 is undefined without anyone explaining it to them) and at the same time ask them to practice multiplying and dividing.
jamesblackburnlynch 1 year ago
We bought Singapore math, and an Everyday Mathematics book for home use. I would review the Everyday Mathematics book with my daughter before class, and teach her from the Singapore math book. It worked wonders.
bjalder26 1 year ago
@bjalder26 I'm a big fan of the Singapore books. There is no straw man here either. Both books are excellent, in my opinion. But if you like Singapore better, than by all means you should use it. And try to convince your local schools to use it too. My impression is that parents like it better than Everyday Math. I think Everyday Math is quite a bit more demanding, but I don't think we need to go that far. If students will actually learn the material in Singapore math, they will do fine.
jamesblackburnlynch 1 year ago
The college students I see are poorly prepared for college, because they enter high school unprepared and spend their high school years struggling with basic math, rather than coming to understandings of how numbers relate to each other. As someone who teaches an MCAT preparation course I can tell you that your kids will be at a significant disadvantage if all they do is Everyday Mathematics and they want to become a doctor.
bjalder26 1 year ago
@bjalder26 Yes indeed...we do agree, I think. "Coming to understandings of how numbers relate to each other" is exactly what I'm talking about. Students who memorize procedures and don't step back and think about their answers (because they've learned not to do that) add 1/2+3/5 and some how come out with something less than 1. This is not a failure in skills. This is a failure in understanding. Everyone makes mistakes. But we can see the mistake and fix it. They don't.
jamesblackburnlynch 1 year ago
The point for the traditional method is that it builds lifelong skills, and builds on those skills, to help children understand the concepts. Everyday Mathematics tries to force feed concepts to children before they know anything to relate them to. More importantly, is it’s been proven as a less effective method over and over again now and Everyday Mathematics has moved to become more “traditional”.
bjalder26 1 year ago
@bjalder26 I haven't seen that proof. I've asked for it, but I can't seem to find any real studies either way. Perhaps no one is willing to "experiment" on children in this way.
As a college professor, I can tell you that the problem my students have (those that are truly deficient in math) is not that they haven't memorized skills. Many have. It's that they have no expectation of understanding. And, eventually, they get flustered.
This is just my opinion but it comes from my experience
jamesblackburnlynch 1 year ago
It’s a straw man argument to say you need to choose between learning concepts vs traditional algorithms. My daughter’s school uses Everyday Mathematics, and it’s been close to useless for her. Before 3rd grade my daughter learned the multiplication table backwards and forwards, but they reinforce those skills so little in 3rd grade, that we’re reviewing them again now.
bjalder26 1 year ago
@bjalder26 I certainly don't think it's a straw man argument. One could legitimately take that position. But I do not. I'm disappointed that my video clearly has not laid out my position so that everyone hears it. My conclusion is we should do both concept-teaching and skills teaching. But that conceptual-learning should be first and foremost. But skill learning must be there too.
I believe Everyday Math always goes back, to learn things more deeply.
jamesblackburnlynch 1 year ago
Why don't we teach student to write essays without teaching them vocabulary? I mean, there are dictionaries, right?
Brain research shows that the primary years are best utilized by learning facts. The brain truncates synapses at age 10 to increase efficieny, which means that facts become much more difficult to learn new facts after age 10.
I am agree with the need to have conceptual understanding while the facts are being learned. The simple truth is, though, that facts are key.
kyop69 1 year ago
@kyop69 While I'll agree it's true that children learn to memorize facts more easily than adults, I don't agree that the evidence suggests kids cannot learn conceptually as well. There are some types of concepts that need to wait. (I don't advocate teaching algebra to small children. That's a level of abstraction that is neither necessary nor possibly ideal to teach at that age). But many do not. Again, if we teach kids that math is (only) memorization at the earliest age, we will not fix it
jamesblackburnlynch 1 year ago
I caution that it is not developmentally appropriate to teach big math concepts - that drive upper level math - at a 4th/ 5th grade level. Your talk is being approached from the perspective of a college professor - not a 5th grade teacher. Basic skills in elementary lead to investigation of concepts in middle school, which leads to application in high school: culminating in college readiness. Good teaching uses logic to support skills. It cannot, however, function as the entire curriculum.
mattybohan4 1 year ago 2
@mattybohan4 I'm not sure what level of concepts you believe I am advocating. Many others, in the past, have thought I meant far more than I do. I think what I want is reasonable. I have a five year old and a seven year old that suggest it may be so. I remember struggling with place value myself in the 2nd grade. It isn't easy. It's much harder than just memorizing the times tables, I agree. But it is more worthwhile. The struggle itself is worthwhile. As long as it can lead to success.
jamesblackburnlynch 1 year ago
@jamesblackburnlynch No worries. I responded only because I HAVE taught out of the Everyday Math program. It's shortcomings are frightening IF (huge IF) the teacher sticks strictly to the curriculum and methods given in the book. Parents are unable to be of help usually because they are unfamiliar even with the way that questions are asked. Students are confused because they are asked to "think deeply" about a topic that they are still being taught.
