The new question-of-the-week is:
What is an instructional strategy and/or teaching concept that you think is under-used/under-appreciated in the classroom that you think should be practiced more widely?
In Part One, Kathy Glass, Amber Chandler, Carol Salva, Jennifer Davis Bowman, and Janet Allen proposed their “nominees.” You can listen to a 10-minute conversation I had with Kathy, Amber, Carol, and Jennifer on my BAM! Radio Show. You can also find a list of, and links to, previous shows here.
Part Two‘s contributors were Jo Boaler, Katie Brown, Rachael George, Laura Greenstein, Dan Rothstein, David Jacob, and Greg Brown.
Today, Ron Berger, Debbie Zacarian, Greg Walton, Christopher Panna, Kathy Dyer, Barb Pitchford, Dr. Paul Bloomberg, and Malke Rosenfield share their responses.
Response From Ron Berger
Ron Berger is Chief Academic Officer for EL Education, working with public schools across the country. He was a classroom teacher for over 25 years, and is the founder of Models of Excellence, an open source website of the nation’s best student work:
Models of Excellence
We spend a lot of time in education thinking about how to teach, but not so much time thinking about how people learn. I believe that most of us—adults and children—learn much of what we know through models. If there is one practice that is under-utilized in classrooms, it is a lack of strong models that provide students a vision of what they are aiming for.
We need to analyze models with our students to understand what quality looks like in a particular domain or format, and we need to help our students chart a path to reach the quality that good models represent.
This is a simple idea that does not go over well much of the time. As teachers, we worry, understandably: “What if students copy those models?” We have been taught since we were young that copying is cheating, and if we provide good models for students, they will inevitably start copying. We tend to forget that much of what we learn, perhaps most of what we learn, we actually learn through copying.
Let’s say we, as adults, wanted to learn something new—perhaps woodworking, or guitar, or Spanish, or tennis, or writing code to create a website. We would start with models, and we would use models throughout our learning process. We would look at well-crafted furniture to learn what we can copy, and we would also try to copy techniques with tools. We would listen to guitar music to learn technique, and we would also carefully watch someone play. We would listen to Spanish being spoken by a native speaker. We would watch videos of tennis professionals, or watch a friend model tennis strokes for us in person. We would study well-written computer code to understand how and why it works. We would copy everything we could copy in our quest to get better. And we would seek ongoing critique from peers and experts: are we copying this correctly; are we doing this well? Eventually we would begin to improvise and make our technique more our own. But we would always start by copying.
One thing we would not do is attend a class with a teacher who refused to show us models of what we are trying to learn. But this is what often happens for our students.
Every day in school we ask students to create things: to write persuasive essays or history papers, to explain the mathematical thinking involved in solving a complex problem. We tell students what we expect from them in terms of quality; we name features of quality in that genre and sometimes we give them a rubric of how they will be assessed. Those are all good supports. But students have no picture in their minds of what excellence looks like. As teachers, we have that picture, but students can’t read our minds. If students have never read and analyzed great persuasive essays, no rubric or list can give them the inspiration and guidance to get there.
As an instructional coach, I observed a talented high school physics teacher—an 18-year veteran—give a beautiful lesson to her seniors. When I asked her what she was looking for in terms of coaching, she said it was not her lessons. She complained that her students wrote terrible lab reports, and it drove her crazy. I asked her how long this had been a problem for her and she said, “Eighteen years.” I asked her: “Have your students ever seen a good physics lab report?” She said “No; I told you I don’t have any. Their reports are awful.”
But after more conversation it turned out that she actually had one student who wrote very strong lab reports, and we were able to copy one of her best examples as a model for the next physics section. The students were amazed when they read it. They marveled over its language, its sophistication, its depth and thoroughness. They couldn’t believe a student in their school had written it. One student raised his hand for the teacher: “Mrs. Johnson? Is this what you wanted us to do?” She replied, “Yes; absolutely.” The student responded: “Then why didn’t you show us this in September?”
We need to bring models into the classroom. The first step in this practice is for teachers to build a library of models of what quality looks like in the format they are asking students to use. Those can be models from the professional world (e.g., high school science students reading professional journal articles; ELA students reading professional book reviews). Even more powerful is to provide students with models created by other students so they can see that students their age can do work of great quality. Because we as teachers tend to give similar assignments every year, a good practice is to save the best work every year (with student permission and names redacted) for possible future use as models.
