 Good afternoon and welcome to likeable science here on think tech Hawaii. I'm your host Ethan Allen. Thanks for joining us today. Likeable science is all about how science is likeable. What can I say? It's a dynamic interesting process, a field of study, something we should all embrace and enjoy and it's not something that is confined to the people in white coats and in distant laboratories. Today we are branching out a little bit from science and we're actually going to sort of likeable math today and I'm joined from North Carolina by Dr. Malkeet Singh. Welcome Malkeet. Thank you Ethan. It's nice to be on the program. Glad to have you and as you may have seen our the title list was Math is Fun and Malkeet is one of these people who actually did not hate math, did not run from math, did not find math apparently unpleasant as so many people do. He learned math and he's gonna tell us today a little bit about about that experience. Maybe that's actually a good place to start Malkeet is how is it what was your early experience with math that helped sort of shape your interest and liking for math? Yes, when I was younger I left in Singapore. I grew up born and raised in Singapore. I also taught math and science in Singapore and before coming to the States and I find math intriguing. It's really elegant. It is known as the queen of the sciences so if we want to be really good scientists we need to get a good grip on mathematical principles and I find that when it's when we are teaching the kids they need math to be concrete and we want to show the beauty and the elegance of the mathematical principle. It's really writing and it's it's in nature and it's all around us. Absolutely it's an important part of science and nature and as I often talk about now computational thinking is a really important skill in becoming science literate but I think you really hit on a good one is if you can help kids really begin to appreciate math and like math then you really made a huge stride and helping them to do that by showing sort of the concrete nature by helping them understand it relates to real things it's not just some arbitrary scribblings of numbers on a page right it relates to real things and real processes that's that's a key part of early exposure to math right? Yes absolutely I think if they have bad experiences then they'd get turned off from mathematics doing math is hard and it's boring it's not exciting but if they had a good experience that builds up their confidence and at the same time they will start liking math because the experiences are good and they will explore studying math so so I think initial experiences are really important we do not want to put them off and everybody can do math and making math concrete is one of the ways to engage students for example when teaching fractions you can bring in things like ribbon and like a lot of kids might find it difficult when we are dividing fractions and fractions is a crucial topic in the early grades especially once they master the fundamentals of whole numbers and then they move on to fractions and that's a topic that stumbles a lot of students because maybe the examples given to them may not be too engaging so for example you can bring concrete stuff like ribbons so if we look at a ribbon and we say what is one divided by half and that's a division problem so we can take the ribbon for example in this case if we cut the ribbon into half how many pieces do we have so we can ask students to cut or kids to cut the ribbon into two half pieces so they will have two and then we can also get it to another fraction which is one quarter so we can ask what if you divide this into one quarter how many one quarter pieces do we have and then they can work with the ribbon and they get four and then you can move on to eight and so it becomes concrete understanding rather than just saying that whenever you divide by a fraction you take the reciprocal and multiply so that's just like a heuristic method where they you just follow a principle rather than here they are holding this right the object and making sense of the math and it makes sense to them when they can actually see it they can fill it and they understand why it always works right I was so struck as as an adult I didn't run into these until I was in little so-called math cubes or arithmetic cubes just sets of identical cubes you can begin to to look at and move about multiplication when you put you know you make a little grid of four cubes and then you make four lines of four cubes and suddenly you see that four times four or sixteen and you begin to understand the principle of squaring something right and that that sort of concrete thing when I thought it was just like wow this just suddenly makes clear so clear what you know that any kid and then you can look at three dimensions and begin to think four times four times four right if you built this up you begin to really understand that the power of using a concrete object or concrete objects to teach kids math I had never that was not part of my original math training at all and maybe why I'm not not particularly fond of half-mouth at all yeah I mean multiplication is directly related to finding area of for example rectangles where they you can give a one cube one centimeter by one centimeter cube or one inch by one inch cube and you let's say you you give 24 cubes and they can put six on the length side and oh and they fill up the whole rectangle and that you can say okay well why don't you come up with a theory on why when you put them length by width and you fill up the whole rectangle you get 24 so they can figure oh you are multiplication six times four is 24 cubes right you let explore and so they can relate multiplication to finding areas of rectangles and then they get they can see it that it works it it is a concrete to them math is existing it is right in front of them exactly exactly and they understand them the equivalents of six times four and four times six because they can look at that rectangle and say there are four rows of six where there are six rows of four depending upon how they look at it it's all the same yeah so when when you get the students to explore they will and get them to discuss and look as exactly like what you said some will see it six times four some will say it as four times six but then they come to the same conclusion and you can guide them along and that is more fun than just teaching them memorize this six times four six seven four and so and so then they can see those same 24 cubes can be done in three rows of eight or eight rows of three right and it's the same 24 you know it's a whole yes you know suddenly they even get that notion of equivalence in a very very real very authentic way yeah no very powerful and I so much wish in retrospect that I had been taught that way originally because because of course how we learn math early on really shapes I think how we think