mattybohan4 1 year ago
@jamesblackburnlynch @jamesblackburnlynch Good teaching and learning, rooted in explanation always trumps simple answers. The problem is that I now teach middle school (pre-algebra/algebra) and have students that lack SO much of basic understanding (BOTH the algorithm and the reason behind it) that they get stumped mid-way through a problem. It is difficult to teach the harder concept when there is a need for basic explanation at every step of the process.
mattybohan4 1 year ago
@jamesblackburnlynch @jamesblackburnlynch Once again - good math teaching cannot and should not have to teach MULTIPLE skill sets all at once... and students with lack of basic computational skills are in this category. So to reiterate - it is not that I totally disagree with you - I just specifically feel that the Everyday Math program never teaches to mastery and focuses more on the big ideas while forgetting about skill base.
mattybohan4 1 year ago
@jamesblackburnlynch Good number sense exists when you are able to make the link between the two worlds. In theory, I believe that is what good math education does in elementary and middle school - it builds and informs, rather than trying to work backwards from ideas that students HAVE NEVER HEARD OF. It makes sense for us. Of course - we have done it for a long time. But Everyday Math places a lot of emphasis on an implicit assumption that students GET the big underlying math concepts and
mattybohan4 1 year ago
@jamesblackburnlynch then homework sets work in this reverse method. In my classes, students do a lot of practice problems based on what we are studying - YET, they are continually quizzed on WHY we are doing what we are doing, explain what we are doing. That is to say - it ADDS to what we are doing, rather than replaces it. Everyday Math is too one-sided to truly be effective. I really wanted to share my feelings on the Everyday Math program, as the original video post describes all too
mattybohan4 1 year ago
@mattybohan4 I hope it works. What I'm saying in this video, and this comes from my experience with the students that struggle with math in distinction to those that don't, is that many students have managed to succeed in math without understanding what they are doing. They just memorize and plug and chug. And that's enough to survive, it seems. But it's not enough to understand and therefore they just get worse and worse. I'm all for skill mastery. Just after concept understanding.
jamesblackburnlynch 1 year ago
@jamesblackburnlynch well the difficulties that actual classroom teachers face. She is quite astute as to how the program works in a practical setting. Finally - I applaud you for teaching college - where every level of math skill comes to you - impressive as well to take on the challenge of remedial courses. I see the disparity already in 8th grade and it is a challenge. Best of luck to you!
mattybohan4 1 year ago
@mattybohan4 Of course you can and should teach the big concepts at all levels... true it looks different at different levels.
My two-year old loves proto-multiplication games. He groups objects (usually dinosaurs), counts the groups, and counts the objects. He uses a meter stick to measure "how many sticks" long everything is. Unfortunately very few people understand what the "big ideas" are... and they thus have trouble understanding how they express at different levels.
jmleblan 1 year ago
I'm for the most part in agreement with you, I work with 4th and 5th grade exclusively however an in a school district where I feel the kids have great teachers but low support from home (I am an instructional assistant, not a full time teacher). I recently was challenged with creating a curriculum for an after school program. The problem I ran into is that I am trying to teach problem solving skills, but the students can't do basic arithmetic. They lose confidence, give up, and shut off. hmm...
beatisagg 1 year ago
Yes, yes, Yes, Yes, yes, yes, Yes, Yes, Yes!
I grew up with TRADITIONAL math.
My kids grew up with everyday math (thus, I did everyday math my second time through).
I went back for my certificate in elem. ed and TAUGHT everyday math.
Everyday math teaches THINKING math. And understanding that people THINK math in many DIFFERENT ways. It doesn't matter if it's a fast way or a round about way as long as you get the answer. Give kids the permission to THINK math ON THEIR OWN.
McKennahLane 1 year ago 2
@geniusinthehouse I'm familiar with the math of perspective. Is that fine art? As for tennis, I can only hit right-handed. I see you can hit with both hands. The math of it...only the basic physics.
jamesblackburnlynch 1 year ago
@geniusinthehouse Seriously? What about physics? And chemistry? And accounting? And engineering? And biology? And psychology? Etc. Math is too universally applicable to restrict it to only one field.
jamesblackburnlynch 1 year ago
Thank your for taking the time to share your thoughts. It is appreciated. However, you, as most do on this issue, offer a false choice - that one must choose one way over the other. Why must it be reform math or traditional math? Why not a blend? My children (12 and 9) are using Everyday Math. They are not flourishing. Part of the reason is the curriculum - it is counter intuitive to learning - coupled with teachers who are not knowledgeable or enthusiastic about math.
HorologicalRex 1 year ago
@HorologicalRex, Did you watch the whole video? I tried to say the same thing as you did. There is no reason why we can't have both. I want students to understand, first and foremost, and then practice until mastery of skills is there too.
I do think that much of the counter-intuitiveness of EM is due to it being so different from the past. If we all had learned that way, then it wouldn't seem counter-intuitive. It's tricky to make dramatic changes like this.
