Math Curriculum Makeover

The following video is Dan Meyer’s talk  brilliant talk about mathematics teaching — math problem solving in particular.  Dan focuses on “reconstructing” ordinary textbook problems so that they  become more interesting and would elicit rich class discussion.  Dan also discusses the characteristics of good problems.

Dan Meyer is the author of dy/dan, a blog about mathematics and mathematics teaching.

When do mathematical definitions matter?

In the movie Hanna, Hanna was a 16 year old  girl who grew in the wilderness of Finland. Since two years old, she never had contact with the real world and modern technology.  Hanna learned about the world from Erik, his adopted father, and by reading books.  In one of the father-daughter conversations, Hannah asked about music. Their conversation was as follows.

Erik: Music is a combination of sounds with a view of beauty to form.
Hanna:  But how does it feel?
Erik: Good. It feels good. It’s, uh,nice.
Hanna:  Tell me properly. Can you play music?
Erik: Your mother could. She used to sing very well.
Hanna:  I’d like to hear it for myself.

Hanna probably feels the way students feel when we define an unfamiliar concept.  To students who are mathematically matured, definitions at the beginning of the lesson are probably understood, but for those who are just learning the basic concepts, it might be a little vague. Imagine a teacher saying that a function is a correspondence between two sets A and B, where each element in A has exactly one and only one corresponding element in B to students who have no prior experience of the said relationship.

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Are you a good math teacher?

Here is a list I found in  a research paper about good teaching practices, and I think most of us teachers will agree on these.

A good teacher

  • raises questions that give for all students to contribute an answer;
  • makes students think;
  • provides problems/questions that may have many different ways of solving and/or may have many different correct answers;
  • uses real-life situations whenever possible and relevant;
  • develops mathematics concepts, ideas, and skills based on problems;
  • builds on students’ previous knowledge and experiences;
  • requires students to argue clearly and convincingly about the correctness of their answers; and
  • makes available follow up tasks to reinforce what students have learned.

For Fun

If you’re a math teacher, give yourself one point if you do the item on the list and zero for not doing it.  The perfect score should be 8/8.

What’s your score?

The  above list was the output of the APEC Conference on Innovations in Teaching and Learning Mathematics in Tokyo, Japan on January 15-20, 2006

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