Solving Equations: Exploring Instructional Exchanges as Lenses to Understand Teaching and Its Resistance to Reform

2019 ◽  
Vol 50 (1) ◽  
pp. 51-83 ◽  
Author(s):  
Orly Buchbinder ◽  
Daniel I. Chazan ◽  
Michelle Capozzoli
Keyword(s):  
Teacher Beliefs ◽  
Mathematics Teaching ◽  
Explanatory Variable ◽  
Linear Equations ◽  
Classroom Interaction ◽  
Media Representations ◽  
Theoretical Construct ◽  
Mathematics Classrooms ◽  
Rich Media ◽  
Solving Equations

Many research studies have sought to explain why NCTM's vision for mathematics classrooms has not had greater impact on everyday instruction, with teacher beliefs often identified as an explanatory variable. Using instructional exchanges as a theoretical construct, this study explores the influence of teachers' institutional positions on the solving of equations in algebra classrooms. The experimental design uses surveys with embedded rich-media representations of classroom interaction to surface how teachers appraise correct solutions to linear equations where some solutions follow suggested textbook procedures for solving linear equations and others do not. This paper illustrates the feasibility of studying teaching with rich-media surveys and suggests new ways to support changes in everyday mathematics teaching.

Take Time For Action: Reasoning about Linear Equations

2002 ◽  
Vol 8 (3) ◽  
pp. 146-148
Author(s):  
A.Susan Gay ◽  
Charlotte J. Keith
Keyword(s):  
Linear Equations ◽  
Semantic Feature ◽  
Feature Analysis ◽  
Mathematics Classrooms ◽  
Literacy Strategy ◽  
Semantic Feature Analysis

Have you heard of or used semantic feature analysis? It is a literacy strategy that can help students determine relationships among related vocabulary terms (Cooter and Flynt 1996). In mathematics classrooms, the use of semantic feature analysis is relatively new.

Critical Thinking and Mathematics Teaching and Learning

2019 ◽  
pp. 234-253
Author(s):  
Kelli Thomas ◽  
Douglas Huffman ◽  
Mari Caballero
Keyword(s):  
Critical Thinking ◽  
Mathematics Teaching ◽  
Teaching And Learning ◽  
Methods Course ◽  
Teaching Behaviors ◽  
Mathematics Methods ◽  
Mathematics Classrooms ◽  
Mathematics Methods Course ◽  
Mathematics Teaching And Learning ◽  
And Mathematics

The purpose of this chapter was to investigate pre-service teachers' noticing of children's critical thinking and views towards eliciting and using students' critical thinking in mathematics teaching. A mixed method study was used to provide a range of perspectives on pre-service teachers' views towards mathematics. The results indicated that the pre-service teachers initially held beliefs that mathematics teaching and learning consist of transferring information and students absorbing and memorizing information. The pre-service teachers based their instructional responses on experiences they had as students in elementary mathematics classrooms. The pre-service teachers described what they had observed about teaching mathematics as the ideal without regard for how the teaching behaviors they observed might influence children's critical thinking about mathematics. After completing a mathematics methods course, the pre-service teachers held beliefs more consistent with a reform-oriented classroom and demonstrated growth in their ability to notice children's mathematics thinking.

Conversation Analysis

2021 ◽  
pp. 9-32
Author(s):  
Jenni Ingram
Keyword(s):  
Conversation Analysis ◽  
Classroom Interaction ◽  
Mathematics Classrooms ◽  
Inductive Approach ◽  
Teachers And Students ◽  
Patterns Of Interaction

Conversation analysis offers an inductive approach to the analysis of classroom interaction. With its roots in ethnomethodology, conversation analysis is underpinned by some key principles that focus on how the learning of mathematics is made visible through teachers’ and students’ interactions. Using the tools developed by conversation analysts, the structures and patterns of interaction within mathematics classrooms can be described to reveal what it means to learn, and what it means to do, mathematics in school classrooms. This approach foregrounds what teachers and students themselves treat as learning and doing mathematics and reveals the multifaceted role of interaction in these processes.

Representing, Solving, and Using Algebraic Equations

1989 ◽  
Vol 82 (8) ◽  
pp. 608-612
Author(s):  
Joe Dan Austin ◽  
H. J. Vollrath
Keyword(s):  
Linear Equations ◽  
Algebraic Equations ◽  
Beginning Algebra ◽  
Physical Problems ◽  
Solving Equations ◽  
Physical Objects

Students of beginning algebra are quickly expected to solve linear equations. The solution procedures are generally abstract, involving the manipulation of numbers and algebraic symbols. Many students, even after completing a year of algebra, do not understand variables, equations, and solving equations (cf. Carpenter et al. [1982]). One way to help students learn to solve equations is to use physical objects, diagrams, and then symbols to represent equations. (Bruner [1964, 1967] calls such representations enactive (concrete), iconic (pictorial), and symbolic.) Although solving equations symbolically is essential, many students can benefit from working with physical problems that can also be symbolized mathematically. This article describes one way for students to learn to solve certain linear equations using pan balances, diagrams, and then symbols.

scholarly journals Solving equations in dense Sidon sets

2021 ◽  
pp. 1-10
Author(s):  
SEAN PRENDIVILLE
Keyword(s):  
Linear Equations ◽  
Alternative Proof ◽  
Translation Invariant ◽  
Sidon Sets ◽  
Solving Equations

Abstract We offer an alternative proof of a result of Conlon, Fox, Sudakov and Zhao [CFSZ20] on solving translation-invariant linear equations in dense Sidon sets. Our proof generalises to equations in more than five variables and yields effective bounds.

Supporting Mathematics Teachers to Build Deep Understandings of the Home Contexts of their Students

2019 ◽  
pp. 96-99
Author(s):  
Marta Civil ◽  
Roberta Hunter
Keyword(s):  
Mathematics Teaching ◽  
Mexican American ◽  
Immigrant Students ◽  
The United States ◽  
Theory And Practice ◽  
Mathematics Classrooms ◽  
Mexican American Students ◽  
American Students ◽  
Strength Based ◽  
Home Context

Teachers face many challenges in meeting the cultural diversity they encounter in current mathematics classrooms. To avoid marginalisation of specific groups of students we advocate for a strength-based approach in which teachers are supported to build deep understandings of the lived home context of their students. We discuss findings from our research projects with immigrant students (Pāsifika) in New Zealand and with Mexican American students in the United States. While our contexts are quite different, our approaches have much in common, in particular through their focus on teachers learning from and about their students’ communities to then build on this learning in their mathematics teaching. Bridging theory and practice, we share specific strategies that we have used to support teachers as learners of their students’ home contexts (e.g., home visits; parents’ classroom visits; school meetings led by parents).

Sign in / Sign up

Export Citation Format

Share Document