Effects of Reform-Based Mathematics Instruction on Low Achievers in Five Third-Grade Classrooms

Baxter, Juliet A.; Woodward, John; Olson, Deborah

doi:10.1086/499686

Cited by 117 publications

(109 citation statements)

References 27 publications

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“…Or, would it be fair to group them with low-achieving students, in an effort to support the low-achievers and perhaps narrow gaps in achievement? On the other hand, if low-achievers are marginalized in group work (as in Baxter, Woodward, & Olson, 2001; L. H. King, 1993), perhaps they should be grouped together, to provide more opportunities to engage in mathematical discussion, rather than just copying the work of their high-achieving peers.…”

Section: Ideas and Identities 26mentioning

confidence: 99%

Ideas and Identities: Supporting Equity in Cooperative Mathematics Learning

Esmonde

2009

Review of Educational Research

173

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This review considers research related to mathematics education and cooperative learning, and discusses how teachers might assist students in cooperative groups to provide equitable opportunities to learn. I define equity in this context as the fair distribution of opportunities to learn, and argue that identity-related processes are just as central to mathematical development as content learning. I consider the link between classroom social ecologies, the interactions and positional identities that these social ecologies make available, and student learning. I close by considering unresolved questions in the field and proposing directions for future research.

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Section: Ideas and Identities 26mentioning

confidence: 99%

Ideas and Identities: Supporting Equity in Cooperative Mathematics Learning

Esmonde

2009

Review of Educational Research

173

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“…However, recommendations for this kind of instructional approach are somewhat at odds with the literature on problem solving instruction for low achieving students in the field of special education, which has found that low achieving students benefit far more from direct instruction and practice at problem solving than competent problem solvers (Baker, Gersten, & Lee, 2002;Jitendra & Xin, 1997;National Mathematics Advisory Panel, 2008;Tuovinen & Sweller, 1999;Xin & Jitendra, 1999). In fact, research conducted in reformoriented classrooms suggests that many low achieving students (particularly those with learning SCHEMA-BASED INSTRUCTION 6 disabilities) may assume passive roles and may encounter difficulties with the cognitive load of the discovery-oriented activities and curricular materials (Baxter, Woodward, & Olson, 2001;Baxter, Woodward, Voorhies, & Wong, 2002;Woodward, Baxter, & Robinson, 1999). Yet, despite the robust literature from special education in support of more direct instruction for low achieving students and those with learning disabilities, many in the mathematics education community have strong negative reactions to this instructional approach, in part because of perceived associations and historical links between direct instruction and the development of rote, inflexible knowledge.…”

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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

100

142

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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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“…However, not all students seemed to have benefitted from this. This was demonstrated in a study by Baxter, Woodward and Olson (2001) where they observed that low achievers tend to be passive in group discussion and during learning activities. The Integration of content instruction with constructivist-based strategies: An approach to engineering mathematics…”

Section: Learning Mathematics In a Constructivist Learning Environmentmentioning

confidence: 82%

Integration of content instruction with constructivist-based strategies: An approach to teach first-year engineering mathematics

Choy¹,

Yeo²

2016

IJRSE

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This paper proposed an approach to teaching first-year engineering mathematics, based on constructivist strategies, through careful integration of interactive lectures and small-group learning. Students' perceptions of learning mathematics through this approach were examined through both quantitative and qualitative approaches (N = 425). The results from the student feedback scores indicated strong consensus among students that the integrated approach was useful in helping students gained knowledge and skills in solving mathematical problems (M =3.85, SD = .62). Further insights gathered from the qualitative data revealed that students relished having more opportunities for practice under close guidance of the facilitator and resources. The discussion points to the appropriateness of using different teaching approaches to meet the diverse needs of learning of mathematics.

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Effects of Reform-Based Mathematics Instruction on Low Achievers in Five Third-Grade Classrooms

Cited by 117 publications

References 27 publications

Ideas and Identities: Supporting Equity in Cooperative Mathematics Learning

Ideas and Identities: Supporting Equity in Cooperative Mathematics Learning

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

Integration of content instruction with constructivist-based strategies: An approach to teach first-year engineering mathematics

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