Questions that Encourage Creative Thinking-2

A lot of educators agree that creative thinking is a crucial skill for students to learn and develop throughout their mathematical study. But how to design our questions and lessons to allow the development of creative thinking is a common struggle for most teachers.

Following Questions that Encourage Creative Thinking-1, here is another good example that encourage students to develop creative thinking skills demonstrated in the video "Who Students in the US need Common Core Math" given by Professor Jo Boaler.

Geometrical pattern problem is a very common type of question solved in K-12 mathematics education. Many adult tests even use it for assessing intelligent quotient (IQ). In Professor Boaler's video, she used three four ways to explain the pattern of growing.

The last method - Square Method, in particular, can lead to a more higher level of mathematical thinking. By moving the blocks and creating squares or creating a table to list the number of blocks, students may be able to see that the number of blocks actually are square numbers. Through this analysis, they may even be able to find out the pattern by using mathematical induction or simply common sense and the concept of variable, derive the formulae of number of blocks of case n is (n+1)^2.

This entire thinking process involve all the higher order thinking skills defined by Bloom's Taxonomy: analysing, evaluating and creating. Students analyse change in number of blocks in different cases, create their hypothesis of possible pattern, and evaluate their hypothesis by testing their created pattern in each case.

This is an excellent example that has low entry - every student can try, but also have high ceiling - it requires all different levels of higher order thinking skills as well as understanding of variable (abstract concept) and mathematical induction.