丁香园AV

Close your eyes and picture the most recent math class you taught. Who is doing the math? Who is doing the talking? Who is doing the thinking? Three years ago, my answer would have been 鈥渕e鈥濃�攖he teacher. My students were doing math, but I was probably telling them how to think and what to do most of the time.

My big aha moment was being introduced to the research of , a professor at 丁香园AV. Liljedahl proposes three strategies that you can implement in order to create what he calls the : Start with good problems, use visibly random groups, and work regularly on vertical nonpermanent surfaces. I started using these three strategies in my math classes, and they have been an absolute game-changer. I can confidently say that my students now do most of the thinking and talking in my classroom.

Begin With Good Problems

Liljedahl鈥檚 first strategy is to start with good problems. He suggests using rich, engaging problems that are not necessarily curriculum-based at the start of the school year in order to establish the norms of the thinking classroom. Once a problem-based learning approach has been established, you can begin to choose problems that are curriculum-based to meet your learning goals. Liljedahl offers  such as Dueling Dice or Pirates and the Diamond to get you started. Gone are the days of notes, then worked examples, then practice routine. For every learning goal, we start with a problem.

Use Visibly Random Groups

Every day I greet my students as they enter class and hand them a playing card from a deck to assign their group for the day鈥攅ach day they鈥檙e randomly assigned to a new group with new partners. I like to use groups of three students as much as possible; any bigger and it becomes easy for one or more group members to disengage from the task. The key features of the visibly random grouping strategy are:

• Neither the students nor the teacher chooses who works together. I find that my students are willing to work with any of their classmates since they know it鈥檚 just for one day.
• The group-making process must be visible to the students so that they don鈥檛 think you鈥檝e prearranged the groups.

I used to diligently orchestrate a new seating plan on the first day of every month. Yet my students and I were never fully happy with the groups I made. Now, my students work happily and productively with each of their classmates. Liljedahl notes many benefits of using visibly random groupings every day:

• Students are willing to work with any of their classmates, despite previous social barriers.
• Students learn to depend on their partners rather than only their teacher.
• Knowledge is shared between students more readily; they learn from each other.
• Students are more engaged in and more enthusiastic about math class.

Implementing visibly random groups has fostered a more positive and collaborative classroom environment for me and my students.

Work on Vertical Nonpermanent Surfaces

Now that you鈥檝e grouped your students and presented them with a rich problem, where will they show their thinking? On any available vertical nonpermanent surface: whiteboards, chalkboards, and/or windows (which they can write on with whiteboard markers). Have each group stand and work at a vertical station. The writing surfaces should all be vertical (not lying horizontally on desks) and nonpermanent (so students can easily erase things as they work through the problem-solving process). Use one writing implement per group so that partners have to work together to solve the problem.

Liljedahl notes several positive effects of working on these surfaces:

• Students start writing down their thinking faster and aren鈥檛 afraid to make mistakes when they know those are easily erased.
• Students get engaged, participate, and discuss problems.
• Students learn from each other鈥攇roups can see other boards to get ideas when they鈥檙e stuck.
• Students persevere longer with tough problems.

I love being able to look around the room and see all of the thinking on all the boards at once. This allows me to easily identify groups that need help so I can offer prompt and in-the-moment feedback for learning.

What Are You Waiting For?

My favorite thing about these strategies is that they can easily be implemented in any classroom. Pick a great problem, greet each student at the door with a random playing card, and get groups solving at the whiteboards, chalkboards, and windows that are already in your classroom. You鈥檒l be amazed at the rich discussions you鈥檒l hear and the deep thinking your students will share.

Further Reading

To see how teachers around the world are implementing these strategies in their classrooms鈥攏ot just in math classes鈥攃heck out #VNPS and #VRG on Twitter.