Amanda (Mandy) Jansen
“The core principle is moving between 'right and wrong' to 'what's the strength in this idea and what can be revised?', and everyone can keep revising and improving.”
About the article:
This post is a part of an ongoing series in which I interview educators and education researchers to supplement the articles on AJ’s Takes on Why. All speakers have my sincerest gratitude and are acknowledged below.
Speaker Bio:
Amanda (Mandy) Jansen is a Professor in the mathematics education program area in the School of Education at the University of Delaware with a joint appointment in the Department of Mathematical Sciences. Earlier in her career, she taught middle school mathematics in Mesa, Arizona. Mandy earned her PhD in educational psychology from Michigan State University. As a mathematics teacher educator, she facilitates professional learning for in-service teachers in grades K-12, and she teaches future elementary and middle school mathematics teachers in UD’s undergraduate program. She conducts research on motivation and engagement in mathematics classrooms, and her latest work addresses how teachers foster engaging mathematics lessons. For her book, Rough Draft Math: Revising to Learn, she curated strategies that teachers have used to teach mathematics in ways that honor strengths in students’ in-progress thinking and that emphasize growth in thinking through revising.
Can you tell me a bit more about the motivation behind your book, Rough Draft Math?
I'm interested in supporting students so they feel safe to take intellectual risks in math classrooms. I was originally really invested in reducing math anxiety when I was thinking about what I wanted to do research on earlier in my career. And instead of thinking about it from the perspective of trying to change the kid to be less anxious, I realized it's better to try to change the environment to be more welcoming.
So that's the way I got into this line of work. I'm doing Rough Draft Math specifically because I was collaborating with a group of high school and middle school math teachers in Delaware. We were trying to develop ways to have better classroom discussions with more students participating, and we were thinking about how to create a more welcoming environment where students would talk to one another about their ideas. We were reading a book called Exploring Talk in School about the concept of exploratory talk. Douglas Barnes was writing about that concept.
And he contrasted exploratory talk with final draft talk. The final draft would be like: I raise my hand, I figured it all out, and I'm going to perform what I know. And so the teachers decided to say, instead of exploratory talk, let's call it rough draft talk, because it's different than final draft talk.
My desire to help improve classroom discussions so that students were more involved, and my desire to create an environment that reduced anxiety for students, came together when the teachers and I co-developed this idea of rough drafts in math classrooms. We wrote a small article about it that came out in Mathematics Teaching in the Middle School, a journal published by the National Council of Teachers of Mathematics, at the end of 2016.
Then, teachers kept saying to me at conferences and in other gatherings that the ideas of sharing your rough drafts, sharing your thinking when you're not sure, and continued revision help students feel more welcome in the math classroom. They kept telling me different ideas they had for doing this, different ways they welcome students' drafts, and different ways they engage students in revising. So, the ideas culminated in a book. There have been a lot of studies, and now we're conducting follow-up research with people who have read the book.
What are some of the core philosophies that you've uncovered in your research for teaching math?
Specifically in the realm of rough drafts and revising in the math classroom, one core idea is just drafting and revising, and that creates many ways for teachers to creatively put this into practice.
We welcome a student's thinking at any time. We welcome all ideas. All ideas are treated as drafts. They're going to have some strengths, and they're going to have some opportunities to be revised for every single person. If we're going to welcome drafts and encourage revisions, it's less about math thinking being either right or wrong, but based on your solution, based on your explanation, how much is correct, where are all the strengths, and how much can you revise?
Revising isn't about fixing a mistake. It could be about having a clearer explanation or adding an alternative strategy. It could be about adding a visual representation to help illustrate relationships. The core principle is moving between 'right and wrong' to 'what's the strength in this idea and what can be revised?', and everyone can keep revising and improving. Everyone is constantly growing together, and you can emphasize growth in what you understand rather than your performance at a period in time.
What are some of the tangible benefits that you've seen in students using the rough draft method?
When teachers say to students, "It's fine, you can share your rough draft ideas," that helps students feel safer, like, "Oh, I don't have to figure it all out. I can just share what's on my mind."
The idea of drafts is very welcoming for students. They also really appreciate that they can revise. If they know they'll be able to revise, it creates more desire and opportunity for persistence because they can revisit their work. They get less frustrated because they're not expected to know it right away. In classrooms where there's rough drafting and revising, there's often collaboration, so it becomes collective knowledge building rather than a single person trying to figure it out alone.
We're actually conducting research on students' experiences with rough drafting right now. I have a grant from the National Science Foundation to investigate middle school students' experiences with drafting and revising. We have conjectures that students may feel a stronger sense of belonging in a classroom where their thinking is treated as having strengths, and where revision through collaboration helps them feel more connected to their peers. They may develop a stronger sense of self-concept when their ideas are recognized for their strengths and they have multiple opportunities to try.
They might also develop a more positive math identity. They may begin to see learning as trying to understand, rather than simply trying to perform. We have a number of conjectures about these experiences, but soon we'll have empirical data over the next couple of years to see how much this is happening—and where it may not be. We're also studying the teaching to see whether different approaches to rough drafts and revising are more effective than others for motivating students.
What are some ways to encourage students who tend to only offer correct or polished answers, especially in collaborative settings where there seems to be more of a perceived "risk"?
First of all, it's usually the kind of math problem we ask students to work on. There's a problem that I've seen: "Would you rather have one big ice cube or a lot of smaller ice cubes with the same amount of water?"
Some of it is preference, like "I want to chew on my ice cube so I want the smaller pieces" or something like "the big ice cube's pretty." Still, once you get underneath the math of that, there ends up being a discussion on comparing the surface area of the ice with a bunch of smaller cubes and then the bigger cube. You could still prefer one over the other, not necessarily based on surface area.
Either answer could be correct, but it's how you justify it mathematically that would matter. If it's a challenging problem and every single person in the group is needed because the problem is so hard that you can't really do it by yourself, that leads to greater collaboration.
I teach a math class right now for future teachers, and I gave my students a set of different ways you could be smart in math. Maybe you're good at identifying patterns, maybe you're good at explaining your thinking, maybe you're good at thinking of an alternative explanation, all of these different strengths, and I had them rate their strengths. They realized they had different strengths from other people in the group, and they were trying to grow in other dimensions.
Then, I gave them a challenging problem to work on together, and they realized they needed each other's strengths. They recognized that there are many ways to be good in math, and we need the strengths of the other people in the group for challenging problems, so we can all be successful together. Those are two different strategies that make a difference.
