PROBLEM SOLVING STRATEGIES IN MATHEMATICS
Jean Mistele Katherine Hilden Jennifer Jones Powell
This session shares the research conducted by Drs. Mistele, Hilden and Powell that joins together mathematics and reading. They seek to integrate these two disciplines to create Thinking Strategies that support children when they engage in mathematics problem solving activities. This collaboration began approximately two years ago and in this session we share our progress and session participants will code 3rd grade mathematics problems.
Our theoretical framework attempts to join reading comprehension strategies (e.g. Pressely & Afflerbach, 1995) and problem solving strategies (e.g. Polya, G. 1945). Scholars, such as Fluentes, (1988) and Hyde, (2006) tout the importance that reading comprehension has in the problem solving process. Our goal is to integrate these two types of strategies in order to develop integrated thinking strategies. The following sections provide a brief description of the literature that informed our research.
Reading Comprehension Literature
Some literacy researchers describe the strategies used by good readers to inform reading comprehension instruction to include a before, during, and after reading framework (e.g. Duke & Pearson, 2002). Others place emphasis on integrating reading comprehension across disciplines that creates a new type and advance form of literacy - discipline literacy (Shanahan & Shanahan, 2008). Unfortunately, research on disciplinary literacy for mathematics is lacking. For example, Goldman and colleagues (2016) provided disciplinary literacy frameworks for literature, science, and history but ignored mathematics.
Mathematics Problem Solving Literature
The research on mathematics problem solving is marked by the work of Shoenfeld (1985). However, his focus is on the meaning of mathematical thinking and how to help students do it such as using heuristics. Yet, reading comprehension appears to be assumed. Today there continues to be a reliance on Polya’s (1945) four step problem solving process: 1) understand the problem, 2) devise a plan, 3) work the plan, and 4) look back (e.g. Beckman, 2018; Shoenfeld, 1985). Polya’s method is process oriented, similar to reading comprehension instruction. However, we found a lack of consensus on problem solving strategies.
Our goal is to identify thinking strategies –integrating problem solving strategies and reading comprehension strategies- to support all children when they solve word problems, including struggling learners and English Language learners. We began our research by coding reading comprehension strategies when solving mathematics problems. Initially 12 reading comprehension strategies were reduced to eight through an iterative coding process using third grade and fifth grade standardized released tests. The inventory of comprehension included: problem and me, compare and contrast, cognitive flexibility, clarifying, graphics, fluency, activating prior knowledge, and think and search. We validated our coding of the strategies with two third grade teachers and two fifth grade teachers. Our interrater reliability was between .90 and .91. Next, we examined the relationship between the coded strategies with the mathematics content strands: number and number sense; computation and estimation; measurement; geometry; probability and statistics; and patterns, functions, and algebra. We found students need a repertoire of strategies to solve mathematics problems regardless of the content strand, which is consistent with reading comprehension research. That is, good readers use multiple strategies depending on the text, much like in solving a range of different types of mathematics problems.
It was during our tutoring of third graders that we shifted our thinking from teaching reading comprehension strategies to identifying the need for integrated thinking strategies. We focused on third grade students’ mathematics problem solving using two strategies: 1) problem and me and 2) think and search. These two strategies are differentiated by the structure of the problem. For example, the Think and Search strategy could be used when students are required to pull information from different parts of a graph but performing a calculation is not required to answer the question. On the other hand, Problem and Me strategies are used when the child integrates information from the problem with his or her prior knowledge to perform multiple operations. We met twice each week for eight weeks with 16 third graders for our experimental design study. The students solved algebra problems (patterns – repeating and growing) and data analysis problems (bar graphs and combinations). The control group received mathematics instruction both days. The intervention group received mathematics instruction on the first day each week with the control group followed by an integrated mathematics and reading comprehension instruction for the second day each week in a separate room. We found both groups significantly improved their mathematics test scores between the pre- and post-tests (F = 7.24, p = .021, η2 = .397). However, the intervention group did not show improvement over the control group as we had hypothesized.
ACTIVITY IN THE SESSION
Participants in this session were given a set of third grade Common Core mathematics problems to code. Working in small groups they coded the problems based on our third grade inventory. More than one code could be used for each problem. In addition, each group identified the location in the problem solving process: beginning, middle or end in which most students would struggle. The small groups shared their code choices and explained the reasons for their choices.
We will switch to the Common Core problems as we intentionally focus on reaching consensus on integrated thinking strategies used by strong problem solvers. We noticed both disciplines are process oriented and they identify the before, during, and after framework (Duke & Pearson, 2002; Warshauer, 2015). We will incorporate this as we reach consensus with our thinking strategies. For example, are some strategies more likely used at particular points in the problem solving process? Ultimately, our goal is to taking our thinking strategies from theory into classroom practice. We will work with two students who finished third grade and are beginning 4th grade moving forward.
Beckman, S. (2018). Mathematics for Elementary Teachers with Activities (5th Edition). New York, NY: Pearson.
Duke, N. K. & Pearson, N. P. (2002). Effective practices for developing reading comprehension. In S. J. Samuels and A.E. Ferstrup, (Eds.), What Research Has to Say about Reading Instruction. (3rd. Ed.). Newark, NJ: International Reading Association.
Goldman, S. R., Britt, M. A., Brown, W., Cribb, G., George, M., Greenleaf, C., Lee, C. D., & Shanahan, C. (2016). Disciplinary literacies and learning to read for understanding: A conceptual framework for disciplinary literacy, Educational Psychologist, 5(2), 219-246.
Fluentes, P. (1988). Reading comprehension in mathematics, The Clearing House, 72(2), 81-88.
Hyde, A. (2006). Comprehending Math: Adapting Reading Strategies to Teach Mathematics, K-6. Portsmouth, NH: Heinemann
Pressley, M., & Afflerbach, P. (1995). Verbal protocols of reading: The nature of constructively responsive reading. Hillsdale, NJ: Lawrence Erlbaum.
Schoenfeld, A. H. (1985). Mathematical Problem Solving. Orlando, FL: Academic Press, Inc.
Shanahan, T. & Shanahan, C. (2008). Teaching disciplinary literacy to adolescents: Rethinking content-area literacy, Harvard International Review, 78(1), 40-59.