Math in Focus is good too.
jamesblackburnlynch 1 year ago
@jamesblackburnlynch I'm with on understanding and mastery. Sadly, EM doesn't succeed on either front, in my experience. What is counter intuitive isn't using lattice, partial product, etc., but the utter lack of mastery, or at least a firm grasp, of the subject before moving on, is. Only through repetition is mastery of any subject or task achieved. And, sometimes, such work is laborious but it is necessary if one wants to succeed. EM's spiral method of teaching doesn't allow for this.
HorologicalRex 1 year ago
@HorologicalRex, But...the "spiral" method is exactly that of repetition. They aren't opposed at all. When you talk of an "utter lack of mastery" I have to wonder: of what? A mastery of addition and multiplication tables? Or of the concept of addition and multiplication? As I've said before, the second is the much more important. With it, we can get the first. But if we only do the first, we will teach students (as they do today) that math is not something to be understood, but memorized.
jamesblackburnlynch 1 year ago
@jamesblackburnlynch If you are suggesting the "spiral" method is one of repetition, i.e., the material is studied and practiced until a firm grasp of the material is achieved before moving on... you couldn't be more wrong. The spiral method is, "we'll teach a, b, c, and d and we'll do each for a few days, then circle back, touch on them again, and then move onto e, f and g, circle back, etc... . And, to be more accurate, it isn't normally a, b, c and d. It is more like a, f, p, and y
HorologicalRex 1 year ago
@HorologicalRex, clearly the spiral method is one of repetition by your own explanation. I don't think repetition fairly gets to include "mastery." But your point is still there. If there isn't sufficient repetition until mastery (and I've said in my videos that I think that is the case) there should be. I don't think we have to be slaves to the text. Supplement with practice. Nothing wrong with that. I do it all the time. Sounds to me like you are doing this at home.
jamesblackburnlynch 1 year ago
@jamesblackburnlynch Clearly, you don't understand me. For me, and as framed by the current "Math Wars," teaching by repetition is not the spiral method, but rather by the traditional "drill and kill" and "teaching by rote" manner. I don't see, however, teaching a skill for a couple of days and then dropping it for a month and revisiting it for a couple of days, as teaching by repetition. It appears, however, this is a point we will agree to disagree.
HorologicalRex 1 year ago
@jamesblackburnlynch Yes, I do work with both kids in the evening and we have two tutors, math majors from our local university, who help us, too. The biggest problem, more so than the curriculum, is the lack of math mastery from the educators. I suspect a skilled, motivated and enthusiastic instructor can educate and inspire most any class regardless of the textbook and curriculum being employed.
HorologicalRex 1 year ago
@HorologicalRex, I couldn't agree more. It just kills me that people hate math as much as they do. And see it as useless. When I tell people (doctors, dentists, anyone who is forced to ask) what I do for a living, they usually respond "Oh, I always hated math." It's so sad because when I talk to them for a while usually I find how they learned to hate math. So they weren't born with it. We just torture them in this country.
I wish that elementary schools teachers didn't hate it.
jamesblackburnlynch 1 year ago
@jamesblackburnlynch Again, you offer a "this or that" choice. I, for one, don't see them as exclusive. One can be taught the tables and told the concept. I was taught that way. I agree a conceptual/theoretical understanding is important, and should be taught, but without the practical skills... you can talk the talk, but can't walk the walk. I restore watches and clocks for a living - I meet loads of people who can talk the theory, but can't sit at my bench and put it into practice.
HorologicalRex 1 year ago
@HorologicalRex, where do I speak of "this or that?" Perhaps you are reading that too often in other comments, because it is not in mine. I have repeatedly said I want both. I spoke of emphasis. I want the emphasis on conceptual understanding. That is followed by practice until mastery. What I observe as a professor who sees math students of all types is that few think of math that way. It is memorize first. And believe me, that doesn't work. There is simply too much to memorize.
jamesblackburnlynch 1 year ago
@jamesblackburnlynch You're right. My mistake. You didn't offer a "this or that" choice, but, of the two, you'd take "this" (conceptual) over "that" (practical.) We split the atom and put men on the moon starting with memorizing first, as well unravelling the mysteries of the universe by memorizing first, so to say "it doesn't work" is fallacious. It is true memorizing first isn't fashionable now, but to say it doesn't work... world history differs. Continued.....
HorologicalRex 1 year ago
Your students have probably suffered through substandard teachers, maybe they don't care for math to begin with, just as some students don't care for literature and see it as something to simply "get through," or.... Society biases young minds to think math is to be feared, not cool, worse than going to the dentist... ugh... Anyway, thanks for your videos, I will continue to view them and comment. I think your students are fortunate to be under your instruction.
HorologicalRex 1 year ago
@HorologicalRex, Thanks for saying that. I really do care, no matter if I'm wrong or right. And I love math. And was always uncool. (With or without the math.)
