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The (Activity-)Effect of Manipulatives on Algebraic Generalizations: A Constructivist Teaching Experiment
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Karen Zwanch; Brooke Mullins – Educational Studies in Mathematics, 2025
To understand the ways that manipulatives might support changes in students' reasoning about algebraic generalizations, a constructivist teaching experiment was conducted with two sixth-grade students. The students interpreted numerical situations with units of one and could construct units of units in mental activity. Initially, the students'…
Descriptors: Mathematics Education, Mathematics Instruction, Teaching Methods, Algebra
Developing the Concept of Task Substitution and Transformation by Defining Own Equivalences
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Tirpáková, Anna; Gonda, Dalibor; Wiegerová, Adriana; Navrátilová, Hana – Educational Studies in Mathematics, 2023
The presented article is dedicated to a new way of teaching substitution in algebra. In order to effectively master the subject matter, it is necessary for students to perceive the equal sign equivalently, to learn to manipulate expressions as objects, and to perceive and use transformations based on defining their own equivalences. According to…
Descriptors: Mathematics Instruction, Teaching Methods, Instructional Innovation, Mathematical Concepts
Children's Use of Variables and Variable Notation to Represent Their Algebraic Ideas
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Brizuela, Bárbara M.; Blanton, Maria; Sawrey, Katharine; Newman-Owens, Ashley; Murphy Gardiner, Angela – Mathematical Thinking and Learning: An International Journal, 2015
In this article, we analyze a first grade classroom episode and individual interviews with students who participated in that classroom event to provide evidence of the variety of understandings about variable and variable notation held by first grade children approximately six years of age. Our findings illustrate that given the opportunity,…
Descriptors: Elementary School Mathematics, Elementary School Students, Grade 1, Algebra
Mathematical Critical Thinking Ability through Contextual Teaching and Learning Approach
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Kurniati; Kusumah, Yaya S.; Sabandar, Jozua; Herman, Tatang – Indonesian Mathematical Society Journal on Mathematics Education, 2015
This research aimed to examine the effect of the application of contextual teaching and learning (CTL) approach to the enhance of mathematical critical thinking ability (MCTA) of Primary School Teacher Students (PSTS). This research is an experimental study with the population of all students PSTS who took algebra subject matter of one university…
Descriptors: Foreign Countries, Mathematics Education, Critical Thinking, Mathematics Instruction
Flawed Mathematical Conceptualizations: Marlon's Dilemma
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Garrett, Lauretta – Journal of Developmental Education, 2013
Adult developmental mathematics students often work under great pressure to complete the mathematics sequences designed to help them achieve success (Bryk & Treisman, 2010). Results of a teaching experiment demonstrate how the ability to reason can be impeded by flaws in students' mental representations of mathematics. The earnestness of the…
Descriptors: Adult Education, Adult Learning, Developmental Programs, Mathematics Education
The Acquisition of Problem-Solving Skills in Mathematics: How Animations Can Aid Understanding of Structural Problem Features and Solution Procedures
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Scheiter, Katharina; Gerjets, Peter; Schuh, Julia – Instructional Science: An International Journal of the Learning Sciences, 2010
In this paper the augmentation of worked examples with animations for teaching problem-solving skills in mathematics is advocated as an effective instructional method. First, in a cognitive task analysis different knowledge prerequisites are identified for solving mathematical word problems. Second, it is argued that so called hybrid animations…
Descriptors: Foreign Countries, Prerequisites, Task Analysis, Problem Solving