Latest / Math Therapy / Math ed needs more conversations like this w/ Pam Harris

Transcript

Math ed needs more conversations like this w/ Pam Harris · Math Therapy

• 0:02
  Pam Harris: one of my favorite things to do is to ask how do you think about this problem?
• 0:05
  Pam Harris: 99% of the time people will go, well, you know, that's how you think about it, but you're supposed to do the right way.
• 0:10
  Pam Harris: And I'm like, what if we could teach all math the way you just logiced your way through that one.
• 0:14
  Pam Harris: Algorithms amazing human achievements.
• 0:17
  Pam Harris: They're just not very good teaching tools because, people like me can get trapped in them and believe that math is something that it isn't.
• 0:26
  Vanessa Vakharia: Okay guys, it's me, Vanessa, and I could not be more excited for you to hear today's episode Okay, I know I say that every single episode is gonna change your life, but this one is seriously going to change your life.
• 0:37
  Vanessa Vakharia: Because the conversation I'm sharing with you today is not just about how we can improve math education, but literally about how we can improve the way we all talk to each other as people.
• 0:47
  Vanessa Vakharia: The first time I actually had a conversation with Pam Harris was literally an hour long argument because we were both guests on the Debate Math Podcast, so we were debating, we were actually discussing whether students should be able to use algorithms or tricks.
• 1:01
  Vanessa Vakharia: See, Pam is the founder of Math is Figureoutable, and by that she means that students can make sense of math through reason and shouldn't be taught to rely on memorization or shortcuts.
• 1:11
  Vanessa Vakharia: I, on the other hand, just don't like believe in black and white rules or thinking, and I believe that students should have access to whatever tools work for them because everyone's different.
• 1:21
  Vanessa Vakharia: Now on social media, most arguments would just end there, right?
• 1:25
  Vanessa Vakharia: Like, you're wrong.
• 1:26
  Vanessa Vakharia: No, you're wrong.
• 1:26
  Vanessa Vakharia: Okay, cool.
• 1:27
  Vanessa Vakharia: The end.
• 1:28
  Vanessa Vakharia: So I wanted to have Pam on to really dive into these big questions with nuance and truly get to the root of what we each believe.
• 1:36
  Vanessa Vakharia: Spoiler, we have more in common than we initially thought.
• 1:40
  Vanessa Vakharia: This convo is a must listen for anyone passionate about teaching and learning math.
• 1:44
  Vanessa Vakharia: We explore not just where we differ, but also the shared goal that unites us, which is helping students truly think, reason, and understand, rather than just memorizing steps or like spitting out answers.
• 1:57
  Vanessa Vakharia: I hope this episode inspires you to have deeper conversations with every single person in your life because it certainly inspired me.
• 2:06
  Vanessa Vakharia: I was trying to explain to David how I knew you and I was like, you know, I didn't really know Pam until Chris and Rob got us on their Debate Math Podcast.
• 2:14
  Vanessa Vakharia: So our first real interaction was a debate, which isn't like the best way to form like a, a relationship with someone.
• 2:21
  Vanessa Vakharia: You would think, especially because our debate was a little heated, which if you guys haven't listened to it, go to the Debate Math Podcast, listen to me and Pam's first conversation via debate, about algorithms, which we're obviously gonna talk about later.
• 2:33
  Vanessa Vakharia: But my point is that like you would think after like a debate where two people are disagreeing, we wouldn't like become friends after necessarily,
• 2:40
  Pam Harris: Sure enough,
• 2:41
  Vanessa Vakharia: No, but we kind of did.
• 2:43
  Pam Harris: Well, I I maybe we both went into it, I think with, the best intention, desire to have a conversation.
• 2:51
  Pam Harris: We listened to each other and we spoke back to each other's points.
• 2:54
  Pam Harris: And we didn't just have our, you know, our thing that we were gonna say, and I'm not listening to you, whatever.
• 3:00
  Pam Harris: And I think it was a real conversation.
• 3:03
  Vanessa Vakharia: For some reason, whatever it was, I didn't think the debate was going to be as like pleasant as it was.
• 3:10
  Pam Harris: Huh?
• 3:10
  Vanessa Vakharia: I, that's all I can say.
• 3:11
  Vanessa Vakharia: Like it had nothing to do with you.
• 3:13
  Pam Harris: in your face or something like,
• 3:14
  Vanessa Vakharia: I mean, maybe just the term debate and also just because, I don't know.
• 3:18
  Vanessa Vakharia: I've heard so many great things about you.
• 3:20
  Vanessa Vakharia: I think maybe I was a bit intimidated, like maybe I was like, I don't know if like, your brand Math Is Figureoutable is really based on the idea that algorithms should not be used as teaching Tools and we can figure out math, right.
• 3:34
  Vanessa Vakharia: Would you say
• 3:35
  Pam Harris: those so
• 3:35
  Vanessa Vakharia: Yeah.
• 3:36
  Vanessa Vakharia: Flip it?
• 3:36
  Pam Harris: emphasis is we can
• 3:38
  Vanessa Vakharia: Yes.
• 3:39
  Pam Harris: It's not rote memorizable, it's figureoutable.
• 3:42
  Pam Harris: And then there's a sort of corollary that, a thing that follows.
• 3:47
  Pam Harris: If we are about figuring out math, if, if, if it means that we can actually teach kids to logic their way through problems, which helps them create mathematical connections and relationships, which then helps them logic through new problems, which then helps them create new mathematical relationships, the algorithms can get in the way of that and it can actually trap students into not knowing that we can do that, that that's, that those are actually the mental actions of a mathematician.
• 4:14
  Pam Harris: Algorithms aren't evil.
• 4:16
  Pam Harris: They're amazing human achievements.
• 4:18
  Pam Harris: They're just not very good teaching tools because, I'm pointing at me, people like me can get trapped in them and believe that math is something that it isn't.
• 4:28
  Vanessa Vakharia: Okay.
• 4:28
  Vanessa Vakharia: I wanna get into this so much, and I wanna say just as to wrap up the, the what I said before, so it doesn't seem like I thought you were some mean person, that's not it.
• 4:35
  Vanessa Vakharia: I really admire you, I think there are so many cool things about you, and I think this whole philosophy is something I'd never really considered before.
• 4:42
  Vanessa Vakharia: But more than that, I hadn't seen it in action.
• 4:44
  Vanessa Vakharia: And I want people to get a little taste of what you're talking about.
• 4:47
  Vanessa Vakharia: But first I was explaining this to David, okay.
• 4:51
  Vanessa Vakharia: And he said to me, you and your guests keep talking about algorithms.
• 4:55
  Vanessa Vakharia: So like, what is an algorithm, exactly?
• 4:59
  Pam Harris: These are excellent questions because we as a mathematics education community have gotten muddy and we use words to mean different things, and I don't know that we know that.
• 5:10
  Pam Harris: a true algorithm means I can you any numbers, throw'em in, you follow the steps, all the steps every time, and you will come out with the correct answer.
• 5:19
  Pam Harris: It took humankind until we had the, uh, Roman Arabic numerals to get to where we were in about seven 800 AD when Al-Khwarizmi created both algebra and he wrote a book that then, um, he created our, at least precursors to our digits focused algorithms.
• 5:39
  Pam Harris: So first we needed the, the numer system that we have today, and then he said, Hey, we could actually align these numbers up and just focus on digits.
• 5:49
  Pam Harris: You don't actually have to know what's going on at all.
• 5:52
  Pam Harris: You just have to be able to do these steps in a certain order.
• 5:56
  Pam Harris: Start with the smallest digits, and then the next digits, and then the next digits.
• 5:59
  Pam Harris: Without even really understanding what's happening or the numbers involved, you can just do a bunch of steps, you'll always get the correct answer.
• 6:05
  Pam Harris: Well, that was an amazing, historic step for mankind because before that, the only people who were able to do lots of digit computations people who had money.
• 6:17
  Pam Harris: were in the sort of intelligentsia, they were the upper crust that could afford to send their kids to school to learn to, to work an Abacus.
• 6:25
  Pam Harris: So when Al-Khwarizmi created the algorithms, it was almost like Gutenberg's printing press.
• 6:32
  Pam Harris: Like Gutenberg's printing press is when he was able to print the Bible and gave the word to the common man.
• 6:37
  Pam Harris: And all of a sudden the common man could read.
• 6:40
  Pam Harris: And we had the Renaissance.
• 6:42
  Pam Harris: Well, Al-Khwarizmi's algorithms were very similar.
• 6:45
  Pam Harris: All of a sudden you didn't have to go to school to learn to work an Abacus.
• 6:49
  Pam Harris: Could use an algorithm and all of a sudden the common man could compute.
• 6:53
  Pam Harris: So hear me clearly, the algorithms are amazing, historic achievements.
• 6:57
  Pam Harris: They are amazing that we came up with them.
• 6:59
  Pam Harris: We can do better.
• 7:00
  Vanessa Vakharia: Okay, but hold on.
• 7:01
  Vanessa Vakharia: I need an example of an algorithm.
• 7:03
  Vanessa Vakharia: Like give us an ex, like do you know what I mean?
• 7:05
  Vanessa Vakharia: Like what's, give us a one that we all would kind of be,
• 7:08
  Pam Harris: 99 plus 67.
• 7:10
  Pam Harris: The algorithm would say, line those numbers up.
