Curriculum and Classroom Resources
This page contains resources and ideas for teachers who would like to use Collaborative Mathematics in the classroom.
For a start, we offer the Collaborative Mathematics Lesson Outline, with tips and suggestions for structuring a 45-minute (or so) class period around the exploration and discussion of a Collaborative Mathematics video challenge.
We also offer a student handout for each of the challenges:
For a start, we offer the Collaborative Mathematics Lesson Outline, with tips and suggestions for structuring a 45-minute (or so) class period around the exploration and discussion of a Collaborative Mathematics video challenge.
We also offer a student handout for each of the challenges:
Alignment to the Standards
Collaborative Mathematics is focused more on mathematical processes, practices, and habits of mind than on specific pieces of mathematical content. The challenges are designed to engage participants in those aspects that are called "Process Standards" by the US National Council of Teachers of Mathematics (NCTM) and "Standards for Mathematical Practice" by the Common Core.
For example, the NCTM puts problem solving at the top of its list of process standards. The Common Core emphasizes that students should "make sense of problems and persevere in solving them", for example by developing their ability to "look for and make use of structure". Problem-solving is clearly at the heart of Collaborative Mathematics.
By recording and sharing response videos, students can develop their skills of mathematical communication as they "communicate their mathematical thinking coherently and clearly to peers, teachers, and others" (in the words of the NCTM). By watching and discussing the responses videos of others from around the world, students are able to practice analyze, evaluate, and critique the reasoning and strategies of others -- another skill emphasized both by NCTM and the Common Core.
For example, the NCTM puts problem solving at the top of its list of process standards. The Common Core emphasizes that students should "make sense of problems and persevere in solving them", for example by developing their ability to "look for and make use of structure". Problem-solving is clearly at the heart of Collaborative Mathematics.
By recording and sharing response videos, students can develop their skills of mathematical communication as they "communicate their mathematical thinking coherently and clearly to peers, teachers, and others" (in the words of the NCTM). By watching and discussing the responses videos of others from around the world, students are able to practice analyze, evaluate, and critique the reasoning and strategies of others -- another skill emphasized both by NCTM and the Common Core.
Implementation Ideas
Although we encourage participants to record and share response videos with their solutions, that is certainly not the only way to participate in Collaborative Mathematics! Here are a few ideas for ways to use the CollaboMath challenge videos in the classroom.
Develop communication and problem solving skills.
Teachers might use a challenge video as a standalone lesson about developing communication and problem solving skills. For example, Challenge 02: Multiply and Flip provides a rich context for discussing what makes a good mathematical explanation (or mathematical proof).
In that challenge, for instance, we might be tempted to say that only one four-digit number is flipped when multiplied by 4... but we certainly don't want to check all four-digit numbers. How can we make a convincing general argument for this? What counts as evidence? What counts as proof?
In that challenge, for instance, we might be tempted to say that only one four-digit number is flipped when multiplied by 4... but we certainly don't want to check all four-digit numbers. How can we make a convincing general argument for this? What counts as evidence? What counts as proof?
Launch a new unit in an engaging and challenging way.
Teachers might use a challenge to launch a new unit. For example, an algebra teacher might use Challenge 08, The Confetti Problem (Part 1) as the engaging kick-off to a unit on linear relationships. Throughout the unit, important concepts about linear functions (slope, y-intercept) could be connected back to this anchoring experience of tearing up sheets of paper.
Assess student learning in an alternative format.
Rather than launching the linear unit with Challenge 08, a teacher might use that challenge as an alternative form of assessment at the end of the unit. In this case, students could be asked to solve and analyze the challenge as a way to demonstrate their ability to apply and analyze linear functions in a problem context.
Help students to appreciate alternative points of view.
We can learn a great deal about our own thinking when we try to understand and appreciate the thinking of others. So, teachers might ask students to respond to the response videos that have been sent in to Collaborative Mathematics. After exploring a challenge, students might be asked to watch some of the video responses and write a paragraph reflecting on one that stands out to them. What is that video's biggest strength? What is one piece of constructive criticism the student might give to the video's creator?
Instructors of teacher education and teacher certification programs, may find benefit in sharing these "real student responses" with pre-service teachers. After imagining a lesson around Challenge 03: Finger Counting, for instance, how would a teacher-to-be respond to the thinking evidenced in Don's response video? What about Kaylyn's response? What about Maile's response?
Instructors of teacher education and teacher certification programs, may find benefit in sharing these "real student responses" with pre-service teachers. After imagining a lesson around Challenge 03: Finger Counting, for instance, how would a teacher-to-be respond to the thinking evidenced in Don's response video? What about Kaylyn's response? What about Maile's response?
How have you used Collaborative Mathematics? Click here to get in touch and share your story!