My colleagues at EL Education and Harvard Graduate School of Education and I have created a collection of free, open source models of high-quality student work, housed on a website, Models of Excellence. We welcome you to download any models that are useful, and also to submit models of student work to the site from your own classrooms.
Once you have strong models, we suggest leading critique lessons in which students view models to analyze what is working in them: what features of the work are high quality and what strategies the author of the work used to make it good. That analysis is different from typical critique—it is not in service of improving the work. Instead it is a search for only the positive dimensions of the work that we can learn from. From that analysis, the class can create criteria lists for quality in that genre, rubrics for assessment in that genre, and can choose features and strategies that students want to borrow and use themselves.
Within a strong academic culture, borrowing strategies from model work is not a hidden process that is frowned upon; it is an explicit, valued strategy that is discussed openly. Students are able to say “I borrowed this idea from this model; I borrowed that idea from this other model.”
I spend a good deal of time visiting classrooms around the country in which students are, to be blunt, doing low-quality work. For example, I recently walked into a middle school social studies classroom where students were creating posters describing ancient civilizations. The students were polite and earnest, but the work was awful. I wished I could have called “Time Out,” and pulled out high quality posters—professional posters from museums or great posters done by students—and started a conversation, right then, about what a quality poster looks like. The students deserved that clarity.
Using models of high-quality work is an instructional practice that has the power to raise the bar for what all students can do.
Response From Debbie Zacarian
Debbie Zacarian (email@example.com) is known for her work in advancing student engagement and achievement. She is an education consultant and the author of many books, including two co-written books from which this response was drawn: Teaching To Strengths: Supporting Students Living with Trauma, Violence, and Chronic Stress (ASCD, 2017) and In It Together: How Student, Family, and Community Partnerships Advance Engagement and Achievement in Diverse Classrooms (Corwin, 2015):
In theory, we all understand the importance of family-school engagement. We hold a number of routine activities and events for this purpose (e.g., Curriculum Nights, Parent Conferences, Parent Council Meetings, School Plays and other performance-based events). These are so common that it’s likely that we have an image of each event and can describe what it looks like. However, deepening family engagement is something we often grapple with—especially when it comes to including the very families that feel the most distanced from us. Classroom-based events have the power to engage everyone, especially when we use strategies that are designed to build connections between home and school and in the process enhance students’ success. Here are three strategies for engaging families as partners.
- Inviting families for social events greatly helps in building trusting relationships. There are a variety of forms for these (e.g., a potluck family picnic, a dance, a movie, or a game event). Each can create positive momentum for and throughout the school year. Steps to best ensure its success include:
- Meeting with administrators in advance to secure their support.
- Collaboratively planning the event with colleagues (e.g., specialists, counselors, and others), current and former families, members of our local communities (e.g., religious and community leaders), and districts’ family liaisons.
- Collectively selecting a date and time that will yield the most participation.
- Using various conventions to invite families to the event including school newsletters, social networks, and phone calls.
- Including greeters (staff, students, former students, and families) at the school door to escort and welcome families and engage them in conversation during the event.
- Creating a warm welcoming atmosphere.
- Closing the event by asking for ideas for future events and including a suggestion box for these.
- Inviting Families For Curriculum Showcase Events are wonderful opportunities for students to share what they have learned, take the mystery out of what’s being studied, and receive acknowledgement for their efforts. While it’s important to follow the same steps as we would a social event, it’s also important to:
- Provide students with time to practice their presentations, prepare invitations, and plan the event.
- Acknowledge students’ efforts and family’s participation during the event.
- Drawing on the rich resources, talents, and assets of families can greatly help a unit of study be brought to life. An example is a middle school English and social studies teacher who are doing a unit of study on contemporary issues in the Middle East and invite family members to discuss their experiences growing up or serving in the military in these areas. There are a myriad of ways that families can be involved. It’s helpful to include the following steps:
- Talk with them ahead of time about the start and end time of the class they will be attending, the number of students and adults in it, and what to expect during it.
- Explain the goals of the unit of study.
- Provide tips and strategies that will support the family member to have a successful experience.
- Share questions that students might ask.
- Share information with the class about who is coming to build excitement about family member’s visit.
- After the event, work with students to write and send a thank you note.
Using these strategies can greatly help us in building strong home-school partnerships on behalf of our students’ success in school and beyond.