• 7:13
  Pam Harris: So 99 plus 67, I gotta even picture this in my head.
• 7:16
  Pam Harris: So 99 67, that means there's a seven and a nine in the smallest.
• 7:20
  Pam Harris: Those are smallest numbers, right?
• 7:22
  Pam Harris: So we would add the seven and the nine together, we know that 16.
• 7:25
  Pam Harris: We'd write down the, the six of the 16 part, carry the one or the 10 depending on how well you understand what you're doing.
• 7:32
  Pam Harris: And then I would add that second column together.
• 7:34
  Pam Harris: and then notice I've written the sum of the smallest numbers down and now the sum of the biggest numbers down.
• 7:40
  Pam Harris: And then I would to read the answer, I have to go the other direction.
• 7:43
  Vanessa Vakharia: So let me just make sure I understand.
• 7:45
  Vanessa Vakharia: The algorithm part of it is the, can I call it a rule?
• 7:49
  Vanessa Vakharia: The rule that when we add things, we line up the digits on top of each other in order from smallest to largest.
• 7:56
  Vanessa Vakharia: We line up the ones, we line up by place value, and we add them vertically.
• 8:01
  Vanessa Vakharia: That is an algorithm.
• 8:02
  Pam Harris: Yeah.
• 8:02
  Pam Harris: And then you have to regroup, then you have to carry
• 8:04
  Vanessa Vakharia: Yeah.
• 8:04
  Vanessa Vakharia: Like the, the whole, the whole thing of it would be like, that is
• 8:07
  Pam Harris: our traditional addition algorithm.
• 8:09
  Pam Harris: Notice I called it the traditional addition
• 8:11
  Vanessa Vakharia: yep.
• 8:13
  Pam Harris: because people will call things standard algorithms, and I'm gonna push on that hard because the way that my mom, who grew up in Switzerland, learned to multiply and divide, doesn't look anything like our traditional multiplication and division algorithms.
• 8:25
  Pam Harris: I was just in Croatia, um, last winter.
• 8:28
  Pam Harris: Their division algorithm looks nothing like our long division algorithm.
• 8:32
  Pam Harris: Uh, many Latin and South American countries, we, they use a different subtraction algorithm than we do.
• 8:38
  Pam Harris: So we have to be careful that we don't assume that our traditional algorithms are standard.
• 8:44
  Vanessa Vakharia: I, It's funny'cause David just held up a question to me, which he very rarely does, he said, why is she calling that an algorithm as opposed to just doing addition?
• 8:54
  Vanessa Vakharia: And I think, so tell me if I've understood you right.
• 8:57
  Vanessa Vakharia: I think it's called an algorithm because there's a specific rule about how you're supposed to do it and a pattern you're supposed to follow.
• 9:04
  Pam Harris: Well, it's a pattern you have to follow every time, no, no matter what the numbers are.
• 9:08
  Pam Harris: So let me ask David this question, the problem I used before was 99 plus 67.
• 9:13
  Pam Harris: if you think the definition of addition is to follow that algorithm, you line it up, you add the numbers, and then you're like, duh, that's what you do.
• 9:20
  Pam Harris: what if I were to say something like 99 Do you get an urge right now?
• 9:26
  Vanessa Vakharia: Exactly, I, because I've, because I've seen Pam, I'd be like 99 plus 67.
• 9:30
  Vanessa Vakharia: It's a hundred plus 67 minus one, right?
• 9:33
  Vanessa Vakharia: It's 166.
• 9:35
  Vanessa Vakharia: I can just round that 99 up to a hundred.
• 9:37
  Pam Harris: face right now.
• 9:37
  Pam Harris: Like, what is
• 9:38
  Vanessa Vakharia: Oh my God,
• 9:39
  Pam Harris: Yeah,
• 9:39
  Vanessa Vakharia: I, here, David, he's like, no, he's thinking about it.
• 9:43
  Vanessa Vakharia: Well, but why is that not an algorithm, but because that's, okay.
• 9:46
  Vanessa Vakharia: So now he, here's his question.
• 9:47
  Vanessa Vakharia: Why is that not an algorithm?
• 9:49
  Pam Harris: Because I wouldn't want to do that strategy for something like 32 plus 67.
• 9:56
  Pam Harris: I wouldn't wanna go 33 plus 67 minus one.
• 10:01
  Vanessa Vakharia: Can I try, can I chime in here and tell me if, well, if what I've learned from you is accurate, I think what Pam might say, even though I could just ask her, but I wanna see if I've learned, is the point is if you understand what addition is as a concept, you can, uh, change your strategy based on the numbers.
• 10:19
  Vanessa Vakharia: 'cause you understand what adding means.
• 10:21
  Vanessa Vakharia: So you could be like 32 plus 67, it makes more sense to do it this way.
• 10:25
  Vanessa Vakharia: 99 plus 67, oh, I'm gonna do this because I understand the concept of addition and I can draw on all this prior knowledge instead of being like, no matter what the numbers are, I have to line them up.
• 10:36
  Vanessa Vakharia: Am I right?
• 10:36
  Pam Harris: Yes.
• 10:37
  Pam Harris: And, and
• 10:38
  Vanessa Vakharia: You're so kind.
• 10:40
  Pam Harris: No, no, that was very well said.
• 10:42
  Pam Harris: I just wanna add in a little bit of an additional thing.
• 10:44
  Pam Harris: So a lot of really good people would say, if we really get some conceptual understanding down, then then good, you're, you're good to go.
• 10:51
  Pam Harris: And I'm gonna say there's actually a small set of major relationships that lead to a small set of major strategies that we need kids to own.
• 11:00
  Pam Harris: Or when we say, well, you understood addition, go ahead and add'em any way you want.
• 11:03
  Pam Harris: They're gonna be like, I don't know what to do.
• 11:06
  Pam Harris: they don't own enough relationships.
• 11:07
  Pam Harris: We need to help them own.
• 11:09
  Pam Harris: So the, the strategy you just used was, I'm gonna start at 99, I'm gonna go to a hundred, add the 67 and then back up one.
• 11:16
  Pam Harris: great strategy.
• 11:17
  Pam Harris: But another kid might say, I'm just gonna give one from the 67 to the 99.
• 11:22
  Pam Harris: So now I have that a hundred that you had, and I'm gonna add what's left over the 66.
• 11:27
  Pam Harris: Those are slightly two different ways of thinking about the problem that will be important when the numbers get done as, as trivial.
• 11:34
  Pam Harris: So 99 and 67 I use because, and we're, we're on a, we're on a podcast here, so we're trying to make sure people can,
• 11:40
  Vanessa Vakharia: I was like, Pam, don't talk too much about math.
• 11:42
  Vanessa Vakharia: It's been 10 minutes,
• 11:45
  Pam Harris: so, so people might hear, well, of course you can do that.
• 11:48
  Pam Harris: Pam, it's 99.
• 11:49
  Pam Harris: Well, okay, but what about 98 plus 67?
• 11:51
  Vanessa Vakharia: but wait, so why aren't, but now I'm kind of with David because now you've gone into, there's a bunch of different, like, kind of,
• 11:58
  Pam Harris: a small set.
• 11:59
  Pam Harris: It's a, it's a very small
• 12:00
  Vanessa Vakharia: But how are those not algorithms?
• 12:02
  Pam Harris: because again, I'm gonna let the numbers influence which of those small set of relationships I'm gonna use that,
• 12:10
  Vanessa Vakharia: Hold on, let me, uh, let me think here.
• 12:13
  Pam Harris: So I have a son who would actually agree with you right now.
• 12:16
  Pam Harris: He would say, all of your strategies are algorithms, mom.
• 12:19
  Pam Harris: It's just that for many they won't work well.
• 12:22
  Vanessa Vakharia: Right.
• 12:23
  Pam Harris: One of the relationships that I would develop in kids, I call the Over strategy.
• 12:28
  Pam Harris: Um, I got this from my co-host Kim, uh, on our podcast Math is Figureoutable podcast, where if she was adding something like, and I'm gonna write this down'cause I don't hold numbers in my head, all that great.
• 12:37
  Pam Harris: So I'm writing down 23 and plus 49, um, 23 plus 49.
• 12:43
  Pam Harris: I might think about, I could line those up and I could do the thing because I can do that for any problem.
• 12:49
  Pam Harris: I could also think about what do I know about 23 and 49?
• 12:52
  Pam Harris: Well, 49 is pretty close to 50.
• 12:55
  Pam Harris: Well,
• 12:55
  Vanessa Vakharia: 50.
• 12:56
  Pam Harris: I know what 23 and 50 are.
• 12:58
  Pam Harris: So 23 and 50, that's 73.
• 13:03
  Pam Harris: I didn't want 23 and 50, I wanted 23 and 49.
• 13:06
  Pam Harris: So it's gotta be one less, it's gotta be 72.
• 13:09
  Pam Harris: So that's an, that's an over strategy that works really well when you're adding 49.
• 13:14
  Pam Harris: That's, that's a, it's a good strategy.
• 13:16
  Pam Harris: What, what if you were adding 89?
• 13:17
  Pam Harris: What if you were adding 149?
• 13:19
  Pam Harris: What if you were adding 999?
• 13:21
  Pam Harris: What if you're adding 3,496
• 13:25
  Vanessa Vakharia: we have to stop.
• 13:26
  Vanessa Vakharia: We have to stop.
