Teaching Math to Non-Math Teachers

by Angie Hodge

I know how to sell freshman calculus students on math and, in particular, on math taught using inquiry-based learning (IBL). Undergraduate math majors also buy into IBL pretty easily. They like math no matter how it is taught.

The same cannot be said of my students this summer. I've taught graduate courses to secondary mathematics teachers before, and my summer students were teachers, too. They were mostly elementary teachers, though, elementary teachers who had enrolled in a two-year master’s program focused on learning middle school math deeply. They recognized weakness in their mathematical preparation and wanted to learn math better for the benefit of their students.

photo credit Lindsay Augustyn

This is very brave of these teachers. To recognize that you are not the best at something is one thing, but to face that fear head on and enter into a master’s program focusing entirely on your fear takes courage.

I spent five days (8 a.m.-5 p.m.) in the last couple of weeks with 29 teachers who were taking their first math course in a math master’s program for teachers. During these five days, I witnessed the teachers undergo amazing transformations in both attitude toward math and knowledge of it. And I learned a lot, too.

Here are some reflections on the lessons learned over the five-day period. The course was taught in partnership with two middle school math teachers, one elementary school teacher, and two grading assistants. When I say "we" or "the instructional team" that is who I am referring to.

Day 1: Be firm and friendly
We all tried to be firm, but friendly on Day 1. Setting the tone for an entire master's program is a big task, and our instructional team didn't take this lightly. We spent lots of time discussing the importance of working together, having a positive attitude, knowing the importance of productive failure, taking chances, thinking outside the box, and learning to communicate in a mathematically correct manner. We dug right into the mathematics and the mathematical habits of mind. On Day 1, the teachers were "good students," but they were still very timid. They made lots of negative comments about math and moaned when asked to justify the "whys" rather than just memorizing rules. Despite the moans, we kept pushing: friendly but firm.

Day 2: Persevere (pep talks are a must!)
"Ugh" is all I have to say about the first hour of this day! Imagine being swarmed as you walk into your classroom by 15-20 upset people, all of them near tears. "Tough it out," I told myself. "Things will get better for you as an instructor if you persevere as you want the teachers to persevere." 

Teachers wanted to quit. Teachers were really not happy about math or the amount of time it took to think about the homework problems. They did not understand why an answer wasn’t good enough and why they had to "show us" their thinking process.

For all the tears and griping we somehow pulled together and even bonded as a team/class on Day 2. How? There was a lot of pep talking. We talked about productive failure. We talked about the importance of struggling. We cheered for progress. We gave praise for positive attitudes. We rallied and threw energy around like it was going out of style.

Day 3: The calm before the storm
Day 3 was one of our best days and one of the days when we saw the teachers grow the most. Teachers who were barely talking earlier were taking risks to present (but only if they knew they were correct) and were talking more to the instructional team and to their group members. Although it worried us (the instructional team) that some groups weren't talking as much as we had hoped, some were working really well. We debated switching up the groups and decided to try it for Day 4. We didn’t have to do much on Day 3 other than teach and continue to compliment progress, positive attitudes, and good work ethic.

Day 4: Beware of your first "hit" of hard material
We switched up the groups. Maybe not the best idea on the hardest day of class. Fractions!!! Need I say more? :) Wow. At the end of this day I truly wanted to cry. Our evaluations were lower than usual (still pretty decent, but we all strive for perfection). The teachers were frustrated. We were frustrated. How could we use this as a teachable moment to help them persevere?

Day 5: Make every moment a teachable moment
We started Day 5 as we started every day, talking about the evaluations. We discussed evaluations daily to make sure the teachers knew that we heard their voices. We commented on why we were or were not changing things based upon the feedback they gave us. We used negative comments about confusion as a teachable moment. We talked about what it meant to be confused and how it was part of the learning process. We also discussed the importance of speaking up if you are confused or stuck. We stressed the team aspect of the course again and emphasized that even though it was hard we were here to learn together. Since these were teachers, we were able to do this in an IBL manner, asking the teachers how they would respond to students who were confused but did not tell them this until after the fact. This discussion set the stage for a new tone. No matter how clear you think you are with your expectations and no matter how approachable you think you are, you need to remember that your students come pre-programmed to try to get the correct answer quickly. "Unprogramming" this takes time. Be a broken record about this and praise your students when they finally believe you!

Boom! (as Dana Ernst would say) On Day 5 I saw remarkable growth in nearly every single teacher. They made it over many mental hurdles and they realized they made it. Somehow making it past that tough hurdle on Day 4, they had become a team. We let the teachers sit anywhere they wanted to on Day 5. Some sat with their original groups and some paired up with new people they met from switching. Some sat in pairs, some sat in triples. Honestly, I didn’t care how big the groups were. What was important was that everyone had found someone whose learning style complemented his or her own. The day could not have gone better. The teachers did some really tough problems really well (even showing multiple solution paths). They were even asking each other to "prove it" and asking why things worked. Teachers wanted to know when they would get to see the team again. Right then it was clear that the connections made were ones that would extend beyond the one course.

Somehow, 29 individual teachers (and the instructional team) went from strangers to a team in five days. We all problem solved together and bonded—IBL Style. Boom.