Response From Greg Walton
Greg Walton is an Associate Professor of Psychology at Stanford University. His research explores students’ sense of social belonging in school as well as how to motivate his two-and-a-half year-old to go potty on the potty.
Supporting Students’ Sense of Belonging
One of the many lame things I did in the first year of college occurred when an In-N-Out Burger truck pulled up on campus. Kids were so excited they waited in line for 45 minutes. But I stomped right past to the dining hall to eat alone.
Why was I so ridiculous? Twenty years has given me some perspective. I went to college in California but I was brought up in the Midwest. California seemed a world apart. For Californians, In-N-Out Burger was a familiar taste of home. But I felt like I wasn’t invited to the party.
My disadvantage, such as it was, was having been brought up in another state. But what if you look around yourself in school and find that few people look like you, and pervasive stereotypes say that your group is less able and less worthy than other students?
Fifty years ago, the great sociologist Erving Goffman wrote, “The central feature of the stigmatized individual’s situation in life...is a question of...'acceptance.’” Indeed, social stigma can breed a profound uncertainty about whether other people will include, value, and respect you—about whether you belong.
Supreme Court Justice Sonia Sotomayor tells of her experience in college as a first-generation Latina student, "[At Princeton, I felt like] a visitor landing in an alien land...I have spent my years since Princeton, while at law school, and in my various professional jobs, not feeling completely a part of the worlds I inhabit.” If people as successful and well-respected as Justice Sotomayor experience this doubt, surely it is common.
My colleagues and I call this “belonging uncertainty.” Everyone worries at times about whether they belong, like when you go to a new school or take a new job. But this worry is deeper and more pervasive when you face disadvantage in a setting. Then you can wonder: Do people like me belong here? And if you look out at the social world with this question in mind, even little things can seem to harbor the threat that the answer might be no—like enthusiasm for In-N-Out, or feelings of loneliness or disrespect. And that inference is debilitating.
In my research, I have asked: Could we change this inference? Could we give students a different narrative for understanding challenges in school so they don’t impugn their belonging?
In one approach, my colleagues and I tell first-year college students stories from older students—stories about worries that the older students felt about their belonging early in college, and how they came to feel at home with time. Our goal is to help students see belonging as a normal process that takes time and effort to develop, not as an either/or condition defined in part by group identity. We also ask students to tell us how this process of change is reflected in their own lives, stories we can share with future students.
In one study, this exercise, delivered in an hour-long session in the first year of college, raised African-American students’ grade-point-average through senior year, reducing the achievement gap between African-American and White students by half, and made students happier and healthier, relative to a randomized control group. Years later, a post-doc, Shannon Brady, surveyed students in their mid-20s about their lives as young adults. Strikingly, Shannon found that African-Americans who had completed the exercise nearly a decade earlier reported greater life and career satisfaction.
How could an hour-long exercise in the first year of college improve people’s lives?
The answer involves the different path the intervention set students on. Early in college, the exercise changed how students interpreted daily challenges. Freshman year students told us about their days for a week—struggles in class, difficulties with friends, romantic boondoggles. All students reported similar kinds of adversities. But African-American students who didn’t complete the belonging exercise reported lower levels of belonging when they faced more adversity. It was as if adversities meant to them that they didn’t belong. But for those who competed the exercise, belonging stayed high even on bad days. They had a different narrative. The same events didn’t mean they didn’t belong.
That change in interpretation altered students’ developing lives. In the same survey, Shannon asked students about mentors. Students who completed the belonging exercise reported having developed more significant mentor relationships in college, relationships that continued after college. And those relationships predicted life success.
So what happened? The intervention removed a critical psychological barrier early in a major school transition—a pervasive worry about belonging, rooted in an awareness of negative stereotypes. That helped students develop the kind of supportive relationships that everyone needs to succeed.
One of my favorite quotes of all time is from Urie Bronfenbrenner, a co-founder of Head Start: “In order to develop normally, a child requires activity with one or more adults who have an irrational emotional relationship with the child. Somebody’s got to be crazy about that kid. That’s number one, first, last, and always.”
And that is one of the most important implications of this work. Schooling is about relationships—maybe more than anything else. And it’s our job as teachers, as researchers, and as policy makers to facilitate the kind of productive, secure relationships that help students stay engaged, take risks, and learn.
