Shalinee Sharma: Revolutionizing Math Education for Every Student

0:00:08 [MUSIC]
0:00:10 Hello, my name is Guy Kawasaki.
0:00:13 This is the Remarkable People podcast.
0:00:14 Thank you for joining us.
0:00:17 As you know, we’re on a mission to make people remarkable.
0:00:20 And today we have another remarkable guest.
0:00:25 Her name is Shalini Sharma, and we’re going to talk about math.
0:00:28 Now, she’s the CEO and co-founder of Zern,
0:00:32 and this is a non-profit educational organization
0:00:34 to help kids learn math.
0:00:37 And what a wonderful goal and what a wonderful implementation
0:00:40 of this lovely strategy of hers.
0:00:45 And she has written a new book that I think you will find
0:00:46 fascinating.
0:00:52 It’s called “Math Mind,” subtitled “The Simple Path to Loving Math.”
0:00:54 That is a nice cadence to it, Shalini.
0:00:56 I like that cadence.
0:00:59 Anyway, so we’re going to be talking about math today.
0:01:03 So, Shalini, welcome to Remarkable People.
0:01:04 Thank you so much, Guy.
0:01:08 I’m so excited to be here, and I so enjoy your podcast.
0:01:11 Oh, you say that to everybody who interviews you, but–
0:01:14 [LAUGHTER]
0:01:18 I read your book, and as I’m reading it, I’m thinking, my god,
0:01:24 this book is like a combination of Carol Dweck meets Ken
0:01:27 Robinson meets Mary Murphy.
0:01:31 It’s like the growth mindset and educational mindset
0:01:35 and unleashing the power of youth all combined.
0:01:38 So I loved it, as you can tell.
0:01:39 Let me just jump in here.
0:01:42 So first, a really basic question,
0:01:47 which is, tell us why learning math is important at all.
0:01:48 Yeah.
0:01:50 Thank you so much, first of all, for what
0:01:53 you shared about the book, and for actually asking
0:01:57 such an important baseline question, why does math matter?
0:02:01 And one could even ask, why does math matter now?
0:02:05 But let me just start with the basics that we know as facts.
0:02:08 Leaving aside the heart, let’s just hit the head first.
0:02:13 Algebra completion is the most predictive activity
0:02:17 that a young person can do kindergarten through 12th grade
0:02:21 to predict that they’ll graduate from high school,
0:02:25 get admission to college, and graduate from college.
0:02:28 That one single activity, algebra completion.
0:02:31 And on the other side, failing algebra
0:02:35 is predictive of dropping out of high school.
0:02:38 In career, algebra completion, again,
0:02:41 eighth grade or high school algebra completion,
0:02:46 is predictive of massive difference in lifetime earnings.
0:02:49 And so what we can see in the actual facts
0:02:54 is how important math is in K-12 for your whole life.
0:02:57 And I think then we can start to explore why.
0:02:58 Why is that happening?
0:03:00 And what I would posit is that math
0:03:03 is the place that every child gets to participate
0:03:05 in a reasoning course.
0:03:08 And if you think about the core ways
0:03:11 we get through any job and lots of interesting problems
0:03:14 that we experience as grownups, that they require
0:03:17 two core skills, reasoning through the problem
0:03:19 and being able to communicate effectively
0:03:21 to navigate the problem.
0:03:24 So algebra and math, in general, is the reasoning course
0:03:26 we all get to take.
0:03:29 And what I’d say is that when you and I were in school,
0:03:33 the marketplace didn’t demand numeracy like it does now.
0:03:36 And so when we think about participating in jobs
0:03:39 in the marketplace, numeracy is even more important
0:03:40 than it used to be.
0:03:43 Further, just with the kind of information
0:03:46 that we get overloaded with to solve problems
0:03:49 in our everyday life, to even participate in our democracy
0:03:53 to understand the news, numeracy is a baseline.
0:03:56 Let me ask a really simplistic question.
0:04:00 People throw around the phrase math and algebra.
0:04:05 But can you precisely define what is algebra?
0:04:08 If you buy two oranges and they’re 50 cents each,
0:04:09 how much did you spend?
0:04:13 Is that algebra or what exactly is algebra?
0:04:16 So we know what is so predictive.
0:04:18 – I love that question.
0:04:22 What is algebra is actually a more than century-long debate.
0:04:24 (laughing)
0:04:25 – We only got an hour.
0:04:26 – Yeah.
0:04:30 And the debate ends with two options of what algebra is.
0:04:33 So algebra is either solve for X.
0:04:38 So it’s teaching the schema structures, tools, procedures
0:04:43 to allow young people and adults to solve for X.
0:04:47 Does that mean that when a first grader is doing a problem
0:04:49 where there is an X hidden,
0:04:53 you have, there are six pencils all together.
0:04:55 One friend grabbed three.
0:04:59 How many pencils were left in the container?
0:05:00 Is that algebra?
0:05:01 It actually is, right?
0:05:03 So that’s all for X.
0:05:05 Now the second thing that then makes it the classification
0:05:08 of algebra that is typically a later middle school
0:05:12 or early high school course is where we introduce
0:05:15 moving to almost exclusively notation
0:05:18 as opposed to concrete context and objects
0:05:20 that we still can utilize that.
0:05:23 And we start to move to multiple variables
0:05:26 where we’re solving for a system of equations.
0:05:27 So set another way.
0:05:31 If I have two equations, X plus Y equals five,
0:05:36 and then I have another equation, two X plus Y equals 17,
0:05:39 I can solve both variables.
0:05:43 And so these are the kind of the arbitrary and real lines.
0:05:45 But I think when we think about what’s most predictive
0:05:48 and what’s most important is solving for X,
0:05:51 which we do all the time in our lives.
0:05:54 – You got me with the solving for X
0:05:57 is something we do all the time in our lives.
0:06:02 But when do you ever solve for X and Y in life?
0:06:06 Normal life, maybe in some,
0:06:09 somebody at Google in statistics or something,
0:06:12 but when does a normal, quote, normal person
0:06:17 shopping at Costco ever solve for two variables?
0:06:18 – Every time they’re at Costco
0:06:21 and they may not need to do that in pencil and paper,
0:06:24 but having that structure in their brain and that schema
0:06:27 will make that Costco treasure hunt way more fun.
0:06:29 So it will.
0:06:31 So let’s assume for a minute
0:06:34 that your Costco monthly budget is $100
0:06:36 and you’re wandering Costco
0:06:39 and there’s things you are definitely going to get.
0:06:42 For example, almonds or coconut water,
0:06:44 like those you have to get on your list.
0:06:46 But then you have a little bit of money left
0:06:49 for some fun at Costco, which Costco always presents.
0:06:53 And the X and the Y is what I have to get
0:06:56 in what quantities and what I might want to get.
0:06:59 And I still have to solve inside $100.
0:07:01 And so we’re actually doing that every day all the time
0:07:03 in budgets when we think about
0:07:06 how much can we spend on a trip to the movies
0:07:08 or a trip to Disney World versus how much we can spend
0:07:10 on the things we have to spend.
0:07:13 Those are actually multivariable equations.
0:07:15 Now, we may not lay them out that way
0:07:17 and there may not be utility in laying them out,
0:07:19 but that doesn’t mean that that way of thinking
0:07:20 isn’t in the mind.
0:07:24 – Now, if I were talking to the sholony of physics
0:07:27 or statistics or chemistry,
0:07:31 wouldn’t that sholony say physics is everywhere around us
0:07:35 when your car breaks or doesn’t break and hits the wall?
0:07:36 What makes an orange?
0:07:39 Physics is everywhere, chemistry is everywhere,
0:07:41 reading is everywhere.
0:07:44 So like pretty soon everything is everywhere.
0:07:49 So is math special or is it, this is your area of expertise?
0:07:52 – I think math needs a little bit of a boost.
0:07:54 So the idea that reading is everywhere
0:07:58 and literacy is non-negotiable
0:08:01 is really what I hope we get to with numeracy.
0:08:04 And I think physics is one of the most beautiful applications
0:08:07 of math that there is.
0:08:10 But what I’d say is that the reason for my focus on math
0:08:13 or the reason that I wrote the book about math
0:08:16 is I really do think in our world today,
0:08:16 math needs a boost.
