Multiple Representations for Problem Solving
The Common Core State Standards in mathematics and the Standards for Mathematical Practice encourage students’ fluency with multiple representations and mathematical modeling of routine and non-routine situations. The Standards emphasize the application of knowledge, including the use of representations such as tape diagrams, double number lines, charts and tables, pictures, and schematic diagrams and algebraic notation. The three videos in this collection discuss the importance of using multiple representations for mathematical modeling, as well as selecting the appropriate representation for a situation.
Algebraic Notation in Problem Solving stresses the importance of using notation for even simple problems and suggests strategies to help students understand the relationship between problem and notation. Next, Matching Visuals to Purpose in Problem Solving encourages representing the problem in various ways, highlighting the importance of purposeful selection of the representation. In the third video, Number Lines: A Key Representational Tool, UC Santa Barbara's Yukari Okamoto discusses misconceptions regarding fractions and how the choice of representation can confuse or clarify students’ understanding of a concept.
These interviews reflect research-based recommendations from the IES Practice Guide, Improving Problem Solving in Grades 4-8. For more details, download and read the Practice Guide.
Ken Koedinger provides examples that demonstrate the importance of bringing mathematical notation into the problem-solving process.