Hi Robin,

This is a great question.  One way I do that in this project is through the course I developed as a part of this work.  Teachers take part in a Mathematics Strengths Project, which has several components (e.g., clinical interview, use of a redesigned curriculum task using UDL principles, observation of and conversation with students about perspective of math, number talks, 3 act tasks, worked examples).  Anyway, teachers begin this project by asking a researchable question about a focus student and then work to use what they learned from the above to make strengths based claims about the student's reasoning.  Some of these claims align with established research, some claims extend it, and some challenge it.  The project gives teachers a space to present and discuss their findings, which positions us as a community that learns together and pushes forward knowledge.

Oooo, "strengths-based claims" is a phrase I'm adding to my vocabulary. I really like the idea of asking teachers to focus on one student, and emphasizing that they need to ask a researchable question about what the student can do. So it's not about comparing students to each other, or directly to external frameworks using some checklist. It's about teachers arming themselves with current research, then looking at the relationship between that research and what they see students doing. They can feed the research into their work with kids, and can feed their discoveries of kids' thinking back to their understanding of research.

Yes!  This has really made a difference in my work with teachers in terms of positioning them to use tools like interviews to focus on student thinking from a basis of strengths.

Hi Robin,

 

Thank you for taking the time to think critically about how to help share our framework with teachers. We have worked in the past in introducing the framework with pre service teachers' in our methods courses. In these courses, we introduced the framework and received constructive feedback on its usability and how to improve it. In addition to sharing our framework, we have also created an interview tool for teachers to use with children. This interview tool will allow teachers to investigate student reasoning in similar ways that we do in the project were teachers can compare and contrast their experiences with our framework.

Hi Catherine,

The general ideas behind the protocol are here.  For the actual questions and tasks, we are refining the originally developed document and will make it available publicly this summer or early fall here.  I am also partnering with American Institutes for Research on Clinical Interviewing development for coaches and teachers this month and aim to have a report and possible publication from this work within the year.

 

Hi Katie,

This is a great question.  I view disability as a form of neurodiversity, so I agree that elements of this work go a long way in promoting knowledge for learners in a broad sense.  For example, using principles from frameworks that promote access to different ways of reasoning (universal design for learning, for example) or using tasks that have a high cognitive demand yet are also accessible to many ways of reasoning are promising.

I would also say that variations of these design principles make a world of difference for students with disabilities in particular. For example, students who have access to, say, using a solution strategy that is unique and being able to share that reasoning in different ways (e.g., with pictures as opposed equations; talking and showing thinking first with a partner; choice in how to share with the group) is significant to the student's participation in the content.  Also, providing a task in different ways - and allowing students a choice for which task they will engage with - supports students productive struggle for students who may not have engaged previously. We also hypothesize that these design elements may support perseverance for students.

In our ongoing analysis of two intervention studies we just concluded, we are seeing differences both in terms of how students' participation in the groups (how much they talk, the nature of their talk in terms of standards for mathematical practice) grows and changes and their conceptual advance (learning trajectories).  We are also showing significant differences in score on a curriculum based measure of the curriculum from pre to post intervention.

Katie,

I definitely think this is something that can help all students. If you start with student's own reasoning when teaching you can help them to build on their own reasoning. Students can then build conceptual understanding, because you are starting from what they understand. This is important for all students, but even more so for the populations that we work with, because they are frequently taught in ways that ignore their reasoning. 

For example, many children already have an intuitive understanding of fair sharing which can then be formalized as multiplication or division through actions such as "dealing" or "splitting."

Hi Amy,

Thanks for this great question. 

By Zooming out, I mean beginning intervention by creating an accessible learning environment, where many ways of engaging in a task, representing thinking, and expressing ideas is commonplace. We use elements of Universal Design for Learning Principles and also draw from CGI and differentiation in terms of task design (choice; number values) that support the cognitive demand of the task yet also allow access. 

Another mechanism at work in Zooming out is establishing group norms that may be different from what students are used to when they think of “math intervention time”.  For example, establishing what it means to have discussions of mathematical thinking, or establishing explicit roles around that (solver and questioner, for example).  I also link zooming out to anticipating students’ reasoning in the group and building up a model of how students are thinking toward a key idea. I use the research to anticipate thinking and refine based on what I see in the midst of instruction.

