If you doubt it, substitute y/(1+y) for x in equation 1 and simplify. Of course, if you couldn't solve the first, you probably have no chance ........
If there is a science of possibility that helps one go from the smallest choices, to the largest, while respecting the sum of limitations, and the chance for error, then it is Mathematics. Science reveals the way choices are, but without a theory of representation, we are voiceless in a confusing world. There are deeper structures to be found, even if simple, that only deep concentration may provide. When people say mathematics is beautiful, it is not a stepchild of euphoria, it is a new sun.
Good video! Education is not something to be put in a box and forgotten, no matter which approach we use. We need to keep examining the approaches to education and the curriculum that are being used in public school classrooms. We, as taxpayers, should have some say in the way students are being taught and what standards they are expected to meet.
An international standard is the wisest course.
Of course, this video shows just one more reason that families are home schooling their students.
sleeper2345 is correct. Many of the math teachers who have been teaching for a 30 years, hate the Investigative approach. Not because it doesn't work, but because it required them to teach outside of their comfort zone. They taught the curriculum poorly so they could say, "I told you so." The old way of teaching worked...for some of the students, but not for every student! We used to be OK with 40-50% of kids failing math. But not anymore, and Investigations grabs kids and draws them in...
sleeper2345 is correct. Many of the math teachers who have been teaching for a 30 years, hate the Investigative approach. Not because it doesn't work, but because it required them to teach outside of their comfort zone. They taught the curriculum poorly so they could say, "I told you so." The old way of teaching worked...for some of the students, but not for every student! We used to be OK with 40-50% of kids failing math. But not anymore, and Investigations grabs kids and draws them in...
Outstanding video, as is the one by M J McDermott. Reform Math was a poisoned well. Trouble is, the con artists who create this stuff are now back in their dank labs, concocting Core Standards. More of the same, I'm afraid.
I'm struck by the evil parallel between Whole Word in reading and Reform Math in arithmetic. Both curricula seem to be designed not to work.
Geometric demonstration and discovery of a " geometric sacred boss " used very presumably in the construction of The Great Pyramid of Gizéh's plateau and his chance? Relation with the number "pi" (with a simple rule and / or compass) 2300 years B. Arquimedes (4600 years B.J.C.) for the farón Jufu-Keops.
sleeper2345 is typical of the thinking among math teachers who believe in this nonsense. As he says, the problem with EM is tha teachers are not teaching it properly. Well, how good can it be if the teachers can't teach it. I learned standard algorithims, earned a degree in economics and never touched a slide rule. Maybe my teachers were just good. Reasoning through problems won't work unless students first understand standard algorithims.
@tubeview72 Nice condescending remarks--attempting to marginalize my statements without support. Your comment is laughable: "Reasoning through problems won't work unless students first understand standard algorithims." So you don't reason with the standard algorithms? Where did they come from? didn't someone need to reason to invent them? Reasoning is embedded in mathematical activity. However, this is not true in US mathematics instruction, reasoning is hardly ever addressed.
@linesronda Cliff isn't worried about the evidence that supports his point of view, he just wants to share his misinformed conclusions. He assumes that all students are being taught differently than he was 30 years ago, despite the overwhelming evidence that little has changed related to math teaching in the US.
All college freshman should be on the same level of mathematical ability as Kurt Godel and Julian Schwinger. That would solve the problem wouldn't it?? :D
nothing wrong with the standards or constructivism per se -- it could be other factors (e.g. teachers, assessment, in-grained expectations etc.). but most people (teachers included) never learned how to learn by discovery themselves, so it might be better to forget about even trying. right?
@Heissenburger No one is suggesting that student learn by "discovery." However, the individual in the video and the National Mathematics Panel would like to provide a distorted view of what is suggested by reform mathematics. The suggestion is that students actually think and use mathematical reasoning rather than memorize procedures. However, for most adults in the US, thinking and reasoning was not part of their school mathematics experience and they cannot help their children.
@sleeper2345 so the problem is the implementation (lack of comprehensive thinking through and ground preparation), rather than the idea itself, right?
@Heissenburger As with most ideas, they are distorted and difficult to realize. This is certainly true in school where there are no mechanisms to support implementation of research findings. Instruction continues as it did 30+ years ago.
Unfortunately Cliff seems to have limited understanding of research. You can't test college students on their performance and blame the poor results on particular instruction unless you know the students actually experienced it! Cliff: You forgot to study what math the students experienced in high school. Perhaps it was the traditional math you so dearly love! Try supporting you argument with real evidence next time!
i am not being prejudiced, nor am i that type of a person, so don't take this the wrong way, it is my experience. i used to cheat on my math tests all through school or i never would have graduated. i am nearly 60 years old now, for some reason the oriental students were always every one of them, excellent in math. why? is it the style of way they were taught the math from the begiinning? obviously, they were learning the right way, it isn't an ethnic thing, but what is the method they used?
As an old bastard, I attest that modern math teaching dramatically reduced understanding & increased incomprehensibility. Our kids had trouble with math until my wife (also an engineer) sat down with them every night & practiced from old text books.
Kids today are not stupid. They get bored and distracted easily, especially in large classes with dreary teachers and their "modern" methods.
Math is simple; but only when presented well.
Those who control schools do not want educated citizens.
I think your faulty generalizations from a small "n" are quite dangerous. Such "proof" is not valid mathematically or scientifically.
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I do agree that kids are much smarter than we think, too bad the math teaching of yore does not encourage thinking.
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Also, math is not simple, it involves some very difficult ideas. Our number system itself is a very complex system that was developed over 100s of years, hardly simple.
Simple Mathematics It began in 1907 when Minkowski tried to understand SRT using 4D space Nobody knows what Minkowski negative space really is. Trying to understand it, Kaluza in 1921 created 5D space Nobody knows what it is too So If we don't know what 1+1 = 2 how can we know what 5 + 4 = 9 ? And if we don't know what is 4-D how can we understand 10-D, 11-D ? Israel Sadovnik Socratus
I can really appreciate your perspective, it is very common among university professors, and it is from a perspective that understands certain things that the typical parent, or pre-college math educator can't see,
They also have a perspective that includes a part of the story totally unseen by Cliff.
Take it from a person 10 years in a variety of settings in secondary, and 10 years teaching undergrad courses at a University Level, neither side sees the picture clearly.
Note that this is just a misleading video with someone "searching" for conclusions. Cliff doesn't know what instruction students receive, but tries to draw conclusions anyway. I suggest actually asking students how they were taught math. This may be over Cliff's head.
Cliff is really on to something though with regard to the curricula and the Textbook companies he's just a little to naive in believing that the ITBS is any better than the WASL, it's still totally created by teachers that go "by the book" out of the fear of not being enough. Where's the mathematics indeed. That's the whole problem, all memorized process, no grasp of concepts. AT ALL!
This video is VERY well named though. Although it should really be called THE typical University Veiw,
I don't know what method Iowa Test of Basic Skills uses for their math proficiency, but the state has gone to these inefficient models for teaching math. Check it out at Iowa Core Curriculum - Home
Definitely a worldwide problem! Same problem exists in Ireland. The key is teaching the component skills (or buidling blocks) to fluency (accuracy plus speed). How can a child master a simple composite skill like addition if they have not been given enough practice opportunities to become fluent at reading or writing numbers! Teachers need to start changing the instructional form not necessarily the actual maths content.
In the 80's there were fewer distractions that affected me from doing my studies. But today if you don't have a phone with internet, a PS2, a PC with a gaming card, email address, facebook account, watch utube videos at least 3 times a day, download stuff from piratebay etc, etc.. then you are not considered to be normal. I too in recent years see my personal decipline decline 'cause of too many distractions. I am in the process of remedying - delisting from soclal n/w sites is just the start.
Nothing that you list is "research." These are opinion pieces without empirical support. The "new math" that you refer to is designed to support memorization of facts. However, the memorization is not meaningless, but builds on how we know students progress to having their facts memorized. See "Cognitively Guided Instruction" in a search for more on this.
All I could see are opinion pieces for the search you describe. Can you give a citation? Again, see CGI for how kids actually learn their facts without silly memorization techniques like 5, 6, 7, 8 for 7 x 8 = 56.
The information about CGI is interesting. Now let's imagine college students are using manipulatives to figure out differential equations.
I think the professor teaching the class might put a video on YouTube about his frustration over trying to teach students who do not know basic math concepts.
Saying CGI is about using manipulatives is like saying that playing chess is about moving wood around. From a particular perspective, you are right. However, children reason about facts (e.g., 5 + 6 = 11 because 5 + 5 is 10). I can understand you not wanting students to reason like this if you are opposed to mathematical rigor. Mathematics is about memorizing and not reasoning. Student use models in diff equations, (e.g., graphs). Would you rather have students who don't reason about quantities?
Do a search for "Carpenter & Moser, 1984" or "Carpenter, Fennema". See "Adding It Up" for a synthesis of research by the National Research Council. It matters very much how students learn in grades K-8 and the reasoning they use. I'm assuming that you are "for" mathematical rigor, but I'm not sure.
I am "for" mathematical understanding, specifically for my own kids. The public schools have failed them so far, not in grades, but in concepts. The schools here use "Everyday Math," and my kids are completely confused with the concepts they were learning.
Everyday Math came up in my search for Carpenter & Moser. EM states that it uses Carpenter & Moser's methodology, which I completely disagree with for middle school students.
I don't know what is meant by "Carpenter and Moser's methodology." EM has been demonstrated to help students who are struggling in math. Of course, this is complex, as the teacher must understand the purpose and goals of the curriculum. Most teachers teach as they were taught, encouraging students to practice following procedure that students do not understand. Do a search for "schoenfeld ed researcher everyday math" for an excellent study.
"EM has been demonstrated to help students who are struggling in math." Maybe, but EM turns otherwise potentially bright, motivated NORMAL students into drooling morons... mathematically speaking. Typical progressivism: drag everybody down to the lowest level instead of letting the brightest excel.
Typical misleading statement spoken in ignorance. It is traditional math that turns bright students with strong reasoning into bumbling mathematical idiots who don't trust their own reasoning. Google "parrot math" to see what traditional math does. I see it everyday with even our brightest students. They don't know why they follow the rules they do, they just do! This, to them, is math.
sleeper2345 is talking thru his/her/its hat. The Seattle schools have adopted EM; consequently, local for-fee math tutors have never had brisker business, duh.
