Teacher Background

 Background for teaching with a Standards-based approach    Practical teaching approaches to problem solving

"Teachers' actions are what encourage students to think, question, solve problems, and discuss their ideas, strategies, and solutions." (NCTM, 2000, p.18)

Problem solving and creative thinking come naturally in some settings, but sometimes not so naturally in math class. We selected each resource below to help teachers broaden their understanding of problem solving and to facilitate using a problem-solving approach with students. The first set of resources illustrates actual teaching in the spirit of the NCTM Standards, where problem solving, reasoning and proof, communications, connections, and representation are the essence of mathematics learning. The second set features examples of teaching strategies that support problem solving.

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Background for teaching with a Standards-based approach

Private Universe Project in Mathematics: Workshop 4: "Thinking Like a Mathematician" http://www.hsdvl.org/video.php?record_serial=345

This 25-minute video offers a peek into the lives of two professional mathematicians as one engages in real-world problem solving, and the second turns the familiar Tower of Hanoi puzzle into a mathematics problem-solving investigation with a sixth grade class. This is a must-see! MSP full record

Petals Around the Rose Game

This simple number game played with dice can be used as a student problem solving activity. The resource below features ideas about how to set up a critical thinking activity that is accessible to all students, regardless of ability. Students can expand the activity by sharing the game with families and friends. Check out the online resource below to get the thinking and fun started!

Petals Around the Rose: Identifying Patterns in a Dice Game
http://illuminations.nctm.org/index_d.aspx?id=576

Learning math: geometry http://www.learner.org/channel/courses/learningmath/geometry/index.html

Feel like you need a little review in problem solving? This site offers a college-level online mathematics course designed to teach geometry content to teachers of elementary and middle school. The site uses geometric reasoning to highlight problem-solving methods as it engages teachers through video lessons, problem-solving activities, and online demonstrations. The course contains 10 sessions, each providing video lessons, activities, and homework problems. The final session furnishes case studies that teachers may use to examine problem-solving processes in their own classrooms from the perspective of a student. MSP full record

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Practical teaching approaches to problem solving

Searching for solutions http://faculty.goucher.edu/jcampf/searching_for_solutions.htm

Here is a problem-solving unit you may want to use to introduce students to strategies and real-life practice activities for applying problem-solving skills. Students can investigate real problems through a variety of web sites and group activities. The unit is divided into five sections: task description, process, evaluation, web resources, and conclusion. The task description outlines a wide range of the problem-solving strategies for student use. The process section offers details about each strategy, along with exercises and examples. The evaluation section includes five problem-solving activities. MSP full record

Math WebQuests http://www.wfu.edu/~mccoy/NCTM99/

If you haven't tried one yet, a webquest is an excellent technique to develop students' problem solving, reasoning, communication, connections, and representation process skills as they develop an understanding of data collection and analysis. This site describes the purpose of a webquest, offers sample webquests, and explains how teachers can create their own web-based projects that incorporate cooperative learning and real-world problem solving. MSP full record

Classic Problems http://mathforum.org/dr.math/faq/faq.classic.problems.html

Teachers can use these problems to show how math can answer questions about everyday life, including questions about birthday probability, the old favorite about the missing dollar, and trains leaving a station. The illustrated problem solutions are very helpful. MSP full record

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Reference

National Council of Teachers of Mathematics. (2000). Principles and Standards for School Mathematics. Reston, VA: Author.

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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.