0:08:19 The way I would describe it is,
0:08:22 if you think about a classroom full of kindergartners
0:08:24 and you think about all the grownups
0:08:26 that love those kindergartners.
0:08:28 So those can be their teachers, their families,
0:08:30 their caregivers.
0:08:32 When those kids are in their kindergarten classroom,
0:08:37 there is an expectation that they will learn to read.
0:08:41 And then there’s a hope that they’ll love to read.
0:08:42 We don’t approach math that way.
0:08:45 So we don’t have an expectation
0:08:48 that every single child will be numerate.
0:08:50 And we don’t even dare have a hope
0:08:54 that they would all have some part of mathematics they love.
0:08:57 I think about when my 13-year-old boys became eight years old,
0:08:58 when I was eight years old,
0:09:02 my favorite book series was the C.S. Lewis Narnia series.
0:09:04 And it was really magical for me.
0:09:07 And I tried over and over to get my eight-year-olds
0:09:09 to love Narnia too.
0:09:11 For the parents out there, you know how that went.
0:09:14 So it didn’t work.
0:09:16 But I was filled with this hope and desire
0:09:19 that they could love this book the way I did.
0:09:23 And I want people to be filled with that hope and desire
0:09:26 that their children can love math too.
0:09:28 – And how did we get to this place
0:09:32 where people don’t have an expectation
0:09:34 about math that they have about reading?
0:09:36 What happened?
0:09:38 Does math have a marketing problem?
0:09:40 – I think so.
0:09:42 I think math does have a marketing problem.
0:09:45 How I’d say how we got to this place is
0:09:49 we just haven’t gotten to the other side yet.
0:09:51 If we could transport ourself in a time machine
0:09:54 200 years into the past,
0:09:57 when the majority of humans were not literate
0:09:58 and couldn’t read,
0:10:00 then we might encounter,
0:10:04 we’d likely encounter similar beliefs and stereotypes
0:10:06 about who could read and who couldn’t read
0:10:08 and how magical and special reading was.
0:10:12 And maybe even thinking of it as some rare genetic ability,
0:10:17 which we know and have proven as all of humanity is nonsense.
0:10:19 Today there are more people on earth,
0:10:21 the population growth has been explosive
0:10:24 and a greater percentage of them are literate.
0:10:26 And it’s because amongst other things,
0:10:29 it’s because we all have a common belief and expectation
0:10:32 that every human can read.
0:10:35 We don’t yet have that in math though it is emerging.
0:10:37 The second thing I’d say though is that
0:10:42 the experience of learning math can feel humiliating.
0:10:45 And that is shaped by our attitudes in mathematics.
0:10:49 One of the things that to share like a Carol Dweck
0:10:51 or a Mary Murphy and the mindset,
0:10:53 you might see in a math classroom,
0:10:57 a poster that says making mistakes is how you learn.
0:11:00 But in a lot of classrooms that poster,
0:11:03 children don’t feel that making mistakes is how they learn.
0:11:06 They feel that making mistakes is how they get punished.
0:11:08 And so they don’t make mistakes,
0:11:11 which means they don’t learn.
0:11:13 And so this is one of the tricky parts we have
0:11:15 in math teaching and learning today,
0:11:20 which is opening up both the pedagogy, the way we learn,
0:11:24 as well as the mindsets, the learner mindsets,
0:11:27 to really support an openness to learning
0:11:30 in math classrooms for all kids.
0:11:32 – But why, Shalini, why?
0:11:34 Why are we in this place?
0:11:35 What happened?
0:11:38 – I mean, I think one way to ask the question is,
0:11:40 why are we behind other countries
0:11:42 who are ahead of us?
0:11:45 So for example, there’s a test
0:11:47 that’s taken across all the countries
0:11:49 and it’s called the PISA test.
0:11:53 And it’s a high school test of proficiency in mathematics
0:11:55 and the United States scores very low
0:11:58 compared to other wealthy nations.
0:12:00 And for example, one nation that scores very high
0:12:02 on that test is Taiwan.
0:12:04 And in that test, at the end,
0:12:07 they ask that sample of students who take the test
0:12:10 that’s like a randomly sampled test.
0:12:12 They ask them different interesting questions.
0:12:16 Like, if I work harder in math, will I get better at math?
0:12:19 And in Taiwan, the students uniformly say yes.
0:12:22 And in the United States, the students say no.
0:12:26 And so I think what we have that’s quite important
0:12:30 to realize is that we have built up a large system
0:12:32 that costs a lot of money,
0:12:34 that educates 55 million students,
0:12:38 that is oriented more towards sorting children
0:12:41 in mathematics than teaching them all.
0:12:44 The deepest reason of why we have a fixed mindset
0:12:46 towards mathematics versus other countries,
0:12:49 I don’t know that I have the expertise
0:12:50 to answer all of that.
0:12:53 But I think the evidence that we do have that system
0:12:56 that we put a lot of money and time into
0:12:58 is one definitely worth reflecting on.
0:13:00 And we built our system,
0:13:04 which therefore means we could build a different one.
0:13:09 Do you think that for a long time prior to the pandemic,
0:13:14 lots of people were obsessed with the math SAT score
0:13:17 and then the SAT score became optional.
0:13:20 So do you think that that is gonna make the situation
0:13:22 better or worse?
0:13:25 The case for making it worse is that
0:13:28 without SATs necessary,
0:13:31 people aren’t gonna be forced to learn math.
0:13:34 The opposite argument could also work
0:13:37 that now people explore math with less risk
0:13:40 because they don’t have to worry about this SAT thing
0:13:41 hanging over them.
0:13:44 What do you think of standardized testing of math
0:13:48 now that you just discussed how low we score in math?
0:13:51 – Yeah, I’m not an expert on standardized testing,
0:13:53 but I can still share some thoughts.
0:13:56 What I would say about the SATs,
0:13:58 and this is from reading newspapers
0:14:02 as opposed to having personal deep expertise on the SATs,
0:14:05 is that many universities that took away the SATs
0:14:06 are now bringing them back.
0:14:09 And they find that they can actually get to
0:14:12 a more diverse and qualified candidate pool
0:14:15 for their universities by bringing the SATs back.
0:14:18 I think both Brown University and Dartmouth University
0:14:20 published both research on that
0:14:23 and then altered their orientation to admission.
0:14:27 So the question mark of whether the SATs
0:14:31 are better or worse is still out for public debate.
0:14:32 With regard to standardized tests,
0:14:36 and if they put too much pressure on the learning system,
0:14:38 ’cause I think your question is,
0:14:40 perhaps these standardized tests put too much pressure
0:14:44 onto the learning system, which doesn’t allow us to explore.
0:14:45 In Taiwan, there’s more pressure
0:14:47 with regard to standardized tests.
0:14:52 Same in Japan, which is another very high-performing country
0:14:53 in terms of mathematics.
0:14:55 In Japan, there are more children
0:14:56 who are proficient in calculus
0:14:59 than we have students proficient in algebra.
0:15:02 Singapore is also a very high-performing country
0:15:05 in terms of mathematics, so is Estonia.
0:15:09 And all of them have higher pressure exam structures
0:15:10 than we do.
0:15:13 So I don’t think the kind of broad dataset
0:15:17 would then say that when we take out the exam
0:15:18 and the pressure of the exam,
0:15:22 we could therefore get to something better as a default.
0:15:25 But I think there is no question
0:15:27 that math can be taught
0:15:31 where the orientation is just to get to an answer.
0:15:34 Here’s a simple story or a metaphor that I love to share,
0:15:39 which is, so guy, imagine if you have a reading test tomorrow
0:15:45 and the reading test tests you on, let’s say, 50 words,
0:15:47 but you actually don’t know how to read,
0:15:49 so we can pretend this reading test is in Hindi
0:15:52 or a foreign language that you don’t happen to know.
0:15:54 I’m just making a guess that you don’t know that language.
0:15:57 You aren’t taught the letters and the sounds
0:15:59 and how to sound them out and put them together,
0:16:01 but the way you choose to do it is you memorize the picture.