My niece is sorely challenged by college math remedials, courtesy of the mushy Seattle math taught her. I've seen first-hand the train wreck that EM and similar makes of its victims' ability to clearly solve problems and prepare kids for higher learning. EM could not be better designed to destroy the math talent of those subjected to it.
I'll add that I spoke recently to a Seattle teacher friend, who she told me how the hated EM is *really* taught: after every EM unit, the teachers revert to 3 days' worth of traditional algorithms and math-fact teaching, once the SPS proctor-goons have left the premises.
I suggest that the reason SPS scores have not totally collapsed is due to the continued use of the methods that sleeper2345 sneers at -- and the common hiring of Kumon et al by desperate parents anxious for their kids' futures.
bertwindon: Please try to engage in an intellectual argument over the topic rather than resorting to name-calling. I pointed out a flaw in Cliff's argument:You can't test college students on their performance and blame the poor results on particular instruction unless you know the students actually experienced it! Please support your position if you can.
@sleeper2345 So what is your explanation of the drastic decline in elementary mathematical ability of student to which "Cliff" refers. Is he a liar ? - drunk ?
I think you're describing a different video. This video has nothing to do with elementary math. I'm not sure what he's on. You'll have to ask him. Cliff doesn't teach math, he teaches atmospheric science.
These curricula have only been around for a short period of time. When did she start EM? Were the teachers properly prepared? So you're generalizing from an N of 1 to the population? Sounds like you have some difficulty wiht statistical reasoning.
That is what Mathematics is - RULES ! Obviously we need to be aware of the purpose and effect of applying any given rule, and maybe that is what many students are not shown propperly. I don't know, but I believe "Cliff" gets Results. Do you ?.
- and the ability to not get confused helps immensly in using those rules to achieve a desired result. There is nothing "fuzzy" about it.
You obviously are not a mathematician as no mathematician would say that mathematics is a bunch of rules. However, I understand your position as this is what "school math" is. It is quite distant from the work of mathematicians.
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I'm not sure what results Cliff gets. What are you referring to?
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Most students are quite fuzzy on the rules that they learn in traditional math. This is supported by many studies over many decades.
Cliff's results. Sorry, I assumed that someone employed as a mathematician for 25 years probably got some results that worked.
What results have you got - other than pieces of paper stating that you passed an exam ?. Correct me if I'm making assumptions again - you "don't do applied maths " Hahahahaha you're so funny.
Interesting that the data Cliff cites involves dates before these curricula were released. How could curricula that were not published until 1996 impact the incoming middle school math performance of graduates in 1999? These data have so many holes in them. I'm surprised you don't recognize them.
@sleeper2345 Yes, maybe I'm not up to speed with the way things are in your personal world. Like I tend to try to give an answer questions Have you ever taught anyone anything ? I belirve the teachers when they say it is the curriculum they are pushed into.
Maybe it's mercury and lead in the environment, but I would put my money on the people who at least USED TO get results. And you never answered my question. What results have you to show ?
My suggestion is to look at some actual data that you can draw some conclusions from, not just a convenience sample where Cliff cherry picks what impacts student performance. For example, look at the longitudinal National Assessment of Educational Progress (NAEP). These show that students today and those in the late 90s that Cliff examined, perform better mathematically. Of course, this is just a randomized study as opposed to the limited study that Cliff provides.
@sleeper1234 Or is your qualification for all this bullshit the fact that you failed every maths exam because you were taught badly ? In that case, there's no arguement Q.E.D. ! Cliff will have to stick 'em up !
But it worked ok for his kid. So maybe it's each to his own. You still haven't said what you have to show for your "abilities" - not even so much as a piece of paper. So you found a solution to what ?
So you provide the evidence from a sample of one (you?). Seems like a weak argument. My suggestion is to look to real research to draw conclusions. However, you may have missed the statistical courses that require evidence to support your conclusions. Most US classrooms don't require students to support their conclusions either, just mimic the procedure that the teacher provides. Monkey see, monkey do. My suggestion is to believe evidence, not unsubstantiated ideologues.
So it was a strange odd bit of luck that Cliff's teaching happened to sort-out his son in maths, according to you, was it ?
You still haven't said what you have to show for your "abilities" - not even so much as a piece of paper. So you found a solution to what ? - and what method of teaching can take the credit for this ?
My college student started crying when she had to do the simple business math in her business class. It is essentially too late for her - she has to use a calculator for everything. She has a sales job; she has literally called me to do the math for her when her calculator batteries die. I did the math in my head; she can barely do it with a calculator. (Did I mention that I had memorize the multiplication tables through 12 in grade school? Yeah - I hated it, and yeah - it works.)
Interesting that Mr. Mass assumes that instruction in the US quickly changed based on NCTM. Note, too, that Mr. Mass says that he is "speculating" about this. Have you been in any math classes recently. Teachers are still, primarily, doing what they've always done. Students have struggled with algebra for years. See the research by Booth in 1982. Why? Because algebra is about memorizing facts that are not connected to meaning.
Research shows that the more comfortable kids are with math (new math), the less they are able to compete with other students, worldwide. Students who are pushed to explore the more difficult areas in math, and simply memorize the easy stuff, excel. If you have to think about the easy stuff, you are are not thinking hard enough!
What is this "research" that you refer to? Sure students have to make sense of basics first to move on. There is no research to support that just memorizing a bunch of facts will lead to deeper understanding later. Just look at today's college grads (and yesterdays). Almost all are mathematically illiterate, not even able to recognize situations that involve subtracting of dividing fractions.
As for my links, you will need to add w w w (period) in front of the link, change the "(dots)" to periods, and remove the spaces in the middle (they were added by youtube formatting).
I am not sure if there is a better way to specify links in chat on youtube. I had trouble just getting this accepted.
You have to understand the facts before you can understand the meaning. A you learned to talk, you memorized the words before you understood the meaning of sentences. Then you memorized punctuation before you understood the meaning of paragraphs and more extensive writings.
Mathematics is nothing more than a language used to describe ideas and relationships. You have to memorize the syntax before you can understand the context.
No, I think I learned the meaning before I learned the term. For example, I saw a "cat" before I learned the word. How can you learn that 4 x 8 is 32 before you know what it means? This is senseless information.
No one memorized "cat" but they developed meaning for it that evolved over time. No one wants students to use a calculator to determine 4 x 8. They should have it memorized. However, what we disagree on is how students come to have this memorized. You seem to think that children just recall meaningless information. This is not the case, as the research shows.
The memorization that I think you are referring to is memorizing rote facts without understanding (e.g., using the 5, 6, 7, 8 for 7 x 8 is 56). The memorization that I refer to is quick recall with understanding. Do you see the difference? I don't think you do.
I don't believe there is a difference. If there is, the both are necessary.
Again, thinking of mathematics as language: you must learn the vocabulary forst, then you can gain the ability to put the vocabulary into sentences.
Using "cat" as an example: You may initially know that vocalizing the word "cat" means you are talking about the furry animal running around on the floor.
Wen you see the word "cat" in print for the first time, you have no idea what C A T means. You barely have an understanding of the letters C, A, or T. You have to memorize that combination of letters, and put into context. You have learn that "adding" C and A and T together yields the word "cat." This is memorization.
Vocabulary is very important in language development, and years are spent memorizing words.
I don't think kids see the word "cat" by seeing it. They hear it first and have no ideas how it is spelled. Children know what a "cat" is before they ever learn to spell it. The idea that they see the word and learn what it means seems very strange. Young children use many words without knowing how to spell them.
You are completely missing the point. "Cat" is not important. Vocabulary is the important part of the lesson here. Teachers give vocabulary words to memorize for language skills before they are ever used otherwise. They may use them along with the vocabulary words, but the vocabulary is rote memorization. It is also very important. Look for "Mathematics as Language" for information.
ur 4 more English words and rote memorization, and claim this is the Language of Mathematics?
When we teach a 2nd language, do we teach it in English? or do we speak English for a very short while, and then teach and learn in the language we are learning? But math educators put little emphasis on the symbols, and huge emphasis on English words that point to their meaning? 7-9 grade texts have 2-300 vocab words, DISTRACTION!! its really not that complicated. 9 RULES, 3 DEFINITIONS. NO WORDS
I am "4" exactly the opposite: I am for rote recall. That is, you should not have to think about simple things. For example, when you work with algebra, you should be thinking about how algebra works, not how addition or subtraction works.
How do you learn new rules without using the words that describe the rules?
How does some obtain quick recall? We know that this occurs through developing a deeper understanding. What does your question (about new rules) mean? What are you trying to say?
Know: To have innate congition (originating from the mind, rather than from experience).
How that knowledge is achieved is not as important as the fact that it is achieved.
My question about rules applies to Teachless' assertion that learning vocabulary is unimportant, but learning the rules is. You cannot learn the rules unless you learn the vocabulary that describes the rules.
My definition of understanding: Able to apply mathematical ideas and know why these ideas are valid. Your definition lacks such knowledge. We're loaded with college students who have memorized facts. They can show that two fractions are the same (e.g., 1/2 = 2/4) but they don't know why or when this information can be applied. They've learned the rules, they just don't know when to use them or why.
Having the ability to apply something is not the same as being able to apply it in a testable timeframe.
But in any case, what is your point? Why are you are arguing against being able to use the information quickly and efficiently? I don't believe I ever said that the should not understand the information (by your definition), that they should not be able to apply the rules, or realize what they mean.
I believe I have argued the opposite - they should be able to apply them - QUICKLY.
Sure they should apply it quickly. Right now most students can't because they have learned by memorizing meaningless facts that they don't understand. For example, they can say that (x-1)(x+1) = x^2 -1 but they don't believe that it is true. They can't apply it to numbers. Your focus on rote recall is misguided.
So, if my son can finish a math test in half a day, with reasonable accuracy, because he understand the material, but he fails the test in class because he doesn't know the sum of 3+8, your contention is that I should not drill him the addition problems, thereby allowing him to complete the test on time. Very interesting.
Are you reading anything that I'm typing? No, students should recall it quickly (once they know what it means). However, there is much more to be learned than just these basic facts. You're all for rote recall, but this is the least of our worries. What you're describing can be done by a calculator. What is hard is what needs to be done by the human mind.
"No, students should recall it quickly...more to be learned..." - Why are you arguing then? We agree.
"You're all for rote recall." - When did I say that that was my only concern? You are making false assumptions. I said this because people here are arguing it is not necessary. I disagree.
