# Ep 2: Math Does Not Equal Algorithms!

June 30, 2020 Pam Harris Episode 2
Math is Figure-Out-Able with Pam Harris
Ep 2: Math Does Not Equal Algorithms!
Chapters
Math is Figure-Out-Able with Pam Harris
Ep 2: Math Does Not Equal Algorithms!
Jun 30, 2020 Episode 2
Pam Harris

What do you think math is, a disconnected set of facts to memorize and rules, procedures to mimic or is it something else entirely? In this episode, Pam and Kim talk about discuss that real math teaching is about listening to students - that you must know your content, and know your kids. Also that math is not about mimicking an algorithm, but rather math is about letting the numbers and the structure dictate the strategy. How would you answer the question, "What is 99 plus anything?" or "What is 99 times anything?" How can you use relationships to solve those problems?

Talking Points:

• What are Algorithms? Why are they not Pam's goal?
• How mathematicians approach problem solving
• What is 99 + anything?

Find the transcript here: http://podcast.mathisfigureoutable.com/1062400/3887876-math-does-not-equal-algorithms

What do you think math is, a disconnected set of facts to memorize and rules, procedures to mimic or is it something else entirely? In this episode, Pam and Kim talk about discuss that real math teaching is about listening to students - that you must know your content, and know your kids. Also that math is not about mimicking an algorithm, but rather math is about letting the numbers and the structure dictate the strategy. How would you answer the question, "What is 99 plus anything?" or "What is 99 times anything?" How can you use relationships to solve those problems?

Talking Points:

• What are Algorithms? Why are they not Pam's goal?
• How mathematicians approach problem solving
• What is 99 + anything?

Find the transcript here: http://podcast.mathisfigureoutable.com/1062400/3887876-math-does-not-equal-algorithms

Pam Harris :

Hey fellow mathematicians. Welcome to the podcast where math is Figure-Out-Able. I'm Pam Harris,

Kim Montague :

and I'm Kim Montague.

Pam Harris :

And we're here to suggest that mathematizing is about thinking and reasoning about creating and using mental relationships. We answer the question, if not algorithms, then what?

Kim Montague :

In today's podcasts, we're going to talk about how Pam's work differs from others that you might find out there. There are a handful of people who are doing really good work around numeracy around student thinking and alternate strategies. Math looks different than it did when we were in school, and that can be confusing for parents and teachers. Pam, can you talk to us a little bit about how your work is unique?

Pam Harris :

Kim Montague :

So it's not about mimicking. Could you give us a little summary, if you could share with us a few bullet points. Tell us about your work in math education about teaching mathematics.

Pam Harris :

Yeah, thanks. So math teaching is about listening to students. You've got to know your content and know your kids. Math is also not about mimicking a series of steps. It's not about repeating an algorithm. Mathematics is about letting the numbers and the structure dictate the strategy that you choose.

Kim Montague :

Those are some really important ideas. Can we back up a little bit and I heard you say know your content, know your kids. Can you say more about what you mean by that?

Pam Harris :

Yeah, sure. So there's a lot of really good people out there. And I think most of us when I talk to colleagues at the university, when I go to conferences, most of us agree on that sort of first point that I made that math teacher is about knowing your content, knowing your kids that we need to listen to students, we need to notice what students are thinking, we need to notice the way that they're attacking problems, we need to notice the strategies that they're using, we need to notice the way that they are thinking about relationships. There's a whole thing out there that the Drexel Institute came up with the notice and wonder that's wonderful. A lot of people have picked up on it. And so there's people out there that are doing rich tasks and three act tasks. But for the most part, all of that all of those really good people are agreeing that we need to listen carefully to kids thinking but their end goal is still the algorithm. So they do a lot of really good work towards getting students to be able to estimate and use reasonableness and, and get some number sense and, and all that stuff. Like Of course we should do that. But their end goal is the algorithm is getting kids good at repeating these steps in order to get an answer. Their goal is to get kids good at mimicking all the steps all the time, they're headed towards the algorithm, not me. I'm not headed towards having kids just do this one thing all the time to solve every problem in that class.

Kim Montague :

That's a pretty bold statement you're making that algorithms are not your goal.

Pam Harris :

Yeah. And it's where I differ. So it's one of the reasons that we're talking about this on this podcast so early is to sort of say, my work isn't just about getting kids kind of good, at you know, like some number sense and some being able to, you know, kind of reason a little; nah like, that's actually my goal. My goal is number sense. Number sense, isn't just this little thing about being able to estimate or being able to look at your answer and make sure that it's reasonable number since is a huge part of what it means to be a mathematician that I use relationships and connections I know that instead of looking at a problem and saying, Oh, this is an addition problem, I must now do these steps or, oh, this is solving a proportion, I must now cross multiply and divide. Instead, it's looking at the problem and saying, Ooo, how are these numbers affecting me? What relationships do I see here? And how do I want to then let those relationships influence how I'm going to solve the problem? I let the numbers and the structure dictate the strategy. It's not about one set of solution steps all the time. It's about ooo, based on what I see in this multiplication problem, ooo, I see these numbers, this relationship, I'm going to use those relationships to solve this problem. So, Kim, I happen to know you well enough that if I say, Hey, give me an example of what you do. So I mentioned earlier 99 plus anything, so let's just pick an ugly number, like 47. Give me an example of what you do. If I said, Hey, Kim, what's 99 plus 47? How do you let those numbers influence how you solve that problem? 99 plus 47.

Kim Montague :

Sure. So 99 to me is really close to 100. So I'm gonna think 100 plus 47, which is 147. And then since I only needed to add 99, I'm going to backup one To get 146

Pam Harris :