0:16:04 So you see a picture and you say that means house,
0:16:07 and then you see another picture and you say that means book,
0:16:09 and this is how you learn it.
0:16:11 And because you’re guy, let’s say tomorrow
0:16:13 you get an A on that test, you nail it.
0:16:17 – Let’s say.
0:16:19 – Let’s say, let’s try it.
0:16:21 But because you’re just a normal human being,
0:16:22 what also will happen, well, actually,
0:16:24 you’re a remarkable human being,
0:16:28 but what will happen next week because you have a brain,
0:16:31 that’s a human brain, is you will start to forget
0:16:33 because that learning wasn’t presented to you
0:16:37 in a durable fashion where you developed understanding
0:16:41 of ideas or deeper schema or structures.
0:16:43 You used a different form of learning,
0:16:46 which is just a more disposable form of learning
0:16:48 of just fast memorization.
0:16:51 And also that memorization didn’t have any connections,
0:16:52 right, and so that’s the kind of stuff
0:16:54 we just falls right out of our heads.
0:16:56 And so what would happen is,
0:16:58 while you got an A on that test next week
0:17:01 or two weeks later, you actually would not be able to read.
0:17:03 You would only be able to read for the test,
0:17:05 and then two weeks later, you’d forget how to read.
0:17:08 And this is an approach to math called answer getting.
0:17:11 And so a lot of what you might be learning in math
0:17:13 is just to memorize, but you don’t know
0:17:15 why anything is happening.
0:17:17 And when we teach math that way,
0:17:19 which is not how math is taught
0:17:21 in those top performing countries,
0:17:23 it is a very pressure-filled,
0:17:26 very anxiety-filled experience,
0:17:27 especially when you take tests,
0:17:29 because to study for those tests,
0:17:31 you memorize your way to the answers.
0:17:32 You don’t understand.
0:17:33 I’ll give you a simple example,
0:17:37 which is I didn’t learn ’til I was in my 40s
0:17:41 why anything times zero is zero.
0:17:45 N times zero is zero is a proof.
0:17:48 And on Zern, we teach that to third graders.
0:17:51 And what that means is when you hit
0:17:53 an algebra two or in calculus,
0:17:56 when you hit a quantity times zero,
0:17:59 what I used to do on the test is freeze for a second,
0:18:01 get really anxious for a second,
0:18:03 and say, what’s the rule about times zero?
0:18:04 What’s the rule?
0:18:05 Is it everything zero?
0:18:05 Is everything one?
0:18:06 Is everything?
0:18:10 And then also three raised to the power of zero is one.
0:18:12 And just all these different things to memorize.
0:18:15 But when you actually teach why things are happening,
0:18:18 you teach the axioms, you can release that pressure
0:18:20 and just understand.
0:18:23 So just think about how if you grabbed any book off a shelf,
0:18:25 even if it was difficult,
0:18:27 you could feel calm and confident
0:18:29 because you would be able to read it.
0:18:32 So a reading test wouldn’t be this pressure filled experience.
0:18:33 You’d be like, I can read.
0:18:36 What if a math test felt like that?
0:18:37 Because you understood.
0:18:41 – I think the reading test versus the math test
0:18:45 is because the precision of grading of a math test.
0:18:48 I mean, you either got the right answer, you didn’t, right?
0:18:53 Whereas reading test, I would say is more vague
0:18:55 or more subtle than that.
0:19:07 Did I hear you right?
0:19:10 Did I hear you say that in these countries
0:19:13 that lead in math, it’s very high pressure
0:19:15 and memorization based?
0:19:17 I thought you’re trying to make the case
0:19:20 that high pressure memorization is not good.
0:19:22 But then you’re saying that the countries that lead
0:19:24 use those not good methods.
0:19:29 So did I hear this wrong or is there an explanation there?
0:19:31 – Yeah, no, I appreciate that question.
0:19:33 So what we see in those top performing countries
0:19:35 and what we see in the bright spots
0:19:39 of top performing schools in this country
0:19:43 is what we call integrative complexity.
0:19:44 Two things can be true, right?
0:19:46 It’s not black or white, it’s gray.
0:19:48 And so what does that mean?
0:19:49 The distinction I was trying to make
0:19:51 is that in those high performing countries,
0:19:56 they have a higher pressure test than the SATs, way higher.
0:19:59 For example, those tests determine
0:20:00 which high school you go to.
0:20:03 Those tests you can or can’t stay with your friends.
0:20:06 You can imagine the pressure around that.
0:20:07 What else is interesting in those countries though,
0:20:09 when they present mathematics,
0:20:14 they don’t present math as memorization alone.
0:20:17 And they don’t present math as big ideas problem solving
0:20:22 and that kind of complexity alone, they present both.
0:20:23 So how does that play out?
0:20:25 I’ve spent time visiting math classrooms
0:20:27 in Singapore and Japan.
0:20:29 And so from a firsthand experience,
0:20:32 what you see is I was in this amazing
0:20:34 third grade classroom in Japan
0:20:38 where children were proving that the area of a triangle
0:20:40 was one half base height.
0:20:43 They had construction paper, scissors.
0:20:45 They were cutting up rectangles.
0:20:49 And they were proving that if you cut a rectangle in half,
0:20:52 that’s half, and then you multiply the base times the height,
0:20:55 that will be the area inside.
0:20:57 And they were having lots of fun doing it.
0:21:00 And that’s a deep proof and a deep amount of understanding.
0:21:03 But what preceded that portion of the math lesson
0:21:07 was maybe five or seven minutes of a fun game
0:21:11 where kids were memorizing their multiplication tables,
0:21:13 but in a fun gamified way.
0:21:16 Because the problem is if you have one without the other,
0:21:19 you either have like a memorized rote version of math,
0:21:23 like the reading test, or you have a lot of concepts,
0:21:24 but you can’t do the math
0:21:28 because your working memory gets overloaded
0:21:29 when you’re trying to do algebra,
0:21:33 because adding 13 plus 18 overwhelms your brain.
0:21:36 And so that’s what we can learn from the other countries,
0:21:40 which is this notion of both concepts and procedures
0:21:42 or integrative complexity.
0:21:46 – Now, just to be a devil’s advocate,
0:21:48 what if I said to you, yeah, okay,
0:21:53 so Japan, Singapore, Estonia score very high on math,
0:21:56 but I don’t exactly see a lot of creativity
0:21:57 coming out of those countries.
0:22:02 I don’t see Facebook, I don’t see Google, I don’t see Apple,
0:22:05 I don’t see any of these tech successes.
0:22:08 So yeah, maybe they’re great mathematicians and accountants,
0:22:10 but they’re not creative.
0:22:12 Not that I necessarily believe what I just said,
0:22:15 but somebody could say something like that
0:22:17 to which you would counter what?
0:22:20 – Yeah, so I think we also need to understand
0:22:24 that there are wonderful parts of our education system
0:22:26 and not throw it all away.
0:22:27 There are parts of our education system
0:22:31 that do help produce some of the most valuable
0:22:34 and interesting companies, like the ones you named.
0:22:37 So I don’t think that we can look at these countries
0:22:38 and say, let’s lock stock,
0:22:41 take every dimension of their education system.
0:22:43 Here we’re talking about one thing,
0:22:45 which is math proficiency.
0:22:47 One thing you can see, for example,
0:22:50 in the latest CHIPS bipartisan legislation,
0:22:55 which was a overwhelmingly set of bipartisan legislation
0:22:59 to support the increase of microchip manufacturing
0:23:04 in the United States was the worry across 50 governors
0:23:07 that we don’t have enough tertiary candidates
0:23:10 in STEM in this country.
0:23:13 So those are PhD candidates in STEM fields,
0:23:15 like for example, electrical engineering
0:23:18 or other vital fields to actually build
0:23:21 all those CHIPS manufacturing facilities.
0:23:24 So a lot of the companies you just named
0:23:28 rely on the education systems of other countries
0:23:32 to train people to that level of mathematics
0:23:33 to come and work here,
0:23:35 which is also a great part of our country
0:23:38 and a great part of our country’s innovation,
0:23:41 but we can also help our own students
0:23:43 be that successful as well.
