Ep 47. Mailbag: Math facts vs. calculators, a logic problem, the Southern surge

This transcript was created with speech-to-text software. It was reviewed before posting but may contain errors. Credit to Jazmin Boisclair.

You can listen to the episode here: Chalk & Talk Podcast.

Timestamps:

[00:00:00] Introduction and Mailbag Announcement

[00:01:08] Question 1: Logic Problem from Episode 40

[00:04:47] Question 2: Can calculators replace math fact fluency?

[00:12:00] Comment on states that buck the declining scores trend

[00:00:05] Anna Stokke: Welcome to Chalk and Talk, a podcast about education and math. I'm Anna Stokke, a math professor, and your host. Welcome back to another great episode of Chalk and Talk. I get a lot of emails from listeners with questions, so to help answer them, I'll be recording occasional mailbag episodes. These will be released sporadically in addition to my regular guest interviews, so I'll continue to release my regular episodes typically every three weeks, sometimes every two.

[00:00:43] If you have a question, you can go to my website, annastokke.com, and fill out the form to submit your question, and it might be featured on a future episode. So, for this episode, I'll be answering two questions. One is about a logic problem that was on a previous episode with Therese Markow, and another is about using calculators in place of math fact automaticity.

[00:01:08] I'll also discuss a useful comment I've received about my recent episode on declining test scores. Now without further ado, let's get started. So, my first question is from Pam, and this question concerns Episode 40 From Math to Science: How Weak Math Skills Hurt Students. My guest on the episode was Therese Markow, and she's a geneticist.

[00:01:36] She talked about papers that found that individuals who had taken more math courses were more likely to do well on tests of logic. And in the course of that discussion, she discussed one of the logic questions on the test that was given in one of the research studies that she talked about. So, here's the logic problem.

There are three people: Jack, Ann and George. Jack is looking at Ann, Ann is looking at George. Jack is married, but George is not. The question is, is a married person looking at an unmarried person? And there are three options: yes, no, or cannot be determined.

[00:02:20] So I got a message from Pam, and Pam writes, “I thought I aced the logic problem about Jack, Ann and George,” but not so apparently because Therese did give the answer and it was not what Pam was expecting. Pam says, "My immediate response was cannot be determined because we're not given any information about Anne's marital status. listened to it again when I got home, hoping Theresa's answer would make sense, and it still didn't.

I then got my husband, an irritatingly logical person, to tackle it, and his response was the same as mine. What are we missing? Or should we assume that Ann is so virtuous that she would not look at a man unless she was married to him? Please enlighten us.”

[00:03:07] So I am happy to talk about that logic problem, and I apologize for not going through it on the episode. So, I'm going to repeat the problem. There are three people: Jack, Ann, and George. Jack is looking at Ann, Ann is looking at George. Jack is married, but George is not.

The question: is a married person looking at an unmarried person? Now if you haven't gotten the answer or if you think the answer is undetermined, I'm going to give you a hint. So, we don't know anything about Ann, but we do know that Ann either has to be married or she's not married.

[00:03:46] So, maybe think about it with that in mind. So now I'm going to go through it. So, I'm going to just do it as two cases. So, let's suppose Ann is married. Well, Ann is looking at George and George is unmarried. So yes, a married person is looking at an unmarried person because Ann is looking at George in that case.

[00:04:11] The second case is that Anne is not married well, Jack is married, and he is looking at Ann. So again, a married person is looking at an unmarried person because Jack is looking at Ann. So it doesn't matter whether Ann is married or not, there's always a married person looking at an unmarried person. So that was fun. So, thanks for your question, Pam, and I hope that enlightens you and your irritatingly logical husband.

[00:04:47] So my next question is from Mike, and it's on one of my favourite topics, times tables. So, Mike says, “I was discussing the importance of multiplication fact fluency today, and someone responded that knowing multiplication facts isn't important as kids can just use a calculator. Do you have any tips on responding to this?”

[00:05:10] All right, so I mean, I've heard that a lot and calculators have been around for a long time. They've been commonplace, meaning pretty much everyone has had one since, you know, the seventies or eighties. So, there's really nothing new about this argument. And for that matter, technology has progressed quite a lot.

[00:05:29] Students can use apps to read to them too, but we don't often hear people saying that kids don't need to read anymore. For that matter, AI can write for us, so why bother learning to write? The list goes on.

[00:05:42] The first thing I would say is that kids need to know their math facts because it frees up working memory so they can do other math problems more easily that require using basic facts. Using a calculator does take up cognitive load and it's inefficient, and if you don't know your basic facts and you punch in something wrong on the calculator, you won't even know you made a mistake.

[00:06:06] And if you make mistakes with simple math facts, you'll make mistakes in more complex math problems.

[00:06:13] But more than that, it may seem straightforward to punch eight times six into a calculator, but there are a lot of other ways that students need to use that fact that aren't as straightforward and, you know, relying on various strategies — so that's another, another thing I often hear, that students don't have to memorize times tables because they can just learn a whole bunch of strategies, but that's going to hold students back too. So, for instance, it's going to be really hard to find a common denominator if you don't know your math facts.

