This is final installment of an interview series with Barry Garelick and J.R. Wilson about Traditional Math: An Effective Strategy that Teachers Feel Guilty Using. You can read Parts 1-3, here. It was a fun ride! Who should I interview next?
Q4: How do you build motivation, self-concept and a growth-mindset in students using traditional methods of math teaching?
JR: I work towards having students be successful with their math work. Students seem to enjoy math more when they are successful. Success feeds their confidence, enhances self-concept, and helps develop motivation. So, what do I do to help students be successful?
As a teacher, my attitude towards and enjoyment of math was evident to students. I feel that made a positive difference in my students’ attitude towards math compared to having a teacher who makes it clear they don’t like math. I let my students know, that like them, I make mistakes and would encourage them to point my mistakes out when I make them.
Success often comes as a result of hard work. That doesn’t mean students need to have a load of hard work dumped on them. Having consistent daily practice of intense but short duration helps students be successful, especially when it is leveled practice focused on one fact or skill at a time. I have students set goals for themselves that are reasonable and achievable. They self-check their work and keep a record of their progress. When students reach an established proficiency goal they are able to move to a new level. Students who gain competence with basic math fact fluency are more able to successfully apply their ability to other problems.
As my students would get used to the I Do, We Do, You Do approach they would realize that if they didn’t get something the first few times through, they would have more chances until they were successful. If they missed a problem, they began to be curious as to why so they wouldn’t make the same mistake on other problems.
Most of my incoming sixth grade students weren’t used to checking their own work. They seemed to be oriented to pleasing the teacher and would hurriedly change an incorrect answer without regard for why it was incorrect. Eventually, students would begin to try to figure out why they missed a problem and would ask me to work through a problem if they couldn’t figure it out. Students got immediate feedback on their work and an opportunity for explanations on missed problems. With self-checking, immediate feedback, and opportunity for further explanation, I began to see students take responsibility for their learning and striving to be successful. For most, every problem became a challenge they would tackle with an “I can do this” attitude which is otherwise known as a growth-mindset. As students became successful, they seemed to enjoy math and become intrinsically motivated to apply their ability and skills as well as taking on new challenges.
BG: In math, motivation comes from success at being able to solve problems. Giving students the proper instruction and tools they need to solve particular types of problem leads to their realization that they can do what they initially believed they couldn’t. This is a powerful feeling; students like to know how to do things. Obviously, there are going to be challenges as we gradually step up the complexity of a particular type of problem beyond the initial worked example. But by scaffolding the problems at a pace appropriate to their levels of knowledge and experience, they can make the stretches in reasoning necessary to tackle the increasingly harder problems.
Sometimes students need some help and encouragement as they advance up the ramp, so we give them hints with encouragement. In our book Traditional Math, I give examples of the types of prompts we might give a student who is having difficulty; e.g., “What’s different about this problem than the last one? What are you going to let 𝑥 represent in this problem? I know you can do this!” And so forth.
As JR mentioned, teaching students how to check if their answer is correct is important to building their self-sufficiency. I often told my students: “If you ask me during a test whether the answer you got is correct, I’m not going to tell you. But if you check your answer you can see whether the answer works.” In one class, I remember telling them “By checking your answer, you are your own answer book.” One student remarked, “Wow, that’s deep!” And I suppose it is; knowing how to solve a problem is really only part of it—seeing if it makes sense is the other part, and is equally important, if not more.
I taught in middle school, a time when students are very self-conscious and trying to fit in socially. It’s a time when students are fearful about making mistakes in front of the class. I tried to take the tension out of it by showing that I make mistakes as well—in fact for any student who caught me making a mistake at the board or otherwise, they would get a pack of Goldfish crackers.
While this kept them paying attention and taking joy in catching an error, it still didn’t alleviate their fear of making mistakes in front of their peers. But there was one activity in which students would overcome that fear, and that was presenting them with a challenging problem which I called a “Kit Kat Problem”—so called because whoever got the correct answer, and showed how they obtained it, would receive a Kit Kat bar. Such problems would be challenging enough that even the top students would have difficulty and get it wrong the first few tries. This encouraged most of the class to try for it. There was no penalty for a wrong answer and since many would get it wrong at first, students felt they were all on the same footing. Combined with the ultimate motivation of the Kit Kat bar, students would give it a try.
After seeing the correct answer, I would sometimes hear students say “Oh, I should have got that”, knowing that they had the prior knowledge necessary to solve it. If I heard “There’s no way I could have got that,” that alerted me that this was an area where I needed to provide more instruction, so that they could be successful—and have the motivation to try more problems like it.
Education Rickshaw 
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