about it later I suspect you had very good teachers yeah yeah I I think so I I think teaching teachers make a great impact on students interest and at the same time giving them the confidence that they can do well in math and they shall explore doing higher level math and if they get discouraged in the earlier grades then it's hard to move on to upper grades and and suddenly just get a phony and say oh today I get up and I love that so it builds from foundations yeah yeah and Singapore of course it is renowned for having a very good education system teachers are well-trained professional they generally do a really super good job and really they obviously work for you so whereas I had a my early grade teachers were not necessarily I think of the highest caliber and particularly in things like math so I'm just lucky my folks supported my interest in science I suppose yeah yeah I think it's we have to make maybe teaching math a bit more consistent and and I think so that and get teachers to work together and look at strategies now we have a lot of resources like they have video clips clips on teaching math fractions for example teaching rational numbers and things like that where the teachers can get ideas and they can work together and collaborate and make make teaching more fun in it's rather than just individually coming up with a plan because sometimes when you collaborate you exchange ideas and you you can you you can share ideas and and learn from each other and come up with a better lesson plan perhaps exactly exact in some of those have been gathered into a together into a resource that we have a picture of I think this is from a group called the what's work what works clearinghouse and so they have this this booklet on developing effective thinking about fractions there so and we have the URL at the bottom if viewers want to go to get that they can get it from the Institute for educational services IES there you can find that by googling it on the web and look at their resources you can find this so you you've used this particular resource yes I have used this resource and what the resource does is it it gathers all the evidence from the research findings and they look at different practices and they rate those practices according to the available evidence so some of the practices have very strong evidence some of them may have moderate evidence depending on how many research studies have found an impact to improve student performance and some of that the principles that that I think worked for me I actually the same that is being shown in that case guide so from my own personal experience I think those are strong evidence or moderate evidence depending on how much research is available but it just can use those as a guide yeah and you know different teachers of course have different styles and different approaches but there is overall our approaches that are known to be shown to be now demonstrated and proven to be better and more effective than other approaches and it's good for teachers to be able to know this and know that you know you hear some tried and true approaches here are some basic things I really ought to be doing on teaching math and then there are other things that I could try it if I want but you know it may be less effective so it's it's valuable for teachers to have that kind of resource yes because now they they don't need to search for what works or what doesn't work they have a resource that the what works clearing house which is body of the Institute of Educational Sciences and they have done all the hard work to put it together so that the teachers don't have to hunt for what works what doesn't work they can have the evidence at their fingertips basically knowing what research is available out there so they don't they just have a resource and they can adapt that and they know that okay this practice works then they can use that and develop their lesson plans or they can discuss and make it more exciting but at least they are they are in the ballpark yeah absolutely absolutely that's great it's great great guide to have and great group is this Institute for Educational Services has done really remarkable work we're gonna explore more about math and why math is fun but first we're gonna take a one-minute break here my guest Malkeet Singh will be back with me Ethan Allen your host here on likeable science on think why we'll be back in one minute hello I'm Dave Stevens host of the cyber underground this is where we discuss everything that relates to computers that's just kind of scare you out of your mind so come join us every week here on think tech Hawaii calm 1pm on Friday afternoons and then you can go see all our episodes on YouTube just look up the cyber underground on YouTube all our shows will show up and please follow us we're always giving you current relevant information to protect you keep in you safe hello hi I'm Rusty Komori host of Beyond the Lines on think tech Hawaii my show is based on my book also titled Beyond the Lines and it's about creating a superior culture of excellence leadership and finding greatness I interview guests who are successful in business sports and life which is sure to inspire you in finding your greatness join me every Monday as we go beyond the lines at 11 a.m. Aloha and you're back here on likeable science on think tech Hawaii with me your host Ethan Allen and with our guest today Dr. Malkeet Singh from North Carolina thanks again for being here Malkeet and we are we've been exploring why math is interesting why math is fun looking at some of the keys to really helping engage young learners in math and we're talking for a bit there about the concrete nature of helping kids understand by using real tangible objects ribbons or a little cubes of things objects they can see they can feel they can manipulate and they can then get a real sense of what this math really mean and but I think you wanted to delve a little more deeply into a little bit higher levels you had talked in your our earlier correspondence about something called the distributed property of math yes yes so I think the second important thing that we have to consider is making sure that the math that we are teaching we make strong connections to the mathematical principles for example when customers why is a negative number multiplied by a negative number is positive the typically we make teachers may give a response like well that's that's a rule it's always positive negative number multiplied by negative is positive but actually it is you can prove why negative number multiplied by a negative will always be a positive number so what principle can we use we use what properties distributive property it we can build on the foundational principle so that they appreciate that the distributive property can be used to prove why a negative number multiplied by a negative number will always be positive for example if you look at this