Challenging Student Thinking and Creativity

We can look at mathematics instruction as question and answer or as an opportunity to examine, think, and draw conclusions. Is it strictly one or the other? No—students need to develop not only skills with straight-forward problems, but also understanding with problems where the approach is not stated and the answer is not a forgone conclusion.

If you want to nurture students who are problem solvers, you must make them comfortable with the practice of explaining their solutions and methods. Converting a typical mathematics problem into a problem solving activity can be challenging work for teachers. But any problem—big or small—that the student does not know exactly how to approach can be an opportunity to foster problem-solving strategies. A teacher who encourages students to explain their methods and solutions can turn most lessons into meaningful problem-solving and learning experiences. The teacher's approach is essential to making mathematics challenging in ways that are deeper than those found in doing drill-type lessons with progressively harder numbers.

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Problems with a point http://www2.edc.org/mathproblems/default.asp

Here is a great place to start fusing math skill with understanding. This searchable problem database classifies problems by topic, time required, suggested technology, required mathematical background, and the habits of mind that students develop or use as they work. Problems can be sequenced to build on student knowledge and to create individualized learning sequences. The list of favorite problems selected by teachers is a great place to start learning about the resources at this site. MSP full record

Hot math! Hands-on tasks in the mathematics classroom http://projects.edte.utwente.nl/hotmath/index.html

These classroom activities link mathematics to real-world problems and situations. Each of the 13 activities takes less than 30 minutes and is designed to get students actively involved in mathematics. Teachers are encouraged to customize the activities for their students. MSP full record

Word problems for kids http://www.stfx.ca/special/mathproblems/welcome.html

Teachers can select grade-appropriate problems from this list to help students improve their problem-solving skills. Students are encouraged to carefully think about how they would solve a problem and to make sure that they understand all parts of the solution. Each problem contains a link to helpful hints and the solution. MSP full record

Pre-Algebra Problem of the Week http://mathforum.org/prealgpow/

This site is a good source for math problems keyed to holidays and seasons. The problems are designed to foster students learning algebraic reasoning, identifying and applying patterns, ratio and proportion, and geometric ideas such as similarity. The problems are non-routine and focus on communication with students putting their solutions into words. The detailed solution to the previous posted problem and information about resources offered by Math Forum are available for a fee. MSP full record.

More advanced problems are available from Algebra Problem of the Week at http://mathforum.org/algpow/.  MSP full record

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Copyright March 2005 — The Ohio State University. This material is based upon work supported by the National Science Foundation under Grant No. 0424671. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

This work is licensed under a Creative Commons License.