Learning by Understanding: The Role of Multiple Representations in Learning Algebra

Brenner, Mary E.; Mayer, Richard E.; Moseley, Bryan; Brar, Theresa; Reed, Barbara Smith; Webb, David J.; Durán, Richard P.

doi:10.2307/1163353

Cited by 19 publications

(18 citation statements)

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“…In relation to their findings, we hypothesised that diagnostic accuracy would be associated with greater use of semantic qualifiers to characterise the chief complaint. The results of a case‐control study 23 showed that indeed diagnostic accuracy was associated with greater use of semantic qualifiers to mentally represent the chief complaint, a result that mirrored findings from mathematics education research 24 showing the key role of abstract problem representation in solving algebra problems.…”

Section: Key Pointsmentioning

confidence: 76%

Conceptual frameworks to illuminate and magnify

2009

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Context In a recent study of the quality of reporting experimental studies in medical education, barely half the articles examined contained an explicit statement of the conceptual framework used. Conceptual frameworks represent ways of thinking about a problem or a study, or ways of representing how complex things work. They can come from theories, models or best practices. Conceptual frameworks illuminate and magnify one’s work. Different frameworks will emphasise different variables and outcomes, and their inter‐relatedness. Educators and researchers constantly use conceptual frameworks to guide their work, even if they themselves are not consciously aware of the frameworks. Methods Three examples are provided on how conceptual frameworks can be used to cast development and research projects in medical education. The examples are accompanied by commentaries and a total of 13 key points about the nature and use of conceptual frameworks. Conclusions Ultimately, scholars are responsible for making explicit the assumptions and principles contained in the conceptual framework(s) they use in their development and research projects.

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Section: Key Pointsmentioning

confidence: 76%

Conceptual frameworks to illuminate and magnify

2009

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“…The Number test was a better fit with the activities of the in‐service, which emphasized understanding of mathematical ideas, rather than obtaining the correct answer to basic algorithms. Brenner et al (1997), in a study involving a full spectrum of student abilities, also found that a Standards‐based teaching approach had a positive effect on student performance on conceptual tasks (e.g., word problem representation) but not on algorithmic tasks (single variable linear equations).…”

Section: Discussionmentioning

confidence: 94%

“…But we had little confidence in the results because in both instances the model was not positive definite, indicating a problem with the covariance matrix. Rigdon (1997) suggested that not positive definite matrices can result from small samples. Treatment condition was not a statistically significant predictor in any of the other models.…”

Section: Resultsmentioning

confidence: 99%

The Effects of a Teacher In‐Service on Low‐Achieving Grade 7 and 8 Mathematics Students

Ross

Ford³

2008

School Sci & Mathematics

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Previous research (e.g., Woodward & Baxter, 1997) found that Standards‐based mathematics teaching provides marginal or no benefits for low achievers, in contrast with positive effects for middle and high ability students. A randomized quasi‐experiment in 52 Canadian schools found that low achieving grade 7 and 8 students who received support consisting of placement on a learning continuum, instruction focused on their specific learning needs, and concrete materials to represent mathematical constructs, benefited from teaching that emphasized construction over transmission of knowledge. Treatment students showed small but statistically significant improvements over controls in student achievement, and controversially, in mathematical beliefs, and attitudes. The latter finding raised issues of the appropriate balance between Type I and Type II error in educational research.

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“…Algebraic thinking is crucial for developing thorough mathematical habits of mind (NCTM, 1989(NCTM, , 2000. Algebra has been the stumbling-block for many high school students, who have difficulty in making the transition from arithmetic to algebra (Brenner et al, 1997) due to the lack of expertise in problem representation, which involves understanding word problems. Research in high school mathematics has been limited to problem-solving tasks prepared by researchers (Nesher, Hershkovitz, & Novotna, 2003); few studies have looked at students' performances on state-mandated standardized tests, such as Iowa Test of Basic Skills.…”

Section: Algebraic Problem Solvingmentioning

confidence: 99%

“…For example, to determine the function between two sets of numbers in a word problem, a learner must simultaneously use his or her understanding of the concept of representation, variable, and function. Brenner et al (1997) and Nesher et al (2003) have supported the interrelated nature of these concepts, pointing out that symbol manipulation and problem representation (which involves translating the text of the problem into algebraic representation) are important for successful algebraic story problem solving.…”

Section: Algebraic Problem Solvingmentioning

confidence: 99%

Investigating the changes in teachers' pedagogical practices through the use of the Mathematics Reasoning Heuristic (MRH) approach

Akkuş

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This study examines the pedagogical differences when three teachers change their practices from traditional teaching to student-centered practices. The student-centered approach adopted-the Mathematics Reasoning Heuristic (MRH) approach-was developed by the researcher. A professional development program was implemented over one semester where the MRH approach was initially modeled for teachers before the three teachers implementing the approach. The level of student-centered teaching in the MRH classes varied as a result of the feedback provided by the researcher, while the teachers' traditional-style teaching level stayed the same. The patterns of the change for all three teachers, with different scales, were similar; that is, their MRH teaching stayed at the level of their control teaching for a while and began to move up depending on the pedagogical area on which they put emphasis. Their questioning was the first move to change, yet it was not aligned with other areas at the beginning. However, variations existed in the differences between the teachers' control and MRH instructions.

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Learning by Understanding: The Role of Multiple Representations in Learning Algebra

Cited by 19 publications

References 0 publications

Conceptual frameworks to illuminate and magnify

Conceptual frameworks to illuminate and magnify

The Effects of a Teacher In‐Service on Low‐Achieving Grade 7 and 8 Mathematics Students

Investigating the changes in teachers' pedagogical practices through the use of the Mathematics Reasoning Heuristic (MRH) approach

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