Academic journal article Middle Grades Research Journal

The Effects of a Mathematical Problem-Solving Intervention on the Errors Made by Middle School Students with and without Learning Disabilities

Academic journal article Middle Grades Research Journal

The Effects of a Mathematical Problem-Solving Intervention on the Errors Made by Middle School Students with and without Learning Disabilities

Article excerpt

Over the last decade, the landscape of the workforce has changed dramatically. Particularly in the fields of science, technology, engineering, and mathematics (STEM), job opportunities are increasing even in a time of economic downturn (National Math and Science Initiative, 2011). However, American students continue to struggle in foundational STEM fields. According to the Trends in International Mathematics and Science Study 2011, for Grade 8, only 7% and 10% of United States students attained the "advanced" benchmark in mathematics and science, respectively, and only 30% and 40%, respectively, attained the "high" benchmark; percentages for leading nations, meanwhile, ranged from 30-50% for the advanced benchmark and 70-80% for the high benchmark. As a result, foundational STEM concepts have been incorporated into middle and high school instruction in the United States. For a better understanding of how STEM concepts have been integrated into the mathematics standards, consider reading the article in this issue titled STEM Integration in Mathematics Standards (Capraro & Nite, this volume). According to Basham and Marino (2013), STEM education reflects interdependence among its fields (i.e., science, technology, engineering, and mathematics). It utilizes a teaching approach that emphasizes inquiry-based learning, which allows students to gain a deeper understanding of contextualized problems (Basham, Israel, & Maynard, 2010; Basham & Marino, 2013). While each of the four fields stands alone, mathematics is considered essential to the development of STEM education (National Science Board, 2010). Further, student achievement in high school mathematics courses frequently predicts success in college majors for the other three fields (Atanda, 1999). That is, key mathematical ideas or skills are critical to developing proficiency in science, technology, and engineering. Problem solving represents one such skill.

The National Council of Teachers of Mathematics (NCTM, 2000) defines problem solving as "engaging in a task for which the solution method is not known in advance" (p. 52). Though our study uses routine and close-ended word problems that may not immediately resonate with the NCTM definition provided above, it is important to note that problem solving is a subjective term that applies to a task but reflects the problem solver. In other words, mathematical word problems that may appear to be straightforward and procedural to a proficient problem solver may, for a struggling student, represent NCTM's conceptualization of problem solving (i.e., "a task for which the solution method is not known in advance"); as the population of interest in the present study was students with and without disabilities who were lowachieving in mathematics as well as their average-achieving peers, we assumed that the problems selected aligned with NCTM's definition. As the goal of the intervention was to support students with poor problem solving abilities gain the cognitive and metacognitive strategies needed to understand, analyze, and ultimately solve word problems, they are developing skills critical to inquiry-based learning and thus STEM education. Starting in kindergarten, students must demonstrate the ability to build new mathematical knowledge, solve problems in mathematics as well as other contexts, and apply and adapt various problem-solving strategies effectively (NCTM, 2000). The importance of problem solving has been underscored as a critical skill for success in both higher education and the workplace (Hudson & Miller, 2006; NCTM, 2000; Wilson, 1993). Despite the call for an increased focus on the teaching of mathematical problem solving and for reformations in curriculum, American students continue to perform poorly in relation to other developed countries on measures related to problem solving (Vigdor, 2013). There has been a noticeable decline in U.S. middle school mathematics achievement from that of the elementary level (Reys, Reys, Lapan, Holliday, & Wasman, 2003; Xin, 2007). …

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