• 13:27
  Pam Harris: or, or even better, 3,996.
• 13:29
  Pam Harris: But 3,996 is so close to 4,000.
• 13:33
  Pam Harris: No, hang with that one.
• 13:35
  Pam Harris: 3,996 is so close to four.
• 13:38
  Pam Harris: Come on, you can do it.
• 13:41
  Pam Harris: Vanessa.
• 13:41
  Vanessa Vakharia: on.
• 13:42
  Pam Harris: if I had some random four digit number
• 13:45
  Vanessa Vakharia: I know, I'm sure.
• 13:46
  Vanessa Vakharia: Yeah.
• 13:47
  Vanessa Vakharia: Okay.
• 13:47
  Pam Harris: was
• 13:47
  Vanessa Vakharia: Okay.
• 13:48
  Pam Harris: it, 4,996, what if we, 4,996?
• 13:52
  Pam Harris: What if we
• 13:52
  Vanessa Vakharia: I would add four.
• 13:53
  Vanessa Vakharia: I would put four.
• 13:55
  Pam Harris: So,
• 13:56
  Vanessa Vakharia: then I would take four away from whatever the answer is.
• 13:58
  Pam Harris: You're now thinking about, what do I know about 4,996.
• 14:02
  Pam Harris: Ooh, it's really close to 5,000.
• 14:05
  Pam Harris: I could use that.
• 14:06
  Pam Harris: Notice that, that, that thought process is,
• 14:09
  Vanessa Vakharia: Okay,
• 14:09
  Pam Harris: think about the numbers.
• 14:11
  Pam Harris: Let me actually consider the numbers here
• 14:13
  Vanessa Vakharia: okay.
• 14:14
  Vanessa Vakharia: Okay.
• 14:14
  Pam Harris: I dive and choose what to do.
• 14:17
  Pam Harris: That's the crux of the difference between a strategy and an algorithm.
• 14:22
  Vanessa Vakharia: I think you just, I think you just, something clicked, even though literally what happened is you threw a bunch of numbers into the ether and that some No, it was, it kind of worked because I think, I think something you said just clicked where you said the difference is that you're thinking about the numbers.
• 14:39
  Vanessa Vakharia: There I think is it.
• 14:41
  Vanessa Vakharia: Is that with a traditional algorithm of just line up the digits by place value and add, there is zero thinking.
• 14:47
  Vanessa Vakharia: You are simply following.
• 14:49
  Vanessa Vakharia: If however, you have a boatload of, not a boatload, but you've got a range of strategies to choose from that require a small set that require your prior knowledge and thinking and you get to be empowered to say, I'm gonna choose this because I know this, all of a sudden the student is in the seat of power, they're thinking and they're not just following and now it is no longer simply an algorithm.
• 15:12
  Vanessa Vakharia: Did I get it?
• 15:12
  Pam Harris: And they're using their agency.
• 15:14
  Pam Harris: I'd throw that in.
• 15:15
  Pam Harris: Yes.
• 15:15
  Vanessa Vakharia: Their agency.
• 15:16
  Vanessa Vakharia: I love it.
• 15:16
  Pam Harris: have agency, they get to choose, they get to, they, they get to be
• 15:19
  Vanessa Vakharia: I got to choose
• 15:20
  Pam Harris: they get to be influenced by the numbers.
• 15:22
  Pam Harris: And then say, for this, for this problem, I think I'm actually, how about No.
• 15:26
  Pam Harris: Ooh, this, I have, I have, I have my, my oldest son, I was teaching high school math, knew what I was doing.
• 15:34
  Pam Harris: Vanessa, I could tell you every, give me a high school problem, I knew the algorithm, I knew the steps well because if I didn't, I would have major imposter syndrome.
• 15:43
  Pam Harris: So I knew that in order to be a high school math teacher, I needed to know all the things.
• 15:47
  Pam Harris: But what I knew was to recognize which algorithm to do and then be able to do those steps.
• 15:53
  Pam Harris: What I didn't ever do was let the problems influence how I would attack the problem.
• 16:00
  Pam Harris: My young son was growing up and he would logic his way through problems.
• 16:05
  Pam Harris: I literally went to him one day and I was, I just had a conversation with my kids' teachers who were saying, Pam, we're kind of concerned that our kids don't know facts anymore because we've been told not to give him time fact math and so we stopped'cause we don't wanna give him math anxiety.
• 16:19
  Pam Harris: So we stopped giving him time fact math tests'cause we don't wanna give him math anxiety and now they don't know their facts anymore.
• 16:23
  Pam Harris: Is that important?
• 16:24
  Pam Harris: And I was like, that's important.
• 16:25
  Pam Harris: Like kids need to know their facts.
• 16:27
  Pam Harris: I went home to my own kid, but, but just like you, I don't wanna give kids math anxiety.
• 16:31
  Pam Harris: So this is,
• 16:31
  Vanessa Vakharia: Right.
• 16:32
  Pam Harris: was fussing with this.
• 16:33
  Pam Harris: I'm a high school math teacher.
• 16:34
  Pam Harris: Think I know everything.
• 16:36
  Pam Harris: I know it sounds so arrogant, but y'all, I had to be that almost to be able to survive in that, that place.
• 16:41
  Pam Harris: Anyway, I went home to my own kid and I'm thinking in my head, do you know your multiplication facts?
• 16:46
  Pam Harris: And I, what I asked him was, do you know your fives?
• 16:49
  Pam Harris: I just picked one.
• 16:50
  Pam Harris: And he said no.
• 16:52
  Pam Harris: And I was like, I'm sorry, what?
• 16:54
  Pam Harris: Like, dude, thou shalt know thy facts.
• 16:57
  Pam Harris: Like this is I, I, as a math teacher, I panicked like my own personal kid has to know his F like he's got.
• 17:04
  Pam Harris: So in that panicking, he goes, mom, mom, mom, you don't have to know your fives if you know your tens.
• 17:10
  Pam Harris: And I said, what?
• 17:12
  Pam Harris: And he goes, you don't have to know your fives if you know your tens.
• 17:14
  Pam Harris: I was like, dude, I heard what you said.
• 17:16
  Pam Harris: I don't know what you mean.
• 17:17
  Pam Harris: Like Vanessa, at that point in my life I could not follow.
• 17:20
  Pam Harris: Now maybe some of your listeners are like, duh Pam.
• 17:23
  Pam Harris: Well you can look down on me all you want, but I am the product of the current system.
• 17:26
  Vanessa Vakharia: Yeah.
• 17:27
  Vanessa Vakharia: Yeah, yeah.
• 17:27
  Pam Harris: I was a very successful high school math teacher who had no idea what he meant.
• 17:32
  Pam Harris: Now many, your listeners are like, I don't either, Pam tell me.
• 17:35
  Pam Harris: So I said to him, give me an example.
• 17:37
  Pam Harris: said, okay, let's say that you don't know five times nine.
• 17:40
  Pam Harris: Well do you know 10 times nine?
• 17:41
  Pam Harris: That's 95 is half of 10.
• 17:43
  Pam Harris: So half of 90 is 45.
• 17:45
  Pam Harris: To which I said, good heavens, that is nine times five.
• 17:48
  Pam Harris: Does that work every time?
• 17:50
  Pam Harris: Give me another example.
• 17:51
  Pam Harris: he said, okay, what about five times 23?
• 17:56
  Pam Harris: Vanessa?
• 17:56
  Pam Harris: I'm thinking about single digit facts and he's playing around with a pattern with relationships that can find five times 23.
• 18:04
  Pam Harris: So in that moment I was like, wait, okay, 10 times 23 is 230 five is half of 10.
• 18:10
  Pam Harris: So half of 230 is 115.
• 18:13
  Pam Harris: And then I literally had to say to myself, is that five times 23?
• 18:16
  Pam Harris: I did the algorithm to make
• 18:17
  Vanessa Vakharia: Yeah, yeah,
• 18:18
  Pam Harris: but then I thought if you have 10 groups of things and you cut it in half, you'll have five groups of things.
• 18:23
  Pam Harris: And times 10 is so brilliant in our Base
• 18:26
  Vanessa Vakharia: yeah, yeah, yeah.
• 18:27
  Pam Harris: that it makes it a relationship worth knowing.
• 18:30
  Pam Harris: Does that, does that track?
• 18:32
  Vanessa Vakharia: It totally tracks.
• 18:33
  Vanessa Vakharia: I love this story, by the way.
• 18:35
  Pam Harris: I'm gonna suggest that that relationship, that five is half of 10, is one of the small set of major multiplication relationships that we need to build in kids.
• 18:43
  Pam Harris: Like I could've thought that way, if I knew it was a thing, if I'd had a teacher say, Hey, it's sort of important that you know five is half of 10, and look how you can use it, would've used it.
• 18:51
  Pam Harris: Like I could have let that influence how I solve things, but nobody ever shared that with me.
• 18:56
  Pam Harris: So Vanessa, my work is interviewing, studying naturally math people and going, wait, wait, wait, wait.
• 19:03
  Pam Harris: How do you do that?
• 19:04
  Pam Harris: Oh,
• 19:05
  Vanessa Vakharia: What's a naturally mathy person?
• 19:06
  Pam Harris: Ok i'm gonna suggest, and I know there are good math minds out there, math education, people who would disagree with me on this, and I would love to have the respectful conversation with them.
