2.1 PROBLEM TYPES: ADDITION AND SUBTRACTION Mathematical Thinking for Instruction K-3

Joining Carpenter et al., 1999

Common Misconceptions Related to Problem Types MisconceptionAccurate Explanation A student’s strategy determines the problem type. The problem type’s label is unrelated to the solution strategy. However, problem types often influence the choice of strategy. Number sentences are problem types.Only a few problem types can be represented by number sentences. Problem types are contextual. Solving contextual problems is a different ‘type’ of mathematics than bare computation. Problem-solving is the essence of mathematics. Problem-based instruction was the foundation of math courses for centuries until the early 20 th century. Students should solve word problems any way they want. Students should be given every opportunity to solve realistic problems any way they choose. The instructor must guide students to increasingly accurate, generalizeable, and efficient methods.

Task 1 Write 3 problems JRU, JCU, JSU Use the same context and number sets for each problem The number sets and context must be appropriate for the grade-level you teach

Separating Carpenter et al., 1999

Task 2 Write 3 problems SRU, SCU, SSU Use the same context and number sets for each problem The number sets and context must be appropriate for the grade-level you teach

JRU Join Result Unknown JCU Join Change Unknown JSU Join Start Unknown SRU Separate Result Unknown SCU Separate Change Unknown SSU Separate Start Unknown Active Static

Part-Part-Whole ? 14 ? 26 Carpenter et al., 1999

Task 3 Use the context of soccer teams to create a Whole- Unknown and a Part-Unknown problem. Change the wording for each of the Part-Whole problems to turn them into any type of Join problem you choose.

JRU Join Result Unknown JCU Join Change Unknown JSU Join Start Unknown SRU Separate Result Unknown SCU Separate Change Unknown SSU Separate Start Unknown PPW:WU Part-Part-Whole: Whole Unknown PPW:PU Part-Part-Whole: Part Unknown Active Static

Compare ? Carpenter et al., 1999

Task 4 Create a CDU, CQU, and CRU problem using the word ‘more’ in the context. Re-write your Compare problems using the word ‘less’ or ‘fewer’.

JRU Join Result Unknown JCU Join Change Unknown JSU Join Start Unknown SRU Separate Result Unknown SCU Separate Change Unknown SSU Separate Start Unknown PPW:WU Part-Part-Whole: Whole Unknown PPW:PU Part-Part-Whole: Part Unknown CDU Compare Difference Unknown CQU Compare Quantity Unknown CRU Compare Referent Unknown Active Static