I have this very problem with them. I show them every day (even in, say, Calculus II) that there is a great deal of math that they don't understand that is high school and earlier...and I demand that they understand. But it's so hard for them to change 12 years of learning. They really want to, often. But it's still not easy.
jamesblackburnlynch 1 year ago
@HorologicalRex,I would indeed do just as you say. I don't however agree that that's the way it was taught. Instruction was so much more demanding in the past. Most people didn't go to college. They got much further in high school and that's both conceptually and in rote. But even then (the 40's and so on) we were struggling with these same problems. I have the letter from a professor in the 40's to prove it. Understanding was essential then too.
jamesblackburnlynch 1 year ago
so you want 1st and 3rd graders to undertstand and see the beauty of math? Good luck with that. Also not everyone hates math, I like it because it is all about rules, 6xs 2 will always be 12 no matter what. How easy is that?
I think word problems should be taught more because that really trips up everyone for some reason. Even if you just write "one minus three" people freak out because its not 1 -3 lol.
cgravier 1 year ago
@cgravier, I don't know what gave you that impression. I harbor no illusions that the average person sees math the way I do. My whole point is that "the beauty of math" isn't a reason for almost anyone to study it. That's why I advocate applications, such as they focus on in EM. For most people, math without purpose is boring and nearly unlearnable. At the same time, they hate word problems. So, I definitely agree more word problems. Until they understand that is when math is useful to them.
jamesblackburnlynch 1 year ago
I think people should know math at least up to differential equations. That would really help. Just my 0.02$
gvsfgdf 1 year ago
@gvsfgdf, help with what? Hell, I'd be satisfied if people understood percent and ratios. Once we get there we can talk about differential equations.
jamesblackburnlynch 1 year ago
I gad fine teachers in 1-5 and mostly fine teachers 6-12. I slacked off a lot in my teens. Algebra was the Achilles heel for me. That started my "I'll never use this" attitude. But I see now I could use it sometimes in daily life. 90% of what I learned was in 1-5.
usaruss 1 year ago
@usaruss, So which grade as Algebra? I would've thought that was somewhere in that 6-12 stretch. I also had a rotten experience in algebra, though I don't think the teacher was the main cause of that. She wasn't great, but I was the real problem. I didn't come back until geometry in 9th grade.
I think most people still have most of their problems with the 1st-5th grade material. That's that percents and ratios material I was referring to before.
jamesblackburnlynch 1 year ago
But all my early teachers told why we needed it. We did tables, had word problems, etc. Mae sense to me.
usaruss 1 year ago
@usaruss, I'm glad to hear it. Explains why you still understand and value math to this day. I wish everyone had had your experience.
My love and understanding of math came from my father. Without him, I would've been stuck on place value in 2nd grade and epsilon-delta proofs in calculus. I didn't run into many teachers of quality in my first 12 years of education.
jamesblackburnlynch 1 year ago
The students still do not have multiplication & division down well. Volume can wait until they are better equipped for it. So your students are in the advanced sciences and you think math without formulas is easier for them? The methods I saw on Inconvenient Truth were formulas themselves and much more confusing ones at that. Than too, a couple were just guesswork. I don't claim to be a math genius. I am good in basics & and see my daughter having troubles I did not have.
usaruss 1 year ago
@usaruss, I don't agree that those "formulas" were more confusing. If you already have a system memorized and mastered, of course, anything less familiar with seem less clear at first. But for the kid who hasn't already mastered the so-called "standard algorithm" the "partial product" method is much clearer. The act of "carrying a digit" is confusing at first. But that's because it's hiding what is really going on. The partial product method is exactly that, but without hiding it.
jamesblackburnlynch 1 year ago
@usaruss, You see, this is probably where you and I disagree. We agree they should memorize multiplication tables. But I think that is a secondary goal. The first goal to get across is that math is useful and makes sense. I don't want students blindly memorizing how to do math as their early exposure. That's exactly what hurts most of the students I see even in college. They don't ask themselves: "what is this for" and "how does this work?" They just try to memorize it.
jamesblackburnlynch 1 year ago
That just doesn't work for long. Eventually you can't memorize anymore. There's too much. I much prefer understanding, followed by memorizing what doesn't just come naturally. The purpose of having volume calculations early would be to have a nice, simple use of multiplication. Then students might have a clue how to answer "why do I need to know math?"
In college, kids struggle most with percents and fractions. That's crazy. It's only because they've memorized their way. Not enough.
jamesblackburnlynch 1 year ago
My daughter has also brought home worksheets with volume calculations, with illustrations that don't give full info on some dimensions, such as depth. Volume calculations have no place until the basics are learned.
What real life math situations do you teach your students to prepare for?
usaruss 1 year ago
@usaruss, Why shouldn't volume be early? It's just basic multiplication. I don't see how they could do it without all the dimensions, but I haven't seen the assignment either. Volume is a real life situation and it can help build up the uses of multiplication. And, better yet, it can begin a good discussion of units. Dimension is such a basic part of math and is often overlooked.