• 19:17
  Pam Harris: I think we all have natural talents.
• 19:19
  Pam Harris: you're
• 19:19
  Vanessa Vakharia: Okay.
• 19:20
  Pam Harris: the video, you'll notice there's a basketball behind me.
• 19:23
  Vanessa Vakharia: Yeah.
• 19:23
  Pam Harris: a baller.
• 19:24
  Pam Harris: I played semi-pro basketball in Switzerland.
• 19:27
  Pam Harris: the game.
• 19:28
  Pam Harris: Um, I, I, I think I have some natural talent.
• 19:31
  Pam Harris: To play that game.
• 19:32
  Pam Harris: But I gotta be honest, there were people who were much better than me.
• 19:35
  Pam Harris: One of the reasons why I was any good is I worked blooming hard at it.
• 19:38
  Pam Harris: So I had some natural talent.
• 19:40
  Pam Harris: I put a lot of effort into it.
• 19:42
  Pam Harris: I think my personal kid, the story I just told, has some natural talent to run into a low dose of mathematical patterns and pull them together make new relationships in his head.
• 19:55
  Pam Harris: And now that he owns those, pull those together, uh, he ran into the same low dose of patterns we all do.
• 20:01
  Pam Harris: And for whatever reason, he had both the, the sort of talent and the interest.
• 20:07
  Pam Harris: Like I think both of those go together.
• 20:09
  Pam Harris: If you have the talent and the interest, I think pull out a favorite athlete of yours.
• 20:13
  Pam Harris: Ooh, Alanis Morissette.
• 20:16
  Pam Harris: Did I get a name?
• 20:18
  Pam Harris: I think she has some natural talent.
• 20:22
  Vanessa Vakharia: Dying
• 20:22
  Pam Harris: She's
• 20:23
  Vanessa Vakharia: fam.
• 20:23
  Vanessa Vakharia: I love you an athlete,
• 20:27
  Pam Harris: Well, okay, because, so, so we should probably tell everybody, you introduced me to Alanis Morissette.
• 20:31
  Pam Harris: You were like comparing I I hadn't heard of her before.
• 20:36
  Vanessa Vakharia: but you know who she is now, right?
• 20:37
  Vanessa Vakharia: Do you know that song?
• 20:38
  Pam Harris: no, not really.
• 20:39
  Pam Harris: Sorry.
• 20:40
  Vanessa Vakharia: like rain on my wedding day.
• 20:43
  Pam Harris: to it.
• 20:43
  Pam Harris: Now I know it.
• 20:44
  Vanessa Vakharia: You've never heard that song?
• 20:45
  Pam Harris: before then.
• 20:46
  Pam Harris: I don't think so.
• 20:47
  Vanessa Vakharia: Really?
• 20:48
  Vanessa Vakharia: Okay.
• 20:48
  Vanessa Vakharia: No problem.
• 20:48
  Vanessa Vakharia: Go on.
• 20:49
  Pam Harris: me
• 20:49
  Vanessa Vakharia: It's fine.
• 20:49
  Pam Harris: ignorant.
• 20:50
  Pam Harris: Maybe that's probably
• 20:51
  Vanessa Vakharia: No, no, no, it's fine.
• 20:52
  Vanessa Vakharia: It's totally cool.
• 20:53
  Vanessa Vakharia: Yeah.
• 20:53
  Vanessa Vakharia: I'm not trying to shame you.
• 20:54
  Pam Harris: has natural talent and drive and eth work ethic and, and when after interest she's interest in it.
• 21:02
  Pam Harris: So I'm gonna suggest there are naturally mathy people who a, have maybe some natural talent or, or have enough natural interest that they go for it.
• 21:10
  Pam Harris: And either one of those is enough for them to sort of take interest.
• 21:13
  Pam Harris: Here's the rub, not the rub.
• 21:15
  Pam Harris: Here's my point.
• 21:16
  Pam Harris: We can all be mathy people, but we have to know what the actual mathy thing is.
• 21:25
  Pam Harris: I
• 21:25
  Vanessa Vakharia: Oh, boy.
• 21:26
  Vanessa Vakharia: Okay.
• 21:26
  Vanessa Vakharia: Yep.
• 21:27
  Pam Harris: I want, I want we, everybody can do more real math than fake math.
• 21:32
  Pam Harris: I know you hate those words.
• 21:33
  Pam Harris: Sorry.
• 21:34
  Vanessa Vakharia: Oh my God.
• 21:34
  Vanessa Vakharia: Okay, so there's so much happening here.
• 21:36
  Vanessa Vakharia: Okay, so first of all.
• 21:38
  Pam Harris: take a
• 21:38
  Vanessa Vakharia: Let's just, let's take a drink.
• 21:39
  Vanessa Vakharia: We'll both take a drink.
• 21:40
  Vanessa Vakharia: What water?
• 21:41
  Vanessa Vakharia: Okay.
• 21:41
  Vanessa Vakharia: Decaf latte for me.
• 21:42
  Vanessa Vakharia: Okay.
• 21:42
  Vanessa Vakharia: So, mm, but electrolytes are gonna be next, so I'm gonna need to hydrate for what's happening next.
• 21:47
  Vanessa Vakharia: Okay.
• 21:47
  Vanessa Vakharia: So first, I guess we probably don't have time to go into this.
• 21:52
  Vanessa Vakharia: I will have to respectfully disagree about the term"naturally mathy", we, we likely don't have to, and I'll only say, I'm actually, I'm gonna respectfully disagree because that's cool.
• 22:02
  Vanessa Vakharia: But my actual question I don't wanna tell, I wanna ask.
• 22:07
  Vanessa Vakharia: No, I, I'm gonna respectfully disagree'cause I'm wondering if this is an opinion you have or something that's corroborated by evidence.
• 22:14
  Vanessa Vakharia: Because all of the evidence I've seen is that there is no.
• 22:18
  Vanessa Vakharia: Um, you know though, no, because it's such a big conversation.
• 22:21
  Vanessa Vakharia: 'cause are we talking about like at birth they pop out and they're naturally mathy?
• 22:25
  Vanessa Vakharia: Or are we talking about culturally they become more naturally mathy because there's no actual scientific evidence that there is like a mathy gene in the brain.
• 22:33
  Vanessa Vakharia: That's all.
• 22:33
  Vanessa Vakharia: Something to add on is have you ever read, um, Outliers by Malcolm Gladwell?
• 22:39
  Pam Harris: And, do I think that some people have a math gene and some people don't?
• 22:43
  Pam Harris: Absolutely not.
• 22:44
  Pam Harris: We all have the math gene.
• 22:46
  Pam Harris: Do I think some people pay basketball better than others?
• 22:49
  Pam Harris: Yes.
• 22:49
  Pam Harris: Is that because they were in the gym a lot with their dad, who was the coach?
• 22:53
  Vanessa Vakharia: Yeah.
• 22:53
  Pam Harris: so as from a young kid, they had a ball in their hands.
• 22:55
  Pam Harris: Like, so my high school coach, we, we called his kids gym rats.
• 22:59
  Pam Harris: Like he, his
• 23:00
  Vanessa Vakharia: Yeah.
• 23:01
  Pam Harris: in the gym.
• 23:01
  Pam Harris: Were they?
• 23:02
  Pam Harris: And, and then they grew up to be, uh, basketball coaches as well.
• 23:06
  Pam Harris: that because they were naturally basketball players or is it because they grew up in the gym with a
• 23:10
  Vanessa Vakharia: Yeah.
• 23:10
  Vanessa Vakharia: Yeah, yeah,
• 23:11
  Pam Harris: So I think nature, nurture, there's a lot of, um, I, when I meet people who say, Ooh, I've always thought about numbers that way, and I just assumed everybody else did too.
• 23:21
  Pam Harris: Are you
• 23:22
  Vanessa Vakharia: yeah.
• 23:22
  Pam Harris: that you didn't?
• 23:23
  Pam Harris: And I'll smile and I go, I didn't.
• 23:24
  Pam Harris: And
• 23:24
  Vanessa Vakharia: Mm-hmm.
• 23:25
  Pam Harris: at me like, really?
• 23:27
  Pam Harris: if I ask that person, did you have some, so I would call that person kind of naturally math for
• 23:33
  Vanessa Vakharia: Okay.
• 23:34
  Pam Harris: As they were growing up, they played with relationships.
• 23:37
  Pam Harris: I did not,
• 23:39
  Vanessa Vakharia: Yeah.
• 23:39
  Vanessa Vakharia: Okay.
• 23:39
  Pam Harris: thought about using relationships and they assumed the rest of us did too, or they weren't sure why the rest of us weren't.
• 23:46
  Pam Harris: did not.
• 23:46
  Pam Harris: Many people that I meet, the majority of the math teachers I work with will say to me, I was like, you, Pam, believed that math was wrote, memorizing and mimicking.
• 23:55
  Pam Harris: And that's what I did.
• 23:57
  Pam Harris: I did not, I never played with numbers.
• 23:59
  Pam Harris: Now, I, I don't know if the reason some people kind of did that on their own was because.
• 24:05
  Pam Harris: They had a natural inclination, more talent, or it was because they had more interest or it was because they had a mom, a dad, an uncle, an aunt a a, some other significant person in their life who played with numbers with them.
• 24:18
  Pam Harris: So often when I meet that person I'll say, did anybody play with numbers with you when you were a kid and they'd say oh my gosh, my granddad would put me on his knee and we played cards and we always had to figure out our score.