0:23:46 So what I would say is we’re not looking totally
0:23:48 at every part of these education systems
0:23:50 and saying, let’s transplant them,
0:23:53 but we’re looking really specifically
0:23:55 at specific parts of the education systems,
0:23:59 like the percentage of children who know algebra
0:24:01 and thinking about what are some of the great things
0:24:03 we can bring over into our education system.
0:24:06 – I read your book about the horror stories
0:24:10 of people making these decisions where there’s 18 chairs
0:24:13 and there’s 20 students and the teacher says,
0:24:14 look to your right, look to your left,
0:24:18 one of you is gonna be gone, that kind of thing, right?
0:24:21 Like, why?
0:24:23 – I don’t understand this.
0:24:25 You would not say that in an English class
0:24:27 or a Spanish class or anything.
0:24:32 Why is math so linked with anxiety?
0:24:34 – Yeah, and cumulation too.
0:24:38 I think there’s so many myths around math
0:24:40 that start quite young,
0:24:43 and they might be in the movies
0:24:45 or they might be in popular culture,
0:24:49 but they’re also in math class every day.
0:24:52 So for example, my ninth grade classroom,
0:24:53 which you might be referencing,
0:24:55 actually amazing math teacher,
0:24:57 I learned so much mathematics,
0:25:01 but he really thought it was important to let us all know
0:25:03 that he would be failing a portion of us
0:25:06 out of the ninth grade honors math class
0:25:09 because we wouldn’t all make it to calculus.
0:25:11 Crazy, that was a group of kids
0:25:14 who had selected themselves into honors math,
0:25:15 had all the motivation in the world,
0:25:17 might have needed some additional supports
0:25:18 to get to calculus.
0:25:19 There might have been some kids
0:25:21 who needed some additional supports,
0:25:23 but that was the mindset.
0:25:27 I can’t fully get myself back into the ’90s mindset
0:25:29 of why one might have thought that way.
0:25:34 But I’d say today with digital tools and with AI tools,
0:25:36 any child in that ninth grade math class
0:25:40 who was struggling with, I don’t know, inverse functions
0:25:43 or whatever sort of chapter we were on
0:25:46 can Google their way to a great YouTube video,
0:25:48 can get unbelievable amounts of supports.
0:25:51 Google Gemini, they can take a picture of their math problem
0:25:53 and see it laid out step by step.
0:25:58 Tools like Zern, there is not a scarcity of supports.
0:26:02 And maybe in my teacher’s mind in ninth grade,
0:26:04 maybe he did see this as a very scarce amount
0:26:09 of learning input that could be provided.
0:26:11 And he had to ration that
0:26:13 across 18 students instead of 20,
0:26:17 which today is truly silly and nonsense.
0:26:21 – But couldn’t you make the case that
0:26:23 if you went out for the football team,
0:26:26 the football coach would say there’s 60 people here,
0:26:27 50 are gonna make the team.
0:26:29 So one out of five of you is not,
0:26:31 I hope I did the math right just now,
0:26:35 but one out of five of you is not gonna be on this team.
0:26:37 And that’s basketball, that’s football,
0:26:38 that’s the debate club.
0:26:42 Not life is not necessarily a no-cut sport.
0:26:45 – What’s the problem if your math teacher said that?
0:26:49 – Yeah, I think that is okay for advanced mathematics
0:26:51 or for things that people are choosing.
0:26:56 So if I cut you from reading,
0:26:58 because in second grade you weren’t showing
0:27:00 the kind of progress I needed you to show.
0:27:01 And so I was like, forget it,
0:27:02 you will finish elementary school,
0:27:04 but you will not be able to read.
0:27:05 (laughing)
0:27:07 – That sucks.
0:27:09 – It’s criminal and certainly sucks.
0:27:11 Now if, for example, we cut you
0:27:13 because there’s only a certain number of children
0:27:17 in a senior elective on Shakespeare
0:27:18 and only eight students can join
0:27:20 and everyone had to write an essay
0:27:21 to talk about how they wanted to join
0:27:25 and your essay didn’t make it, you’re the ninth student,
0:27:28 you were going to be fine, that’s fine.
0:27:30 I didn’t take away anything essential from you,
0:27:33 I didn’t take away your ability to read
0:27:35 and maybe you’ll take a different elective about,
0:27:38 I don’t know, dystopian novels, you will be fine.
0:27:41 It’s completely fine if at upper mathematics
0:27:43 one child is pursuing physics
0:27:46 and another is pursuing statistics
0:27:49 or they’re choosing not to pursue upper math whatsoever
0:27:51 and they have found another passion,
0:27:55 like history or science, it’s all fine.
0:27:58 But to take away what I would say is basic numeracy
0:27:59 is not fine.
0:28:02 Now, people can do it in different speeds.
0:28:04 I am a believer in the fact
0:28:06 that there is a bell curve of talent.
0:28:08 A simple example could be people are very tall
0:28:12 and if you’re six foot seven,
0:28:13 you have a different chance
0:28:16 at being able to play professional basketball
0:28:18 than if you are five foot seven.
0:28:22 So of course there’s talent and passion
0:28:24 and those are different by person
0:28:26 and of course they fall in a bell curve
0:28:29 but that is unrelated to what I’m talking about.
0:28:32 So of course there are subset of children
0:28:34 who will grow up to be professional NBA players
0:28:37 but that doesn’t mean every single child can’t play sports
0:28:40 and can’t participate on a team sport
0:28:42 and get all the value of it.
0:28:45 And no one ever opposes those two things, right?
0:28:46 I would just say another example I’d say
0:28:48 is of course there are gonna be people
0:28:50 who write Pulitzer Prize winning novels
0:28:52 but that doesn’t mean that you spending time
0:28:56 in creative writing isn’t extremely valuable for you
0:28:58 and for others who get to read it and enjoy it.
0:29:01 – What if somebody says I can go to Siri
0:29:06 or I can go to Alexa and say I have $100 to spend at Costco
0:29:09 I gotta buy $50 worth of broccoli and meat
0:29:10 how much do I have left over?
0:29:15 And Siri and Alexa and chat, GBT, anything will answer you.
0:29:18 Why do I have to learn math?
0:29:20 What do you say to that person?
0:29:22 – The same question could be asked
0:29:25 which is I can have Siri read any book allowed to me
0:29:27 or Alexa for example.
0:29:29 – I have asked other teachers that question, yes.
0:29:31 – Yeah and during the pandemic
0:29:34 when my sons were in third and fourth grade
0:29:35 and I was working a lot of times
0:29:39 we would just have Alexa read books allowed to our kids
0:29:41 as something that was a reasonable activity.
0:29:44 So I think these tools are amazing
0:29:48 and they increase engagement, they increase accessibility.
0:29:51 Sometimes a child might be a later reader
0:29:53 and this still lets them participate.
0:29:57 So we can use a lot of these tools to support accessibility,
0:29:59 to support on ramps for kids.
0:30:01 But what we also know is the other side of a world
0:30:06 with these kinds of tools is one with a lot more information
0:30:08 is one with a baseline of numeracy
0:30:12 expected to be a lot higher as well as literacy.
0:30:14 It’s this funny kind of double-edged sword
0:30:17 which is we can use these tools and we should.
0:30:18 They are phenomenal on ramps.
0:30:20 We use them all through Zern
0:30:23 and so we should use these tools as on ramps for students
0:30:27 but also know that this world, this digital
0:30:31 and AI driven world now sets higher expectations
0:30:32 of what humans can do.
0:30:35 And so that’s what’s actually happening right now.
0:30:37 – Let’s say that your kids
0:30:39 or one of your sons has dyslexia.
0:30:44 So reading is extremely hard for him, right?
0:30:47 And before you would say, wow, if you cannot read
0:30:50 how are you gonna get information about how to do things
0:30:54 and how to learn anything that’s written in text?
0:30:58 But now you could son, you can just go to YouTube
0:31:01 and ask the question, how do I add an HP printer
0:31:02 to a wireless network?
0:31:03 You don’t need to read that.
0:31:06 There’s a YouTube, there’s probably 500 YouTube videos
0:31:07 that explain that.
0:31:10 So don’t worry about your dyslexia son.
0:31:12 You don’t need to be able to read.
0:31:14 You can do everything is online.