[00:06:43] So, for example, if your two denominators are six and eight, your best common denominator is 24. And someone who knows their math facts can see that pretty quickly, whereas someone who doesn't, cannot. But you know, the same thing applies to reducing fractions and it goes further to simplifying complex algebraic expressions to factoring polynomials. Like it's going to be very hard to factor a quadratic like x^2 + 2x – 48 if you can't quickly see that six times eight is 48, and now you're going to be behind all your peers in algebra class. And so again, the same goes for reliance on strategies.

[00:07:23] Instead of just knowing automatically your times tables, they're not going help you in these kinds of situations. So, to do more complex problems, particularly algebraic type questions, you need to know your math facts quickly and effortlessly. It’s gotta be automatic, it's gotta be instantaneous. So, when we don't ensure that kids memorize math facts, we're really crippling them, and the calculator is a crutch that ends up being fairly useless when the problems get more difficult.

[00:07:59] And honestly, I've been teaching university math for 20 years, and I've never had a student in an introductory calculus class who didn't have their times tables memorized. That's because they don't often make their way up through the higher-level math classes. They're shut off to them when they don't have the foundational skills because then they start struggling in later classes.

[00:08:24] We do have a lot of students at the university level, though, in the remedial classes who don't have their times tables memorized and it holds them back in those classes too. It's also rather humiliating to be an adult who has to pull out their calculator to figure out seven times six. So now there may be students who exist who didn't memorize their times tables, but were able to take higher-level math.

[00:08:50] I've heard people say that. I've even heard people claim that there are mathematicians who haven't memorized their times tables. I've never actually met one, I'm a mathematician and I've met lots of mathematicians. But regardless. I want to be clear, these individuals are outliers. The probability that a student will be able to succeed in higher-level math without knowing their tables is very low.

[00:09:17] So, please don't choose to take that risk for a student. So, take the time to ensure that students memorize their times tables. It's an investment in their mathematical future. Probably one of the most important gifts an elementary math teacher can give their students. So please put in the time. Do the work and make sure kids have their times tables committed to memory.

[00:09:40] And just a reminder, I did record an episode How to Build Automaticity with Math Facts: A Practical Guide that will help with that. It's short, it's practical, and it's based on empirically validated techniques. I got help from Brian Poncy and Amanda VanderHeyden with that one. Please check it out. Now I also reached out to Bruno Reddy. He is the creator of T imes Table Rock Stars, and I asked him what he thought about this question.

[00:10:10] I wanted to share what he said because it's kind of a unique perspective. So, he says that his instinct is to “get to the heart of why someone is saying that. Why are they saying that kids don't need to memorize math facts?” He says, “They likely wouldn't believe it's unnecessary to learn to spell because we have Siri.

[00:10:28] So what's the big deal with times tables? They can't think times tables are unlearnable because,” Bruno says, and I agree, “everyone can learn their times tables.” He thinks that “it could be that they're concerned about kids not enjoying mathematical pursuits if they're having to do lots of tables practice.

[00:10:48] They may think that they can protect kids from disengaging in maths” — and Bruno's British, by the way, so, he says maths — “disengaging in maths by not having them learn the tables. That they're worried that kids will see maths as a battery of memory tests and not develop any understanding of the concepts.”

[00:11:11] Bruno thinks that “perhaps there have been scare stories about times tables practice being done badly, which actually has perhaps put some kids off math in the past.” He goes on to say that, “That doesn't mean that we don't learn the tables at all because we very much need to learn them despite having calculators.

[00:11:32] It means we need to address how they're being practiced.” Now, Bruno will be coming on the show in a few weeks to talk about times tables and other math things, so stay tuned for more from him. And please, Mike, have your colleague listen to my episode, Math Fluency Matters with Brian Poncy. I'll put a link in the show notes.

[00:12:00] Anna Stokke: The third thing I'm going to address today, Karen Vaites reached out to me and offered some comments on the Mike Petrilli episode, Examining Falling Test Scores. She wanted to mention that in addition to Mississippi, there are three other states who had strong gains in reading outcomes.

[00:12:23] Louisiana. Tennessee and Alabama. All four states stood out for reading growth, both on NAEP and state testing, and they seem to weather the pandemic better than most other states. Karen mentions that all four states have done similar reforms, which essentially boiled down to building better reading foundations, knowledge-building curriculum, investing in teacher knowledge on those things, and making sure that kids have foundations before they move to upper grades.

[00:12:56] Something that's really important, not just in reading, but in math. So, Karen's feeling is that perhaps other states can ignore it when one state makes changes and sees vast improvements, but they can't ignore a trend.

[00:13:14] And so her argument is there are now these four, there are actually these four states who have managed to really improve reading growth, and we're starting to see a trend in what they're doing, and Karen has written about it on Substack in a post called The Southern Surge: Understanding the Bright Spots in the Literacy Landscape.

[00:13:35] Karen blogs at karenvaites.org, and I am going to link to her blog post in the show notes so you can go ahead and check that out.

[00:13:42] So that's it for today. Just a short episode to answer a few questions. And again, if you want to submit a question, you can go to my website and fill out the form. Thanks for tuning in.

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[00:14:28] You can follow me on X, Blue Sky, or LinkedIn for notifications, or check out my website, annastokke.com for more information. This podcast received funding through a University of Winnipeg Knowledge Mobilization and Community Impact grant funded through the Anthony-Swaity Knowledge Impact Fund.