This week the Institute of Education Sciences released their publication of the “New Practice Guide: Improving Mathematical Problem Solving in Grades 4 Through 8”. In this they offer five recommendations of research-based practices for teaching problem solving:
1. Prepare problems (both routine and non-routine) and use them in whole-class instruction.
2. Assist students in monitoring and reflecting on the problem-solving process.
3. Teach student how to use visual representations.
4. Expose students to multiple problem-solving strategies.
5 Help students recognize and articulate mathematical concepts and notation.
The authors of the study actually rated the five practices as to the strength of evidence they had to support its recommendation. Two were rated with “strong evidence”. Can you guess which two they were? Reflection and representation. This was no surprise to me.
Reflection is a part of self-assessment, which, according to Dylan Wiliam, when used with peer-assessment, makes “distinct contributions to the development of students’ learning. Indeed, they (self- and peer-assessment) secure aims that cannot be achieved in any other way” ( “Working Inside the Black Box”, Phi Delta Kappan, Sept. 2004).
Representation is one of the Five Process Standards listed in Principles and Standards for School Mathematics (NCTM, 2000), referring to the processes through which students should acquire and use mathematical knowledge. Representation, along with problem-solving, reasoning and proof, communication, and connections, are seen as integral components of all mathematics learning. They direct the methods or processes of doing all mathematics.
Click here for a link to the IES site where you can download the full study.