My students are college students. We do physics, biology, chemistry, agriculture, computer science, etc.
jamesblackburnlynch 1 year ago
Well, my mother was a math teacher for many years. She agreed with me that new methods of teaching did more to confuse kids than to help them. My daughter, in 4th grade had been doing fair with math, but now is having trouble remembering her addition & subtraction. I'm going to have to make up worksheets she can understand, just to keep her from falling behind. I just found out from her teacher that Every Day Math is the book they use. She is sending a copy home for me to see.
usaruss 1 year ago
@usaruss, The question is what is important to be able to do in math? Is the most important thing memorizing addition, subtraction, multiplication, division tables? As I've said before, I think it's important for students to memorize. But that isn't the most important part of math.
I don't know what your experience has been, but I don't think people in the past loved or understood math. People in their 40's and up often talk about how much they fear and hate math. Memorization didn't work.
jamesblackburnlynch 1 year ago
Well, I'm pretty sure these students were taught by the new methods, not the old ones. No one I graduated with had that much trouble on a consistent basis.
BTW, I started giving the test because so many employees could not add up
the $ properly.
usaruss 1 year ago
@usaruss, Remember these are elementary books. They'd have to have encountered them when they were children. 10 years later you'll see the effects. These books are only a few years old. There do exist, of course, kids who have been taught only their last few years with this series, but it doesn't really work if you only have it for a couple of years. It's a system to build on itself.
So..why can't your employees add? Calculators. Social passing. Helicopter parents. And much more.
jamesblackburnlynch 1 year ago
I was hiring people to work in a mall video arcade. They had to keep up with $100 in a cash box. Took in bags or jars of mixed coins from kids and gave them out quarters or tokens in the right amount. Sometimes helped me do collections from the games. Yes, it was rather important to be able to count change. It may also be important if they buy something and are shortchanged by a clerk. If they can't count change, they won't know they were shortchanged.
usaruss 1 year ago
@usaruss, As I said, I'm not for it, but if everything is done electronically, they can be guaranteed not to be short-changed. Well...the thing is...if people don't have number sense at all, they won't be able to see huge errors that come from typing mistakes. Back to this book...it's great at building number sense. That is, approximating. Something normal people do all the time, but is rarely taught in school. If the thing was $19.23 and they paid $20, they obviously don't get $5 back.
jamesblackburnlynch 1 year ago
My nephew worked at a store with a college girl. Someone called that some
appliance had broken down & he needed a new one. Said the space was a yard wide; did they have units that would fit? Girl told him "our's aren't measured in yards, they're measured in inches". Overhearing this, he got to the phone before she could hang up and dealt with the customer. Should a college student be able to think back and forth from yards to inches, etc ? I would hope so.
usaruss 1 year ago
@usaruss, well, yes, there are idiots everywhere. That one is pretty hysterical, actually. But it has nothing to do with this argument. These books cover all of that in detail. They insist that students think about these things and are able to understand the use of math (such as converting from yards to inches and so on) in a context like the one you described.
And yet, many people learn nothing. The solution isn't to go back to what has failed in the past. The solution is to demand more.
jamesblackburnlynch 1 year ago
When should a student be able to make change back from a dollar without a calculator? Many clerks out there cannot do that. They are better with computers because they have been raised on them. I know many kids who can do anything with a computer but can't pass a simple math test, have poor reading comprehension & can't write a legible sentence..
usaruss 1 year ago
@usaruss, What is a simple math test to you? A bunch of addition and multiplication and so on? Perhaps you are testing people today on stuff based one what you were taught. Maybe that's not so relevant anymore. Why should they be able to make change?
Personally, I think they should, as I said in the video. I think we should ask our students to learn to understand math AND to master the skills involved. But many people argue that you and I are trying to keep the slide rule alive.
jamesblackburnlynch 1 year ago
If your new methods work so well, why are students who used it so weak in math? Why can HS grads not add up values of rolls or bags of coins? Why can so many not read a tape measure? Why are calculators being allowed when we did not even have them available? Why use a longer equation and draw those silly brackets which takes longer to do? The world is pushing people to work ever faster & math is being taught that requires more time than ever to do.
usaruss 1 year ago
@usaruss, First of all, and this is obvious, as you said these methods are "new." The kids you are talking about learned math the old way. That doesn't mean these "new" ways will solve the serious, endemic problems of math in our society. But it points out the first serious problem with people complaining about these "new" methods.
If students really learned from these books, they'd be able to do all you are talking about. They know the uses of math, like tape measures.
jamesblackburnlynch 1 year ago
3 minutes into this & he's still babbling without saying anything. I learned multiplication/division very well in 4th grade. We were also told why we needed it, had worksheets that gave common uses. I have worked with HS grads who can't use a tape measure, can't add up a column of figures, etc. He babbles about thinking; the formulas are to help thinking along.
usaruss 1 year ago
@usaruss Yes, if you think math is a bunch of formulas to be memorized, any
discussion of what math is would sound like "babbling." Your contention that "formulas are to help thinking along" isn't my expierence. Have you taught many students math? My experience indicates most don't use them to help with thinking.
