Know the ROPES!

Debbie Cargill
Sep 14, 2009

Learning to solve problems in mathematics is about knowing what to look for.  Knowing and using a process leads students to try solving problems more readily.  When students are familiar with a variety of strategies for problem solving, they are more likely to choose appropriate strategies for a given situation or problem.  And, as they become more proficient, they recognize the value of approaching problem solving in a systematic manner.

Standardized tests include math items which require a higher level of thinking and the use of strategies to recognize and analyze data presented to solve the problems.  "Solving problems is not only a goal of learning mathematics but also a major means of doing so.  Students should have frequent opportunities to formulate, grapple with and solve complex problems that require a significant amount of effort and should then be encouraged to reflect on their thinking." (NCTM)

LEARNING-FOCUSED recommends a problem solving process called ROPES.  Each letter in ROPES represents a step in solving word problems:

R - Read the problem thoroughly and underline the important data.
O - Omit unnecessary data.
P - Plan, using the strategies.
E - Efficiently carry out the plan, checking as you solve.
S - Study results and check for accuracy.

Once learned, this structure will give students an effective way to approach problem solving, examine information, and organize data.  "Effective problem solvers constantly monitor and adjust what they are doing..." (NCTM)

Additionally, problem solvers need specific strategies to make sense of situations.  Early on, students learn to explore and build concepts in mathematics through the use of manipulatives, patterns, drawing pictures, etc.  As they mature and become more proficient at solving problems, they develop their own toolbox of strategies for mathematics.  "Different strategies are necessary as students experience a wider variety of problems... Strategies are learned over time, are applied in particular contexts, and become more refined, elaborate, and flexible as they are used in increasingly complex problem situations." (NCTM)

Both a problem solving process and problem solving strategies shou! ld be ta ught directly and explicitly so that students internalize and make them a part of their own repertoire or mathematics toolbox.  Initially, the teacher models the process and the "thinking about" appropriate strategies to choose.  The ultimate goal is that students will use the process and select a strategy for multiple and diverse situations.

View the LEARNING-FOCUSED Math Instruction Collection by clicking here.