"...can be done by a calculator." False assumptions again - no calculators for tests. Try again.
"What is hard...' Agree again - what is easy should be memorized and not waste time.
You can't just memorize facts without understanding what they mean. For example, many college students think that 3/4 is the same as 6/8 because you double 3/4 to arrive at 6/8. Without this understanding they can't perform other operations. They have to understand what things mean, not just memorize meaningless information.
Once the idea is understood, repeat it enough times so that you don't have to think about it anymore. You will then know it, and can use it to think about something else.
You keep referring to memorizing and recalling rote facts. Your rhetoric infers that you are focusing on facts devoid of meaning. This is that rote recall insinuates: that there is no connection to meaning. I suggest a change of terminology so that you can better relay information.
Create your own new definitions if you wish. However, this will not facilitate communication. Wikipedia: Rote learning is a learning technique which avoids understanding of a subject and instead focuses on memorization. The major practice involved in rote learning is learning by repetition. The idea is that one will be able to quickly recall the meaning of the material the more one repeats it.
You tell me to change terminology, and then get mad when I do. My definitions came from Merriam-Webster - they are not mine.
I am communicating my ideas, and I have explicitly stated that I am a proponent of rote RECALL, not rote LEARNING. Understanding is just as important as being able to effectively and quickly use what is known.
You are continuing to argue against me for things we agree on. Discussing this any further is pointless.
The wikipedia article you reference includes these notes:
"Progressive reforms such as Outcomes-based education which have put an emphasis on eliminating rote learning in favor of deep understanding have produced a storm of controversy as a generation of students are failing new math assessments which were aimed at increasing math performance."
Exactly, why do students who have done traditional math think that 2/4 is double 1/2? They learned a rule without a reason. Thus they think that 1/2 x 2 = 2/4 (sorry for the typo below, I meant to type that 1/2 is the same as 2/4).
Since it is not discussed why 1/2 is the same as 2/4, they invent a reason. Some correctly make sense of it. Others do not. I think it would be better if all students could explain why 1/2 is the same as 2/4.
I'm surprised most of your students actually went through traditional mathematics instruction; the NCTM standards were created before many of those students were born. I know where I came from it took a while for the fad to wash over my school system but outside of small-town flyover country traditional mathematics was likely considered outmoded during the '90s and the decade that just ended.
Evidently you have not seen the results of the TIMSS video study. Teachers teach as they were taught. Any change in mathematics instruction is minimal. I've been in hundreds of classrooms and have seen little change in the teaching of mathematics since the 1970s.
I saw the results of the study and it's a damning indictment of *reform* mathematics, not the traditional way.
And teachers do teach as they are taught...by schools of education, many of which adopted reform mathematics from a misguided belief that it would aid disadvantaged groups.
I now know what the warnings to parents that their kids may not be taught as they themselves were taught actually meant; my older sister entered kindergarten in 1989, the year the NCTM standards were published.
You'll have to be more specific about the TIMSS study. I have no idea what you're referring to.
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You statement about schools of education could not be further off. The research shows just the opposite. Teacher teach as they were taught. They are not convinced to change much of anything based on their teacher education programs. If you think you are correct, cite one study that supports your findings. I can find 100s that support mine.
Findings from the TIMSS video study: US teachers do not focus on mathematical ideas. They focus on procedures. Teachers in the high performing countries focus on the mathematical ideas that underlie procedures. In the US, public explanations to mathematics involves describing procedures and giving answers, whereas all other countries focus on the ideas supporting procedures.
In other words, mathematics teaching the US remains where it always has and student performance remains poor.
Findings from the TIMSS video study: US teachers do not focus on mathematical ideas. They focus on procedures. Teachers in the high performing countries focus on the mathematical ideas that underlie procedures. In the US, public explanations to mathematics involves describing procedures and giving answers, whereas all other countries focus on the ideas supporting procedures.
In other words, mathematics teaching the US remains where it always has and student performance remains poor.
Based on your conclusions, students in inner city schools should perform the best in relation to mathematics scores. We know that in these locations, students are drilled on algorithms and memorization is the norm.
Anyone that cannot work-out that one half is the same as 2 quarters must be not really in this world. So is "new maths" teaching helping this sad condition ?
Hmm. Interesting that most of my college students think that doubling 1/2 gives them 2/4. Their traditional mathematics instruction gives them the correct answer, but they don't understand what the symbols mean or why 1/2 is the same as 2/3. The new mathematics textbooks actually develop meaning for 1/2 and 2/4 and expect students to be able to explain and show why 1/2 and 2/4 are the same.
You are completely missing the point. "Cat" is not important - it is the concept that individual words must be taught before they can be used in any context.
Another analogy might be describing online usage. You have to define "YouTube" before you can discuss what it does, means, or whether it is even useful.
What is the definition of "You Tube." I don't think I could define "cat." I suggest reading Vygotsky for how meaning are constructed. These are socially negotiated, not defined and memorized. Please share you memorized definition of "cat."
If words are not defined, then why do dictionaries exist?
For what it's worth, math information is also negotiated. Roman numerals are not used for normal math because they do not work for most numerical discussions. Mathematical theory, its meaning, and its understanding are discussed and negotiated on a regular basis by far more knowledgable people than you or I.
I have already shared my understanding of cat. That is irrelevant.
I agree, the meaning is shaped over time, just like 12 - 5. It means different things in different situations.
Note, too, that you meaning of cat does not distinguish it from other animals. You have a more complex image of a "cat" or you would not distinguish it from dog.
I'm not sure what you mean by "Roman numerals do not work for numerical discussions." Roman numerals have as much meaning as our Hindu-Arabic system.
It appears that learning higher math skills is irrespective of memorization.
"The final step in cognitive development (Piaget) is the formal operational stage. Only 35% of people ever achieve formal operational thought (Huitt & Hummel, 2003). This stage provides the ability to master abstract thought, use symbols in relation, and complete intricate problems in subjects such as Algebra. Hypotheticals are also processed during this stage." ~ Davison, 2006
Yes, of course they do, but what tjhombs was talking about was the learning of reading and writing. Are you gonna tell us that that's all history too ?
The word "cat" does not embody the image of a cat. Children learn what a cat is not by reading the word, but by creating mental images of what a cat is.
To but-in on your deal with thombs, only You could have got the impression:
" You seem to think that children just recall meaningless information" I did not get any such impression, neither do I believe that anyone not in need of phychiatric help would have got such. Indeed I don't believe that thombs has any such view. It is unfair to "tar" people with your own problems.
"Because algebra is about memorizing facts that are not connected to meaning" -- more BS hat-talking, & pure nonsense, as anybody who was good at algebra would know.
Algebra's about a mind-set and tools for approaches to solving problems. One learns basic algorithms, & things take off from there. '2345 probably failed at maths. so his/her/its holding forth so, spewing gibberish, is tragicomic.
Slide rules, log tables & algebra/calculus sent men to the moon; EM is good for basket weaving.
Algebra involves mathematical reasoning, not memorizing a unch of facts. EM can engage students in mathematical reasoning, if properly used. However, most teachers don't implement it properly, as demonstrated by research. Don't worry, we continue to teach math just as we did with slide rules, very poorly without connection to meaning of involving reasoning. See the TIMSS video study for more information on this.
Do a search for "the good old days that never were" to see that US instruction in mathematics has never been helpful for developing student understanding of mathematics. I love your reminiscing of mathematical understanding, though no evidence exists that students actually learned mathematics better at that time. It is time to return to reality rather that live in dreamland.
Right! I have a master's degree in mathematics (4.0 GPA). I've also won an award as the outstanding grad student in the math department. I'd be happy to test my mathematical prowess against yours.
*
I also have taught mathematics for 20+ years and have seen how little knowledge students have after receiving instruction at our finest high schools. The research on algebra backs this up: students have little sense of what algebraic symbols mean.
I completely agree with Mr. Mass, even though I don't live in Washington.
I tutor kids on the weekends in high school mathematics, and I continually see the same type of crap. The kids don't "feel" the math. They are just taught to memorize a minefield of rules to get the correct answer, which quickly become un-navigable to even the most powerful of minds.
There needs to be a reckoning in this country with the way math and science are taught. The way its done now just ain't cutting it.
Unfortunately, Mr. Mass is not advocating thinking. He is advocating moving away from textbooks that encourage students to think and doing what we've always done. What he doesn't realize is that most students have a traditional math experience, thus resulting in their poor performance. However, Mr. Mass forgot to ask them what their instruction was like. He wants them to memorize more rules and think less.
What "kids" are you referring to? Cliff didn't look at the backgrounds of the students he assessed. He just assumed that all of his students came from the less than 5% of students who use these curricula. Quite the "leap of faith" by Cliff. However, he needs to support his conclusions, so twisting the data is his only option.
Ask this guy to use a computer and I guaranty you he'll fuck up someone. What's important in life is relative to the decade and society one lives in.
Math isn't important when computers can do it for us. Math majors, don't flame me for this comment and give me the BS about how math made computers to blah blah blah... fact of the matter is, I can live life with basic math skills -- anything more means nothing to me.
Ask this guy to use a computer and ...wrong...numerical simulation of atmos sci. You think(sic). You want to create a society of luddites. No engineers physicists etc but only common duh heads like yourself...you think(sic). A society where there is a ceiling to intellectualism with you being the king duh head...you think(sic). Is the US going to be the next 3rd world economy...maybe if you and the luddites had your way it would. We have the same issues in Canada as does Wash state.
You really can't engineer a product without even bothering to get familiar on how the assembly line works. Your "engineered" product either won't be able to be produced at the mass and speed you want, or the cost you want, or, more likely, both.
You need to feel like popping an oillie comes as natural as walking before you get creative with your skateboard..