0:31:17 Can’t you say the same thing about math?
0:31:20 – Yeah, I think for children who have learning differences
0:31:23 I don’t think that parents of children who have dyslexia
0:31:26 would want, I have a very good friend
0:31:27 whose son is diagnosis dyslexic.
0:31:32 She doesn’t want her son to not be able to read,
0:31:34 but she wants a little more space and time
0:31:36 to help her son read successfully,
0:31:38 but then still be able to participate
0:31:40 in everything with rigor.
0:31:43 Actually, her son is very good at mathematics
0:31:46 and loves it and feels really smart in math class.
0:31:49 But if he has to read the problem, the word problem
0:31:50 then he doesn’t feel that way.
0:31:52 And so a read aloud support,
0:31:55 like Zern has read aloud supports everywhere in YouTube.
0:31:57 There would be accessible read aloud supports.
0:31:59 That lets him still participate.
0:32:02 And so maybe another child will be proficiently reading
0:32:06 by second grade and this child might need till fifth or sixth.
0:32:09 But in that time, what we wanna be able to do
0:32:11 is still let that child participate.
0:32:14 For example, this child has an amazing ability to draw,
0:32:16 an amazing ability to participate in math.
0:32:20 Just a phenomenal athlete, a great thinker,
0:32:21 such a funny person.
0:32:24 These are all the other attributes of the child.
0:32:27 And if being unsuccessful in reading
0:32:29 holds him back from participating in everything,
0:32:32 you can imagine his confidence, his personality,
0:32:34 all of that getting crushed.
0:32:35 And so instead what we wanna do
0:32:37 with when children do have learning differences,
0:32:40 we don’t wanna lower our expectations and goals
0:32:41 for those children.
0:32:44 There are no parents out there who want that,
0:32:46 but they just want different timelines
0:32:49 and different supports so that kids can still access it.
0:32:51 And so I would say the same in math.
0:32:53 If digital tools are supporting your participation
0:32:56 in mathematics, that’s wonderful.
0:32:57 And we should use all those tools,
0:33:00 but that doesn’t mean that we have a lower expectation.
0:33:02 We still want that child to participate.
0:33:04 – When it comes to math,
0:33:06 I’m constantly on this question about
0:33:09 why math is so different.
0:33:12 When it comes to math, I swear there are people
0:33:17 who say of their kids, Johnny or Jane just isn’t good in math.
0:33:20 He’s an athlete or she’s creative.
0:33:23 She can write, but she just cannot do math.
0:33:25 They’re saying, well, you cannot do math,
0:33:26 but you can do other stuff.
0:33:28 So don’t worry about math,
0:33:31 but aren’t you kind of saying that everybody should have
0:33:36 a basic level of mathematical facility?
0:33:40 – Yeah, what I’m saying is math is taught.
0:33:42 Of course, there are a small set of people
0:33:45 who have genetic gifts and they can learn to read much faster
0:33:48 or they can play music much more quickly
0:33:51 or they can break a four minute mile and others can’t.
0:33:55 So of course that is true and that will always be true.
0:33:59 But what I’m saying is that norm where parents themselves
0:34:02 will say, oh, this kid just not a math kid,
0:34:07 where we describe it as a rare genetic ability is wrong
0:34:11 and has no science behind it
0:34:14 and that math can be taught.
0:34:17 And it is totally okay if it comes slower to others
0:34:18 and faster to others.
0:34:20 Let me give you an example with my own twins.
0:34:24 I had a twin who was reading pretty successfully
0:34:27 in kindergarten, which makes him an early reader.
0:34:31 It was sort of odd how fast he learned how to read.
0:34:32 And then the other twin wasn’t really
0:34:36 a fully successful reader till the back half of second grade,
0:34:40 which makes him a late reader against these kinds of norms.
0:34:42 Can you imagine if in our household,
0:34:45 we said or one of those children were to think
0:34:47 that only one was supposed to read?
0:34:50 (laughing)
0:34:52 – That’s a great story,
0:34:57 but I believe in fact that is happening with math.
0:34:59 – I assure you it’s happening.
0:35:01 That is your belief and I’m here to bring you data.
0:35:03 It is happening.
0:35:06 And at Zern, we prove every day
0:35:10 that the primary way to learn math is to do math
0:35:14 and that when kids do math, they learn math.
0:35:17 And so it isn’t the case that now kids can develop
0:35:19 at different paces, that’s normal,
0:35:22 but it isn’t the case that we need to sort for those
0:35:23 who have the rare genetic gift.
0:35:25 We can teach all kids math.
0:35:30 – So then let’s just numerate for us
0:35:34 the basic myths of math so that people know
0:35:37 when they’re like basically saying something wrong
0:35:39 or copying the wrong attitude.
0:35:42 What are the myths that we should avoid?
0:35:45 – Yeah, so three myths I think and there could be more,
0:35:46 but I’ll share three.
0:35:48 First, let me start with the top line,
0:35:50 that there’s a math kid, that’s the top line myth,
0:35:52 but let me share three in detail.
0:35:56 One is that the math is just about speed.
0:35:59 So let’s say you have minute math.
0:36:02 So there’s a problem and you have 60 seconds to do it.
0:36:04 You can imagine that children will look at a problem
0:36:06 and say, and we have research that proves this,
0:36:08 that children will say,
0:36:10 I can’t do this problem in 60 seconds.
0:36:13 So I’m dumb, but there’s somebody else
0:36:15 who can do this problem in 60 seconds.
0:36:17 So this problem is for them.
0:36:21 As opposed to I can learn how to do this problem.
0:36:22 I can get started in this problem.
0:36:26 I can share how I’m approaching solving this problem.
0:36:27 Now, as I said earlier,
0:36:30 there is an integrative complexity here.
0:36:35 Without automaticity or fluency of your math facts,
0:36:37 math becomes too hard.
0:36:39 It’s just like how your computer,
0:36:41 if you have too many simultaneous programs running
0:36:44 and your computer just turns off, crashes,
0:36:46 that metaphor is really apt.
0:36:48 That’s what happens to our brains.
0:36:50 So if we’re doing advanced mathematics
0:36:52 and adding, as I shared earlier in example,
0:36:56 13 plus 18 takes all our computing power.
0:36:58 What ends up happening is we can’t do
0:37:00 that advanced mathematics.
0:37:03 So we do need automaticity,
0:37:07 but math is not a running race with only one person winning.
0:37:09 That is not math.
0:37:10 But sir, and we have a team of engineers
0:37:12 when they’re solving interesting,
0:37:15 hard computer science problems that are math,
0:37:18 they’re not shouting out answers as fast as they can.
0:37:22 And they’re not racing each other.
0:37:24 They’re calmly solving problems.
0:37:27 There’s a professor who’s now the president
0:37:31 of Dartmouth University, Sian Bailak.
0:37:33 And she wrote this great book called “Choke.”
0:37:36 And what she did was she was testing speed
0:37:38 and whether or not experts go faster
0:37:40 and testing these hypotheses.
0:37:42 So she structured this great experiment
0:37:44 where she had physics undergraduates
0:37:47 who had completed one course in physics,
0:37:50 compete against physics graduate students
0:37:52 and professors of physics.
0:37:54 And she gave both groups an accessible,
0:37:56 it was a difficult problem, but accessible
0:37:59 to the physics undergraduates who had done one course.
0:38:01 And she was measuring and she timed them.
0:38:02 And she was measuring the speed at which
0:38:05 they’d finished the problem plus the accuracy.
0:38:08 And one prediction was that the undergraduates
0:38:09 would be less accurate
0:38:12 and that prediction turned out to be correct.
0:38:13 But the second prediction she had
0:38:16 was that the graduate students and the professors,
0:38:21 the experts would be faster and they were in fact slower.
0:38:24 So the graduate student and physics students
0:38:27 took much longer to set up the problem.
0:38:28 But when it came to calculating,
0:38:29 they actually flew through that.
0:38:33 They were able to calculate correctly and quickly.
0:38:36 But they took a lot of time to pause
0:38:37 and set up the problem.
0:38:40 The undergrads sped through setting up the problem
0:38:43 and sped through the calculations.
0:38:46 And often they set up the wrong problem.
