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Showing 1 to 15 of 18 results Save | Export
Nathan D. Lang-Raad – Solution Tree, 2025
Transform mathematics instruction with the comprehensive mathematical competencies (CMC) framework--a research-based model that integrates seven essential competencies: conceptual and procedural integration, problem solving, logical reasoning, communication, tool use, pattern recognition, and student engagement. Through practical classroom…
Descriptors: Mathematics Instruction, Competence, Mathematics Skills, Elementary Secondary Education
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Wares, Arsalan; Custer, David – Mathematics Teacher: Learning and Teaching PK-12, 2023
Generalizing, conjecturing, representing, justifying, and refuting are integral parts of algebraic thinking and mathematical thinking in general (Lannin et al., 2011). The activity described in this article makes a case for generalizing as an overall mindset for any introductory algebra or geometry class by illustrating how generalization problems…
Descriptors: Mathematical Logic, Geometry, Algebra, Spatial Ability
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Symons, Duncan; Holton, Derek – Australian Primary Mathematics Classroom, 2020
Duncan Symons and Derek Holton discuss the different types of mathematical reasoning and what each of these might look like in the classroom. By suggesting language that can be used to describe the different methods of reasoning, they hope to provide teachers with the tools they need to better recognise and assess student reasoning.
Descriptors: Mathematical Logic, Logical Thinking, Mathematics Instruction, Elementary School Mathematics
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Mulligan, Joanne; Woolcott, Geoff; Mitchelmore, Michael; Busatto, Susan; Lai, Jennifer; Davis, Brent – Mathematics Education Research Journal, 2020
As part of the "Connecting Mathematics Learning through Spatial Reasoning" project, a Spatial Reasoning Mathematics Program (SRMP) intervention was implemented with one cohort of 30 students in grades 3 through 4. The SRMP embedded transformation skills in learning sequences comprising repeating and growing patterns, 2D and 3D…
Descriptors: Program Evaluation, Spatial Ability, Mathematics Instruction, Mathematical Logic
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McGarvey, Lynn M. – Teaching Children Mathematics, 2013
This article describes how in early mathematics learning, young children are often asked to recognize and describe visual patterns in their environment--perhaps on their clothing, a toy, or the carpet; around a picture frame; or in the playground equipment. Exploring patterns in the early years is seen as an important introduction to algebraic…
Descriptors: Mathematics Instruction, Pattern Recognition, Mathematical Concepts, Preschool Children
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Huang, Rongjin; Prince, Kyle M.; Schmidt, Teresa – Mathematics Teacher, 2014
The importance of developing reasoning and justification has been highlighted in "Principles and Standards for School Mathematics" (NCTM 2000). The Common Core State Standards for Mathematics (CCSSI 2010) further reiterates the importance of reasoning and proof in several standards for mathematical practice. Students of all grades are…
Descriptors: Algebra, Mathematics Education, Mathematics Instruction, Mathematical Applications
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McGarvey, Lynn M. – Mathematical Thinking and Learning: An International Journal, 2012
Mathematics curricula in the early years emphasize exploring patterns as an important stepping stone to algebraic thinking. Key expectations for young children are for them to recognize and describe visual patterns in the environment. When children are asked to identify patterns, what criteria do they apply to make a decision and on what do they…
Descriptors: Criteria, Algebra, Young Children, Mathematics Instruction
Miller, Jodie – Mathematics Education Research Group of Australasia, 2014
This paper explores how young Indigenous students' (Year 2 and 3) generalise growing patterns. Piagetian clinical interviews were conducted to determine how students articulated growing pattern generalisations. Two case studies are presented displaying how students used gesture to support and articulate their generalisations of growing patterns.…
Descriptors: Foreign Countries, Generalization, Nonverbal Communication, Grade 2
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Beigie, Darin – Mathematics Teaching in the Middle School, 2011
Initial exposure to algebraic thinking involves the critical leap from working with numbers to thinking with variables. The transition to thinking mathematically using variables has many layers, and for all students an abstraction that is clear in one setting may be opaque in another. Geometric counting and the resulting algebraic patterns provide…
Descriptors: Pattern Recognition, Geometric Concepts, Algebra, Mathematics Instruction
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Bell, Carol J. – Mathematics Teaching in the Middle School, 2011
Most future teachers are familiar with number patterns that represent an arithmetic sequence, and most are able to determine the general representation of the "n"th number in the pattern. However, when they are given a visual representation instead of the numbers in the pattern, it is not always easy for them to make the connection between the…
Descriptors: Preservice Teachers, Methods Courses, Teacher Education Curriculum, Geometric Concepts
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Stump, Sheryl L. – Teaching Children Mathematics, 2011
What is the role of patterns in developing algebraic reasoning? This important question deserves thoughtful attention. In response, this article examines some differing views of algebraic reasoning, discusses a controversy regarding patterns, and describes how three types of patterns--in contextual problems, in growing geometric figures, and in…
Descriptors: Algebra, Mathematical Logic, Mathematics Instruction, Geometric Concepts
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Whitin, Phyllis; Whitin, David J. – Young Children, 2011
The habit of looking for patterns, the skills to find them, and the expectation that patterns have explanations is an essential mathematical habit of mind for young children (Goldenberg, Shteingold, & Feurzeig 2003, 23). Work with patterns leads to the ability to form generalizations, the bedrock of algebraic thinking, and teachers must nurture…
Descriptors: Investigations, Young Children, Grade 3, Algebra
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Mulligan, Joanne; Mitchelmore, Mike; Kemp, Coral; Marston, Jennie; Highfield, Kate – Australian Primary Mathematics Classroom, 2008
Virtually all mathematics is based on pattern and structure. A mathematical "pattern" is any predictable regularity, usually involving numbers or space. In every pattern, the various elements are organised in some regular fashion. The way a pattern is organised is called its "structure," which may be numerical or spatial. In…
Descriptors: Intervention, Kindergarten, Mathematics Instruction, Mathematical Logic
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Booth, Lesley R. – Australian Mathematics Teacher, 1989
Discusses the importance of identifying and describing the pattern by students in algebra class. Provides some examples showing the usefulness of the method seeing the pattern from mathematical materials. (YP)
Descriptors: Algebra, Mathematical Concepts, Mathematical Formulas, Mathematical Logic
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Slesnick, Twila – Arithmetic Teacher, 1984
The problem-solving skills of logical thinking, critical thinking, visualization, and communication skills are linked with some activities for students. Sample activities with logic, strategies and patterns, breaking fixed notions, open-minded problems, spatial visualization, and communication are described. (MNS)
Descriptors: Elementary School Mathematics, Elementary Secondary Education, Learning Activities, Mathematical Enrichment
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