An Investigation of Teachers' Beliefs of Students' Algebra Development

By Mitchell J. Nathan, K. Koedinger. Cognition and Instruction, 2000

215 citations recorded by the source corpus.

Elementary, middle, and high school mathematics teachers (N = 105) ranked a set of mathematics problems based on expectations of their relative problem-solving difficulty. Teachers also rated their levels of agreement to a variety of reform-based statements on teaching and learning mathematics. Analyses suggest that teachers hold a symbol-precedence view of student mathematical development, wherein arithmetic reasoning strictly precedes algebraic reasoning, and symbolic problem-solving develops prior to verbal reasoning. High school teachers were most likely to hold the symbol-precedence view and made the poorest predictions of students' performances, whereas middle school teachers' predictions were most accurate. The discord between teachers' reform-based beliefs and their instructional decisions appears to be influenced by textbook organization, which institutionalizes the symbol-precedence view. Because of their extensive content training, high school teachers may be particularly susceptible to an expert blindspot, whereby they overestimate the accessibility of symbol-based representations and procedures for students' learning introductory algebra.

Subfields: Education, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/48c8ed5fc9ce273025af5a76d004751014af23cb

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Citations in the corpus

Teachers’ Knowledge and the Teaching of Algebra (2004, background): “In a similar study of practising teachers (N=105 elementary‚ middle‚ and high school teachers)‚ Nathan and Koedinger (2000a) investigated the match between teachers’ beliefs about the development of students’ algebraic reasoning and the actual performance of students on a set of beginning algebra ”
Expert Blind Spot Among Preservice Teachers (2003, methodology): “We also note that the middle and high school teachers studied by Nathan and Koedinger (2000a) accurately predicted student performance differences in arithmetic and algebraic problems, even though the teachers differed in their views about symbolic and verbal problems.”
Spring cleaning for the “messy” construct of teachers’ beliefs: What are they? Which have been examined? What can they tell us? (2012, unknown): “Several studies demonstrated that teachers believed that they were implementing inquiry- or reform-based practices but were in reality still using traditional methods of instruction (e.g., King, Shumow, & Lietz, 2001 ; Nathan & Koedinger, 2000 ).”
The Symbol Precedence View of Mathematical Development: A Corpus Analysis of the Rhetorical Structure of Textbooks (2002, methodology): “As reported, middle school teachers did not support the symbol precedence view as strongly, however, and they were more likely than high school teachers to rank algebra story problems as easier than symbolically presented algebra equations (Nathan & Koedinger, 2000a).”
When Am I Ever Going to Use This in the Real World? Cognitive Flexibility and Urban Adolescents’ Negotiation of the Value of Mathematics (2017, background): “Some teachers may also believe that providing TMAs is only appropriate for advanced students (Nathan & Koedinger, 2000), as they have demonstrated mastery over the pure mathematics and are more likely to understand the applied connections.”
"Playing the game" of story problems: Coordinating situation-based reasoning with algebraic representation (2012, background): “…suggested by the verbal precedence work, verbal skills develop prior to symbolic skills, and thus verbal contexts ay allow entry into problem solving through the use of informal, invented strategies (Carraher, Carraher, & Schliemann, 987; Koedinger & Nathan, 2004; Nathan & Koedinger, 2000b, 2000c).”
Middle School Mathematics Teachers' Knowledge of Students' Understanding of Core Algebraic Concepts: Equal Sign and Variable (2007, background): “ Nathan and Koedinger (2000) suggest that tasks such as the ones employed in these studies be used in professional development and teacher education settings to confront teachers’ misconceptions about students’ mathematical learning and”
The Real Story Behind Story Problems: Effects of Representations on Quantitative Reasoning (2004, methodology): “The results of DFA1 and DFA2 contradict the common belief in the ubiquitous difficulty of story problems as well as the predictions of teachers and education researchers (Nathan & Koedinger, 2000a) and cognitive researchers (Cummins et al., 1988).”