0:38:48 So even if they calculated correctly,
0:38:49 they got the answer incorrect.
0:38:51 And so this is something to understand
0:38:54 which is that it is about fast and slow.
0:38:58 But a lot of times we position math as it’s about fast.
0:39:00 The last story I’ll tell you, which I love,
0:39:05 a famous UCLA professor studied American first graders
0:39:07 versus Japanese first graders.
0:39:09 And he gave both groups of students
0:39:12 a problem that was impossible to complete.
0:39:16 And the American students sat for less than one minute
0:39:19 and then handed the problem back to the teachers.
0:39:21 And the Japanese students sat for 45 minutes
0:39:23 trying to solve the problem.
0:39:26 So just an example of that speed myth.
0:39:28 I’ll share a couple others more quickly though.
0:39:32 So two others are that there’s only one way
0:39:33 to do a math problem.
0:39:35 That the teacher up there showed me the way
0:39:37 and I have to copy that way.
0:39:39 So math is actually not creative.
0:39:43 Math is about memorizing one way.
0:39:44 Actually, that’s not what math is at all.
0:39:46 Now there is one right answer.
0:39:48 And that’s actually beautiful.
0:39:52 That makes math empowering and autodidactic.
0:39:53 You can teach it to yourself
0:39:56 because you can check to see if you got the answer.
0:40:00 But there are hundreds of ways to solve a problem.
0:40:02 And that invites you into engaging
0:40:04 and exciting problem solving.
0:40:08 And so that’s another really important myth
0:40:11 that we see in this country that children come to believe
0:40:14 but we don’t see in top performing countries.
0:40:16 And then the last myth is one where
0:40:18 math is a series of tricks.
0:40:20 So how do I solve this problem?
0:40:23 I memorize this trick to do this problem.
0:40:27 What is two divided by one half?
0:40:28 Whenever I divide by a fraction,
0:40:30 I change the division sign to a time sign
0:40:32 and I flip the numbers.
0:40:33 It’s four.
0:40:34 Okay.
0:40:37 Well, what is two divided by one half?
0:40:40 Like why would I divide anything by a fraction?
0:40:43 Can you give me a real world life example?
0:40:46 What is two divided by one half?
0:40:47 I don’t know, I don’t care.
0:40:48 I just flip and multiply.
0:40:52 That’s not a way to learn and love math.
0:40:55 And so I’ll give you a concrete example of that could be
0:40:57 I have two giant cookies
0:41:00 and they’re too big to give to someone to eat
0:41:01 because they’re just, they’re enormous
0:41:03 and unappetizing and too much sugar.
0:41:06 So I’m gonna break them each in half.
0:41:09 And so now I have four pieces.
0:41:10 And so that’s a real world example
0:41:12 where the math has meaning.
0:41:13 So those are myths.
0:41:15 Up next on Remarkable People.
0:41:17 And so the most interesting question
0:41:20 that we have in mathematics that pertains to kids
0:41:23 who, let’s say you wanna help your child in ninth grade
0:41:25 really turn it around in math
0:41:28 is how do you catch up and move forward?
0:41:40 – Thank you to all our regular podcast listeners.
0:41:43 It’s our pleasure and honor to make the show for you.
0:41:45 If you find our show valuable,
0:41:47 please do us a favor and subscribe,
0:41:50 rate and review it even better.
0:41:52 Forward it to a friend.
0:41:54 A big mahalo to you for doing this.
0:41:59 Welcome back to Remarkable People with Guy Kawasaki.
0:42:04 – I have to say that one of my favorite stories
0:42:07 in your book was about the Burger King promotion
0:42:11 where they said that our burger is a third of a pound
0:42:15 and McDonald’s is selling a burger that is a quarter pound
0:42:18 and people thought that a quarter pounder weighs more
0:42:21 than a third pounder.
0:42:23 That was a great story.
0:42:28 And why are we at that point that it is something like that
0:42:30 which that’s pretty basic.
0:42:33 We’re not talking about Steve Wolfram level
0:42:34 Mathematica here.
0:42:37 Where did we go wrong to be in a place like that?
0:42:40 – Yeah, so that’s such a great story.
0:42:43 The A&W third pounder versus quarter pounder,
0:42:46 the test infractions that America failed.
0:42:50 That to me is the exact myth of memorizing math.
0:42:53 If I teach you, you were really, we’re all really lucky
0:42:56 that we didn’t memorize what four is.
0:42:58 We know what four is.
0:43:01 So you see four, you can count four.
0:43:04 If I ask you, prove to me this is four,
0:43:06 you would hold four items and you’d say there are four.
0:43:09 You know, you wouldn’t even, you’d think I was nuts.
0:43:14 But when I say one fourth, what image comes into your mind?
0:43:17 What concrete context do you think of?
0:43:19 You might, because I just said that,
0:43:21 might think of a quarter of a piece of cake
0:43:25 or a quarter of a full cake or a quarter of a pizza.
0:43:27 You might think of something concrete.
0:43:29 But a lot of times the way you would think of it is
0:43:31 numerator, denominator, one fourth.
0:43:34 Now I need to reduce to the common denominator.
0:43:39 You just go right into this disembodied stuff
0:43:40 you had to memorize.
0:43:43 But you can take two four-year-olds
0:43:45 and you can show them a quarter of a cake
0:43:49 or a third of a piece of cake and ask them which one they want.
0:43:53 They’re all intuitively going to know which one they want.
0:43:56 And so a lot of times by the time we teach fractions,
0:44:00 we stop teaching the intuition in the mathematics.
0:44:02 In whole numbers, every child gets to experience
0:44:03 the intuition, right?
0:44:06 Five crackers, they’re just shouting at you
0:44:10 when they’re three years old for the quantity they want.
0:44:12 And that’s really great ’cause they get that intuition.
0:44:16 In other countries, the intuition continues.
0:44:17 So what I told you about Singapore,
0:44:19 the third grade classroom where they were cutting
0:44:24 with construction paper to prove one half equals base height
0:44:27 by cutting rectangles, that’s because they get
0:44:30 to continue their intuition in mathematics.
0:44:32 – Since you brought up the subject of intuition,
0:44:37 now let’s make a transition to what are the best practices
0:44:39 of teaching math.
0:44:41 There’s five I outlined in my book
0:44:44 and I’d love to hit one deeply
0:44:46 ’cause we didn’t get to talk about it as much.
0:44:50 And then Guy, I’ll let you lead me if we wanna cover more.
0:44:54 The one I’d love to hit most deeply is pictures,
0:44:59 using pictures and concrete objects to make math make sense.
0:45:00 The kind of hidden secret I will tell you,
0:45:02 which I think Guy, you’ve experienced
0:45:06 in your professional career is that top of their game,
0:45:10 top of their field, mathematicians, economists,
0:45:12 they’re still using pictures.
0:45:14 Now, those pictures are graphs
0:45:18 and they’re often like line charts or functions
0:45:22 and that’s how they’re describing a lot of what they’re doing.
0:45:24 But you can think of Watson and Crick,
0:45:26 we’re able to understand the double helix
0:45:29 when they could see it, when they could imagine a picture.
0:45:32 Folks at the top of STEM are incredibly concrete
0:45:35 or pictorial when they’re describing what they’re doing.
0:45:37 But along the way, as we teach mathematics,
0:45:41 we use concrete items in kindergarten or first grade.
0:45:43 And then by the time you get into a fourth
0:45:46 or fifth grade classroom, like the fractions classroom,
0:45:49 it is all symbolic notation.
0:45:53 Now that symbolic notation is actually shorthand
0:45:56 to represent a set of pictures.
0:45:58 And it’s this fabulous shorthand
0:46:01 that mathematicians came up with
0:46:03 as the base 10 system was designed
0:46:06 and this beautiful common language of mathematics.
0:46:10 But what’s happened is now we only work in the shorthand
0:46:12 and teach the shorthand,
0:46:15 but the fastest way to teach what the shorthand means
0:46:17 is by bringing back pictures.
0:46:20 A simple example I’d give is in third grade,
0:46:24 we teach fractions and we also teach a fraction
0:46:27 where the numerator, the number on top,
0:46:30 is bigger than the number on the bottom, the denominator.