Yet these relationships can be tenuous. When students come to school from disadvantaged social positions, they can reasonably worry whether they will be included and valued, whether they will get a fair shake. That’s why it’s so important for teachers to reach out and listen to students, to build relationships of trust; to make sure that students know that school is a process of growth and development, and that you have high standards and believe students can meet those standards with hard work; and then to help students learn and grow.
The belonging intervention also tells us something about potential and success. Some say that success is about great contexts—attending a terrific school, say. But all the students in the intervention attended a great university. A great school is necessary but not sufficient.
Others say it’s about having internal qualities that promote success, such as being smarter and more self-controlled than the rest. But in the belonging intervention, a group of students that traditionally performed worse did far better even with no change in their ability, reducing a long-standing achievement gap. Certainly, a minimum of academic preparation is necessary. But far more than we commonly recognize, students are capable of terrific growth and learning if key conditions are met.
Instead, the belonging intervention is a story about how we make sense of the world—the meanings that we draw, from events as little as a long burger truck line: How those meanings arise from the social positions and identities we find ourselves in. And critically, how those meanings can be changed at key times and then, as we engage in the world, become embedded in the structure of our lives. Those meanings we make are pliable but they can become fixed, like clay—for better or for worse.
Response From Christopher Panna
Christopher Panna is a social studies teacher and technology specialist at the Walworth Barbour American International School in Israel. Find him on Twitter @signorpanna:
Project-Based Learning: An Underappreciated Strategy
When I switched my Economics course to a project-based format, it made me consider some fundamental questions about student projects. What exactly is their purpose? Are they summative assessments for students to apply concepts already learned? Or can they be something more?
In project-based learning, students take on a challenge BEFORE they’ve gained all the necessary skills and knowledge. Students discover what they need along the way and the project becomes a vehicle for framing the entire learning journey. Project-based learning is powerful yet easily accessible because it’s rooted in a familiar concept. It only requires a change in mindset.
What is different in a project-based approach? Presenting a challenge early creates engagement and a “need to know” in which students have a clear purpose to research and build their skills. A project becomes the main dish of learning rather than the dessert. The teacher’s role also changes, as he or she becomes a guide and collaborator rather than the source of knowledge.
My particular reason for choosing the project-based format was to give students more choice and responsibility in their learning. In my Economics course they worked in teams to create an original business plan or consulting report. I’d used a similar end-of-year summative assessment before, but introducing the project at the beginning of the course fostered greater excitement among students and a sense that everything they learned could immediately be useful.
This excitement was not without some anxiety, so I provided plenty of foundational knowledge and support. We had teacher-led lessons on basic economic principles, we perused real examples of business plans and consulting reports, and we invited business professionals to visit and share their experiences. Perhaps the most valuable activity of all was conferencing with the teams. By meeting with them multiple times throughout the project, I could help them generate ideas and see their thinking evolve.
The result was sustained engagement at every stage. Compared to past years, students understood key concepts better and created higher quality products because they worked to build their projects throughout the course, rather than only at the end. We further raised the bar by inviting our professional guest speakers to return as judges for the final presentations.
Based on their feedback, students found the experience quite valuable. They appreciated the freedom to pursue their interests and the challenge of presenting an original idea to real business professionals. One student observed that because the teacher didn’t have all the specialized knowledge needed for her business plan (a high-tech walking stick for the blind), she became more responsible and self-reliant. I also learned plenty by working alongside the students as they researched, brainstormed, and designed something completely new.
Project-based learning yielded great results and I’m already thinking about how to bring this approach to my other classes. If you’re interested in the full story, I made a documentary video and a series of blog posts about the project-based Economics course. For both the students and myself, the journey was as important as the destination.
Response From Kathy Dyer
Kathy Dyer is a senior professional learning specialist at NWEA. She designs and delivers professional learning, and coaches educators around the world. She is a regular contributor to the Teach. Learn. Grow. blog and edCircuit and has written for ASCD Express. Follow her on Twitter @kdyer13:
When was the last time that you used a pre-assessment (or had one used on you)? You may use entrance/exit tickets in your class, but do you use them as pre-assessments? Have you ever used a synectic to start a new unit to get a feel for where kids are in their thinking about the unit topic—what they think they know? And how often do you employ a KWL chart at the beginning of a unit? All three of these strategies are examples of effective pre-assessment strategies. Now let’s talk about what pre-assessment is and why you should be using it more often—for both your benefit and the benefit of your students.
