Jo Boaler: Mathematical Mindsets

Chapter 5: Rich Mathematical Tasks

"Teachers are the most important resource for students.  They are the ones who can create exciting mathematics environments, give students the positive messages they need, and take any math task and make it one that piques students' curiosity and interest.  Studies have shown that the teacher has a greater  impact on student learning than any other variable." (Darling-Hammond, 2000).

Engaging maths = curiosity, connection making, challenge, creativity and usually collaboration.

 Maths excitement = maths engagement.

Number sense is crucial.
Students have to be taught to listen to and respect each other's thinking.
It is crucial to engage in "low floor, high ceiling" tasks.

What comes first?  The chicken or the egg?  THE EGG!  Give the real problem first as this engages the students and ignites their curiosity and then give them the method.

We want students to think intuitively about the problem.

We want students to be filled with sense making and understanding.  "Explain why your solution makes sense."

When students are stuck, can they draw the problem out?  Seeing a problem visually can help.

To open maths tasks and increase their potential for learning:

  1. Open up the task so that there are multiple methods, pathways and representations.
  2. Include inquiry opportunities.
  3. Ask the problem before teaching the method.
  4. Add a visual component and ask students how they see the maths.
  5. extend the task to make it lower floor and higher ceiling.
  6. Ask students to convince and reason; be skeptical.
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