0:46:32 What does that mean?
0:46:33 You know, it means, well, you can reduce it
0:46:34 and get to what?
0:46:37 No, literally, what does it mean?
0:46:39 And so what does eight fourths mean?
0:46:43 In Zern and in great math classrooms,
0:46:47 you’ll see a teacher will take, let’s say, two objects,
0:46:51 two oranges and cut each one into four pieces.
0:46:54 And then so what is eight fourths?
0:46:58 Eight fourths is two ’cause there were two oranges.
0:47:02 Eight fourths is two groups of four fourths.
0:47:04 All of a sudden, you can so deeply understand
0:47:06 what eight fourths is
0:47:08 because you’re connecting the intuition.
0:47:11 Now, that doesn’t mean you also shouldn’t get to learn
0:47:15 this fabulous symbolic notation, which is pretty cool.
0:47:18 When I was in classrooms in Japan, once the math started,
0:47:20 I asked the translator to stop talking
0:47:22 ’cause I could follow the mathematics
0:47:27 because we all, as humans, all eight billion of us
0:47:29 have one beautiful common language
0:47:30 to describe mathematics.
0:47:33 I believe that learning that symbolic notation
0:47:34 has tremendous value.
0:47:37 It’s really important to teach eight fourths,
0:47:41 but not completely disconnected from meaning, with meaning.
0:47:42 – Since you brought up pictures,
0:47:45 I love the part in your book where you said
0:47:49 that there was this multiple choice test
0:47:52 about what’s the closest thing to–
0:47:53 – One half.
0:47:57 – One half, and Americans answered two over two,
0:47:59 which is one.
0:48:02 And, but they didn’t pick five over eight,
0:48:05 which is very close to one half.
0:48:07 And then you explained that using pictures,
0:48:09 and I really said, wow.
0:48:12 See why people might say two over two is closer
0:48:15 to one over two than five over eight,
0:48:19 but I know five over eight is closer.
0:48:21 – And for the folks who love math
0:48:26 or when parents identify one kid is just gets math,
0:48:29 what they’re actually describing is that child
0:48:32 or that adult can picture it.
0:48:35 And that’s it, because the asset test
0:48:38 of understanding in math is can you picture it?
0:48:39 And that’s it.
0:48:42 And so guess what you can offer the other child
0:48:44 who can’t picture it?
0:48:45 You can offer them a picture.
0:48:48 And then they’re in the game too.
0:48:50 Then they get to participate too.
0:48:51 And we don’t have to hold it against them
0:48:54 that they couldn’t think of the picture the first time,
0:48:56 because once you give them pictures,
0:48:58 then they can think of pictures, right?
0:49:00 So, and I’ll tell you something so fun,
0:49:02 which is guy, you could share your pictures
0:49:04 of how you think of something,
0:49:07 and I could share my pictures and they’d be different,
0:49:10 but your pictures would shape my problem solving
0:49:12 and mine would shape yours.
0:49:15 And so we would really get to start talking
0:49:17 about the process of problem solving,
0:49:20 and then we’d enjoy it and we get better together.
0:49:22 And that’s what happens when we start to move past
0:49:25 only the symbolic notation to the meaning,
0:49:29 and we start to share the meaning is that in the pictures,
0:49:32 we can actually have math be very fun
0:49:35 and we can increase our problem solving acuity.
0:49:37 We can get better at problem solving.
0:49:41 – Now, what if I’m a parent and I’m listening
0:49:44 to this podcast and I’m saying, oh my God,
0:49:45 I did things all wrong.
0:49:47 I stand convicted.
0:49:49 I told my kid that, oh, it’s okay.
0:49:50 You’re not good at math.
0:49:53 There’s focus on your writing or your art.
0:49:56 And now I’m hearing this and I now like,
0:49:58 the scales have been removed from my eyes,
0:50:01 and now I believe that my kid could be good at math
0:50:02 and should love math,
0:50:06 but he or she’s already in the ninth grade.
0:50:07 What do I do?
0:50:08 – Yeah, it’s not too late.
0:50:11 That gives me a window into the second thing
0:50:12 that I would love to share.
0:50:15 There’s another sort of point of view.
0:50:18 – Do you hear an ambulance or am I imagining that?
0:50:20 – That’s me, I apologize.
0:50:22 I’m in New York City, so that’s an ambulance going by.
0:50:23 I’m sorry.
0:50:28 – Well, you know, this is real life, all right, so.
0:50:32 – Yeah, so for students who are further along
0:50:35 in their math career, let’s say ninth grade or middle school,
0:50:37 and they don’t feel like math kids and they’re behind.
0:50:39 They have certain parts of mathematics
0:50:43 that they have missed or are not strong at.
0:50:46 I think that we think it’s over.
0:50:49 And there’s a lot of problems with that idea,
0:50:51 but one is actually just the structure of math.
0:50:55 So there’s an idea that math is cumulative, it is.
0:50:57 There would be no point in me teaching you calculus
0:50:58 if you couldn’t add.
0:51:00 That would be truly nuts.
0:51:02 But this idea that math is cumulative
0:51:05 is sometimes understood in both an inaccurate
0:51:07 and really literal way,
0:51:11 that I have to get 100 on each day of math that preceded.
0:51:13 So I have to get 100 yesterday
0:51:14 to be able to do the math today.
0:51:16 And that just isn’t true.
0:51:17 And I’ll give you an example
0:51:20 of how math is only a few big ideas,
0:51:23 and while cumulative, there are access points along the way.
0:51:26 So this is a real example in the Zern platform.
0:51:28 In seventh grade, irrespective of the pandemic,
0:51:30 we teach negative numbers.
0:51:33 But post-pandemic, what we see is that a lot of children
0:51:36 are shaky on decimal division.
0:51:40 And so let’s say in seventh grade, we present a question.
0:51:42 We’re not working in negative numbers.
0:51:43 We’re making it really concrete.
0:51:45 We’re climbing a mountain for positive numbers.
0:51:47 We hit C level for zero.
0:51:49 We’re down in the ocean for negative numbers.
0:51:50 It’s an engaging lesson.
0:51:51 It makes sense.
0:51:54 Negative numbers are coming to life for this child.
0:51:57 And then they hit a problem.
0:52:01 Negative 1.4 divided by two.
0:52:04 And their decimal division is shaky.
0:52:07 Now there’s two options at this fork in the road.
0:52:09 One option is we stop teaching negative numbers,
0:52:12 and we spend two or three weeks in decimal division.
0:52:14 But then the problem is the child
0:52:16 is two to three weeks behind in negative numbers
0:52:18 and perpetually behind.
0:52:20 And so the most interesting question
0:52:24 that we have in mathematics that pertains to kids who–
0:52:26 let’s say you want to help your child in ninth grade really
0:52:28 turn it around in math–
0:52:32 is how do you catch up and move forward?
0:52:34 And it is such an interesting and difficult question,
0:52:36 but let’s come back to this problem.
0:52:40 What we find is when we present to children, OK,
0:52:42 leave aside the negative number.
0:52:44 Leave aside the decimal.
0:52:46 What is 14 divided by two?
0:52:48 And Guy, what is it?
0:52:49 Seven, what do you mean?
0:52:50 Seven.
0:52:52 So every kid says that.
0:52:55 And then we say, OK, almost everything
0:52:58 you need to know about 1.4 divided by two.
0:53:00 So first, before we do instruction
0:53:03 on the decimal system, we say, now let’s try one more time.
0:53:05 What is 1.4 divided by two?
0:53:07 The vast majority say 0.7.
0:53:10 And then we say, OK, now what is negative 1.4 divided
0:53:11 by two?
0:53:13 So we just break it down and connect it
0:53:15 to the knowledge they already have.
0:53:17 And that helps most kids.
0:53:21 Some kids need additional support to understand, OK,
0:53:23 how does the decimal point work?
0:53:24 How does base 10 work?
0:53:29 And we can add that as a short bit of extended instruction
0:53:32 and still stay in the negative number’s work.
0:53:34 And so that’s what I would say for a lot of older children
0:53:36 in eighth graders, ninth graders, who
0:53:39 have these kinds of gaps in their learned mathematics.