• 24:29
  Pam Harris: And like often, often, so this was research I would love to do when I have a minute, be to like, like they have some influential person who early in their life helped them do the mental actions of math then that set them on the course of math.
• 24:47
  Pam Harris: And sure, that could be, that could absolutely be true.
• 24:51
  Vanessa Vakharia: Okay, so then we're kind of fine.
• 24:52
  Vanessa Vakharia: Then.
• 24:52
  Vanessa Vakharia: You know what, actually, I think you and I are so funny in this way because I am, so, like, I think it's, for us, most of our like quote unquote disagreements are simply in language.
• 25:03
  Pam Harris: Yeah.
• 25:04
  Vanessa Vakharia: I actually think we're saying the same thing.
• 25:05
  Vanessa Vakharia: 'cause when you say"naturally mathy", it sounds like you're like, some people are just kind of born with this, like abil.
• 25:11
  Vanessa Vakharia: But you're not saying that at all.
• 25:12
  Vanessa Vakharia: You're you're not saying that at all.
• 25:13
  Vanessa Vakharia: And that's exactly, and you know what, all the research actually corroborates what you are saying, which is what outliers is all about.
• 25:19
  Vanessa Vakharia: Which is when we look at these people that are like the most skilled mathematicians or athletes or whatever it is usually nothing genetic.
• 25:25
  Vanessa Vakharia: It is about this 10,000 hours of practice.
• 25:27
  Vanessa Vakharia: Right.
• 25:27
  Vanessa Vakharia: And whether you get that
• 25:28
  Pam Harris: born.
• 25:29
  Pam Harris: Glad.
• 25:29
  Pam Harris: We'll also talk about right when the, when the hockey players in Canada were born,
• 25:33
  Vanessa Vakharia: at different times of the year.
• 25:35
  Vanessa Vakharia: Yeah,
• 25:35
  Pam Harris: year.
• 25:35
  Pam Harris: So if they were born so that they were the oldest kids in their
• 25:38
  Vanessa Vakharia: exactly.
• 25:39
  Pam Harris: magically they looked like they had more talent.
• 25:41
  Pam Harris: So Yeah, absolutely.
• 25:43
  Pam Harris: I, I completely can.
• 25:44
  Pam Harris: I think you are right.
• 25:45
  Pam Harris: I think often where you and I are have to, where we dive in to have a longer conversation is when there's some vocabulary that we're like,
• 25:52
  Vanessa Vakharia: It is a vocab.
• 25:53
  Pam Harris: do, what do we mean.
• 25:54
  Pam Harris: Vanessa, I just wanna encourage anybody listening to this podcast, we in math education, need to have more conversations like this where we don't just nod at each other and
• 26:04
  Vanessa Vakharia: Mm-hmm.
• 26:04
  Pam Harris: yeah, you're good.
• 26:05
  Pam Harris: So sure, I'm gonna agree.
• 26:06
  Pam Harris: Like, we need to parse out what we're talking about because too many people think we're all on the same page when I don't know that we are
• 26:14
  Vanessa Vakharia: Yes.
• 26:15
  Pam Harris: the same page, when in fact we are.
• 26:18
  Vanessa Vakharia: Which is actually, you know what's so ironic about this?
• 26:20
  Vanessa Vakharia: Which by the way, Alanis Morissette's, uh, key song was called, isn't it Ironic?
• 26:24
  Vanessa Vakharia: Um, what's ironic is that so far this whole podcast has actually, this whole interview has just been about language.
• 26:31
  Vanessa Vakharia: What is an algorithm?
• 26:32
  Vanessa Vakharia: What do we mean when we're saying algorithm?
• 26:33
  Vanessa Vakharia: You know, it's funny, it's like when we use the term common sense, it bugs me'cause I'm like, my common sense is not the same as someone else's common sense, right?
• 26:40
  Vanessa Vakharia: So it's like there's no definition of common sense that we're all gonna be like, well it's common sense that blah, blah, blah.
• 26:45
  Vanessa Vakharia: Because depending what you grew up, depending what your values are, it's not common.
• 26:49
  Vanessa Vakharia: It's actually not common.
• 26:50
  Vanessa Vakharia: And like when we use the term algorithm, we don't all mean the same thing.
• 26:54
  Vanessa Vakharia: So we're having this conversation and we're actually saying completely different things because we have a different definition than we're going on.
• 26:59
  Vanessa Vakharia: And actually as mathematicians isn't the number one rule to define our terms, isn't that literally what we're supposed to do before we get into any problem?
• 27:07
  Pam Harris: It
• 27:07
  Vanessa Vakharia: Okay.
• 27:07
  Vanessa Vakharia: So,
• 27:08
  Pam Harris: would be a good idea.
• 27:08
  Pam Harris: Yeah.
• 27:09
  Pam Harris: This is, this is tricky and super subtle and so let me
• 27:11
  Vanessa Vakharia: Okay.
• 27:12
  Pam Harris: what
• 27:13
  Vanessa Vakharia: Hmm.
• 27:13
  Pam Harris: You and I, which I love by the way.
• 27:15
  Pam Harris: Thank you.
• 27:16
  Pam Harris: We are not.
• 27:19
  Pam Harris: these terms so that everybody has to use our definitions.
• 27:22
  Pam Harris: We're defining these terms so that you and I can have a conversation
• 27:25
  Vanessa Vakharia: Yes.
• 27:26
  Pam Harris: we can understand what each other means.
• 27:28
  Pam Harris: We're not commanding everybody now take on our definitions.
• 27:32
  Vanessa Vakharia: Yeah.
• 27:32
  Vanessa Vakharia: This isn't like going in the dictionary of Pam and Vanessa.
• 27:35
  Pam Harris: Uh,
• 27:35
  Vanessa Vakharia: No,
• 27:36
  Pam Harris: uh, me trying to be arrogant to say I know best of what the
• 27:39
  Vanessa Vakharia: no.
• 27:40
  Pam Harris: and everybody
• 27:40
  Vanessa Vakharia: Love it.
• 27:41
  Pam Harris: I wanted to
• 27:41
  Vanessa Vakharia: Thank you for clarifying that.
• 27:42
  Vanessa Vakharia: Actually, no, I really, really liked that.
• 27:44
  Pam Harris: Yeah.
• 27:45
  Vanessa Vakharia: We're making sure we're speaking the same language so that we're actually,
• 27:48
  Pam Harris: we can't have a
• 27:48
  Vanessa Vakharia: or we can't have a conversation.
• 27:49
  Vanessa Vakharia: Yeah, exactly.
• 27:51
  Vanessa Vakharia: This is just, I mean, there's so much here.
• 27:54
  Vanessa Vakharia: You know what I wanna ask you now?
• 27:55
  Pam Harris: Yes.
• 27:56
  Vanessa Vakharia: Just to, to bring it all together.
• 27:58
  Vanessa Vakharia: You at one point said, our students deserve, to, learn these reasoning skills.
• 28:03
  Vanessa Vakharia: You know, we don't need them to just pump out an answers anymore.
• 28:05
  Vanessa Vakharia: They, we, they deserve this, and we are robbing them for that.
• 28:07
  Vanessa Vakharia: If we don't um, facilitate that.
• 28:10
  Vanessa Vakharia: How do you think learning in the way that you're proposing versus learning the standard algorithm actually shapes math identity?
• 28:18
  Vanessa Vakharia: you know, obviously this is a podcast about math, trauma and math, anxiety.
• 28:21
  Vanessa Vakharia: How do you think teaching one way versus the other plays into that?
• 28:25
  Pam Harris: Huge, so if I'm in a math class and the teacher says, here is math.
• 28:31
  Pam Harris: I'm gonna give you a problem.
• 28:33
  Pam Harris: I'm gonna work it out.
• 28:34
  Pam Harris: Now we're gonna do it together.
• 28:36
  Pam Harris: Now you go mimic exactly what I just told you to do.
• 28:39
  Pam Harris: Then the student has no agency and this, the math becomes this thing that I'm, uh, uh, I, what, what I do is, is mimic what you have told me to do.
• 28:51
  Pam Harris: And then if I like that, if I'm, if I'm rewarded for that now, I've created, uh, an identity of, ooh, I'm good at, and, and it was exactly the identity I created.
• 29:01
  Pam Harris: Like I, I was, I was a nerd.
• 29:02
  Pam Harris: I didn't have friends, whatever, but hey, I, I won round the world, Arlene Wheeler.
• 29:07
  Pam Harris: I wonder if she would ever listen to this.
• 29:08
  Vanessa Vakharia: Who's that?
• 29:09
  Pam Harris: she was my third grade nemesis.
• 29:11
  Pam Harris: Well, third grade she won the award in middle
• 29:13
  Vanessa Vakharia: Should we find her?
• 29:14
  Pam Harris: two.
• 29:15
  Pam Harris: Oh, I love that.
• 29:16
  Pam Harris: We, it was the two of us that were, we were always like, like we were the quickest we around the world.
• 29:21
  Pam Harris: It was the two of us that were always at the end.
• 29:23
  Vanessa Vakharia: Mm-hmm.
• 29:23
  Pam Harris: division first, like all the things.
• 29:25
  Pam Harris: I got this identity that I was smart and I,
• 29:29
  Vanessa Vakharia: Okay.