we know that multiplying the number by zero is zero so multiplying the number by one gets the same number for example if two multiplied by one we get two and negative two multiplied by one is equals to negative two so for example if we have a distributive property property so in this case if we have a negative here negative one multiplied by one we get a negative one and then we can multiply negative one by a negative one so to get a zero we we negative one multiplied by negative one has to be one so it is a so the students we get the students to explore using the distributive property what and it be negative one multiplied by negative one has to be one to make the right side equals to zero so once we know that negative one multiply negative one is always one we can expand and ask the students explore what do you think negative two multiply negative one will be will it be negative two or positive two and negative two multiply negative and so as they develop it inductively they will understand that oh yeah the distributive property shows that it works a negative number multiply a negative number will always be a positive number so from all this inductive reasoning then they will do then you have a deductive principle that a negative number multiply a negative number will always be positive right right and that's if you can teach math where yes as you say you develop that from some foundational principles and it's not just a matter of learning arbitrary rules it's much more real it stays in our heads much more they can actually use it and apply it much more effectively and they will become you know more computationally literate as the phrasing is and it's a very valuable skill for kids to learn and something that's again I think often not taught in the way it should be but because many of the teachers elementary teachers themselves that were not taught in this good way using concrete examples drawing things out of fundamental principles and using those processes of induction deduction as you just nicely described right yes and so for example if you look at negative two multiply by negative two you you can see that now if the students know that negative one multiply negative one is always one and then they can develop the bill on that foundation and say okay let's use deduct let's use distributive property to see to show why negative two multiply negative two will be positive oh so they can use their distributive property and then expand it accordingly because they have already proven negative one multiply by negative one will always be one and so when you add one plus one plus one plus one that will be four so negative two multiply negative two will always be four so they can build on then so you're drawing the principles out of distributive property and then explaining and making negative multiplications more fun math is fun it's exciting so it makes math elegant rather than if the teacher says well that's a rule right exactly I mean the one at least the nice thing about mathematical rules is they are consistent it was something that always bothered me in uh learning languages was the fact that the rules there are exceptions to all the rules math is very elegant in that sense that its rules are hard and fast but it's it's far better if you say to teach the kids not the rules or let them deduce the rules themselves and see how the rules come out of the underlying properties of numbers basically right yes and you're developing scientific skills as well scientific thinking because you're using inductive reasoning you're you then and then you come up with and then they can based on the inductive reasoning they've developed a principle and the principle and learn to the principle and now they know how to apply that principle to all their other mathematical questions and problems that they when they deal with negative numbers multiplication or negative numbers so they they can use deductive reasoning from that then that point onward so you it's a it's a good scientific thinking tool as well so the teachers when they teach in this manner not only they are answering the students why the curiosity that the students discover for themselves the beauty of math and the elegance and also they develop the scientific thinking that will help them when they do science and do STEM subjects like science, technology, math, yes it works right right this math is clearly very important in in areas like engineering and the process of producing good concrete results out of a engineering challenge you really have to understand the math you have to understand and be able to apply it well so it's really critical so um and go ahead one thing I would point out is if they are if that you develop the interest uh if the students develop the interest for math and and at the upper level like calculus and higher math it comes with effort they need to put in a lot of effort because um the math problems are a bit more complex but then they can persevere because that interest will drive them to find and learn more interesting mathematical principles and think to things that they can actually use and develop right right and that's again you hit on a key point that in order to build to understand you have to have that engagement that interest and that in part is based on that early learning and having early successes right being able to realize hey I I figured that out uh why you know two times two is four why negative two times negative two is also four and you know when they develop that confidence and that interest and together right those two properties lead them to be confident about further explorations both build their curiosity and and their uh self-efficacy as or so they'll they'll persist and push ahead and learn more and more of the critical math they can then apply in other in other areas absolutely yes that's uh that leads to the third important thing that I I wanted to share is that uh math with perseverance effort uh all students can do well in math is not an innate ability that means some can do math and some uh just one not being able to do math but it's those early experiences that shapes much of their uh desire to do math and do engineering and uh to persevere and and do really well in that subject matter so exactly there is a increasing recognition that that math ability and indeed abilities in general are much more plastic than we used to think and be developed by good teaching encouragement uh and and pushing ahead and rather than just saying oh this is something I can't do or I don't do well hey I want to thank you so much for being with me today Malkeet it's been a real pleasure we're coming up on the end of our time however but uh Malkeet Singh uh from North Carolina has been here help helping us learn that that math is fun thank you so much Malkeet and I hope you will I hope you will come back uh next weekend and see more likeable science here on Think Tech Hawaii until then