BUT they can put up a pretty good show if someone (Cliff, for instance) does the maths. for them. (Freaky, trust me). Thanks for pointing-out that the word "math" is all too often used where "arithmetic" is the word. I believe Arithmatic is about numbers, whilst Maths. may be about (odd?) facts to do with numbers. Maths. is maybe also about meaningful ways of re-arranging "truths". The maxim "Rubbish in Rubbish out" will always apply. Even If we made no mistakes. It's about definition
I'm aware of what computers can do.... (They can construct proofs, it slow and you have to write out your axioms in painful detail and then build up all the theorems you need from them, all expressed in painful detail... Then the theorem prover runs it chugs away for a while and you get a proof... They can do all kinds of things I ought to know since I'm almost finished with a Computer Science degree, if I don't know by now I'll have to give it back)
i'd be interested to know more about these proofs. How can a computer prove something for an infinite number of cases? Can it prove that an even + an even is an even? Can it prove that there are an infinite number of prime numbers?
most of these systems are actually not really generating proofs (that's a very hard problem) but they can check any proof you given them (in the appropriate painful detail)
however if you restrict your problem domain they can do more stuff (eg computer algebra systems that can find exact solutions to things, or linear programming solvers)
you can get a computer to try to find a proof of at most a certain length and it will chug away and eventually either come back with an answer, so you just set n large enough that if it says "no proof less than that long" you can reasonably conclude that means no proof (not the same as disproving the theorem). The problem is that we don't think there is a way to do this that will take a reasonable amount of time (unless P=NP) look up P vs NP if want to know more.
I think you're using "proof" differently that a mathematician would. You're looking at whether a procedure can be completed in polynomial time, whereas a mathematician provides a proof for why a statement is always true.
@sleeper2345 No I'm talking about how long it takes a computer to find a proof to a suitably stated theorem
The problem of: Given an arbitrary statement, find either a proof of at most a certain length N (for some def'n of length), or say "No Proof of length less than N"
Is known to be NP-Hard, and it is in NP because you can check the proof in polytime. So unless P=NP your computer won't be prooving things for you.
Even if it can do proofs it still doesn't know what theorems are interesting.
There's the mizar project - The Mizar project started around 1973 as an attempt to reconstruct mathematical vernacular in a computer-oriented environment
coq - Coq is a formal proof management system. It provides a formal language to write mathematical definitions, executable algorithms and theorems together with an environment for semi-interactive development of machine-checked proofs.
While this is mostly true, you will not be able to solve, say, mechanical and statistical problems that easily with a calculator.
Few mathematical packages can actually prove limits of functions, for example. You have to do that part yourself.
I don't know about the States but in the UK, any sort of science degree needs a solid mathematics foundation and after I've seen these videos, I can gather that few students in the States would end up at top UK institutions.
I just finished calculus 3. We weren't allowed to use calculators whatsoever. I really grateful because I understand the material intuitively. If your a math teacher dont use calculators.
So, in 1991, how many of those people had been affected by a set of *recommendations* with no binding power? Certainly not the 40 and 50 year olds. Not the ones my age. (And, from your profile, approximately yours as well, Tom.) The 18 year olds? Do you really think the *recommendations* were quickly implemented, all across the USA, and had a dramatic impact within 2 years.
And again clearly at 9:19: "The decline in math performance in Washington followed the introduction of reform math. A coincedence?...I think not."
As I said in response to another video, I taught at a community college from 1991-1996. Some students were 18. Some were my age (early to mid 20's). Some were in their 40s and 50s? (Why? Remember our last big recession? A lot of people were laid off in my area.)
This guy thinks that problems with adding two fractions, or using algebra, began 10 years ago?!? He hasn't been paying attention! It's been going on for decades longer. Hmmm, could part of it be that universities allow more students in than they used to? What a concept.
I paid very close attention and I have paid attention to trends for the past ***17*** years I have been teaching mathematics. I also know about the trends that were occurring before that. I see you have no response to the statement that the problems existed before 10 years ago. That these problems were widespread. That universities did not see as many of these problems because admittance was tougher, but has progressively eased since the 1960s.)
It's great that in the USA, we have the *opportunity* to receive higher education. That does not mean everyone's ready for it. I could say more, but I've already posted it in response to similar videos.
I'll just leave it at this: he dumbed down Atmospheric Sciences? Then ***he's just as much too blame***. MAINTAIN STANDARDS. Be prepared to work harder to raise students to those standards, but maintain them.
Your post demonstrates quite handily that reading comprehension is as much of a problem as math skills. No one is denying that problems with math competency predate the past 10 years. The issue is they've grown substantially over that period. Dr. Mass has charts demonstrating the decline, evidence that corresponds with my own anecdotal evidence (teaching Physics at the University level).
Your post demonstrates quite handily that making nasty faceless insults over the internet is easy. Yes, there ARE people that claim the problem that began in the 90's. At 1:21, "... doing problems that students in the 1980s had little difficulty doing ... ."
1. y=x/(1-x)
2. y(1-x)=x
3. y-xy=x
4. y=x+xy
5. y=x(1+y)
6. y/(1+y)=x
7. x=y/(1+y)
If you doubt it, substitute y/(1+y) for x in equation 1 and simplify. Of course, if you couldn't solve the first, you probably have no chance ........
64sandal 3 months ago
Can you solve these math?= D-[divided E.BDF] then divide that whit B|B.DBB Then show me the anwser
garcaidavid95 4 months ago
If there is a science of possibility that helps one go from the smallest choices, to the largest, while respecting the sum of limitations, and the chance for error, then it is Mathematics. Science reveals the way choices are, but without a theory of representation, we are voiceless in a confusing world. There are deeper structures to be found, even if simple, that only deep concentration may provide. When people say mathematics is beautiful, it is not a stepchild of euphoria, it is a new sun.
SymbolicSoliloquy 4 months ago
Good video! Education is not something to be put in a box and forgotten, no matter which approach we use. We need to keep examining the approaches to education and the curriculum that are being used in public school classrooms. We, as taxpayers, should have some say in the way students are being taught and what standards they are expected to meet.
An international standard is the wisest course.
Of course, this video shows just one more reason that families are home schooling their students.
Tyreanify 5 months ago
I agree w/ reservations. Close to "Fox News" math
For instance, what was the mean Pre-Calculus Test (PCT) v mean SAT? Why?
1) SATs are standardized. 2)GPAs are not.
Conclusion: PCT v SAT measures intelligence v PCT more reliably than PCT v GPA.
Another question: is there evidence that a more rigorous approach improves PCT scores?
FYI: The "simple" algebra equation given his students, y=x/(1-x), is unsolvable for x. Simplest form is y-xy-x=0. So much for rigor... :)
lxw0052 6 months ago
I agree w/ reservations. Close to "Fox News" math
For instance, what was the mean Pre-Calculus Test (PCT) v mean SAT?
*SATs are standardized versus norms.
*GPAs are not. (Easier grading systems?)
* Thus, PCT v SAT measures intelligence v PCT more reliably than PCT v GPA
Another question: is there evidence that a more rigorous approach improves PCT scores?
FYI: The "simple" algebra equation given his students, y=x/(1-x), is unsolvable for x. Simplest form is y-xy-x=0. So much for rigor... :)
lxw0052 6 months ago
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sleeper2345 is correct. Many of the math teachers who have been teaching for a 30 years, hate the Investigative approach. Not because it doesn't work, but because it required them to teach outside of their comfort zone. They taught the curriculum poorly so they could say, "I told you so." The old way of teaching worked...for some of the students, but not for every student! We used to be OK with 40-50% of kids failing math. But not anymore, and Investigations grabs kids and draws them in...
rad76dude 7 months ago
sleeper2345 is correct. Many of the math teachers who have been teaching for a 30 years, hate the Investigative approach. Not because it doesn't work, but because it required them to teach outside of their comfort zone. They taught the curriculum poorly so they could say, "I told you so." The old way of teaching worked...for some of the students, but not for every student! We used to be OK with 40-50% of kids failing math. But not anymore, and Investigations grabs kids and draws them in...
rad76dude 7 months ago
Outstanding video, as is the one by M J McDermott. Reform Math was a poisoned well. Trouble is, the con artists who create this stuff are now back in their dank labs, concocting Core Standards. More of the same, I'm afraid.
I'm struck by the evil parallel between Whole Word in reading and Reform Math in arithmetic. Both curricula seem to be designed not to work.
Bruce Deitrick Price
Improve-Education
BruceDeitrickPrice 1 year ago
@BruceDeitrickPrice Bruce: I'd love to see you solve the "simple equation in the video for x: y = x / (1-x). Please tell us your result.
sleeper2345 4 months ago in playlist University
I love Maths; i've just started A level maths and it's more than just logic; it's a beautiful language...
Symmetryful 1 year ago
This has been flagged as spam show
Geometric demonstration and discovery of a " geometric sacred boss " used very presumably in the construction of The Great Pyramid of Gizéh's plateau and his chance? Relation with the number "pi" (with a simple rule and / or compass) 2300 years B. Arquimedes (4600 years B.J.C.) for the farón Jufu-Keops.
Pirramides 1 year ago
sleeper2345 is typical of the thinking among math teachers who believe in this nonsense. As he says, the problem with EM is tha teachers are not teaching it properly. Well, how good can it be if the teachers can't teach it. I learned standard algorithims, earned a degree in economics and never touched a slide rule. Maybe my teachers were just good. Reasoning through problems won't work unless students first understand standard algorithims.
tubeview72 1 year ago 2
@tubeview72 Nice condescending remarks--attempting to marginalize my statements without support. Your comment is laughable: "Reasoning through problems won't work unless students first understand standard algorithims." So you don't reason with the standard algorithms? Where did they come from? didn't someone need to reason to invent them? Reasoning is embedded in mathematical activity. However, this is not true in US mathematics instruction, reasoning is hardly ever addressed.
sleeper2345 1 year ago
what about those implementing the curriculum? do you think they don't factor in?
linesronda 1 year ago
@linesronda Cliff isn't worried about the evidence that supports his point of view, he just wants to share his misinformed conclusions. He assumes that all students are being taught differently than he was 30 years ago, despite the overwhelming evidence that little has changed related to math teaching in the US.
sleeper2345 1 year ago
All college freshman should be on the same level of mathematical ability as Kurt Godel and Julian Schwinger. That would solve the problem wouldn't it?? :D
gvsfgdf 1 year ago
nothing wrong with the standards or constructivism per se -- it could be other factors (e.g. teachers, assessment, in-grained expectations etc.). but most people (teachers included) never learned how to learn by discovery themselves, so it might be better to forget about even trying. right?
Heissenburger 1 year ago
@Heissenburger No one is suggesting that student learn by "discovery." However, the individual in the video and the National Mathematics Panel would like to provide a distorted view of what is suggested by reform mathematics. The suggestion is that students actually think and use mathematical reasoning rather than memorize procedures. However, for most adults in the US, thinking and reasoning was not part of their school mathematics experience and they cannot help their children.
sleeper2345 1 year ago
@sleeper2345 so the problem is the implementation (lack of comprehensive thinking through and ground preparation), rather than the idea itself, right?
