Early algebra : repeating pattern and structural thinking at foundation phase

Background: Working structurally with patterns at foundation phase (FP) enhances habits of mind that advance early algebra at this early stage of mathematical learning. The South African curriculum proposes that learners work with and understand the logic of a pattern, but this important idea has la...

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Published in:South African journal of childhood education Vol. 8; no. 2; pp. 1 - 11
Main Author: Du Plessis, Jacques
Format: Journal Article
Language:English
Published: Johannesburg AOSIS 15.11.2018
AOSIS (Pty) Ltd
University of Johannesburg
Subjects:
Algebra
Classrooms
Cognitive ability
Collection development
Curricula
Cyclical processes
Education, Special
Elementary Education
Elementary School Mathematics
Elementary School Teachers
Elementary schools
Foreign Countries
Grade 2
Habits
Handbooks
Language & Linguistics
Learning
Library and information science
Management
Mathematical Logic
Mathematics
Mathematics education
Mathematics Instruction
Mathematics Teachers
Mathematics, Applied
Pedagogy
Preschool education
Public schools
Relational thinking
Researchers
Sequences
Skill development
Skills
Social Sciences, Interdisciplinary
Structural aspects
Teachers
Teaching
Teaching methods
Thinking Skills
Workshops
South Africa
ISSN:2223-7674, 2223-7682, 2223-7682
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Abstract Background: Working structurally with patterns at foundation phase (FP) enhances habits of mind that advance early algebra at this early stage of mathematical learning. The South African curriculum proposes that learners work with and understand the logic of a pattern, but this important idea has largely been neglected in classroom texts and in the supporting texts that guide teachers regarding curriculum implementation. At FP, most problems dealing with cyclical structure operate at a level of extending sequences by producing the next item that continues the order in which items are presented. Aim: The purpose of this article is to examine the curriculum documents and teaching resources used by FP teachers to deal with repeating patterns. Across the elementary mathematical landscape, there are opportunities to work explicitly with structure in its various conceptual embodiments. Setting: Six Grade 2 teachers in public schools participated in three workshops that foreground a structural approach to teaching pattern. Methods: A thorough document study was conducted to ascertain what the curriculum and supporting texts make available for the teaching and learning of repeating pattern. Results: A more structural approach fosters algebraic habits of mind that lead to more sophisticated forms of mathematical reasoning. A typology that summarises the relational features, intended skills development, complexity of sequences and the use of structural features on four levels is proposed to guide practice towards structural exploration. Conclusion: Focusing on the cyclical structural aspects embedded in repeating patterns inducts the young learner into relational thinking that advance early algebra.
AbstractList Background: Working structurally with patterns at foundation phase (FP) enhances habits of mind that advance early algebra at this early stage of mathematical learning. The South African curriculum proposes that learners work with and understand the logic of a pattern, but this important idea has largely been neglected in classroom texts and in the supporting texts that guide teachers regarding curriculum implementation. At FP, most problems dealing with cyclical structure operate at a level of extending sequences by producing the next item that continues the order in which items are presented. Aim: The purpose of this article is to examine the curriculum documents and teaching resources used by FP teachers to deal with repeating patterns. Across the elementary mathematical landscape, there are opportunities to work explicitly with structure in its various conceptual embodiments. Setting: Six Grade 2 teachers in public schools participated in three workshops that foreground a structural approach to teaching pattern. Methods: A thorough document study was conducted to ascertain what the curriculum and supporting texts make available for the teaching and learning of repeating pattern. Results: A more structural approach fosters algebraic habits of mind that lead to more sophisticated forms of mathematical reasoning. A typology that summarises the relational features, intended skills development, complexity of sequences and the use of structural features on four levels is proposed to guide practice towards structural exploration. Conclusion: Focusing on the cyclical structural aspects embedded in repeating patterns inducts the young learner into relational thinking that advance early algebra.