• 29:29
  Pam Harris: math.
• 29:30
  Pam Harris: I've heard you kinda talk about how, I like your take on that by the way, that we have this cultural sort of assumption that if you're good at math, you're smart.
• 29:38
  Vanessa Vakharia: Yeah, it's gross.
• 29:39
  Pam Harris: I'm just gonna say if you're quick at math.
• 29:43
  Pam Harris: even good, but if
• 29:44
  Vanessa Vakharia: Mm.
• 29:44
  Vanessa Vakharia: Mm-hmm.
• 29:45
  Vanessa Vakharia: Yeah.
• 29:45
  Pam Harris: cause you gotta define good, right?
• 29:47
  Vanessa Vakharia: Totally.
• 29:47
  Vanessa Vakharia: Totally.
• 29:48
  Pam Harris: my identity was based on the fact that I was quick.
• 29:51
  Pam Harris: And then I became a high school math teacher, and I thought I was the god of math.
• 29:54
  Pam Harris: Imagine my dismay when I realized wasn't doing the mental actions that other people were doing it all.
• 30:01
  Pam Harris: I was memorizing and mimicking, and there was this whole other world.
• 30:05
  Pam Harris: Now imagine my joy when I realized I could do that too.
• 30:09
  Pam Harris: I just needed to know it was a thing.
• 30:12
  Pam Harris: I bought into the myth and it, it sh completely shaped my identity.
• 30:16
  Pam Harris: Now I realize I, I can do that too.
• 30:20
  Pam Harris: I can be in that club and maybe better, because this is my life mission, I can invite everyone else into that club, like the real club.
• 30:30
  Vanessa Vakharia: Okay.
• 30:31
  Vanessa Vakharia: Okay.
• 30:32
  Vanessa Vakharia: I was asking about, you know, how does, uh, teaching algorithmically and through mimicking affect, you know, one's math identity?
• 30:37
  Vanessa Vakharia: And there's kind of two parts here.
• 30:39
  Vanessa Vakharia: On the one hand, you and your pal, Arlene Wheeler, which if anyone knows where she is, please do locate her.
• 30:44
  Vanessa Vakharia: You actually formed a very strong, confident math identity as a result of this procedure, uh, sorry, as, as a result of being taught this way because you were, for a while, because you were able to nail this.
• 30:56
  Vanessa Vakharia: Okay.
• 30:57
  Vanessa Vakharia: So on the one hand, we've got two kids here who form a very strong math identity.
• 31:01
  Vanessa Vakharia: They're quote unquote good at it.
• 31:03
  Vanessa Vakharia: They're quick at it.
• 31:03
  Vanessa Vakharia: They can follow the steps.
• 31:05
  Vanessa Vakharia: However, later in life, when that becomes challenged in a sense because they are presented with math in a different way, all of a sudden that identity kind of collapses.
• 31:14
  Vanessa Vakharia: There's a bit of an identity crisis, and then there's this beautiful plot twist romcom ending where you discover math in a whole new light and you're like, I can do it to like beautiful, cool, some ups and downs.
• 31:24
  Vanessa Vakharia: Now forget you and Arlene.
• 31:26
  Vanessa Vakharia: Let's think about the rest of the class who are watching you and Arlene just kill it.
• 31:30
  Vanessa Vakharia: And they're like, oh my God, we suck.
• 31:33
  Pam Harris: Yeah.
• 31:34
  Vanessa Vakharia: So now not only like, you know, we have this like kind of partial success story with you two, you and Arlene, that then later ends up in a bit of an existential crisis, but the rest of the class is not quote unquote good at math in this way, and they don't feel good.
• 31:49
  Vanessa Vakharia: They aren't presented with any other options.
• 31:51
  Vanessa Vakharia: They just leave the class thinking, well I guess I'm not a math person and I'm not good at it.
• 31:55
  Pam Harris: Uh yes.
• 31:56
  Pam Harris: And what a tragedy.
• 31:57
  Pam Harris: Because
• 31:57
  Vanessa Vakharia: and what a tragedy.
• 31:59
  Pam Harris: in reality, they are a math person and they
• 32:01
  Vanessa Vakharia: Mm-hmm.
• 32:01
  Pam Harris: can math if they just need to know it's a thing, and, and
• 32:05
  Vanessa Vakharia: Well, yeah,
• 32:06
  Pam Harris: get experiences to help them build their brain to be able to math more and more.
• 32:12
  Vanessa Vakharia: Well, and the crazy thing is everyone is at a disadvantage in this situation, including the two of you or whoever it was that formed a positive math identity.
• 32:21
  Vanessa Vakharia: Because like my mind is now going somewhere else here where I have never thought about it in this way of thinking like.
• 32:28
  Vanessa Vakharia: You know how there's all these dis, this, you know, hoop law now about people being like, well, why can't we just teach it this way?
• 32:34
  Vanessa Vakharia: There are people who are good at it and those are the people who are good at math, whatever.
• 32:36
  Vanessa Vakharia: You're kind of living proof of being like, well, hold on.
• 32:39
  Vanessa Vakharia: And now this doesn't, this is not a general statement, this doesn't apply to everyone, but a lot of people who get through this system and feel good about it, it's not even happening for the reason that I think we'd all like, which is like we'd all, like everyone to deeply understand mathematics and numbers.
• 32:55
  Vanessa Vakharia: I'm not saying that people don't, I really believe that a lot of people who are, who have been taught through this, uh, mimicking an algorithmic way, I being included, and many of us being included still have, you know, number sense and deep reasoning skills and all of this stuff.
• 33:11
  Vanessa Vakharia: They've just gained it in a different way because they certainly didn't learn it at school kind of thing.
• 33:15
  Pam Harris: Yeah.
• 33:15
  Pam Harris: Yeah,
• 33:16
  Vanessa Vakharia: Sorry, I'm saying a million things at once, but I guess I'm kind of like, where I'm, I'm kind of trying to get to is like, it's kind of crazy to think that we're trying so deeply to protect this way of teaching that actually didn't service most people.
• 33:32
  Vanessa Vakharia: Even those who felt good at math were actually being robbed.
• 33:37
  Pam Harris: Yeah.
• 33:38
  Pam Harris: Agreed.
• 33:38
  Pam Harris: Agreed.
• 33:39
  Pam Harris: And can I add a third
• 33:40
  Vanessa Vakharia: Oh, say that again.
• 33:41
  Vanessa Vakharia: I liked it.
• 33:42
  Pam Harris: agree with you.
• 33:42
  Vanessa Vakharia: Okay.
• 33:44
  Vanessa Vakharia: Yes.
• 33:44
  Vanessa Vakharia: A third group.
• 33:45
  Pam Harris: add a third group because
• 33:46
  Vanessa Vakharia: Yeah.
• 33:47
  Pam Harris: people listening who while they were being taught algorithmic mimicking, through it kinda like my kid and said, Ooh, I could logic my way through that.
• 33:57
  Pam Harris: And they use relationships and connections and think that the way they were able to do these real math mental actions is because they were shown algorithms.
• 34:08
  Vanessa Vakharia: Mm-hmm.
• 34:08
  Pam Harris: Like they almost can't, they almost can't separate it out.
• 34:11
  Vanessa Vakharia: Yep.
• 34:11
  Vanessa Vakharia: Yep.
• 34:12
  Pam Harris: this is the way we should teach because it worked for me.
• 34:15
  Pam Harris: So does that make sense?
• 34:16
  Pam Harris: In other words, there's me who,
• 34:17
  Vanessa Vakharia: I wanna talk about this.
• 34:18
  Pam Harris: it didn't actually work for me.
• 34:19
  Pam Harris: And I'm clear on that.
• 34:20
  Pam Harris: But there are people who are successfully math, they're doing the mental
• 34:24
  Vanessa Vakharia: Yep.
• 34:24
  Pam Harris: and they think it's because of the way they were taught.
• 34:28
  Pam Harris: And I'm gonna respectfully invite the, that if you're listening, I respectfully invite you to consider if your teacher hadn't given you things to mimic?
• 34:37
  Pam Harris: What if your teacher had actually helped you, knew, knew the things you were developing on your own, helped you do that intentionally.
• 34:44
  Pam Harris: What if they had set up experiences for you so you could have developed those things you kind of did on your own, quicker, faster, better, because the teacher knew what they were and helped you intentionally build it.
• 34:55
  Pam Harris: Think of how far and fast you could have gone if you hadn't had to do it on your own.
• 35:01
  Pam Harris: Does that make sense?
• 35:02
  Pam Harris: I don't think
• 35:03
  Vanessa Vakharia: it makes, it makes so much sense.
• 35:05
  Pam Harris: to try to parse out.
• 35:06
  Pam Harris: How
• 35:07
  Vanessa Vakharia: No, I.
• 35:07
  Pam Harris: how did you become the person you are?
• 35:09
  Pam Harris: Well, of course it was the experiences that that created me.
• 35:12
  Pam Harris: I respectfully submit that when you were shown an algorithm for whatever reason, I don't know why you were able to see things through that the rest of us were not, if we were taught differently, all of us could have done what you did in spite of the way you were taught.
• 35:27
  Vanessa Vakharia: Uh, you know what I think is, I think it's just a really hard ask.
• 35:31
  Vanessa Vakharia: I, I don't think it's impossible.
