Kirk Walters is a managing researcher for American Institutes for Research, or AIR, focused on K-12 math teaching and learning. As a teacher in San Bernardino, he joined in a research project and liked it so much that he turned his career toward research. “What I really like about it is I get to work with people who like trying to answer really challenging and important questions,” he said. “Teaching is really complicated and we’re trying to understand how kids learn and how to improve instruction. There aren’t a lot of black and white answers.”
He spoke about his research involving Algebra I instruction through the Better Math Teaching Network in New England at a recent Carnegie Foundation Summit on Improvement in Education. The network, funded by the Nellie Mae Foundation, includes high school algebra teachers, school and district leaders and researchers including Walters. It is focused on making math more interesting to students, especially those considered “at risk” of failing.
Teachers in the group, which started its work 18 months ago, have been testing ways to make math more “personalized, relevant and meaningful,” he said. The network plans to share its successful ideas – which other math teachers throughout the country could try in their own classrooms – on its website this summer.
Walters talked with EdSource after the conference about his work with the network. Below are excerpted comments from our interview.
Q. What’s wrong with the way math is currently taught?
A. If you have ever been a math student, or been around schools, you know the majority of people still aren’t crazy about mathematics. One reason is that math is presented as a set of procedures that are often sort of disconnected from their underlying concepts and from the real world – even though I’m not one of those people that says you can make a real world connection to everything. Math is made up of interesting applications and interesting ideas. It’s just a way of thinking and seeing the world that – unfortunately to a lot of teachers and students, for lots of good reasons – is foreign.
Q. Are you saying most math instruction is boring to students?
A. I think that’s right. I think it’s easier to produce a worksheet and in some cases – for the kids who are used to it – it’s easier for them to just fill out a worksheet. To really push students’ understanding – or explaining ideas through argumentation, or coming up with a real clear explanation, or critiquing someone else – that’s a much harder thing to prepare for as a teacher.
Q. What’s the solution?
A. I think it is to try to make math more engaging to more students. But we’re trying to do this incrementally, rather than making a giant leap, because teachers are at different places in terms of how comfortable they are and how interested they are in this approach. So, we’re trying to look at multiple entry points in aspects of teaching – routines, strategies and practices that teachers already do – and figuring out how we can make small, more concrete adjustments that might lead to improvements, such as more kids that raise their hand or participate. We’re looking at ideas that could grow by the end of the year to have a more ‘student-centered classroom.’
Q. In a nutshell, how can teachers make math more interesting to students?
A. One really important characteristic is when students see that their teacher is just really curious about the content and they get excited about it, like, ‘Wow, can you believe that?’ I find that is more contagious than people might realize, whether it’s math or science or history. That’s important. It seems like in education, we focus more on a teacher’s major and credentials – and that’s important too – but somehow, curiosity seems to be overlooked.
Also, in terms of making it more interesting, we’re finding that’s true with teachers who – instead of just presenting the skills and procedures – are moving onto asking students: ‘I wonder why this procedure works? What’s the underlying concept?’ When pushing students to be more conceptual, pushing for more argumentation and justification, kids are more highly engaged than if it’s just a lecture.
The third aspect is: when students are presented with novel problems where the answer isn’t immediately apparent, that helps on the engagement or interest front.
Q. Why did you choose to focus on Algebra I? Do these ideas apply to other math classes?
A. We wanted to serve teachers and schools and students that were more at risk. Now, if you’re taking Algebra I or the equivalent in 9th or 10th grade, you wouldn’t necessarily be the kind of ‘high flyer’ that zipped through Algebra in middle school.
Also, Algebra is sort of the ‘gatekeeper’ in high school. If you don’t have a solid understanding and foundation in Algebra I, it’s really problematic – not only in the next math class, but also in science.
Q. How do teachers benefit from working with each other in networks?
A. One of the most encouraging things we’re hearing is that the network teachers are saying how valuable it is to collaborate with each other, both in a small group setting – with some in the same schools – or spread across different schools, some in rural settings. The fact that an Algebra I teacher in Maine can talk to an Algebra I teacher in New Hampshire and they’re working on the same ‘change idea’ – that’s really valuable.
And as a group, they share across strategies, so they get other ideas for future improvement projects based on what they’re hearing. It’s highly collaborative and highly job-embedded, because the problems they’re tackling are rooted in their everyday teaching.
Q. What do you mean by, ‘sharing across strategies’?
A. In our network, we’ll have smaller groups of teachers – about three or so – working closely, like through videoconference meetings, every couple of weeks for a quarter. Those small groups are all working on the same idea, the same thing. Maybe they’re all working on strengthening the connections between underlying concepts. But some others may be working on argumentation, some on solving non-routine problems. They hear about these other aspects that still fall under the umbrella of ‘student-centered,’ while working on making small, incremental changes under the premise that it’s really hard to do everything at once.
Q. How is your network sharing its ideas with other educators?
A. Basically every teacher in our network – in some cases, there are pairs of teachers, some individuals – has tested a change idea and refined it over the course of the year. They submitted summaries showing: what you tested, what you learned, what you would recommend for the next teacher to do, data collection instruments, what you used to measure outcomes, and whether it was working… On May 6, teachers presented their strategies they had been testing and refining to each other and also to a group of instructional leaders from New England that included state and district and school department chairs.