Heissenburger 1 year ago
@Heissenburger As with most ideas, they are distorted and difficult to realize. This is certainly true in school where there are no mechanisms to support implementation of research findings. Instruction continues as it did 30+ years ago.
sleeper2345 1 year ago
Unfortunately Cliff seems to have limited understanding of research. You can't test college students on their performance and blame the poor results on particular instruction unless you know the students actually experienced it! Cliff: You forgot to study what math the students experienced in high school. Perhaps it was the traditional math you so dearly love! Try supporting you argument with real evidence next time!
sleeper2345 1 year ago
@sleeper2345
Traditional maths, reform maths, ordinary math, calculator math ? how many different sorts of "math" do rekon there is ?!
bertwindon 1 year ago
i am not being prejudiced, nor am i that type of a person, so don't take this the wrong way, it is my experience. i used to cheat on my math tests all through school or i never would have graduated. i am nearly 60 years old now, for some reason the oriental students were always every one of them, excellent in math. why? is it the style of way they were taught the math from the begiinning? obviously, they were learning the right way, it isn't an ethnic thing, but what is the method they used?
bettygoodbody 2 years ago
As an old bastard, I attest that modern math teaching dramatically reduced understanding & increased incomprehensibility. Our kids had trouble with math until my wife (also an engineer) sat down with them every night & practiced from old text books.
Kids today are not stupid. They get bored and distracted easily, especially in large classes with dreary teachers and their "modern" methods.
Math is simple; but only when presented well.
Those who control schools do not want educated citizens.
OldSchoolSkill 2 years ago 3
I think your faulty generalizations from a small "n" are quite dangerous. Such "proof" is not valid mathematically or scientifically.
*
I do agree that kids are much smarter than we think, too bad the math teaching of yore does not encourage thinking.
*
Also, math is not simple, it involves some very difficult ideas. Our number system itself is a very complex system that was developed over 100s of years, hardly simple.
sleeper2345 2 years ago
socratus1 2 years ago
I can really appreciate your perspective, it is very common among university professors, and it is from a perspective that understands certain things that the typical parent, or pre-college math educator can't see,
They also have a perspective that includes a part of the story totally unseen by Cliff.
Take it from a person 10 years in a variety of settings in secondary, and 10 years teaching undergrad courses at a University Level, neither side sees the picture clearly.
teachless 2 years ago
Note that this is just a misleading video with someone "searching" for conclusions. Cliff doesn't know what instruction students receive, but tries to draw conclusions anyway. I suggest actually asking students how they were taught math. This may be over Cliff's head.
sleeper2345 2 years ago
Cliff is really on to something though with regard to the curricula and the Textbook companies he's just a little to naive in believing that the ITBS is any better than the WASL, it's still totally created by teachers that go "by the book" out of the fear of not being enough. Where's the mathematics indeed. That's the whole problem, all memorized process, no grasp of concepts. AT ALL!
This video is VERY well named though. Although it should really be called THE typical University Veiw,
teachless 2 years ago
I don't know what method Iowa Test of Basic Skills uses for their math proficiency, but the state has gone to these inefficient models for teaching math. Check it out at Iowa Core Curriculum - Home
anonymous915 2 years ago
Definitely a worldwide problem! Same problem exists in Ireland. The key is teaching the component skills (or buidling blocks) to fluency (accuracy plus speed). How can a child master a simple composite skill like addition if they have not been given enough practice opportunities to become fluent at reading or writing numbers! Teachers need to start changing the instructional form not necessarily the actual maths content.
suechopsue 2 years ago
In the 80's there were fewer distractions that affected me from doing my studies. But today if you don't have a phone with internet, a PS2, a PC with a gaming card, email address, facebook account, watch utube videos at least 3 times a day, download stuff from piratebay etc, etc.. then you are not considered to be normal. I too in recent years see my personal decipline decline 'cause of too many distractions. I am in the process of remedying - delisting from soclal n/w sites is just the start.
colinmaharaj 2 years ago
Nothing that you list is "research." These are opinion pieces without empirical support. The "new math" that you refer to is designed to support memorization of facts. However, the memorization is not meaningless, but builds on how we know students progress to having their facts memorized. See "Cognitively Guided Instruction" in a search for more on this.
sleeper2345 2 years ago
Research: the collecting of information about a particular subject. ~ Merriam-Webster
You are free to disagree with the content, but the articles I listed are research, and they dispute your contentions.
tjhombs 2 years ago
All I could see are opinion pieces for the search you describe. Can you give a citation? Again, see CGI for how kids actually learn their facts without silly memorization techniques like 5, 6, 7, 8 for 7 x 8 = 56.
sleeper2345 2 years ago
The information about CGI is interesting. Now let's imagine college students are using manipulatives to figure out differential equations.
I think the professor teaching the class might put a video on YouTube about his frustration over trying to teach students who do not know basic math concepts.
Oh, wait - that's what Dr. Mass did.
tjhombs 2 years ago
Saying CGI is about using manipulatives is like saying that playing chess is about moving wood around. From a particular perspective, you are right. However, children reason about facts (e.g., 5 + 6 = 11 because 5 + 5 is 10). I can understand you not wanting students to reason like this if you are opposed to mathematical rigor. Mathematics is about memorizing and not reasoning. Student use models in diff equations, (e.g., graphs). Would you rather have students who don't reason about quantities?
sleeper2345 2 years ago
The only information I have found on CGI shows that it is a technique used K-3.
The last time I checked, they don't teach chess in third grade. They do use manipulatives.
If your assertion is that CGI applies beyond third grade, it would be interesting to see the references.
tjhombs 2 years ago 2
Do a search for "Carpenter & Moser, 1984" or "Carpenter, Fennema". See "Adding It Up" for a synthesis of research by the National Research Council. It matters very much how students learn in grades K-8 and the reasoning they use. I'm assuming that you are "for" mathematical rigor, but I'm not sure.
sleeper2345 2 years ago
I am "for" mathematical understanding, specifically for my own kids. The public schools have failed them so far, not in grades, but in concepts. The schools here use "Everyday Math," and my kids are completely confused with the concepts they were learning.
Everyday Math came up in my search for Carpenter & Moser. EM states that it uses Carpenter & Moser's methodology, which I completely disagree with for middle school students.
tjhombs 2 years ago
I don't know what is meant by "Carpenter and Moser's methodology." EM has been demonstrated to help students who are struggling in math. Of course, this is complex, as the teacher must understand the purpose and goals of the curriculum. Most teachers teach as they were taught, encouraging students to practice following procedure that students do not understand. Do a search for "schoenfeld ed researcher everyday math" for an excellent study.
sleeper2345 2 years ago
"EM has been demonstrated to help students who are struggling in math." Maybe, but EM turns otherwise potentially bright, motivated NORMAL students into drooling morons... mathematically speaking. Typical progressivism: drag everybody down to the lowest level instead of letting the brightest excel.
seaXcrow 2 years ago
Typical misleading statement spoken in ignorance. It is traditional math that turns bright students with strong reasoning into bumbling mathematical idiots who don't trust their own reasoning. Google "parrot math" to see what traditional math does. I see it everyday with even our brightest students. They don't know why they follow the rules they do, they just do! This, to them, is math.
sleeper2345 2 years ago
sleeper2345 is talking thru his/her/its hat. The Seattle schools have adopted EM; consequently, local for-fee math tutors have never had brisker business, duh.
My niece is sorely challenged by college math remedials, courtesy of the mushy Seattle math taught her. I've seen first-hand the train wreck that EM and similar makes of its victims' ability to clearly solve problems and prepare kids for higher learning. EM could not be better designed to destroy the math talent of those subjected to it.
seaXcrow 2 years ago
I'll add that I spoke recently to a Seattle teacher friend, who she told me how the hated EM is *really* taught: after every EM unit, the teachers revert to 3 days' worth of traditional algorithms and math-fact teaching, once the SPS proctor-goons have left the premises.
I suggest that the reason SPS scores have not totally collapsed is due to the continued use of the methods that sleeper2345 sneers at -- and the common hiring of Kumon et al by desperate parents anxious for their kids' futures.
seaXcrow 2 years ago
So the curriculum has not and will not ever be implemented as intended. We continue to drill students on rules they don't understand.
sleeper2345 2 years ago
@sleeper2345
Has anyone ever told you that you are an arogant moron by any chance ?
bertwindon 1 year ago
bertwindon: Please try to engage in an intellectual argument over the topic rather than resorting to name-calling. I pointed out a flaw in Cliff's argument:You can't test college students on their performance and blame the poor results on particular instruction unless you know the students actually experienced it! Please support your position if you can.
sleeper2345 1 year ago
@sleeper2345 So what is your explanation of the drastic decline in elementary mathematical ability of student to which "Cliff" refers. Is he a liar ? - drunk ?
Seems like a good maths teacher to me - sorry !
bertwindon 1 year ago
Bertw:
I think you're describing a different video. This video has nothing to do with elementary math. I'm not sure what he's on. You'll have to ask him. Cliff doesn't teach math, he teaches atmospheric science.
sleeper2345 1 year ago
Not ever = never. Sorry, but you are going to have to memorize this.
bertwindon 1 year ago
These curricula have only been around for a short period of time. When did she start EM? Were the teachers properly prepared? So you're generalizing from an N of 1 to the population? Sounds like you have some difficulty wiht statistical reasoning.
sleeper2345 2 years ago
@sleeper2345
That is what Mathematics is - RULES ! Obviously we need to be aware of the purpose and effect of applying any given rule, and maybe that is what many students are not shown propperly. I don't know, but I believe "Cliff" gets Results. Do you ?.
- and the ability to not get confused helps immensly in using those rules to achieve a desired result. There is nothing "fuzzy" about it.
bertwindon 1 year ago
You obviously are not a mathematician as no mathematician would say that mathematics is a bunch of rules. However, I understand your position as this is what "school math" is. It is quite distant from the work of mathematicians.
*
I'm not sure what results Cliff gets. What are you referring to?
*
Most students are quite fuzzy on the rules that they learn in traditional math. This is supported by many studies over many decades.
sleeper2345 1 year ago
@sleeper2345
Cliff's results. Sorry, I assumed that someone employed as a mathematician for 25 years probably got some results that worked.
