360 Classroom with Thinking Mathematics

"Their workspace is the Wipebook Flipchart, where they all get to brainstorm together, now that they have their own thoughts chalked out."



At the heart of mathematics is Critical Thinking- the one of the 4Cs - a term often used in education. One of the best ways to encourage this is to give low-floor high ceiling tasks that are rich in content, foster community and and enable open thinking, especially by having no one right answer. My previous experiences have made me realize that investing time early in the year in getting the students engaged in such tasks is very beneficial as we move on ahead in the year. I began this year  but getting my students “on-the-wall” and collaborating on tasks.



Every day, students get a task that they first get to think over independently. Then they get to work with a team to solve the task. Their workspace is the Wipebook Flipchart, where they all get to brainstorm together, now that they have their own thoughts chalked out. Students show their work, their thinking and the flow of conversations become easier when they are at the WipeBook on the wall, talking and doing mathematics.



Critical Thinking Tasks in Mathematics



Critical thinking is at the heart of my mathematics classroom. My philosophy is to let students explore, think, try, make mistakes and go back to the thinking board to revisit the mistakes and track differently, possibly arriving at the right solution. The detail and emphasis is on the process rather than on the solution, per se, and that brings in the depth of learning and the criticality in thinking.






As I began this year, which, arguably, has more unknowns at the moment, than the distance learning last year, I was determined to jump right in with critical thinking tasks in my mathematics classroom. One of my favourite activities is from YouCubed, ‘The Four 4s’. I like to give this task at the beginning of the year because it looks deceptively easy and that makes the students jump right in, and then it gets them engaged easily, and I see students persevere. There is a lot of depth in this task, and students can choose to go as deep as they want, and the mathematical practices and standards it can possibly touch are also many.



Questions include:

  • “Can you use four 4s along with mathematical operations to get the numbers 1 throught 20 ?” 
  • “If so, show how. If not, show why not.” 
  • “What mathematical concept is being used here? Can you think of anything else also”



So Many Answers!!!



Most of these questions don’t have a right or wrong answer, and thus provide lots of space for discussion and note taking in the classroom. A lot of this task is just trial and error, and after a certain number being revealed, students may see a pattern. Students work in small groups to answer the questions on Wipebook. Flipcharts, then rotate to evaluate their peers’ notes and to use that learning to work on their own solution (again).






Using the Wipebook flipcharts for brainstorming along as color markers allows students to edit and make changes to their steps, strategies and answers as they evolve from the discussion. A lot of communication and modelling work happens on these surfaces before they reach the solution to the task.






I also love using these because students can see each others’ work, and in my class, we pause every now and then to take a gallery walk around the class to go and see others’ work. This is a great way for peer reflection, interaction and collaboration. Having these non-permanent surfaces up makes access much easier, even for my shy students.



Make Mistakes- See Mistakes- Erase and Correct the Mistakes!



Another favourite thing about using Wipebook flipcharts is that students are comfortable making mistakes because they know it is erasable. In my class, mistakes are valued way more than no try- so just allow for the confidence to set in, especially in the reluctant early days of class, getting to know their peers while doing mathematics.



Some students choose to draw and diagram the mathematics, and the grid part is especially beneficial for this.  Wipebooks have made it easy for my students to open their minds with ways to think, talk and discuss mathematics. Students have taken ownership of their thinking and that confidence has been a big stepping stone to their success in my class.



Sandhya Raman, Morrill Middle School, Berryessa Union School  District Board.



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