Spurious Correlations in Mathematical Thinking

Ben-Zeev, Talia; Star, Jon R.

doi:10.1207/s1532690xci1903_1

Cited by 31 publications

(23 citation statements)

References 28 publications

(34 reference statements)

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“…While answering the items in the physics test, students likely tried to "imagine" more or less the situation described in these items, rather than treating these items as meaningless "word problems" that, consequently, would elicit a stereotyped or standard mathematical model (see also Van Dooren et al 2007, 2008. Studies in mathematics education have shown that students often perceive mathematical word problem solving at school as a puzzle-like activity with little or no relation to the real world (see Verschaffel et al 2000), which can often be successfully accomplished by relying on superficial cues that help students to decide which operations to perform (Ben-Zeev and Star 2001;Hinsley et al 1977;Schoenfeld 1988). Additional evidence for students' less superficial approach in physics problem solving lies in the fact that students in this study were also influenced by other domain-specific misconceptions.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Students’ Overuse of Linearity: An Exploration in Physics

2010

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In mathematics education, a vast amount of research has shown that students of different ages have a strong tendency to apply linear or proportional models anywhere, even in situations where they are not applicable. For example, in geometry it is known that many students believe that if the sides of a figure are doubled, the area is doubled too. However, also history of science provides several cases of thinkers who inadequately postulated linear relations to describe situations. This article focuses on secondary school students' overreliance on linearity in physics. Now and then, science educators report students' tendency to assume and impose linear relations in physics, but-as far as we know-no substantial efforts were undertaken to study this phenomenon systematically. We conducted an empirical investigation aimed at identifying the competence of 8th-and 11th-gradersbefore and after being taught the relevant physical topics-to qualitatively grasp various situations in physics, as well as their tendency to quantify that qualitative insight linearly. The results provide an ambivalent picture of students' overuse of linearity in physics: Although linear reasoning is sometimes used as a default strategy, even after instruction that addresses the relevant physical contents, this study also indicates that context is taken into account more often than is suggested by research on mathematical problem solving.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Students’ Overuse of Linearity: An Exploration in Physics

2010

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“…The use of keyword methods, focusing on surface level features, does not emphasize the meaning and structure of the problem and thus may not help students to reason and make sense of story situations to be able to successfully solve novel problems (e.g., Ben-Zeev & Star, 2001;Van de Walle, 2007). Our approach moves away from keywords and superficial problem features and more explicitly focuses on helping students see the underlying mathematical structure of problems.…”

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confidence: 99%

Improving seventh grade students’ learning of ratio and proportion: The role of schema-based instruction

Jitendra

Star

Starosta

et al. 2009

Contemporary Educational Psychology

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The present study evaluated the effectiveness of an instructional intervention (schema-based instruction, SBI) that was designed to meet the diverse needs of middle school students by addressing the research literatures from both special education and mathematics education.Specifically, SBI emphasizes the role of the mathematical structure of problems and also provides students with a heuristic to aid and self-monitor problem solving. Further, SBI addresses well-articulated problem solving strategies and supports flexible use of the strategies based on the problem situation. One hundred forty eight seventh-grade students and their teachers participated in a 10-day intervention on learning to solve ratio and proportion word problems, with classrooms randomly assigned to SBI or a control condition. Results suggested that students in SBI treatment classes outperformed students in control classes on a problem solving measure, both at posttest and on a delayed posttest administered four months later.However, the two groups' performance was comparable on a state standardized mathematics achievement test. KEYWORDS: word problem solving, ratio and proportion, middle school students, schema- One of the major difficulties noted in this domain is that students tend to use additive rather than multiplicative solution methods (e.g., "to solve 6:14 = ?:35, they find the difference between 6 and 14 and subtract it from 35 to find 27:35 rather than seek multiplicative relationships," Fuson & Abrahamson, 2002, p. 213). Research in this domain has examined how children reason in various proportionality tasks and the extent to which developmental or SCHEMA-BASED INSTRUCTION 4 instructional factors influence proportional reasoning (e.g., Bright, Joyner, & Wallis, 2003;Lamon, 1993Lamon, , 2002Lo & Watanabe, 1997;Post et al., 1988). Proportional reasoning develops over time and "understanding at one level forms a foundation for higher levels of understanding" (Lamon, 2007, p. 637). Recommendations outlined in the research for developing children's proportional thought processes have included providing ratio and proportion tasks in a wide range of contexts (e.g., measurements, prices, rates) and ensuring that students have experienced conceptual methods before presenting symbolic methods such as cross-product algorithm for solving proportional problems (Lamon, 1999;Van de Walle, 2007).The topics of ratio and proportion are frequently encountered in elementary and middle schools in the form of word problems. Traditionally, word problems are used to teach "mathematical modeling and applied problem solving" (Van Dooren, De Bock, Hessels, Janssens, & Verschaffel, 2005, p. 58). That is, the word problem context provides a description of a problem-solving situation that requires responding to a question by executing "one or more operations (+, -, x, ÷) on the quantities in the problem" (Van Dooren et al., 2005, p. 58).However, word problem solving has proved to be a significant challenge for students, in part because it requires s...

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“…As a result of applying the key word method, students struggling in mathematics have persistent difficulties in mathematical problem solving despite plenty of practice. The keyword method does not emphasize the meaning and structure of the problem and thus may not help students to reason and make sense of problem situations, which is crucial in solving novel problems (Ben-Zeev & Star, 2001). …”

Section: Mathematical Problem Solving and Traditional Instructionmentioning

confidence: 99%