What results have you got - other than pieces of paper stating that you passed an exam ?. Correct me if I'm making assumptions again - you "don't do applied maths " Hahahahaha you're so funny.
bertwindon 1 year ago
bertwindon,
Interesting that the data Cliff cites involves dates before these curricula were released. How could curricula that were not published until 1996 impact the incoming middle school math performance of graduates in 1999? These data have so many holes in them. I'm surprised you don't recognize them.
sleeper2345 1 year ago
@sleeper2345 Yes, maybe I'm not up to speed with the way things are in your personal world. Like I tend to try to give an answer questions Have you ever taught anyone anything ? I belirve the teachers when they say it is the curriculum they are pushed into.
Maybe it's mercury and lead in the environment, but I would put my money on the people who at least USED TO get results. And you never answered my question. What results have you to show ?
bertwindon 1 year ago
Bertwindon,
My suggestion is to look at some actual data that you can draw some conclusions from, not just a convenience sample where Cliff cherry picks what impacts student performance. For example, look at the longitudinal National Assessment of Educational Progress (NAEP). These show that students today and those in the late 90s that Cliff examined, perform better mathematically. Of course, this is just a randomized study as opposed to the limited study that Cliff provides.
sleeper2345 1 year ago
@sleeper1234 Or is your qualification for all this bullshit the fact that you failed every maths exam because you were taught badly ? In that case, there's no arguement Q.E.D. ! Cliff will have to stick 'em up !
But it worked ok for his kid. So maybe it's each to his own. You still haven't said what you have to show for your "abilities" - not even so much as a piece of paper. So you found a solution to what ?
bertwindon 1 year ago
Bert,
So you provide the evidence from a sample of one (you?). Seems like a weak argument. My suggestion is to look to real research to draw conclusions. However, you may have missed the statistical courses that require evidence to support your conclusions. Most US classrooms don't require students to support their conclusions either, just mimic the procedure that the teacher provides. Monkey see, monkey do. My suggestion is to believe evidence, not unsubstantiated ideologues.
sleeper2345 1 year ago
So it was a strange odd bit of luck that Cliff's teaching happened to sort-out his son in maths, according to you, was it ?
You still haven't said what you have to show for your "abilities" - not even so much as a piece of paper. So you found a solution to what ? - and what method of teaching can take the credit for this ?
That's not too difficult, I hope.
bertwindon 1 year ago
My college student started crying when she had to do the simple business math in her business class. It is essentially too late for her - she has to use a calculator for everything. She has a sales job; she has literally called me to do the math for her when her calculator batteries die. I did the math in my head; she can barely do it with a calculator. (Did I mention that I had memorize the multiplication tables through 12 in grade school? Yeah - I hated it, and yeah - it works.)
tjhombs 2 years ago
Interesting that Mr. Mass assumes that instruction in the US quickly changed based on NCTM. Note, too, that Mr. Mass says that he is "speculating" about this. Have you been in any math classes recently. Teachers are still, primarily, doing what they've always done. Students have struggled with algebra for years. See the research by Booth in 1982. Why? Because algebra is about memorizing facts that are not connected to meaning.
sleeper2345 2 years ago
Research shows that the more comfortable kids are with math (new math), the less they are able to compete with other students, worldwide. Students who are pushed to explore the more difficult areas in math, and simply memorize the easy stuff, excel. If you have to think about the easy stuff, you are are not thinking hard enough!
tjhombs 2 years ago
What is this "research" that you refer to? Sure students have to make sense of basics first to move on. There is no research to support that just memorizing a bunch of facts will lead to deeper understanding later. Just look at today's college grads (and yesterdays). Almost all are mathematically illiterate, not even able to recognize situations that involve subtracting of dividing fractions.
sleeper2345 2 years ago
There is plenty of research on this subject. For example:
quickreckoning(dot)com/math_research(dot)htm
achievementtech(dot)com/download(dot)cfm?DownloadFile=25ED2973-9B6D-6E7C-77C77A850A783E22
tjhombs 2 years ago
The link you provide does not work.
sleeper2345 2 years ago
You can simply search for:
"math facts" memorize research
As for my links, you will need to add w w w (period) in front of the link, change the "(dots)" to periods, and remove the spaces in the middle (they were added by youtube formatting).
I am not sure if there is a better way to specify links in chat on youtube. I had trouble just getting this accepted.
tjhombs 2 years ago
You have to understand the facts before you can understand the meaning. A you learned to talk, you memorized the words before you understood the meaning of sentences. Then you memorized punctuation before you understood the meaning of paragraphs and more extensive writings.
Mathematics is nothing more than a language used to describe ideas and relationships. You have to memorize the syntax before you can understand the context.
tjhombs 2 years ago
No, I think I learned the meaning before I learned the term. For example, I saw a "cat" before I learned the word. How can you learn that 4 x 8 is 32 before you know what it means? This is senseless information.
sleeper2345 2 years ago
You memorized what "cat" meant before you able to answer the question, "Why did you paint the cat blue?"
The question makes no sense until you know what the words mean.
Know that the answer is 32 allows you to work with problems that deal with the use of the "X" verb.
If you have to use a calculator to find out what 4x8 is everytime you need to know, you are wasting your time.
tjhombs 2 years ago
Seriously:
당신은 왜 고양이를 파랬던 그렸는가
If you don't understand, it's because you haven't learned the words - duh!
tjhombs 2 years ago
No one memorized "cat" but they developed meaning for it that evolved over time. No one wants students to use a calculator to determine 4 x 8. They should have it memorized. However, what we disagree on is how students come to have this memorized. You seem to think that children just recall meaningless information. This is not the case, as the research shows.
sleeper2345 2 years ago
"He wants them to memorize more rules and think less." ~ sleeper2345
This quote implies that you do not want students to memorize facts.
"They should have it memorized." ~ sleeper2345
You can't have it both ways.
If your assertion is that the information should, in fact be memorized, then what are you arguing about?
tjhombs 2 years ago
The memorization that I think you are referring to is memorizing rote facts without understanding (e.g., using the 5, 6, 7, 8 for 7 x 8 is 56). The memorization that I refer to is quick recall with understanding. Do you see the difference? I don't think you do.
sleeper2345 2 years ago
I don't believe there is a difference. If there is, the both are necessary.
Again, thinking of mathematics as language: you must learn the vocabulary forst, then you can gain the ability to put the vocabulary into sentences.
Using "cat" as an example: You may initially know that vocalizing the word "cat" means you are talking about the furry animal running around on the floor.
tjhombs 2 years ago
Wen you see the word "cat" in print for the first time, you have no idea what C A T means. You barely have an understanding of the letters C, A, or T. You have to memorize that combination of letters, and put into context. You have learn that "adding" C and A and T together yields the word "cat." This is memorization.
Vocabulary is very important in language development, and years are spent memorizing words.
tjhombs 2 years ago
I don't think kids see the word "cat" by seeing it. They hear it first and have no ideas how it is spelled. Children know what a "cat" is before they ever learn to spell it. The idea that they see the word and learn what it means seems very strange. Young children use many words without knowing how to spell them.
sleeper2345 2 years ago
You are completely missing the point. "Cat" is not important. Vocabulary is the important part of the lesson here. Teachers give vocabulary words to memorize for language skills before they are ever used otherwise. They may use them along with the vocabulary words, but the vocabulary is rote memorization. It is also very important. Look for "Mathematics as Language" for information.
tjhombs 2 years ago
ur 4 more English words and rote memorization, and claim this is the Language of Mathematics?
When we teach a 2nd language, do we teach it in English? or do we speak English for a very short while, and then teach and learn in the language we are learning? But math educators put little emphasis on the symbols, and huge emphasis on English words that point to their meaning? 7-9 grade texts have 2-300 vocab words, DISTRACTION!! its really not that complicated. 9 RULES, 3 DEFINITIONS. NO WORDS
teachless 2 years ago
I am "4" exactly the opposite: I am for rote recall. That is, you should not have to think about simple things. For example, when you work with algebra, you should be thinking about how algebra works, not how addition or subtraction works.
How do you learn new rules without using the words that describe the rules?
tjhombs 2 years ago
How does some obtain quick recall? We know that this occurs through developing a deeper understanding. What does your question (about new rules) mean? What are you trying to say?
sleeper2345 2 years ago
Understanding is not the same as knowing.
Understand: Accepting as fact.
Know: To have innate congition (originating from the mind, rather than from experience).
How that knowledge is achieved is not as important as the fact that it is achieved.
My question about rules applies to Teachless' assertion that learning vocabulary is unimportant, but learning the rules is. You cannot learn the rules unless you learn the vocabulary that describes the rules.
tjhombs 2 years ago
My definition of understanding: Able to apply mathematical ideas and know why these ideas are valid. Your definition lacks such knowledge. We're loaded with college students who have memorized facts. They can show that two fractions are the same (e.g., 1/2 = 2/4) but they don't know why or when this information can be applied. They've learned the rules, they just don't know when to use them or why.
sleeper2345 2 years ago
Having the ability to apply something is not the same as being able to apply it in a testable timeframe.
But in any case, what is your point? Why are you are arguing against being able to use the information quickly and efficiently? I don't believe I ever said that the should not understand the information (by your definition), that they should not be able to apply the rules, or realize what they mean.
I believe I have argued the opposite - they should be able to apply them - QUICKLY.
tjhombs 2 years ago
Sure they should apply it quickly. Right now most students can't because they have learned by memorizing meaningless facts that they don't understand. For example, they can say that (x-1)(x+1) = x^2 -1 but they don't believe that it is true. They can't apply it to numbers. Your focus on rote recall is misguided.
sleeper2345 2 years ago
So, if my son can finish a math test in half a day, with reasonable accuracy, because he understand the material, but he fails the test in class because he doesn't know the sum of 3+8, your contention is that I should not drill him the addition problems, thereby allowing him to complete the test on time. Very interesting.
tjhombs 2 years ago
Are you reading anything that I'm typing? No, students should recall it quickly (once they know what it means). However, there is much more to be learned than just these basic facts. You're all for rote recall, but this is the least of our worries. What you're describing can be done by a calculator. What is hard is what needs to be done by the human mind.
sleeper2345 2 years ago
"No, students should recall it quickly...more to be learned..." - Why are you arguing then? We agree.
"You're all for rote recall." - When did I say that that was my only concern? You are making false assumptions. I said this because people here are arguing it is not necessary. I disagree.
