Monday, October 5, 2015

Teaching Effective Math Lessons

Teaching Effective Math Lessons
by Dr. Yeap Ban Har

I was very fortunate to have the opportunity to attend a district math training with Dr. Yeap Ban Har. Here is a summary of some of the things that I learned:

1) Anchor Tasks are used at the beginning of the lesson to engage students in the new learning for the day. An anchor task should be an interesting and rich problem that allows students to explore the mathematical concepts and ideas that are the most integral part of the lesson. This part of the class period should last about 15 minutes which gives students the processing time needed to allow for new learning. 

2) Dr. Yeap encourages his students to find as many ways as possible to solve math problems. He tells his students that it is a clever day when they are able to find more than two ways to solve a problem. He rewards his students when they have 20 or more clever days in one month.

3) Anchor Task Example:  Instead of how can we solve x + 6 = 9, Dr. Yeap said:
  • Can you guess what number I am thinking of?
  • If I increase that number by six then the result will be nine.
  • Can we figure out this number?
  • How can we show it mathematically?
    • Equation
    • Guess and Check (substitution)
    • Balance Scale
    • Mental Math
    • Number Line
4) Students are encouraged to write in their journals throughout the lesson to work out their mathematical thinking and at the end of the anchor task, students are asked to: 
  • Explain in their own words the problem they were solving
  • Show one method to solve it and
  • Give the answer to the problem.

Image result for composition books

5) Dr. Yeap reads his students' journals frequently. He has a system where he is able to read all of his students' math journals once a week. He has two stamps for checking and commenting in the journals:
  • I like this journal entry because it is creative
  • I like this journal entry because it shows initiative.
6) He used a very large pencil pointer. He uses this in his classes to constantly remind the students to WRITE in their journals!

7) Questions Dr. Yeap asks throughout the lesson:
  • Can you imagine that? (He uses this question frequently in his teaching which encourages the students to see the problem in their minds.)
  • Does anyone want to challenge this?
  • Do you think this method works all of the time?
  • Do you accept that?
  • Is my diagram reasonable?
  • How is it the same? How is it different?
  • Do you notice anything?

8) Theories of Piaget and Vygotsky were mentioned frequently:

Multiplicity in Materials: Reggio Inspiration and the Knowledge of Jean Piaget:


9) Differentiation: When students finish their work early he has three possible assignments for them:
  • Write a story for the equation or problem that was solved
  • Write a note in their journal explaining how to solve the problem that they worked on class to a student that was absent. He will then copy the note and give it to the absent student upon their return to class.
  • Can you come up with a new method, an original method, one that no one on earth has ever used before.? If so, you can name it after yourself!

10) Homework:  Pick five problems that you don't think that you can solve (from the exercises page at the end of the section) and then do those five for homework. If they are all too easy, write a paragraph about why they are all too easy and then write three equations that are difficult for you and solve them.