0:53:42 It doesn’t mean that it’s catastrophic,
0:53:44 or that you have to all the way go back to the beginning.
0:53:48 It does need some extended time, but it can be targeted
0:53:48 and focused.
0:53:51 And you can still continue at the learning
0:53:52 that you’re working on.
0:53:54 The other story I would say is just
0:53:58 think of all the stories of late bloomers.
0:54:01 For example, the woman who wrote Hunger Games
0:54:03 was in her mid-40s when she wrote it.
0:54:04 That was her first book ever.
0:54:07 And so there’s this idea that we have to all figure
0:54:10 Yoyomas first started playing the cello when he was four.
0:54:13 That is so wonderful, and he’s a beautiful cello player.
0:54:16 But the world is not only of Yoyomas.
0:54:20 And so excellence can arrive at all these different points
0:54:21 in time.
0:54:24 And there’s lots of room in life for late blooming.
0:54:27 You brought up the story of Julia Child.
0:54:30 She was a spook until her 30s and 40s, right?
0:54:33 She didn’t become the French chef at eight.
0:54:34 That’s right.
0:54:35 That’s right.
0:54:38 And congrats to those who do find their passion at eight.
0:54:41 But that does not stop any of us from finding passions
0:54:43 in our 40s, or 50s, or whenever.
0:54:45 60s, in my case.
0:54:47 Yeah, 60s, 80s.
0:54:48 Like, you can–
0:54:49 yeah, vision.
0:54:52 That’s not how life doesn’t have to work like that.
0:54:54 OK, my last question.
0:54:56 And this is something that I noticed
0:55:02 that we had another math educator on named Joel Bowler.
0:55:05 And she has written a book called Math-ish.
0:55:10 I-S-H. And I noticed in many places in your book,
0:55:12 you didn’t exactly say it that way,
0:55:15 but you talk about intuition, right?
0:55:20 That 5/8 is closer to 1/2 than 2/2.
0:55:23 That’s an ish kind of thing, right?
0:55:26 So tell me about ish.
0:55:28 Do you think that ish is good enough
0:55:30 that you don’t need the exact answer as long
0:55:33 as you were in the ish zone?
0:55:35 I would say it depends.
0:55:37 I think the bigger headline around that
0:55:40 is that everyone can build a bath mind.
0:55:43 And doing so requires adaptability.
0:55:46 So when you get stuck solving a problem,
0:55:49 there are lots of ways you might go about that problem.
0:55:54 So one might be coming down an estimation or an intuition
0:55:55 pathway.
0:55:58 And that may help support your way to solve the problem.
0:55:59 Another, you just may know cold.
0:56:03 So if I ask you what 2 plus 8 is,
0:56:04 you don’t need to estimate it.
0:56:05 You just say 10.
0:56:07 You don’t even know where it came from.
0:56:11 The idea that there is estimation as a tool in problem
0:56:13 solving is vital.
0:56:17 And there is nobody who is going to get to the highest levels
0:56:20 of STEM without really strong estimation.
0:56:22 It’s critical to have very strong estimation.
0:56:25 Often, when you’re doing precision,
0:56:27 you need to pause and say, am I headed in the right direction?
0:56:31 Let me take a second and estimate and then let me keep going.
0:56:34 So what I would say is that’s a critical tool
0:56:37 in the math mind in the math toolkit, which
0:56:38 is around intuition and estimation.
0:56:39 Am I headed the right way?
0:56:41 Should this number be negative?
0:56:45 Should this number be bigger than 3,000, smaller than 3,000?
0:56:47 That’s keeping the intuition going.
0:56:49 It makes math very enjoyable.
0:56:52 It keeps your problem solving mind working.
0:56:55 And it’s also critical when you get stuck.
0:56:58 At the same time, precision in mathematics
0:57:00 is vital without precision.
0:57:02 The bridge will fall down.
0:57:05 You know, it will.
0:57:07 And so I wouldn’t present them as either/or,
0:57:12 but I’d present them as back to that integrative complexity,
0:57:16 that precision is the only way through is not
0:57:17 adaptable problem solving.
0:57:21 It’s not a reasonable way to approach, as you mentioned.
0:57:23 A lot of times in real life, you may not
0:57:26 need to use a precision method.
0:57:28 Sometimes going about a precision method
0:57:32 is silly because the estimation is close enough.
0:57:36 And what that is, is that’s where the real problem solving
0:57:38 is going on, when you need to be precise
0:57:40 and when you can use estimation and intuition.
0:57:43 The other thing I’d say about estimation and intuition
0:57:45 is you can get better at it.
0:57:47 It’s not just something you’re born with.
0:57:48 Same with precision.
0:57:51 You can get better at being precise.
0:57:53 It’s not just something you’re born with.
0:57:57 I would like you to just give a pitch for–
0:57:59 in a sense, we’ve been pitching your book the whole time,
0:58:00 so I think that’s done.
0:58:02 But pitch Zern.
0:58:03 Pitch your company.
0:58:06 What does this company and website do?
0:58:09 Zern’s an online math program for elementary and middle
0:58:10 school students.
0:58:12 Everyday kids in tens of thousands of classrooms
0:58:17 across the country log into Zern to learn and to practice math.
0:58:20 And there’s three things that you need to know about Zern–
0:58:22 how it works, how it’s built, and how to get on it.
0:58:24 So let me start with the last.
0:58:27 As a parent, you can just get on zern.org
0:58:29 and make a free account.
0:58:30 Same with as a teacher.
0:58:32 You can get on zern.org and make a free account.
0:58:35 Schools can also purchase Zern accounts
0:58:37 that have all these additional services.
0:58:40 In terms of how it works, Zern has several parts.
0:58:42 So the first is that when you log in,
0:58:45 you get interactive, guided lessons.
0:58:48 And kids start with a small game that builds fluency.
0:58:51 If you’re in kindergarten, you’re counting the objects
0:58:52 on a train.
0:58:54 If you’re in elementary school, you’re
0:58:57 doing fun games to practice your multiplication tables.
0:59:00 You then move into a video, an interactive video
0:59:04 that has pause points, where a teacher on screen
0:59:09 is presenting mathematics using gifts, pictures, real-world
0:59:12 objects, cutting oranges, as I mentioned.
0:59:15 And then finally, there is an independent practice portion
0:59:18 where students go up a tower of power.
0:59:21 And so there’s a gamified way to get to a badge
0:59:22 at the end of every lesson.
0:59:25 It’s built on a lot of what we just talked about.
0:59:27 But one of the core ways that it’s built
0:59:31 is really trying to build that concrete to pictorial
0:59:32 to abstract understanding.
0:59:35 And the last thing I’d say is there’s so much content.
0:59:40 So there is a fun lesson for every single day of instruction,
0:59:43 kindergarten through eighth grade.
0:59:46 This year, one in four elementary school students
0:59:48 are registered in the country in the United States,
0:59:51 are registered with an account, and more than a million
0:59:52 middle school students.
0:59:56 One in four students?
0:59:57 In elementary school.
1:00:00 In elementary school, have a ZERN account?
1:00:03 Yes, and more than a million of our middle school students
1:00:04 in the country.
1:00:08 Listen, I’m all about Ish, and even a guy who loves Ish
1:00:11 understands that is a humongous achievement.
1:00:13 Congratulations to you.
1:00:14 Wow.
1:00:15 Thank you.
1:00:20 All righty, we have come to the end of what I want to discuss.
1:00:21 Thank you so much.
1:00:24 It’s been most interesting and most remarkable.
1:00:26 And I thank you for being my guest.
1:00:29 And I hope everybody listening to this
1:00:32 has a new appreciation for math, and learning math,
1:00:35 and loving math, but also maybe more
1:00:38 the democratization of math than math is for everybody.
1:00:42 So I hope we’ve accomplished that in this episode.
1:00:46 Thank you very much, Charles Loney, for being on our show.
1:00:47 And good luck with your book.
1:00:52 Remember, it’s ZERN, Z-E-A-R-N.
1:00:54 And her book’s name is Math Mind.
1:00:57 And so that’s the follow-up for all of you listening.
1:01:01 Thank you very much for listening to “Remarkable People.”
1:01:08 This is “Remarkable People.”