"...can be done by a calculator." False assumptions again - no calculators for tests. Try again.
"What is hard...' Agree again - what is easy should be memorized and not waste time.
tjhombs 2 years ago
You can't just memorize facts without understanding what they mean. For example, many college students think that 3/4 is the same as 6/8 because you double 3/4 to arrive at 6/8. Without this understanding they can't perform other operations. They have to understand what things mean, not just memorize meaningless information.
sleeper2345 2 years ago
We agree again. Why are we arguing?
Once the idea is understood, repeat it enough times so that you don't have to think about it anymore. You will then know it, and can use it to think about something else.
tjhombs 2 years ago
You keep referring to memorizing and recalling rote facts. Your rhetoric infers that you are focusing on facts devoid of meaning. This is that rote recall insinuates: that there is no connection to meaning. I suggest a change of terminology so that you can better relay information.
sleeper2345 2 years ago
You disagreed with my earlier change in terminology, but I will present it again, with additions for your sake:
Know: Innate Cognition (A mental process originating from within.) The idea becomes a part of yourself - you no longer think about it. It just IS.
Rote: Rapid
Recall: Experiential Memory
Fact: Experience
Rapid memories of experiences. More = Faster.
BTW: I never said "facts" in my use of rote recall. You are making assumptions again. Ideas are important too.
tjhombs 2 years ago
Create your own new definitions if you wish. However, this will not facilitate communication. Wikipedia: Rote learning is a learning technique which avoids understanding of a subject and instead focuses on memorization. The major practice involved in rote learning is learning by repetition. The idea is that one will be able to quickly recall the meaning of the material the more one repeats it.
sleeper2345 2 years ago
You tell me to change terminology, and then get mad when I do. My definitions came from Merriam-Webster - they are not mine.
I am communicating my ideas, and I have explicitly stated that I am a proponent of rote RECALL, not rote LEARNING. Understanding is just as important as being able to effectively and quickly use what is known.
You are continuing to argue against me for things we agree on. Discussing this any further is pointless.
tjhombs 2 years ago
The wikipedia article you reference includes these notes:
"Progressive reforms such as Outcomes-based education which have put an emphasis on eliminating rote learning in favor of deep understanding have produced a storm of controversy as a generation of students are failing new math assessments which were aimed at increasing math performance."
tjhombs 2 years ago
I couldn't agree more. Have your son learn everything by rote. Good luck! Have him repeat "paper or plastic." There are many jobs available.
sleeper2345 2 years ago
...and there we go with the insults.
In any case, asking, "Paper or Plastic?" seems to have worked out well for this dropout:
ofrf (dot) org (slash) pressroom (slash) organic_news_clips (slash) 050214_forbes_wholefoods (dot) pdf
tjhombs 2 years ago
Hope your son does as well.
sleeper2345 2 years ago
Hard to generalize from an N of 1. However, most students do this anyway and think they are doing algebra.
sleeper2345 2 years ago
Webster Dictionary definition of rote: the use of memory usually with little intelligence. Note that you are not communicating your ideas.
sleeper2345 2 years ago
"Little Intelligence" does not mean lack of understanding.
Intelligence: Skilled use of reason.
You said my example could simply be done on the calculator, which would be using "little intelligence."
Your definition of rote is only one of many.
Rote: Mechanical
Mechanical: Automatic
Automatic: Spontaneous
Spontaneous: Mechanical, Without Deliberation
Rote = Spontaneous, and without deliberation
tjhombs 2 years ago
@sleeper Not wishing to be picky, but if you "double 3/4" you get one and a half.
bertwindon 1 year ago
Exactly, why do students who have done traditional math think that 2/4 is double 1/2? They learned a rule without a reason. Thus they think that 1/2 x 2 = 2/4 (sorry for the typo below, I meant to type that 1/2 is the same as 2/4).
Since it is not discussed why 1/2 is the same as 2/4, they invent a reason. Some correctly make sense of it. Others do not. I think it would be better if all students could explain why 1/2 is the same as 2/4.
sleeper2345 1 year ago
I'm surprised most of your students actually went through traditional mathematics instruction; the NCTM standards were created before many of those students were born. I know where I came from it took a while for the fad to wash over my school system but outside of small-town flyover country traditional mathematics was likely considered outmoded during the '90s and the decade that just ended.
jelewis2 1 year ago
jelewis,
Evidently you have not seen the results of the TIMSS video study. Teachers teach as they were taught. Any change in mathematics instruction is minimal. I've been in hundreds of classrooms and have seen little change in the teaching of mathematics since the 1970s.
sleeper2345 1 year ago
I saw the results of the study and it's a damning indictment of *reform* mathematics, not the traditional way.
And teachers do teach as they are taught...by schools of education, many of which adopted reform mathematics from a misguided belief that it would aid disadvantaged groups.
I now know what the warnings to parents that their kids may not be taught as they themselves were taught actually meant; my older sister entered kindergarten in 1989, the year the NCTM standards were published.
jelewis2 1 year ago
You'll have to be more specific about the TIMSS study. I have no idea what you're referring to.
*
You statement about schools of education could not be further off. The research shows just the opposite. Teacher teach as they were taught. They are not convinced to change much of anything based on their teacher education programs. If you think you are correct, cite one study that supports your findings. I can find 100s that support mine.
sleeper2345 1 year ago
Findings from the TIMSS video study: US teachers do not focus on mathematical ideas. They focus on procedures. Teachers in the high performing countries focus on the mathematical ideas that underlie procedures. In the US, public explanations to mathematics involves describing procedures and giving answers, whereas all other countries focus on the ideas supporting procedures.
In other words, mathematics teaching the US remains where it always has and student performance remains poor.
sleeper2345 1 year ago
Findings from the TIMSS video study: US teachers do not focus on mathematical ideas. They focus on procedures. Teachers in the high performing countries focus on the mathematical ideas that underlie procedures. In the US, public explanations to mathematics involves describing procedures and giving answers, whereas all other countries focus on the ideas supporting procedures.
In other words, mathematics teaching the US remains where it always has and student performance remains poor.
sleeper2345 1 year ago
Based on your conclusions, students in inner city schools should perform the best in relation to mathematics scores. We know that in these locations, students are drilled on algorithms and memorization is the norm.
sleeper2345 1 year ago
@tjhombs Sure this guy is a master with a brush full of tar !
bertwindon 1 year ago
@sleeper1234
Anyone that cannot work-out that one half is the same as 2 quarters must be not really in this world. So is "new maths" teaching helping this sad condition ?
bertwindon 1 year ago
Hmm. Interesting that most of my college students think that doubling 1/2 gives them 2/4. Their traditional mathematics instruction gives them the correct answer, but they don't understand what the symbols mean or why 1/2 is the same as 2/3. The new mathematics textbooks actually develop meaning for 1/2 and 2/4 and expect students to be able to explain and show why 1/2 and 2/4 are the same.
sleeper2345 1 year ago
You are completely missing the point. "Cat" is not important - it is the concept that individual words must be taught before they can be used in any context.
Another analogy might be describing online usage. You have to define "YouTube" before you can discuss what it does, means, or whether it is even useful.
Words come before the ability to discuss them.
Look for "Mathematics as Language."
tjhombs 2 years ago
What is the definition of "You Tube." I don't think I could define "cat." I suggest reading Vygotsky for how meaning are constructed. These are socially negotiated, not defined and memorized. Please share you memorized definition of "cat."
sleeper2345 2 years ago
If words are not defined, then why do dictionaries exist?
For what it's worth, math information is also negotiated. Roman numerals are not used for normal math because they do not work for most numerical discussions. Mathematical theory, its meaning, and its understanding are discussed and negotiated on a regular basis by far more knowledgable people than you or I.
I have already shared my understanding of cat. That is irrelevant.
tjhombs 2 years ago
I agree, the meaning is shaped over time, just like 12 - 5. It means different things in different situations.
Note, too, that you meaning of cat does not distinguish it from other animals. You have a more complex image of a "cat" or you would not distinguish it from dog.
I'm not sure what you mean by "Roman numerals do not work for numerical discussions." Roman numerals have as much meaning as our Hindu-Arabic system.
sleeper2345 2 years ago
It is virtually impossible to perform higher math with Roman Numerals. Therefore, they have less meaning in practical applications.
tjhombs 2 years ago
It appears that learning higher math skills is irrespective of memorization.
"The final step in cognitive development (Piaget) is the formal operational stage. Only 35% of people ever achieve formal operational thought (Huitt & Hummel, 2003). This stage provides the ability to master abstract thought, use symbols in relation, and complete intricate problems in subjects such as Algebra. Hypotheticals are also processed during this stage." ~ Davison, 2006
(Shortened for brevity.)
tjhombs 2 years ago
Yound children do not use words until they know what those words are.
tjhombs 2 years ago
Yes, of course they do, but what tjhombs was talking about was the learning of reading and writing. Are you gonna tell us that that's all history too ?
bertwindon 1 year ago
"You don't think kids see the word cat by seeing it " ? Byeeee !
bertwindon 1 year ago
The word "cat" does not embody the image of a cat. Children learn what a cat is not by reading the word, but by creating mental images of what a cat is.
sleeper2345 1 year ago
@sleeper
To but-in on your deal with thombs, only You could have got the impression:
" You seem to think that children just recall meaningless information" I did not get any such impression, neither do I believe that anyone not in need of phychiatric help would have got such. Indeed I don't believe that thombs has any such view. It is unfair to "tar" people with your own problems.
bertwindon 1 year ago
"Because algebra is about memorizing facts that are not connected to meaning" -- more BS hat-talking, & pure nonsense, as anybody who was good at algebra would know.
Algebra's about a mind-set and tools for approaches to solving problems. One learns basic algorithms, & things take off from there. '2345 probably failed at maths. so his/her/its holding forth so, spewing gibberish, is tragicomic.
Slide rules, log tables & algebra/calculus sent men to the moon; EM is good for basket weaving.
seaXcrow 2 years ago
Algebra involves mathematical reasoning, not memorizing a unch of facts. EM can engage students in mathematical reasoning, if properly used. However, most teachers don't implement it properly, as demonstrated by research. Don't worry, we continue to teach math just as we did with slide rules, very poorly without connection to meaning of involving reasoning. See the TIMSS video study for more information on this.
sleeper2345 2 years ago 6
Do a search for "the good old days that never were" to see that US instruction in mathematics has never been helpful for developing student understanding of mathematics. I love your reminiscing of mathematical understanding, though no evidence exists that students actually learned mathematics better at that time. It is time to return to reality rather that live in dreamland.
sleeper2345 2 years ago 14
Right! I have a master's degree in mathematics (4.0 GPA). I've also won an award as the outstanding grad student in the math department. I'd be happy to test my mathematical prowess against yours.