• 35:32
  Vanessa Vakharia: I think it's actually, this is what like, you know, most therapy is, is this idea of like, let's try and deeply reflect on what, um, you know, we weren't just quote unquote born this way or, you know, these things all played a role, but I actually think it's really hard to be like, okay, so imagine you were taught completely differently because like, it is so hard to parse those two things apart.
• 35:53
  Vanessa Vakharia: Like even I'm trying to do it because obviously I've kind of fall into this camp of being like, yeah, I was taught the algorithm, but I still have these deep reasoning skills and I was able to build relationships.
• 36:01
  Vanessa Vakharia: And I imagine, and I think this might be only because I've sat through a couple of your lessons and been like, oh my gosh.
• 36:09
  Vanessa Vakharia: You know, like, I think, I think people need to experience it in order to, you know, there's this thing I read.
• 36:17
  Vanessa Vakharia: Okay, I think you're gonna like this actually.
• 36:18
  Vanessa Vakharia: So my a, a lot of my work is based around this phrase by Joe Dispenza, who's like.
• 36:23
  Vanessa Vakharia: Let's call him a pseudo scientist.
• 36:25
  Vanessa Vakharia: Um, he's like spiritual science, but I love what he says.
• 36:29
  Vanessa Vakharia: He says, uh, his whole phrase is, believe, behave, become.
• 36:33
  Vanessa Vakharia: It's like you have a belief.
• 36:34
  Vanessa Vakharia: So maybe I believe that what you're saying could be true.
• 36:37
  Vanessa Vakharia: You know, I believe that maybe what you're saying is could be true.
• 36:39
  Vanessa Vakharia: If I was taught in this different way, I'd have a different relationship with math.
• 36:43
  Vanessa Vakharia: I changed my behavior.
• 36:44
  Vanessa Vakharia: So I go to one of your sessions, I actually see it in action and I'm like, oh my God, this actually has changed the way I think.
• 36:50
  Vanessa Vakharia: And now I've become a person who's like, yep, you know what?
• 36:53
  Vanessa Vakharia: I really believe that this can work and now I'm gonna teach this way.
• 36:55
  Vanessa Vakharia: 'Cause when I sat in your problem strings lesson, like I've heard of it, I've read the book, whatever.
• 37:00
  Vanessa Vakharia: I get it.
• 37:00
  Vanessa Vakharia: I was like, this sounds cool, but I, my entire body was on fire.
• 37:04
  Vanessa Vakharia: Like, I was like, oh my goodness.
• 37:07
  Vanessa Vakharia: It's that.
• 37:07
  Vanessa Vakharia: Aha.
• 37:08
  Vanessa Vakharia: That's when we know something to be true.
• 37:12
  Pam Harris: I love that.
• 37:13
  Pam Harris: And, and you're not people will say to me, that's what you mean?
• 37:18
  Pam Harris: Like, they'll sit in a session with their ma with their jaw open.
• 37:21
  Vanessa Vakharia: Yeah.
• 37:22
  Pam Harris: Yeah.
• 37:23
  Pam Harris: And, and I'll be honest, I, I did too when I ran into Kathy Fasno, so she's an elementary math researcher.
• 37:27
  Pam Harris: When I watched her, when I watched kids, it wasn't really watching the teacher at first.
• 37:33
  Pam Harris: It was, it was like me watching learning happening live.
• 37:38
  Pam Harris: I was like, I want that, I want that.
• 37:40
  Pam Harris: I want, I want to.
• 37:42
  Pam Harris: And I had to experience it.
• 37:43
  Pam Harris: And then now my goal is to help us all experience it.
• 37:46
  Pam Harris: Yeah.
• 37:47
  Vanessa Vakharia: Well, and if you think about it when you're teaching a lesson, what you do, this is actually gonna be interesting'cause we're gonna present together soon.
• 37:53
  Vanessa Vakharia: I, I notice this, you guide us through the experience and then you explain what you did, right?
• 37:58
  Vanessa Vakharia: So you're not intellectualizing it first.
• 38:00
  Vanessa Vakharia: You're giving us the experience first, and then you're unpacking it anyways, k.
• 38:04
  Vanessa Vakharia: Fine, fine.
• 38:05
  Vanessa Vakharia: We really do have to wrap this up.
• 38:06
  Vanessa Vakharia: But my point is, the whole thing is
• 38:09
  Pam Harris: You have a point?
• 38:10
  Vanessa Vakharia: well, I, I, I know it's, I don't have a point, but there is one thing I wanna say.
• 38:13
  Vanessa Vakharia: I,
• 38:13
  Pam Harris: Okay.
• 38:14
  Vanessa Vakharia: I wanna make clear, I think, at least from my end, but you can definitely obviously chime in that if you're listening to this and you're a teacher who teaches through algorithms, okay.
• 38:22
  Vanessa Vakharia: I personally wanna make it very, very clear,
• 38:25
  Pam Harris: right?
• 38:26
  Pam Harris: We're not
• 38:26
  Vanessa Vakharia: which we're not, not only are we not blaming because like, you know, yeah.
• 38:32
  Pam Harris: right.
• 38:32
  Pam Harris: We're not.
• 38:32
  Pam Harris: We're not.
• 38:33
  Pam Harris: We're
• 38:33
  Vanessa Vakharia: There's nothing bad happening.
• 38:35
  Pam Harris: we're?
• 38:36
  Vanessa Vakharia: I wanna make it so clear.
• 38:37
  Vanessa Vakharia: I wanna make it so clear that it's like, Hey, first of all, we all learn to teach this way, so whatever you're up to.
• 38:42
  Vanessa Vakharia: Totally cool.
• 38:43
  Vanessa Vakharia: We all have the same mission.
• 38:44
  Vanessa Vakharia: We all want kids to develop reasoning skills.
• 38:47
  Vanessa Vakharia: if you are doing that, you are not doing something wrong.
• 38:49
  Vanessa Vakharia: And this whole episode is meant to be like, oh my God, we're robbing kids like you are not robbing kids.
• 38:54
  Vanessa Vakharia: Everything's cool.
• 38:55
  Vanessa Vakharia: I'm sure they're learning, they're, you know, you're helping them feel confident.
• 38:58
  Vanessa Vakharia: You're helping them build their identity.
• 39:00
  Vanessa Vakharia: That is the most important thing.
• 39:01
  Vanessa Vakharia: And if you're interested in perhaps shifting a little and exploring how you might teach in a different way, maybe you'll like it, there's an opportunity.
• 39:10
  Vanessa Vakharia: Would you agree?
• 39:12
  Pam Harris: Absolutely.
• 39:13
  Pam Harris: Yes.
• 39:13
  Pam Harris: Yes.
• 39:14
  Pam Harris: Very positive.
• 39:15
  Pam Harris: we know better, we can do better.
• 39:17
  Pam Harris: I'm suggesting there might be something worth investigating, worth experiencing
• 39:21
  Vanessa Vakharia: Yeah.
• 39:22
  Pam Harris: that you might find, um, will help you shift you're teaching to reach more students in less time.
• 39:30
  Vanessa Vakharia: Yeah, in less time, that's who doesn't wanna do that?
• 39:34
  Vanessa Vakharia: And also, I also would imagine that there are some teachers that are like, but I don't understand the math fully enough to be doing all this stuff.
• 39:42
  Vanessa Vakharia: Like I learned through algorithms, just so everyone knows that is me.
• 39:46
  Vanessa Vakharia: Like I'm a trained high school math teacher.
• 39:48
  Vanessa Vakharia: That's Pam.
• 39:49
  Vanessa Vakharia: She's pointing at herself.
• 39:50
  Vanessa Vakharia: That's her.
• 39:50
  Vanessa Vakharia: So.
• 39:51
  Vanessa Vakharia: I would personally invite you two to be like, just see what happens.
• 39:54
  Vanessa Vakharia: Like, take one of these workshops, like put, you know, whatever, if you can see Pam present, like go do it.
• 39:59
  Vanessa Vakharia: Um, explore it just for your, I actually think for you, the listener, and I'm talking to myself too, it's gonna build your confidence.
• 40:07
  Vanessa Vakharia: Because what happened is I sat in one of these sessions with Pam and I was like, oh my God, by the way, there's nothing that intimidates me more than elementary school math.
• 40:13
  Vanessa Vakharia: Okay.
• 40:14
  Vanessa Vakharia: Like the worst.
• 40:15
  Vanessa Vakharia: Like, I'm just like, oh God.
• 40:16
  Vanessa Vakharia: So I was very intimidated and yeah, right.
• 40:18
  Vanessa Vakharia: I found myself having so many ahas, like sitting quietly in the back being like, oh my, oh my God, oh my God.
• 40:24
  Vanessa Vakharia: And I was like, oh my God, I feel like I understand more than I gave myself credit for.
• 40:28
  Vanessa Vakharia: So even if you just go as an explor, uh, exploratory, session for yourself, just, I want all teachers to have the confidence themselves.
• 40:37
  Vanessa Vakharia: And you know, I think so many teachers have walked away with so much math trauma from the way we were taught, I just want you to have a good experience.
• 40:44
  Vanessa Vakharia: You know, because yeah, just to see that there's hope.
• 40:47
  Vanessa Vakharia: We can all be learning and growing and changing and there's magic in math and we can discover that every day.
• 40:53
  Vanessa Vakharia: Tell people where to go before I wrap up with the final two questions.
