Wednesday, November 21, 2012

Teaching Math Through Cognitively Demanding Tasks

I have been wanting to blog about how I teach math for quite some time and finally have a moment to sit down and do it. I transferred to a new school and was introduced to a fabulous, student driven way of teaching math. I have meshed this with my own style of teaching and previous methods of teaching to find a happy medium of using best practices, while meeting the needs of students with huge gaps!

I start every math lesson with a pose the problem which is a cognitively demanding task. 90% of the problems are word problems so the students have a context to deal with and not just a "naked" equation. I find these to be more demanding as well. Here is an example of a task:

As a class, we read the task. Depending on the task, I will ask questions to ensure they understand the task. However, sometimes I just say go at it. The students know they have spend a few moments privately thinking about the task at hand. Then, they start the task. They know when they are finished they have to make sure they showed the LOVE.
L: Labels. They label the numbers and any visuals/models.
O: Our Thinking. They have to connect the answer back to the problem by writing a complete sentence answer the question. For example: Instead of just writing 6 R 1, they have to write, Bob will have 6 cookies in each bag, with 1 cookie left over.
V: Visuals
E: Equation. And they have to label each number in the equation by referring back to the word problem.

By this time if I have not stopped them, they begin the process of explaining how they got their answer and justifying why they know it is correct.

As the students are completing the task, I am walking around, looking at their work, asking facilitating questions of some students, and choosing a sequence of student work that I want to share.

When I call the students back together, I ask several students to come up one at a time and show all of their work or part of their work on the ELMO. The other students have to try to make sense of the student's work. I ask questions of the other students to try to get them to pay attention and make sense of other people's strategies. We discuss misconceptions, strategies, and new thinking while we analyze student work. When we are finished analyzing, I will have the students who were correct or parts were correct, tear their work out to go on the chart.

We then move into our lesson. Depending on the results of the task, I use the rest of my math time to do one or more of the following:
  • Have the students complete a similar problem using a newly learned strategy from another student. 
  • Will use a few minutes to do some conceptual understanding teaching to bridge some gaps. 
  • Have the entire class move to independent practice of the skill from the task.
  • Have the higher students play an enrichment game or complete an enrichment activity while I do some intensive remediation and bridging of gaps for the rest of students who are lacking an entry point for the lesson.

In the meantime, here are some more examples of tasks completed by my students.


  1. I love this! I've been wanting to add more student centered activities during my math block. I love how this involves the students from the start of the lesson and gets them thinking about applying the math concept to a "real life" situation. Thanks so much for sharing!
    Lattes and Laughter

  2. How long is your math class? Are you writing your own problems or do you have a resource you can share? I am looking to add more rigor to my class and transition into the common core method of teaching.

  3. I'm starting this TOMORROW!! It will be our 1st day of small group instruction. YIKES. 6th grade. I'm diving in.

    I've written a blog post about it and linked to your blog. Would you mind if I shared some LOVE cards I made???



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