Per Wikipedia, pre-assessment is a way to save teachers time when it comes to teaching new material. For me, it is a valuable formative instructional practice that supports both the teacher and the students. Pre-assessment is about 1) previewing the content, 2) surfacing and connecting to what students know and don’t know, 3) beginning to uncover misconceptions/misunderstandings, and 4) helping students and teachers know where to go with the learning. Let’s consider each of these ideas.
Previewing content: A pre-assessment can provide students a preview of new content, along with expectations for learning. This content preview also helps the teacher plan changes to lessons or even create new lessons that might include review or further instruction.
Surfacing and connecting: One of the major beauties of pre-assessment is that the data tells students and teachers if topics or skills are already mastered. This is a time-saver for both parties. Brain research tells us that if we want learning to stick, we need to make connections to what is in long-term memory. Finding out what students have already learned (right or wrong) before starting instruction can allow the instruction to be more focused. If only a few students are missing content, we can individualize to get them where they need to be. If the majority have gaps, we can plan more whole-class instruction . . . until we assess again.
Beginning to uncover: The National Research Council highlighted that teachers need to place emphasis on conditions that allow students to apply what they know—the when, where, and how to use their knowledge. Sometimes in looking at the application, teachers find that students have misinterpreted knowledge or converted something that worked in one instance into a universal rule. When these misunderstandings and misconceptions are surfaced prior to introducing more or new content, teachers and students can adjust so better connections are made.
Helping students and teachers: Absorbing new knowledge and skill is dependent on preexisting knowledge and skill. Identifying what students know and don’t know before embarking into new content means that instruction and learning are focused on what students need and are ready to learn. Connections can be made and reinforced. Both parties can build off the starting points once those points are identified. It is determining a student’s zone of proximal development (ZPD)—where the student needs teacher or peer support to understand something new.
Identifying students’ preparedness to learn about a topic through pre-assessment affects instructional plans, strategies employed, students’ learning goals, students’ ability to connect to and with the content, and the level at which students and teachers engage with the content. I’d like to be ahead of the game on all of those.
Response From Barb Pitchford & Dr. Paul Bloomberg
Barb Pitchford is a lifelong educator—principal, teacher, counselor—specializing in impactful leadership practices that make a difference for all students. Barb is the co-author of Leading Impact Teams: Building a Culture of Efficacy (Corwin Press), and a Visible Learning consultant.
Dr. Paul Bloomberg is the founder and chief learning officer for the Core Collaborative, a professional learning network that specializes in student-centered approaches to learning. Paul is the co-author of Leading Impact Teams: Building a Culture of Efficacy, published by Corwin Press:
PEER REVIEW: A Powerful Practice to Accelerate Learning
We all know that feedback done well can at least double the rate of learning (Wiliam 2011). And the source of the feedback does not have to always be the teacher. In fact, feedback to self, self-assessment, and feedback to/from peers, peer review, is equally effective as long as there are clear criteria for the learning intention. Hence, we define peer review as students giving and receiving feedback on a specific task.
This is not a new concept, rather an underutilized practice that is often abandoned when it doesn’t initially reap the desired results and causes confusion and chaos in the classroom. However, we argue that peer review done well has the potential to not only double the rate of learning, but to empower students by engaging them in critical and analytical thinking that strengthens their self-efficacy as learners.
The heart of peer review is feedback so let’s take a moment to delve a little deeper into that concept.
- Feedback is what closes the gap between where you are in your learning and the learning goal.
- Feedback doubles the rate of learning.
- Feedback thrives on errors and misconceptions.
- Feedback is not a one-way street.
- Effective feedback requires trust to be effective and to be heard.
- Feedback is actionable.
- Feedback is specific to the criteria (process, performance, or product)
The good news about peer review is that students are already responsible for 80 percent of the feedback in classrooms. The bad news is 80 percent is incorrect! (Nuthall 2007) So how do we leverage the resource of peer to peer feedback to move learning forward?
We have identified five steps to developing effective peer review:
THE CONTENT / Teachers
The teacher(s) identify a standard that students commonly struggle with and unpack (deconstruct) the standard to determine the success criteria or rubric.
- Teachers develop assessment tasks to generate evidence that reflects where students are in the learning process.
THE PEER REVIEW PROCESS / Students
Define criteria: Teachers and students define the success criteria together using examples and non-examples of student work so students have a clear understanding of the knowledge and skills required to reach the learning goal.