Students often bring in reasoning that I do not expect.  By Zooming in, I mean utilizing the models of student thinking to promote the student to engage in action, representations, and discussions that should support them to advance their reasoning or make connections.  For example, many students I have worked with have learning differences (e.g., working memory) and evidence actions that are representative of prior compensations made to support their thinking in some way yet often sustain disconnected actions or reasoning. To help, I work to promote the student’s noticing and reflecting. To support noticing, I've used revoicing and reshowing of exact explanations so student can remember his or her activity or notice activity not previously noticed.  I’ve also used multiple representations that act as "reshows" of the child’s reasoning.  To promote reflection, I draw from Tzur's work as well, using questioning to respond to students' activity and (at times) constrain materials or representations (covering once visible materials, for example) and ask students to imagine the activity.  

We are planning more cross case analysis to further examine each in our project and how they interact.

 

This is great rundown Jessica, and I really appreciate your thoughtful integration of UDL in this work.  Kudos for thinking about learner variability widely.  It seems like you are doing a lot of work at the teacher level, such as supports teachers/instructors provide like questing, curriculum, and implementation decisions or planning.  Does your work deal in any way with student-initiated supports, such as metacognitive or self-regulatory supports that the students themselves are taught to use? 

Kudos on an exciting project!

Hi Todd,

This is a great question and thank you for the kudos!

We do not at this time.  For me, the use of reshowing and restating exactly what was said - acting as a 'mirror', in a way - serves a metacognitive purpose for students to consider and reflect upon their thinking.  

I also accomplish this through questioning in the midst of problem solving, such as "Is that what you thought would happen?" or "This is challenging?  What is challenging about it, for you?"  While these do not teach metacognitive strategies explicitly, implicitly they support students to evaluate their activity ("What happened?  Did that work?  Why did it work or not work?") and reflect across situations.

Hi Rebecca,

Thanks so much for your question- you make a great point and I continue to think a lot about this.

One thing I think makes sense is to talk to parents about how to ask questions to support students as they think within tasks suggested for use at home.  So considering what questions open up thinking or support thinking as opposed to questions that close thinking off may be a good start. 

Has your group done outreach to parents?  How do you think about this?

Hi Judy,

This is a great question, and thank you for your feedback.  One way students are supported to make connections among different models of fractions occurs through the multiple means of representation supported in the task design. For instance, some students may draw rectangular bars to partition while others may draw squares or sets to support their reasoning in a sharing task.  In other tasks, such as those that support unitizing, students might interact with nonstandard representations of unit and non unit fractions to promote them to think deeply about their meaning.  For instance, "two thirds" might be represented within a context with a long, unpartitioned rectangle or by four circles; students may be asked to consider what one whole looks like. This is done to promote the idea that, for instance, "two thirds" is not simply two out of three shaded parts....

Hi Ginger,

Thanks for this question!

Currently, we are in our second phase of research.  The first phase of the work involved examining how students were engaged in the tasks, how (and to what extent) students employed the cognitive operations necessary to advance their conceptions of fractions within the tasks, and how students participated in discussion with each other about their reasoning. In the second phase, we are examining similar questions yet are more focused on to what extent students engaged, participated in discussion, and advanced their conceptions. We are also examining within subject pre post test differences in score on a measure of the curriculum. 

Hi Victor,

Thanks for your question!  I do plan to explore the framework with other topics.  One that we have already started to consider is proportional reasoning, although we are in the very early stages :)  

Here are the talk moves I worked from in this article.  I worked mainly from wait time, revoice, and restate to apply UDL principles of multiple means of representation and expression (e.g., re show and revoice; support students to restate each other using more than just verbal expression).  You can find slides from our NCTM presentation on the paper here.  

talk moves-

Chapin, S., O’Connor, C., & Anderson, N. (2009). Classroom Discussions: Using Math Talk to Help Students Learn, Grades K-6 (second edition). Sausalito, CA: Math Solutions Publications.

O’Connell, S., & O’Connor, K., (2007). Introduction to Communication, Grades 3–5. Heinemann