- Sarah Sword
- Senior Research Scientist
- Assessing Secondary Teachers' Algebraic Habits of Mind and Designing for Equity by Thinking in and about Mathematics
- http://mhomresearch.edc.org/
- Education Development Center (EDC)

- Eden Badertscher
- http://ltd.edc.org/people/eden-badertscher
- Senior Research Scientist
- Assessing Secondary Teachers' Algebraic Habits of Mind and Designing for Equity by Thinking in and about Mathematics
- http://mhomresearch.edc.org/
- Education Development Center (EDC)

- Al Cuoco
- Distinguished Scholar
- Assessing Secondary Teachers' Algebraic Habits of Mind and Designing for Equity by Thinking in and about Mathematics
- http://mhomresearch.edc.org/
- Education Development Center (EDC)

- Miriam Gates
- http://ltd.edc.org/people/miriam-gates
- Researcher
- http://mhomresearch.edc.org/
- Education Development Center (EDC)

- Ryota Matsuura
- Associate Professor of Mathematics
- http://mhomresearch.edc.org/
- St. Olaf College

- Glenn Stevens
- http://math.bu.edu/people/ghs/index.html
- Professor of Mathematics
- http://mhomresearch.edc.org/
- Boston University

Public Discussion

## Karen Mutch-Jones

Understanding how teachers' mathematical habits of mind directly connect to student feelings and influence their work in the classroom is important--I'm sure these two projects will make important contributions to the field. To that end, I'm interested in hearing more about the initial findings you present at the end of the video. Could you further describe the types of teacher language changes that are evident on the ASTAHM and types of student responses observed? Also, I was curious about student survey responses, where they indicated they felt more "cared for". Were those related to feelings of marginalization in the classroom--which was a goal of the DEbT-M project?

## Miriam Gates

Co-PresenterThank you for your question. The ASTAHM language domain is defined as designed to measure how clearly one (in this case a teacher) communicates mathematics to others. Examples of this habit include a large range, but include behaviors like providing clear descriptions of mathematical terminology or using mathematical notation appropriately. We saw that a change in this habit on the written assessment was correlated to the student responses on the IQA. Clearly, there are limitations to correlation; however, this outcome suggests that attention to a teacher’s own language may support developing mathematical language in students.

The Tripod states that the “Care dimension” measures the message from teachers to students, “Your success and well-being matter to me in a serious way” (retrieved from https://tripoded.com/teacher-toolkit/toolkit-care/ May 14, 2019). The Tripod does not explicitly address issues of marginalization; however, the statement here suggests that for students who have previously experienced marginalization, it might have some impact. We do not have evidence for whether or not it did in the case of this project. It does suggest, again within the limitations of correlations, that focusing on structural approaches in mathematics can support students’ feeling of being cared for. That is, perhaps, students feel more cared for by their teacher in the presence of increasingly rigorous approaches to doing mathematics in classrooms.

## Sarah Haavind

Interesting!...I was thinking that perhaps students experienced clear descriptions of what they needed to learn from their teachers as their teachers caring that they learned the (math) content: She's telling me because she cares about me. It comes out more perhaps when stated as an opposite - a teacher who doesn't (isn't able to) explain the content clearly doesn't care about me (when actually, the teacher may care about the student, she simply isn't able to describe/isn't doing a good job of explaining the math clearly). This is truly an intriguing finding. Also, isn't the second highest correlated "C" dimension on the TRIPOD scale with positive student outcomes "clarify"? It would resonate with simple logic that a teacher who could "clarify" content best would get better/best student outcomes, but maybe the reason isn't just the delivery of rigorous content but how it is received, as (love) caring for the student. In other words, clarifying is doing more than meets the eye.Will you be pursuing this research yourselves any further or is the project complete? Either way, what would be most useful next steps from your view?

## Miriam Gates

Co-PresenterThanks for this comment. It’s all interesting to consider. From our point of view, this idea is pretty new, so we’re still theorizing about what might be happening in this data. It’s fun (and important!) to consider the many possibilities here. I think what’s particularly compelling to me is that this provides some evidence that growing habits of mind may support both increased mathematical outcomes (mathematical knowledge), and impact other important school factors for students.

This round of the research is complete at this point, but we hope it can move forward in some way. It would be interesting to consider interviewing some of the students to find out more about how they conceive of caring in this kind of a context. In particular, I could imagine prompting them with items about how rigorous content impacts their feelings about classes across these dimensions might be revealing. I’d be curious to know from your point of view what might be substantive next steps.

Karen Mutch-Jones

Sarah Haavind

## Sarah Haavind

Thank you Miriam for your thoughts. Love your ideas and appreciate your sharing.

## Peter Tierney-Fife

I am glad to learn more about these important projects: thank you!

I am hoping you can tell us more about the work educators do as part of DeBT-M and what you've been learning about addressing racially-based inequities in secondary math classrooms. Any specifics and thoughts you can share about effective equitable practices (or that effectively disrupt inequitable practices) at the classroom level is appreciated.