Apply criteria: Teachers model different ways to use criteria to evaluate student work by modeling the process using think-alouds, e.g., color coding, annotating, etc. followed by guided practice (and lots of it).
- Feedback on feedback: Teachers give feedback on student feedback to ensure quality and accuracy. Feedback protocols such as The Ladder of Feedback (Project Zero), Grow and Glow, and TAG provide structure for this practice.
Empowering students to provide one another with specific descriptive feedback moves accelerates learning. Two critical components of the process are essential: 1) teacher clarity-success criteria; and 2) a well-defined student protocol. With clear criteria and a well-defined protocol, plus modeling, practice, and feedback on feedback, all students can become skilled at peer review. It’s time well spent since; it doubles the rate of learning and engages and empowers students in the learning process.
Response From Malke Rosenfield
Malke Rosenfeld is a dance teaching artist, author, editor, math explorer, and presenter whose interests focus on the learning that happens at the intersection of math and the moving body. She also delights in creating rich environments in which children and adults can explore, make, play, and talk math based on their own questions and inclinations. Her book Math on the Move: Engaging Students in Whole Body Learning was published by Heinemann in 2016:
Every day students of all ages come to school with a powerful tool for mathematical reasoning but rarely get the opportunity to harness its full potential. When this tool, our students’ own bodies, are used, the activity is typically relegated to acts of memorization that lead no further than the next test. In contrast, taking math off the page and into the spatial, embodied realm of the whole, moving body has great potential to open up new avenues for understanding. Here are some examples of how a whole body, #movingmath approach can open up new opportunities for learning in a variety of grades and settings:
* Changing the scale: When you change the scale of the math you are already exploring in your classroom you provide learners with the opportunity to get to know math from a completely new and novel perspective. Whether it’s exploring number patterns on a scaled-up hundred chart, physically experiencing magnitude, scale, distance, and direction on an open body-scale number line, or noticing new things about polygons using lengths of knotted rope, learners collaborate, discuss, evaluate, reflect upon, record their activity, and start to connect it to other experiences in which they encounter and use these ideas. “Seeing connections develops intuition,” Dan McQuillan at the University of Norwich tweeted recently. “Proofs are great; just like climbing trees, but the ability to swing from tree to tree is also great.”
* Reasoning in action: During a Proving Center lesson Kindergarten students were asked to work in teams of four or five to find the center of an 11-cell structure, which looks a bit like a ladder. Children were able to find the “center” of the object with their bodies rather quickly but their biggest challenge was to justify their physical reasoning. Lana Pavlova, an elementary teacher from Calgary, Canada told me that some of her students’ reasoning included, “Because five is the same as five,” “Because these two sides are equal,” “Because it is exactly the half.” Another student said that “not all numbers have the middle, six doesn’t. One has the middle and it’s one.” Lana told me, “I was very impressed by the kids’ reasoning. I also want to highlight how important the initial ‘explore’ stage is [and that] the movement IS the reasoning tool.”
* A reason to persevere: Lisa Ormsbee, a P.E. teacher at Fairhill School in Dallas, spent three weeks this past June running an enrichment program using movement and rhythm to explore and deepen enjoyment and understanding of math with intermediate students, many of whom exhibited what she called “math reluctance.” One of her main activities was Math in Your Feet which requires precise physical/spatial reasoning around rotations, categories of pattern properties, unitzing, complex patterning, equivalence, and perseverance to create original foot-based patterns. Lisa told me, “The kids were ALL so engaged in this activity! It was extremely hard for a couple of students, but because they were working with a partner they were more interested in “sticking in there” where it was uncomfortable until they got it!”
* Cognition is embodied: “Conceptualising the body, in mathematics, as a dynamic cognitive system enables students and teachers’ physical, visual, verbal, written, mental, and (in)formal activity to be taken not simply as representations of abstract spatial concepts but...as corporeal and contextually grounded forms of cognition.” [Spatial Reasoning in the Early Years, Davis et al. 2015]
Overall, no math concept can be understood completely in one representation or modality. Similarly, not all math can be explored with the body. Whole-body math may be a novel approach for many, but it’s also clear that it can be a powerful tool for both learners and teachers.
Thanks to Ron, Debbie, Greg, Christopher, Kathy, Barb, Paul, and Malke for their contributions!
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