Professor Alan H. Schoenfeld loves problem solving so deeply that he earned his bachelor’s, master’s, and doctorate degrees all in math and has spent the past 50 years researching the ways students learn math and how to effectively teach it in K–12 classrooms.

“I feel like I’m getting paid to do *The New York Times* crossword puzzle. That’s how much fun I have as a researcher,” he says.

That joy stems not from the fact that he’s that good at math (he doesn’t think about people in terms of being good or bad at it) but from the fact that he stays curious, and what he is good at is asking questions.

His curiosity and subsequent research to find answers earned him the Felix Klein Medal, the highest international distinction in mathematics education, which in 2011 recognized his “sustained, consistent, and outstanding lifetime achievements in mathematics education research and development.”

Schoenfeld, the Elizabeth and Edward Conner Chair, is now ready to retire from Berkeley School of Education in part because he’s finally making good on his promise of 50 years ago.

“I originally set out to understand more about what productive mathematical classrooms look like. If we have with enough knowledge and the right tools in the hands of teachers and administrators, we can make programmatic and systemic change and ultimately better outcomes for students,” he says.

That promise comes in the form of his Teaching for Robust Understanding (TRU) Framework, which provides schools a comprehensive and accessible description of the five dimensions that can create powerful and ambitious learning environments from which all students emerge as knowledgeable, resourceful, and agentive thinkers and problem solvers.

Even still, after a half century, more than 24 books (written, edited or co-edited), and 34 graduate students later, Schoenfeld has questions. “We have a solid base for a lot of content and teaching methods but what about effective targeted interventions? What about the big theoretical picture?"

He plans to spend his retirement supporting research into those questions as co-chair of the EMERG Scholars program, a joint effort with the National Academy of Education and Gates Foundation to support early career education researchers with funding and mentorship. It’s time to re-think (mathematics) education from bottom to top.

“Sure there will be some leisure travel and more cooking. Now that I won’t be in the classroom and be required to attend faculty meetings, I’ll be pursuing all the things I love to pursue with more time to pursue them.”

*In celebration of Professor Schoenfeld's impact on mathematics education, gifts to the BSE Fellowship Fund will be used to support doctoral students in the Graduate Group in Science and Mathematics Education (SESAME). **Visit give.berkeley.edu/Schoenfeld.*

### The big questions Schoenfeld has pursued over time

**Schoenfeld:** I love math, I love rich, powerful math. I want to understand enough so that every single student can experience mathematics in the powerful ways that allow them to become strong thinkers and have productive mathematical identities. That was the goal literally almost 50 years ago when I got started. ... **Read more.**

We didn't know enough back then so the first question was, let me understand thinking and problem solving for one student. My book, *Mathematical Problem Solving* (Academic Press Inc., 1985) gets at that question.

I found that a student’s success in mathematical thinking and problem-solving depends on four things:

- the mathematical resources at their disposal, including content knowledge, mathematical processes and practices;
- the degree to which they have come to grips with problem-solving strategies;
- the degree to which they have developed effective metacognitive tools such as monitoring and self-regulation; and
- the beliefs about themselves and mathematics that they have developed.

**Schoenfeld:** I spent a decade studying tutoring and the decisions tutors made. When I understood that, I looked at some classroom lessons to see how what we learned about tutoring applies to teaching. When we look at why teachers are making particular choices, especially in the moment decision-making, we can better understand how to help them teach mathematics. **Read more.**

So over the next couple of decades, I looked at what resources do teachers draw upon. What enables them to be effective as a teacher? If we know enough about a teacher’s knowledge, goals, and beliefs, then we can explain every decision they make, in the midst of teaching?

Why? Because the more we understand how teachers think at particular points in their careers, the more we will be able to provide relevant professional development, and that helps teachers get better at helping their students learn.

**Suggested reading:** Schoenfeld’s book, *How We Think* (Routledge, 2010) describes his work in this area, and a chapter he wrote in *The Proceedings of the 12th International Congress on Mathematical Education: Intellectual and attitudinal challenge* (2015), summarizes his research on teachers' thinking.

**Schoenfeld:** You’ve got students. You've got teachers. But there's the whole classroom environment, which involves a lot more than just those two. There are classroom norms involved, there is the dialog between students and teachers, between students and others. That's what shapes not only the mathematics that is learned, but just as important, the student’s identity as a productive mathematical thinker. **Read more.**

It's possible for students to experience mathematics as a sensemaking activity when they're provided opportunities to build ideas, make connections, and come to grips with engaging problem-solving activities. Student can also develop metacognitive competencies and productive beliefs when the environment is appropriately supportive. The challenge, however, is that the supports for attending to these aspects of mathematical thinking are few and far between.

We have to acknowledge that curricula do not support them, testing often undermines them, and teachers themselves may not have had opportunities to develop such understandings themselves.

So it’s hardly a surprise, then, that learning and teaching mathematics are as difficult as they are.

The Teaching for Robust Understanding (TRU) Framework is designed to make teaching mathematics be less of a chore and more of an engaging endeavor for both students and teachers. My research indicates that the quality of the learning environment depends on the extent to which it provides opportunities for students along the following five dimensions:

- Content: the richness of disciplinary concepts and practices available for learning
- Cognitive demand: student sense-making and “productive struggle"
- Equitable access to content: meaningful and equitable access to concepts and practices for all students
- Agency, ownership, and identity: means for constructing positive disciplinary identities through presenting, discussing and refining ideas
- Formative assessment: The responsiveness of the environment to student thinking

I encourage people to watch this video where I explain more about the TRU Framework.

**Schoenfeld:** Robert Moses, the founder of The Algebra Project, talks about math literacy being the civil rights issue of the 21st century. In his book *Radical Equations* (Beacon Press 2001), Moses says: "I believe that the absence of math literacy in urban and rural communities throughout this country is an issue as urgent as the lack of registered Black voters in Mississippi was in 1961." **Read more.**

Underrepresented minorities are largely disenfranchised. They drop out of the math pipeline far faster than anybody else, and that means they're economically disenfranchised.

A world that doesn't support everybody in being mathematically enfranchised, reified in schools in a way that doesn't mathematically enfranchise everybody, perpetuates the structural inequalities that we face and results in the continued disenfranchisement of underrepresented minorities. Moses is right. So that's got to be a nut that we cracked.

When a kid enters the classroom, that kid and the classroom interactions bear the weight of their personal history, the history of cultural practices, including inequities and everything else that shape the institutions, the classrooms and the individuals who enter them.

We don't know how to theorize that yet. So the next big theoretical step is going to be to figure out how to put all that together and use that as the framework for thinking about targeted interventions.

The first step toward that — and this is going to be a radical model — is to build a postdoctoral program with people attending to issues of diversity and equity in math. We have funding from the Gates Foundation and sponsorship from the National Academy of Education for a new program called EMERG (Equity in Math Education Research Grants). Our executive board is made up of people are who are steeped in math education.

What’s different than other postdoc programs is that we’ll have an advisory board made up of people who are experts in other disciplines like the issues of politics, issues of policy, issues of anthropology, sociology, structural racism because all of those issues need to be taken into account as we think about how people grow up mathematically.