Q. What was the outcome?
A. The outcome was that these change ideas or strategies are going to be finalized. The audience of instructional leaders and other teachers provided some more feedback on the presentation and we’re finalizing these into a set of strategies that can be handed off to other people to test and refine. Those will be posted on our website this summer for anyone to use…We will be writing about it and presenting at conferences.
We’re also building a resource library over the summer. That will have things like resources for good change ideas. It could be a research article. Or, if you’re looking for a better problem or task to use that is aligned to the algebra content you’re teaching, you might take this problem to incorporate into one of your routines because it may be better than one out of the textbook.
Q. What types of routines?
A. The routines our teachers are refining are things they do regularly. It could be like a warm up or an ‘exit ticket’ item during the last 10 minutes of class, or, ‘How I sequence my first four lessons in a unit.’
Q. What types of change ideas are teachers testing?
A. The teachers are trying to focus on strategies that are a little smaller and more concrete than say, ‘I’m going to do a Common Core math lesson.’ The Common Core includes eight ‘mathematical practices.’ We’ve narrowed it down to three aspects of student engagement that really are aligned with the Common Core, but are also aligned with things that have been around forever. These are: connect concepts to each other, justify your answers and persist in solving problems.
Q. What kinds of change ideas are working?
A. Some of our teachers have been working really hard on justification – orally or in writing – as well as students’ critiquing each others’ thinking and writing. We have a number of change ideas that have been tested and refined around critical thinking in math. And we have some measures of quality, so we’re not just looking at getting more of our kids to explain their answers, but are looking at, ‘What is a quality justification? What goes into that?’ I think we’ve made a lot of progress. I think we have some concrete examples of teachers who have really seen improvement in kids’ thinking and reasoning.
Q. What is the process for testing a change idea?
A. The first question a lot of teachers ask themselves about this change idea is: ‘Will I do it?’ The second is: ‘Will I actually get the kids to do what I want them to do?’ The third is: ‘Will they engage with quality?’
So, if I’m implementing a change idea to get my kids to describe their thinking, there are different ways to measure that.
Q. Can you give an example of this?
A. For instance, let’s say the first 10 minutes of my class, I do a warm up activity. The goal is to prime the pump from yesterday – articulate three things students learned yesterday. Some teachers have said: ‘Take 10 minutes and answer these questions.’ But instead, they could break the time into three little chunks and say, ‘I’m now going to give you a problem we learned about yesterday.’ Or, ‘I’m giving you two problems that I looked at that kids in this class solved. See if you can find out what’s similar and what’s different. Explain why you think this approach is correct or not. You get three minutes, then turn and talk to your partner and she’s going to explain.’ It’s highly structured, adapting a routine very specifically.
Q. How would a teacher test this with students?
A. In cycle one, I might have decided to chunk out time in three pieces. Then, I might have decided three minutes was too long. I might involve a group of three students instead of pairs of students. Teachers are paying attention to student engagement to see if it can be maximized. Once they determine that, they’re ready to hand it off.
Q. What is a cycle?
A. Let’s say I have a change idea. I’m going to do it four times over two weeks when I review homework. I’m going to call those four tests part of one cycle. At the end of those four tests, I might have made some tweaks. I get together with other teachers to discuss what happened. There’s accountability. They know what I was testing. If I predicted half of my kids would engage, but only 40 percent did, we talk about why or why not they engaged. At the end of the cycle, teachers can decide to abandon the idea, or adapt or tweak it.
Q. What kinds of change ideas flopped?
A. There were no change ideas where the kids revolted. (Kids are used to) sort of the standard, boring math class where someone just talks the whole time. That’s where the real problem is – apathy. These teachers are trying to make it more interesting to kids. Strategies that didn’t work so well had more to do with: the teacher hadn’t really thought through whether this was the kind of thing you would do on a regular basis, or maybe hadn’t thought through the quality piece. So, maybe I got my kids to talk more, but it didn’t really produce high quality responses. Not that it was a dumb idea. You have more kids talking, but are they learning more?
Here’s an example of a change idea that crashed:
One of our network teachers decided to have her students write and meet their own learning goals. The class was organized such that students worked through the curriculum in small groups at a similar pace, so this idea made sense given the structure of the class. The students did reasonably well the first time they tried it, but the students lost interest in setting their own learning goals over a few week timeframe.
Q. What qualities are you looking for in network teachers?
A. The people in our group are inquisitive, they expect each lesson to be a complicated endeavor, they don’t expect perfection, but they’re interested in the whole dynamic. There’s so much going on in a classroom at any given moment…We don’t believe a single adult talking in front of the whole class for 45 minutes is an effective model. Our teachers are willing to pay attention to whether all their students are understanding. They’re all committed to getting better and all interested in teaching.
Q. What ideas from your network could teachers in California use?
A. There are models you could even do within a school or a couple of schools utilizing common planning time.
I think in states like California, where they really are aligned to the Common Core and it’s not a pejorative term, I think the kind of work we’re doing could be useful – working on the mathematical practices standards… So, I don’t see it as being a one off. What we’ve tried to do by focusing on student engagement is to hopefully diffuse misunderstandings about what Common Core is about.