But it's true that HS grads today aren't as good as adding up columns of figures as people in the past have been. But they sure are better with computers.
jamesblackburnlynch 1 year ago
Apparently the first portion didn't post correctly. Here is a repeat. The second part of the message appears below. I understand what you are saying about teaching them to learn however I do think memorization is a key to that. It is the foundation to build on. The Classical education model is built on this. The Grammar stage up to about 4th grade is heavy in memorization with some explanation, Our ability to memorize is greatest st these ages. The Rhetoric stage begins in 5th grade.
billingsbg 1 year ago
@billingsbg, I don't know. My experience has been that students today have never moved beyond the memorization stage. It could be that when the Classical education model was developed, the culture encouraged memorization which led to greater development. But what I see today suggests that many students who learn to memorize math never do anything but that.
Also, while young kids are great at memorizing, they are pretty clever with understanding too.
jamesblackburnlynch 1 year ago
@jamesblackburnlynch True, to a point. Memorization without understanding is useless. What I am suggesting is either teachers are not teaching or textbooks are not. It could be a combination of the two. This country has moved away from the classical model of education now for several generations. My suggestion is that if we returned to this model we would product thinkers and learners and not memory robots.
billingsbg 1 year ago
@jamesblackburnlynch What you then have are teachers in class rooms that were not taught how to be thinkers and learners teaching our children. How will they do this? The same way they were taught. The Classical method goes back to ancient Rome and was how the great true thinkers were taught. It was the model used for education in this country as well until Horace Mann and others decided that not everyone should be a thinker. I can send you some interesting links.
billingsbg 1 year ago
@billingsbg, It's certainly true that many of the teachers (especially in the elementary level) are folks who learned only to memorize math. Many of them (we have a class just for them) fear and hate math more than the average (which is saying something).
Several books out there are quite good. But they don't do much good if the teachers and parents don't understand or support them. Would they be happier with the classical model? Personally, I don't care what it is, as long as they think.
jamesblackburnlynch 1 year ago
As you continue into the Rhetoric stage you build on the introductory explanations that were given with memorization. The Final stage, Logic, which they enter in later middle and high school years is when they should begin to challenge but only if they have been properly educated in the first two stages. If they haven't, they don't know what to challenge. This applies with all subjects.
billingsbg 1 year ago
You are right that teachers should be able to explain the "whys" in any subject. However memorization, especially at early ages is a way to store vast amounts of information for future in depth explanation. If you look at the classical education models you see this in play. In the grammar stage memorization is vital, The Rhetoric stage begins around 5th grade and builds on that memorization with the whys.
billingsbg 1 year ago
Hi James, I'm an elementary teacher who developed a simple math aid that gives concrete visuals to factors, multiples, multiplication and division-Math in Color. For elementary kids, math should be a means to understanding building construction, economics, and cooking. You're right that too many people lose sight of the core concepts. My calculus teacher only taught only formulas and drove me crazy. My Physics teacher allowed me to conduct experiments and actually understand concepts.
MathinColor 1 year ago
I don't believe in teaching multiplication tables. You can show it, and explain it, but teach the standard formulas to give them a base to grow from. As to why they need to learn math, they need to learn it to develop their minds, to sharpen their minds. Because some day they will be in a field where some knowledge of math will be useful to them, such as an accountant, builder, mechanic, or small business owner. I couldn't stand teachers who couldn't answer the question "why."
tubeview72 1 year ago
@tubeview72, I'm confused by your point of view. Your first thoughts about just "teaching" them the standard formulas but then you end talking about how you couldn't stand it when they couldn't answer "why." It seems like these two thoughts are in conflict.
Almost no student is helped by the vague argument that math will be useful some day. And if you think about it, with your example careers it's clear that most students won't ever need math. Mechanic? Really?
jamesblackburnlynch 1 year ago
My point was I couldn't stand teachers who couldn't explain why we need to learn math. Not the why as to how we got the answer, they taught that. Limited space on letters. Mechanics do math when they review customer bills and count change. Not the toughest math, but they need to know it. I have friends who are mechanics and they are sharp with numbers. I have limited space so my arguement is vague. We don't know what these students will be, but many will end up needing math in some way.
tubeview72 1 year ago
Have you had a chance to look at the regents exams for New York State? That is where I teach. The authors of these exams have tried to address the problem of memorization of formulas and methods by making the problems more application-based. The results, so far, have been horrendous. The curve on the Integrated Algebra 1 exam is so steep that a raw score of 34% is passing. The curriculum itself is too dense and not enough focus is given to mastering basic skills such as solving equations.
AgaMbadi 1 year ago
have really suffered as a result of honest attempts to implement many of these new methods.