*
I also have taught mathematics for 20+ years and have seen how little knowledge students have after receiving instruction at our finest high schools. The research on algebra backs this up: students have little sense of what algebraic symbols mean.
sleeper2345 1 year ago
@sleeper2345 So you instruct a machine in how to describe airflow !! - wow ! (bow scrape !)
bertwindon 1 year ago
@seaXcrow Mostly you are on the ball, but I think the ability to weave a basket would be severely impaired by a prolonged dose of "reform math"
bertwindon 1 year ago
Math sucks assholes.
SIRMaleMan 2 years ago
I completely agree with Mr. Mass, even though I don't live in Washington.
I tutor kids on the weekends in high school mathematics, and I continually see the same type of crap. The kids don't "feel" the math. They are just taught to memorize a minefield of rules to get the correct answer, which quickly become un-navigable to even the most powerful of minds.
There needs to be a reckoning in this country with the way math and science are taught. The way its done now just ain't cutting it.
clustro 2 years ago
Unfortunately, Mr. Mass is not advocating thinking. He is advocating moving away from textbooks that encourage students to think and doing what we've always done. What he doesn't realize is that most students have a traditional math experience, thus resulting in their poor performance. However, Mr. Mass forgot to ask them what their instruction was like. He wants them to memorize more rules and think less.
sleeper2345 2 years ago
Thinking? Start from the basis. This is how Everyday Math have ruined our students, especiailly those low income group.
siuwahchan 2 years ago
So thinking is not a basis. Good point. We don't want kids doing that.
sleeper2345 2 years ago
So if these kids have been taught so well to "think" , can you explain how come they cannot work-out the answer to elementary arithmetic ?
Oh - sorry - I forgot, the teachers didn't teach it rite.!
bertwindon 1 year ago
Bertwind,
What "kids" are you referring to? Cliff didn't look at the backgrounds of the students he assessed. He just assumed that all of his students came from the less than 5% of students who use these curricula. Quite the "leap of faith" by Cliff. However, he needs to support his conclusions, so twisting the data is his only option.
sleeper2345 1 year ago
Well anything that could make you start to tink would be welcome, but so far all efforts appear to have failed !!
bertwindon 1 year ago
Ask this guy to use a computer and I guaranty you he'll fuck up someone. What's important in life is relative to the decade and society one lives in.
Math isn't important when computers can do it for us. Math majors, don't flame me for this comment and give me the BS about how math made computers to blah blah blah... fact of the matter is, I can live life with basic math skills -- anything more means nothing to me.
Rstegs 3 years ago
Comment removed
GetSmart008 3 years ago
This has been flagged as spam show
Ask this guy to use a computer and ...wrong...numerical simulation of atmos sci. You think(sic). You want to create a society of luddites. No engineers physicists etc but only common duh heads like yourself...you think(sic). A society where there is a ceiling to intellectualism with you being the king duh head...you think(sic). Is the US going to be the next 3rd world economy...maybe if you and the luddites had your way it would. We have the same issues in Canada as does Wash state.
GetSmart008 3 years ago
Comment removed
frankbraker 2 years ago
Computers can do arithmetic, they cannot do MATH
arithmetic is NOT math...
arithmetic is to math what an assebly line is to engineering
spudd86 2 years ago 3
You really can't engineer a product without even bothering to get familiar on how the assembly line works. Your "engineered" product either won't be able to be produced at the mass and speed you want, or the cost you want, or, more likely, both.
You need to feel like popping an oillie comes as natural as walking before you get creative with your skateboard..
zilun 2 years ago
BUT they can put up a pretty good show if someone (Cliff, for instance) does the maths. for them. (Freaky, trust me). Thanks for pointing-out that the word "math" is all too often used where "arithmetic" is the word. I believe Arithmatic is about numbers, whilst Maths. may be about (odd?) facts to do with numbers. Maths. is maybe also about meaningful ways of re-arranging "truths". The maxim "Rubbish in Rubbish out" will always apply. Even If we made no mistakes. It's about definition
bertwindon 1 year ago
I'm aware of what computers can do.... (They can construct proofs, it slow and you have to write out your axioms in painful detail and then build up all the theorems you need from them, all expressed in painful detail... Then the theorem prover runs it chugs away for a while and you get a proof... They can do all kinds of things I ought to know since I'm almost finished with a Computer Science degree, if I don't know by now I'll have to give it back)
spudd86 1 year ago
i'd be interested to know more about these proofs. How can a computer prove something for an infinite number of cases? Can it prove that an even + an even is an even? Can it prove that there are an infinite number of prime numbers?
sleeper2345 1 year ago
the same way person would...
most of these systems are actually not really generating proofs (that's a very hard problem) but they can check any proof you given them (in the appropriate painful detail)
however if you restrict your problem domain they can do more stuff (eg computer algebra systems that can find exact solutions to things, or linear programming solvers)
spudd86 1 year ago
creating proofs is NP-Hard,
you can get a computer to try to find a proof of at most a certain length and it will chug away and eventually either come back with an answer, so you just set n large enough that if it says "no proof less than that long" you can reasonably conclude that means no proof (not the same as disproving the theorem). The problem is that we don't think there is a way to do this that will take a reasonable amount of time (unless P=NP) look up P vs NP if want to know more.
spudd86 1 year ago
I think you're using "proof" differently that a mathematician would. You're looking at whether a procedure can be completed in polynomial time, whereas a mathematician provides a proof for why a statement is always true.
sleeper2345 1 year ago
@sleeper2345 No I'm talking about how long it takes a computer to find a proof to a suitably stated theorem
The problem of: Given an arbitrary statement, find either a proof of at most a certain length N (for some def'n of length), or say "No Proof of length less than N"
Is known to be NP-Hard, and it is in NP because you can check the proof in polytime. So unless P=NP your computer won't be prooving things for you.
Even if it can do proofs it still doesn't know what theorems are interesting.
spudd86 1 year ago
@sleeper2345
see wikipedia Automated_theorem_proving and Automated_proof_checking
There's a bunch of people trying to get all of mathematics into an automatically checkable form
If you really want to look at this sort of stuff you'll need to brush up on computability/complexity, Gödel's completeness theorem,
I come from a CS background, so computability and complexity are sorta topics I did a fair bit with even though I'm just an undergrad
spudd86 1 year ago
@spudd86 more stuff:
There's the mizar project - The Mizar project started around 1973 as an attempt to reconstruct mathematical vernacular in a computer-oriented environment
coq - Coq is a formal proof management system. It provides a formal language to write mathematical definitions, executable algorithms and theorems together with an environment for semi-interactive development of machine-checked proofs.
spudd86 1 year ago
@bertwindon Math frequently has absolutely nothing at all to do with numbers (take topology for example, or look at how Turing Machines are defined)
spudd86 1 year ago
While this is mostly true, you will not be able to solve, say, mechanical and statistical problems that easily with a calculator.
Few mathematical packages can actually prove limits of functions, for example. You have to do that part yourself.
I don't know about the States but in the UK, any sort of science degree needs a solid mathematics foundation and after I've seen these videos, I can gather that few students in the States would end up at top UK institutions.
Computers don't solve all.
x42bn6 2 years ago
I just finished calculus 3. We weren't allowed to use calculators whatsoever. I really grateful because I understand the material intuitively. If your a math teacher dont use calculators.
lagrangemultipliers 3 years ago 2
what would you want a calculator for in calculus?
(well other than figuring out specific values of log/sin/cos... if you don't have the important one's memorized... (I don't :P))
spudd86 2 years ago
This is a major point. Maths. doesn't involve calcultors. It involves Reasoning.
- And testing the result of that "reasoning" !!
bertwindon 1 year ago
@bertwindon And also the creative process of figuring out what to reason about :P
spudd86 1 year ago
So, in 1991, how many of those people had been affected by a set of *recommendations* with no binding power? Certainly not the 40 and 50 year olds. Not the ones my age. (And, from your profile, approximately yours as well, Tom.) The 18 year olds? Do you really think the *recommendations* were quickly implemented, all across the USA, and had a dramatic impact within 2 years.
billandandy 3 years ago
And again clearly at 9:19: "The decline in math performance in Washington followed the introduction of reform math. A coincedence?...I think not."
As I said in response to another video, I taught at a community college from 1991-1996. Some students were 18. Some were my age (early to mid 20's). Some were in their 40s and 50s? (Why? Remember our last big recession? A lot of people were laid off in my area.)
billandandy 3 years ago
This guy thinks that problems with adding two fractions, or using algebra, began 10 years ago?!? He hasn't been paying attention! It's been going on for decades longer. Hmmm, could part of it be that universities allow more students in than they used to? What a concept.
billandandy 3 years ago
Pay attention. He's saying the problem has gotten much WORSE in the past 10 years. And it has.
ttowntom 3 years ago
I paid very close attention and I have paid attention to trends for the past ***17*** years I have been teaching mathematics. I also know about the trends that were occurring before that. I see you have no response to the statement that the problems existed before 10 years ago. That these problems were widespread. That universities did not see as many of these problems because admittance was tougher, but has progressively eased since the 1960s.)
billandandy 3 years ago
It's great that in the USA, we have the *opportunity* to receive higher education. That does not mean everyone's ready for it. I could say more, but I've already posted it in response to similar videos.
I'll just leave it at this: he dumbed down Atmospheric Sciences? Then ***he's just as much too blame***. MAINTAIN STANDARDS. Be prepared to work harder to raise students to those standards, but maintain them.
billandandy 3 years ago
Your post demonstrates quite handily that reading comprehension is as much of a problem as math skills. No one is denying that problems with math competency predate the past 10 years. The issue is they've grown substantially over that period. Dr. Mass has charts demonstrating the decline, evidence that corresponds with my own anecdotal evidence (teaching Physics at the University level).
ttowntom 3 years ago
Your post demonstrates quite handily that making nasty faceless insults over the internet is easy. Yes, there ARE people that claim the problem that began in the 90's. At 1:21, "... doing problems that students in the 1980s had little difficulty doing ... ."
billandandy 3 years ago