Abstract only
Background: Working structurally with patterns at foundation phase (FP) enhances habits of mind that advance early algebra at this early stage of mathematical learning. The South African curriculum proposes that learners work with and understand the logic of a pattern, but this important idea has largely been neglected in classroom texts and in the supporting texts that guide teachers regarding curriculum implementation. At FP, most problems dealing with cyclical structure operate at a level of extending sequences by producing the next item that continues the order in which items are presented. Aim: The purpose of this article is to examine the curriculum documents and teaching resources used by FP teachers to deal with repeating patterns. Across the elementary mathematical landscape, there are opportunities to work explicitly with structure in its various conceptual embodiments. Setting: Six Grade 2 teachers in public schools participated in three workshops that foreground a structural approach to teaching pattern. Methods: A thorough document study was conducted to ascertain what the curriculum and supporting texts make available for the teaching and learning of repeating pattern. Results: A more structural approach fosters algebraic habits of mind that lead to more sophisticated forms of mathematical reasoning. A typology that summarises the relational features, intended skills development, complexity of sequences and the use of structural features on four levels is proposed to guide practice towards structural exploration. Conclusion: Focusing on the cyclical structural aspects embedded in repeating patterns inducts the young learner into relational thinking that advance early algebra.
BACKGROUND: Working structurally with patterns at foundation phase (FP) enhances habits of mind that advance early algebra at this early stage of mathematical learning. The South African curriculum proposes that learners work with and understand the logic of a pattern, but this important idea has largely been neglected in classroom texts and in the supporting texts that guide teachers regarding curriculum implementation. At FP, most problems dealing with cyclical structure operate at a level of extending sequences by producing the next item that continues the order in which items are presented AIM: The purpose of this article is to examine the curriculum documents and teaching resources used by FP teachers to deal with repeating patterns. Across the elementary mathematical landscape, there are opportunities to work explicitly with structure in its various conceptual embodiments SETTING: Six Grade 2 teachers in public schools participated in three workshops that foreground a structural approach to teaching pattern METHODS: A thorough document study was conducted to ascertain what the curriculum and supporting texts make available for the teaching and learning of repeating pattern RESULTS: A more structural approach fosters algebraic habits of mind that lead to more sophisticated forms of mathematical reasoning. A typology that summarises the relational features, intended skills development, complexity of sequences and the use of structural features on four levels is proposed to guide practice towards structural exploration CONCLUSION: Focusing on the cyclical structural aspects embedded in repeating patterns inducts the young learner into relational thinking that advance early algebra
Audience Grade 2
Primary Education
Elementary Education
Early Childhood Education
Author Du Plessis, Jacques
AuthorAffiliation University of the Witwatersrand
AuthorAffiliation_xml – name: University of the Witwatersrand
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  givenname: Jacques
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  surname: Du Plessis
  fullname: Du Plessis, Jacques
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ContentType Journal Article
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  article-title: 'Combination and integration of qualitative and quantitative analysis'
  publication-title: Forum Qualitative Social Research
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Snippet Background: Working structurally with patterns at foundation phase (FP) enhances habits of mind that advance early algebra at this early stage of mathematical...
Abstract only
BACKGROUND: Working structurally with patterns at foundation phase (FP) enhances habits of mind that advance early algebra at this early stage of mathematical...
Background: Working structurally with patterns at foundation phase (FP) enhances habits of mind that advance early algebra at this early stage of mathematical...
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SubjectTerms Algebra
Classrooms
Cognitive ability
Collection development
Curricula
Cyclical processes
Education, Special
Elementary Education
Elementary School Mathematics
Elementary School Teachers
Elementary schools
Foreign Countries
Grade 2
Habits
Handbooks
Language & Linguistics
Learning
Library and information science
Management
Mathematical Logic
Mathematics
Mathematics education
Mathematics Instruction
Mathematics Teachers
Mathematics, Applied
Pedagogy
Preschool education
Public schools
Relational thinking
Researchers
Sequences
Skill development
Skills
Social Sciences, Interdisciplinary
Structural aspects
Teachers
Teaching
Teaching methods
Thinking Skills
Workshops
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Title Early algebra : repeating pattern and structural thinking at foundation phase
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