AgaMbadi 1 year ago
@AgaMbadi, if this is so (and it may well be) then we need to fix that. As I'm trying to say in this video we need both of them. Understanding and skill mastery. With understanding, the practicing of the skills can happen outside of the class. But if we only practice the skills, the understanding will not come. More importantly, we need to make students understand that understanding is an expectation by including it in evaluating them. If tests are all memorization, then we fail.
jamesblackburnlynch 1 year ago
sine, cosine, and tangent are built before they learn that there is a direct relationship between the ratios of the sides of a triangle and the angles that form them? I don't think that such an approach is even logical given that you would have to teach them about infinite series first. I hear where you are coming from. Theory cannot be replaced by facts and algorithms and the two must be blended together seemlessly in order for the students to make connections. However, kids' basic skills
AgaMbadi 1 year ago
@AgaMbadi, I don't understand your point about sine and infinite series. Why would we have to teach them infinite series to talk about sine? Are you talking about Taylor Series? If so, I have no idea why that is a necessity to talk about the trig functions.
jamesblackburnlynch 1 year ago
@jamesblackburnlynch I made this point because of the ways in which one can express the ratios as infinite series, (and in many other ways as well) to gain a deeper understanding of why and how the ratios themselves correspond to particular angle measurements. Students are often frustrated by the fact that their calculators "magically" convert the side ratios into angle measurements and vice-versa without understanding the algorithms that the calculator uses to determine such calculations.
AgaMbadi 1 year ago
@AgaMbadi, So you mean, for example, when we take sin^-1 (3/5) or the like? That's the only way I can understand a calculator "converting" ratio of sides into angles.
Do you really encounter students wondering what algorithm the calculator used to find an approximate answer? Do you find them wondering the same thing about how the calculator came up with the square root of 7?
I would much prefer to just draw a picture and leave the infinite series approximation for Numerical Analysis.
jamesblackburnlynch 1 year ago
@jamesblackburnlynch Yes, my students are very inquisitive about how the calculator produces such results for the trig functions. I remember learning about square roots as a student first by the method of interpolation, which is left out of our curriculum because, once again, "caculators can do that for you". I insist that my students first learn about roots by this method using the calculator to assist them only for the sake of saving time.
AgaMbadi 1 year ago
(cont.) This further masks the problems that these new texts have created. There is a point in higher level studies of mathematics where the ability to perform simple calculations quickly and efficiently becomes necessary in order to more readily comprehend certain concepts. Sometimes, I feel, it is better to learn that something is true before you learn why it is true. Trigonometric ratios are another good example of this. Do students really have to learn how the trigonometric functions
AgaMbadi 1 year ago
@AgaMbadi, Are you talking about this particular text book? Have you worked with it? I have them and they don't use calculators the way you describe. They use them very cleverly to investigate and help understanding of mathematics. There do exist books and teachers who advocate whole-heartedly caculator use. This book isn't one of them. If it were, I would not like it.
No calculators. Until you can do it yourself and just don't feel like it. But you could if you had the time.
jamesblackburnlynch 1 year ago
(cont.) they must be able to quickly "see" in their head the possible factors of 24. If they must rely on a calculator to come up with a pair of numbers that multiply to be 24 and combine to be 5. They are going to have a much more difficult time factoring the expression. As a result of this dilemma, the new textbooks teach students to use a graphing calculator to simply look at the parabolic graph's roots, (which can be spotted only because they are real and rational),
AgaMbadi 1 year ago
@AgaMbadi, It's not clear to me if you have missed my point of view or not. Are you clear that in the end of these videos I advocate memorization of times tables? I'm not for calculator use. I'm trying to make the point that we need both conceptual understanding and skill mastery. But we must have conceptual understanding as the first and foremost goal. Otherwise we get students who have memorized their way (badly) through math education. With not expectation of math making sense.
jamesblackburnlynch 1 year ago
@jamesblackburnlynch Great to hear that. Students definitely need to understand why arithmetic operations produce the answers that they do, I just feel that rote methods of learning times tables and pure mental math have become so villified, that primary school teachers refuse to give students the time to master these basic concepts at their own pace. There is a fear prevalent amongst educators at the K-12 level that all students must remain on the same "track" because of Inclusion.
AgaMbadi 1 year ago
@AgaMbadi, I actually haven't really had that experience. The elementary school teachers I've encountered (through my children and my experiences investigating this stuff) are often rote learners themselves. And the biggest problem with these books is that most of the teachers neither understand it nor believe in it. They want to teach rotely. And they do. They just teach this stuff rotely.
It may be they've been told not to do it, but I've found many who undermind all of this work.
jamesblackburnlynch 1 year ago
I have taught at both levels, and I can tell you that the greatest difficulties arise when students begin to enter high school. A great example that I like to use to illustrate the flaws inherent in allowing students to become dependent upon calculators for basic arithmetic is the topic of solving quadratic equations. When teaching introductory algebra, the memorization of basic multiplication tables becomes indispensable. When I ask students to factor an expression such as x^2 + 5x - 24
AgaMbadi 1 year ago
As a college professor, I must first ask you if you have ever had the task put before you of teaching introductory algebra, geometry, or trigonometry to middle school and high school students. Without this perspective, it may be difficult for you to appreciate the frustrations inherent in trying to teach these subjects to increasingly diverse groups of students, many of whom have become hopelessly dependent on calculators for the simplest of arithmetic tasks.
