Teaching Creativity in Mathematics
It's a shame that the arts do not have the same priority as do core subjects such as reading, writing, math and science in public schools. When the fat is in the fire, and budgets need to be cut, they're the first to go. There's even a hierarchy in the arts as music and art are generally given a greater priority than dance and drama. I feel very fortunate working in a school where they are all valued and students are given equal opportunity to develop these interests.
I've always been inspired by the arts and love the creativity that they instill in students. It makes so much sense that to become good at mathematics, students cannot resign themselves to learning the "one right way to do it" in order to derive an answer, but to cultivate multiply ways of approaching a problem and solving it through a variety of ways. I've undergone a metamorphic change in my career as a math teacher by shying away from multiple choice assessments to use assessments that require open-ended answers that require justification and analysis. When students are able to use these skills rather then just fill in the correct "bubble" with a 25% of a correct answer, we really start to see the depth of math education and cognitive skills grow by leaps and bounds. Some things that I like to do generally follow this pattern:
Beginning of the Year
During the first two weeks of class, I share a number of problem solving strategies that I have students repeatedly practice and apply over and over. We have a large poster of these strategies in the classroom and we refer to them throughout the school year through large group or whole class investigations. They are:
During the Year
We have some great math standards that are under the umbrella of "Mathematical Reasoning". The strand is intended to integrate into other strands such as Algebra, Computation, Geometry, etc., but our math program does not exactly dictate where these standards of mathematical reasoning will fall. The standards typically read like this:
"Write a linear equation with "y" and "x" where the solution for "y" will always be 1 whatever is substituted in for "x". Explain and support your equation with mathematical reasoning, notation or other supporting evidence.".
Problems like this really demonstrate not only a students ability to solve a problem but to understand the complexity and underlying relationships inherent in math. Answers for this will be varied and many explanations can explain this relationship. How can we expect this creativity to be measured by computers on a multiple choice test?
I've always been inspired by the arts and love the creativity that they instill in students. It makes so much sense that to become good at mathematics, students cannot resign themselves to learning the "one right way to do it" in order to derive an answer, but to cultivate multiply ways of approaching a problem and solving it through a variety of ways. I've undergone a metamorphic change in my career as a math teacher by shying away from multiple choice assessments to use assessments that require open-ended answers that require justification and analysis. When students are able to use these skills rather then just fill in the correct "bubble" with a 25% of a correct answer, we really start to see the depth of math education and cognitive skills grow by leaps and bounds. Some things that I like to do generally follow this pattern:
Beginning of the Year
During the first two weeks of class, I share a number of problem solving strategies that I have students repeatedly practice and apply over and over. We have a large poster of these strategies in the classroom and we refer to them throughout the school year through large group or whole class investigations. They are:
- Doing a similar problem
- Trial and Error
- Constructing a table
- Making an educated guess
- Working backwards
- Looking for mathematical language
- Drawing a picture
- Looking for a pattern
- Making a list
During the Year
We have some great math standards that are under the umbrella of "Mathematical Reasoning". The strand is intended to integrate into other strands such as Algebra, Computation, Geometry, etc., but our math program does not exactly dictate where these standards of mathematical reasoning will fall. The standards typically read like this:
- Break a problem into similar parts
- Eliminate unnecessary information
- Develop a conjecture about this problem
"Write a linear equation with "y" and "x" where the solution for "y" will always be 1 whatever is substituted in for "x". Explain and support your equation with mathematical reasoning, notation or other supporting evidence.".
Problems like this really demonstrate not only a students ability to solve a problem but to understand the complexity and underlying relationships inherent in math. Answers for this will be varied and many explanations can explain this relationship. How can we expect this creativity to be measured by computers on a multiple choice test?
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