• 40:56
  Pam Harris: Excellent.
• 40:56
  Pam Harris: So the first thing I would do is, uh, suggest, wait.
• 40:59
  Pam Harris: I have a free ebook.
• 40:59
  Pam Harris: That would be a great place for you to start.
• 41:01
  Pam Harris: So you can go to mathisfigureoutable.com/big B.
• 41:05
  Pam Harris: 'cause I think it's big, it's a big, it's a big add to the world.
• 41:10
  Pam Harris: That would be a great place for you to start.
• 41:12
  Pam Harris: We have the math is Figureoutable podcast where Kim, we've talked about a little bit, uh, where she And I talk about all things, Math is Figureoutable from super young all the way through high school.
• 41:21
  Pam Harris: Um, another thing that you could do is join me on social media at the hashtag Math Strat Chat where I threw out a problem on Wednesday evenings to people from around the world chat about their strategies and comment on each other's, uh, thinking.
• 41:33
  Pam Harris: So that's totally fun.
• 41:34
  Pam Harris: Those would be some super good ways to sort of kick off.
• 41:37
  Pam Harris: Uh, joining me to make math more figureoutable.
• 41:41
  Vanessa Vakharia: Oh my God.
• 41:41
  Vanessa Vakharia: I can't believe we have to end this.
• 41:42
  Vanessa Vakharia: We didn't even talk about the fake math thing, but I mean, whatever.
• 41:45
  Pam Harris: We could send'em to the Debate Math Podcast if they wanted to hear a little bit
• 41:48
  Vanessa Vakharia: You can, but I feel like both of us have changed since then.
• 41:51
  Pam Harris: well, okay.
• 41:52
  Vanessa Vakharia: You know, it's not important.
• 41:54
  Vanessa Vakharia: Um, it's not important because I feel like it's old news and I feel like we actually covered it in a way by talking about all these other things.
• 42:00
  Pam Harris: Well, it's
• 42:01
  Vanessa Vakharia: Do you?
• 42:01
  Pam Harris: mean.
• 42:02
  Pam Harris: Everything we talked about today Is the important stuff.
• 42:04
  Vanessa Vakharia: Is what I mean.
• 42:04
  Vanessa Vakharia: David's doing this, by the way.
• 42:06
  Vanessa Vakharia: He is doing the wrap up.
• 42:07
  Vanessa Vakharia: I love telling people that.
• 42:08
  Vanessa Vakharia: It's so fun.
• 42:09
  Vanessa Vakharia: Okay, so final two questions.
• 42:10
  Vanessa Vakharia: Quick fire.
• 42:11
  Vanessa Vakharia: I ask every guest.
• 42:13
  Pam Harris: I'm ready.
• 42:13
  Vanessa Vakharia: Number one, if there's one thing you could change about the way math is taught in school is, what would it be?
• 42:21
  Pam Harris: Holy.
• 42:24
  Pam Harris: I would help teachers experience what it means to do the mental actions of math thing, because that would shift everything they do.
• 42:31
  Vanessa Vakharia: I love it.
• 42:32
  Vanessa Vakharia: Okay.
• 42:32
  Vanessa Vakharia: So what if a teacher's listening to this and they're like, you know, this is so awesome.
• 42:37
  Vanessa Vakharia: It sounds really great, but I just, I'm not a math person and that's just it.
• 42:40
  Vanessa Vakharia: I'm just not a math person.
• 42:41
  Vanessa Vakharia: What would you say?
• 42:42
  Pam Harris: I would say you're, you're not a math person yet, or you actually are a math person.
• 42:49
  Pam Harris: Um, and, and one of my favorite things to do is to ask them, how do you think about this problem?
• 42:53
  Pam Harris: And, and then, and 99% of the time people will go, well, you know, that's how you think about it, but you're supposed to do the right way.
• 42:59
  Pam Harris: And I'm like, what if we could teach all math the way you just logiced your way through that one.
• 43:03
  Vanessa Vakharia: Oh, I love that.
• 43:07
  Vanessa Vakharia: Well, that's all she wrote.
• 43:09
  Vanessa Vakharia: I mean, it's not, I have like 20 more questions, but that's all.
• 43:12
  Vanessa Vakharia: That's all we have time for it on today's segment of Pam and Vanessa, figure out what words and math mean and truly understand each other.
• 43:22
  Vanessa Vakharia: Thank you so much.
• 43:23
  Vanessa Vakharia: This was so much fun.
• 43:25
  Pam Harris: You're a gift.
• 43:26
  Vanessa Vakharia: Oh my God, you're a gift.
• 43:27
  Vanessa Vakharia: This is so sweet.
• 43:28
  Vanessa Vakharia: We should tell Chris and Rob that you know they really were the start of our love story.
• 43:32
  Vanessa Vakharia: Thanks guys.
• 43:33
  Vanessa Vakharia: The matchmaker, the match makers.
• 43:35
  Vanessa Vakharia: Okay, until next time.
• 43:37
  Pam Harris: Woo.
• 43:39
  Vanessa Vakharia: ​Okay, guys, be honest.
• 43:41
  Vanessa Vakharia: When we started that convo, did you think we'd be besties by the end of it?
• 43:45
  Vanessa Vakharia: I loved this talk with Pam.
• 43:47
  Vanessa Vakharia: In a world where our differences and disagreements are amplified.
• 43:50
  Vanessa Vakharia: I just found it so refreshing to have time for actually nuanced debate about some math questions that people seem to lose their minds about online, but that really shouldn't be so controversial.
• 44:01
  Vanessa Vakharia: Especially when we all have the same goal, which is just helping kids learn and feel confident.
• 44:07
  Vanessa Vakharia: So, I have some homework for you this week.
• 44:09
  Vanessa Vakharia: Maybe my biggest challenge for you yet.
• 44:12
  Vanessa Vakharia: I want you to find someone you disagree with about math or like anything, and sit down for an hour, okay, that's, that's a long time.
• 44:19
  Vanessa Vakharia: But like, sit down for like 20 minutes and really talk about it.
• 44:22
  Vanessa Vakharia: See each other's side and truly try to understand where they're coming from and where you actually might share common ground, one piece of common ground.
• 44:30
  Vanessa Vakharia: And, ahem, a good way to break the ice with this person might just be to send them this episode.
• 44:36
  Vanessa Vakharia: And whether you try this challenge out or just wanna share your thoughts on the episode, please text the podcast, DM me on Instagram at the Math Guru, or email me at vanessa@themathguru.ca.
• 44:46
  Vanessa Vakharia: Links to do all of those things are in the show notes.
• 44:49
  Vanessa Vakharia: Also, my audio book is officially out and I cannot believe how many of you guys have already bought a copy and are listening to me narrate Math Therapy in my voice, in your ears, that's actually wild.
• 45:00
  Vanessa Vakharia: You can grab it wherever you buy your audio books, including Audible and actually Spotify where it just got added like today.
• 45:07
  Vanessa Vakharia: Finally, my Math Therapy merch line has dropped and I'm dying for the cute pics you guys are sending me with you in your MT swag, please keep sending me those, and you can shop the drop at maththerapy.com/merch.
• 45:20
  Vanessa Vakharia: Math Therapy is hosted by me, Vanessa Vakharia.
• 45:22
  Vanessa Vakharia: It's produced and edited by David Kochberg, and our theme music is by our band, Goodnight Sunrise.
• 45:28
  Vanessa Vakharia: Okay, that's it.
• 45:29
  Vanessa Vakharia: Go forth.
• 45:30
  Vanessa Vakharia: Trust yourself.
• 45:31
  Vanessa Vakharia: And remember, your inner mathematician is already in there.
• 45:34
  Vanessa Vakharia: You just have to give them the mic.
• 45:41
  Pam Harris: They're logical relationships, but we're not logicing our, see, I've made it my own word.
• 45:44
  Pam Harris: They're logicing.
• 45:45
  Pam Harris: We're
• 45:46
  Vanessa Vakharia: I like it.
• 45:46
  Pam Harris: logicing our way.
• 45:48
  Pam Harris: What is on your shirt?
• 45:50
  Vanessa Vakharia: Brittany Spears, do you know who that is?
• 45:51
  Pam Harris: do, but I, there's two people on your shirt that, so they can't be.
• 45:57
  Vanessa Vakharia: They're, they're both just Brittany.
• 45:58
  Vanessa Vakharia: It's like both, just two different,
• 45:59
  Pam Harris: right now.
• 46:00
  Pam Harris: There's
• 46:00
  Vanessa Vakharia: no,
• 46:01
  Pam Harris: on your shirt.
• 46:03
  Pam Harris: Sorry.
• 46:04
  Pam Harris: Okay.
• 46:05
  Pam Harris: Pop, pop culture ignorant here.
• 46:07
  Vanessa Vakharia: I mean, no, you're not ignorant.
• 46:08
  Vanessa Vakharia: You're, you know who Britney Spears is.
• 46:10
  Pam Harris: mean, ish.
• 46:11
  Vanessa Vakharia: Yeah, it's just a very poorly designed shirt.
• 46:15
  Pam Harris: We won't tell anyone that you said that.
• 46:18
  Vanessa Vakharia: Okay.
• 46:18
  Pam Harris: We won't put that out publicly or anything.
• 46:22
  Vanessa Vakharia: Oh my God.
• 46:23
  Vanessa Vakharia: Okay.