AgaMbadi 1 year ago
@AgaMbadi, Nope. This sabbatical I'm going to go into the HS and middle-schools to at least observe it. My mother-in-law is a high school math teacher and I've hired many of them. They tell me all sorts of scary stories. (Particularly about "social passing.") I would like to see for myself.
jamesblackburnlynch 1 year ago
why play trick with math thats the problem
lovelynann 1 year ago
I agree with you that the underlying ideas are key to understanding math. Investigations does that. However, the next step has to be efficient application of those ideas. Investigations doesn't get there. I draw an analogy to learning derivatives in college. We learned the concept. We spent a few weeks computing derivatives by taking the limit. After a few weeks, the teacher introduced "the short cuts", e.g., f(x) = x^n then df(x)/dx = n*x^(n-1), and so on. These programs never get to...
EvansBurgess 1 year ago
@EvansBurgess, Is there more to your comment? Or was the ellipsis all you needed? I agree after conceptual understanding is worked on applications must be done as well. Or, better yet, they are done in tandem. Those books do exactly that. She complained about the section of the book that did this. It's the "atlas" which is full of good applications of all sorts of math (multiplication, division, fractions, statistics).
By the way, the short cuts are fun, but really...what is the point?
jamesblackburnlynch 1 year ago
Her video was biased. I learned my times tables through 15s but i was STILL horrible at math. She needs to talk about the REASON these alternative books were developed.
True, parents don't know what these books are asking by "clusters" and for many kids, these alternate methods are a waste of time, as these kids may get it the traditional way.
And understanding calculators is ABSOLUTELY ESSENTIAL for college math. I went on, out of sheer refusal to admit defeat, to take college calc and phys,
MethodiousMind 1 year ago
THANK YOU THANK YOU THANK YOU! You said it much better than I could.
diomedes39 1 year ago
PLEASE REPLY: The way you explained 1/0 was excellent. I have had worst maths teachers all my life. I am in college, but my basics are very weak. Could you please tell me some good books? Thank you.
youngnewtonian 1 year ago
@youngnewtonian, I'm not sure what to offer. What kind of books? What level math are you talking about? What do you want to learn? What do you want to do with it?
jamesblackburnlynch 1 year ago
hi james, i totally agree with you on this topic but just fyi, multiplication is NOT repeated addition (negative numbers, fractions, and irrational numbers do not follow the idea of repeated addition) and i dont think you should be telling your students that. When i tell my college students that they go nuts, good video though.
yomrcheng 1 year ago
@yomrcheng , you can watch my video on why 2^0=1 to see that I understand the idea of generalizing a common-sense definition (exponentiation is repeated multiplication) by abstract rules (b^xb^y=b^(x+y) as a defining rule). But it remains that for natural numbers, multiplication is repeated addition. And we are talking about elementary students (3rd graders and lower). We don't really need to introduce them to irrational numbers yet.
jamesblackburnlynch 1 year ago
@jamesblackburnlynch , i am not questioning your math knowledge, the comment was not meant to be offensive. But if you tell elementary students that "multiplication is repeated addition" when they are introduced to fraction/negative number multiplication they will apply that same idea and will find that it doesnt hold. So, are you going to tell the students that those are exceptions to "multiplication is repeated addition?"
yomrcheng 1 year ago
@yomrcheng, no offense taken. No problem. I would actually take it as a great opportunity to discuss the idea of what a fraction is. Same with negative numbers. Both sets of numbers confuse students even in college. They need to understand early on that their confusion is honest. These ideas are generalizations of common sense ideas but are themselves significantly more abstract. Yet they are still physical. Of course, I wouldn't say it like that!
jamesblackburnlynch 1 year ago
....The thing is, these new algorithm "tricks," to me, only seem to distance themselves from the concept and focus on getting a right answer. Forget the tricks, use something concrete like base 10 blocks, and make the numbers and systems MEANINGFUL.
KomodoRogue 1 year ago 2
@KomodoRogue, I am all for manipulatives. Absolutely. The more concrete the better. But about the lattice method...this book, as I think I mentioned in the video, uses other methods that are MORE intuitive than the standard algorithm. These methods don't hide the methodology in the mysterious "carry" digit.
jamesblackburnlynch 1 year ago
The lattice method is even more mysterious than the standard method. But...here's how the book uses it. After they've worked with the other, more intuitive methods, they are given a problem where a student uses the lattice method. Then they make them figure out what the student is doing! Now that would make them think deeply about the concept.
jamesblackburnlynch 1 year ago
Your heart is in the right place and I can see why you might have misgivings with the video but I can't help but feel like you're missing the point. The lattice method, for example, only serves to make place value increasingly abstract, which is one of the most difficult concepts to grasp when learning multiplication. I agree that it's not about the process but about gaining a better understanding of mathematical concepts.... continued
KomodoRogue 1 year ago
A year later...and i have to say that McDermott is still the smartest voice in this discussion. I wish everyone in US would take 15 minutes and watch "An Inconvenient Truth."