## Eden Badertscher

Co-PresenterPeter, thank you for asking. It is a bit challenging to discuss in a short blurb in no small part because DEbT-M provided a 2-year program of professional learning. Addressing racially-based inequities takes significant time and effort so I think being sure to be committed for several years of consistent focus is a critical foundation. Our program was a bit distinct in that we took a systems-based approach. Therefore we did not spend significant time focused on particular practices that teachers could use in their classrooms. We did explore and draw on some key practices included Complex Instruction (Ilana Horn's book was very valuable for teachers) and the Five Practices for Classroom Discussions; and we used key protocols, such as Courageous Conversations about Race, but these were tools for us, rather than the focus.

Rather than being practice-focused, we explored systemic oppression and institutionalized racism through narratives, structures, and tools (which did include system and classroom practices such as grading practices and tracking). We really dig into these- what they are, what mental models contributed to their foundations, who has power within each, what is the impact on different groups of each- focusing on getting multiple perspectives before thinking about how to change the system. A key element was that all participants--from teachers to facilitators to administrators--were to acknowledge how we each independently perpetuate racial inequity in our own practice, something that we have to accept that we wall do; then, through our developing understandings, we made decisions about what to change and how. We did not prescribe what teachers changed. Rather the focus of changes was based on significant study of practice, personal data collection, and collaborative discussions of that data. Ultimately, our goal was to empower teachers as change agents to understand and impact the systems in which they work. This enables them to continue to respond and adapt and grow as needs change and progress is made.

I think a big takeaway is, there is no one pathway to follow to achieve equitable practices; however, the pathway chosen must be purposefully designed with the system, the teacher and the students in mind. Done in this way, many avenues can lead to significant changes as the data in the video suggests.

Sarah Haavind

## Robin Jones

Thanks for introducing us to these projects, and for highlighting some intriguing findings. As someone who grew up in a very informal environment (California in the 70s), I regularly undervalue the development of common formal language. It didn't occur to me until now that the development of that language might actually level the playing field for students - it would give everyone the same set of language tools to work with. Attention to mathematical habits of mind might also make it possible for students to pick up more of them as they become the norm in the classroom.

Do you have any sense of whether students felt cared for because they (the students) were developing habits of mind themselves (i.e. becoming more powerful mathematicians), or whether they felt cared for because they had a teacher who valued the students enough to put effort into careful teaching?

Jessica Hunt

Sarah Haavind

## Miriam Gates

Co-PresenterThank you for this question! As I wrote earlier, I think we are still exploring the possible reasons for this correlation. This is one that came up repeatedly during our conversations. Unfortunately, we do not have data to address this question explicitly. I think whatever was happening was occurring in the presence of an intervention that addressed a number of different classroom factors, so we can’t be sure that MHoM alone had the impact. On the other hand, in previous, anecdotal work, we have heard from teachers (outside of this study) who found their students to be more engaged or responsive as a result of focusing on mathematical habits of mind in the classroom.

Unfortunately, in this study we did not collect the kind of data that would help us make the determination of what the exact nature of the relationship was. This line of work requires and demands further investigation. As I suggested before, I think student interviews might help us unpack some of these relationships in a way that the survey data could not. I’m particularly intrigued by the relationship between growth in use of mathematical structure and classroom management. This relationship did not seem obvious to me at first, but I did wonder if it suggests that classrooms with increasingly rigorous mathematics engage students, resulting in fewer classroom management issues. On the other hand, this could also indicate that a careful person is a careful person in multiple settings as you suggest.

How would you think about trying to understand this a bit more?

Robin Jones

## Karen Mutch-Jones

Thank you, Miriam, for wondering aloud (with us) about these relationships and considering the type of data that might make the correlations even more meaningful in the future. You might find interesting connections between math structure and immediate outcomes like classroom rigor/relevance which, over time, translate into different types of outcomes like inclusiveness (not marginalization) and engagement. It would be interesting to see whether time/dosage matters and to consider variation by student and course demographics. I know, that's a whole other project! Exciting to consider....

## Sarah Sword

Lead PresenterRobin, thanks for this comment. As Miriam mentioned above, we don't have full answers to your question. It's interesting to imagine some theories based on years of teachers' reports. One of the things we see in classrooms with teachers who attend to students' MHoM is careful use of *clear* language (on the part of teachers), but purposeful timing of *formal* language. (In particular, maybe not early in kids' learning about a topic! And just to be clear, we're talking about teachers' use of language - as kids are learning, they're using whatever language seems natural to them - often not clear, and not formal.)

As for students feeling cared for... our teacher collaborators report that a "structural approach" to high school mathematics (as seen in Common Core SMP, for example) feels more "realistic" and "relevant" to kids, even if the contexts they are using are mathematical, which might make them feel cared for. This is something I'd love to try to unpack sometime, but we haven't done it yet.

Robin Jones

## Al Cuoco

Co-PresenterI too would love to look into this. My conjecture is the same as Sarah's: Context is secondary to approach---what hooks kids is what Deborah Schifter describes as ``taking delight in their own mathematical thinking.'' More important that

wheremathematics is applied ishowit is done.In fact, I think context is more of a hook for teachers than students. If a teacher gets excited by a circle of ideas and can convey that excitement to the kids, magic happens.

Further posting is closed as the showcase has ended.