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Teaching Practices for Differentiating Mathematics Instruction for Middle School Students

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Title: Teaching Practices for Differentiating Mathematics Instruction for Middle School Students
Language: English
Authors: Hackenberg, Amy J., Creager, Mark, Eker, Ayfer
Source: Mathematical Thinking and Learning: An International Journal. 2021 23(2):95-124.
Availability: Routledge. Available from: Taylor & Francis, Ltd. 530 Walnut Street Suite 850, Philadelphia, PA 19106. Tel: 800-354-1420; Tel: 215-625-8900; Fax: 215-207-0050; Web site: http://www.tandf.co.uk/journals
Peer Reviewed: Y
Page Count: 30
Publication Date: 2021
Sponsoring Agency: National Science Foundation (NSF), Division of Research on Learning in Formal and Informal Settings (DRL)
Contract Number: DRL1252575
Document Type: Journal Articles
Reports - Research
Tests/Questionnaires
Education Level: Junior High Schools
Middle Schools
Secondary Education
Descriptors: Mathematics Instruction, Teaching Methods, Individualized Instruction, Thinking Skills, Middle School Students, Decision Making, Small Group Instruction, Multiplication, Mathematical Concepts, Concept Formation, Algebra, Fractions, Worksheets
DOI: 10.1080/10986065.2020.1731656
ISSN: 1098-6065
Abstract: Three iterative, 18-episode design experiments were conducted after school with groups of 6-9 middle school students to understand how to differentiate mathematics instruction. Prior research on differentiating instruction (DI) and hypothetical learning trajectories guided the instruction. As the experiments proceeded, this definition of DI emerged: proactively tailoring instruction to students' mathematical thinking while developing a cohesive classroom community. Analysis of 10 episodes across experiments yielded five teaching practices that facilitated DI: using research-based knowledge of students' mathematical thinking, providing purposeful choices and different pathways, inquiring responsively during group work, attending to small group functioning, and conducting whole class discussions across different thinkers. The latter three practices, at times, impeded DI. This study is a case of using second-order models of students' mathematical thinking to differentiate instruction, and it reveals that inquiring into research-based knowledge and inquiring responsively into students' thinking are at the heart of differentiating mathematics instruction.
Abstractor: As Provided
Entry Date: 2021
Accession Number: EJ1292407
Database: ERIC
FullText Text:
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  Data: Teaching Practices for Differentiating Mathematics Instruction for Middle School Students
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  Data: <searchLink fieldCode="AR" term="%22Hackenberg%2C+Amy+J%2E%22">Hackenberg, Amy J.</searchLink><br /><searchLink fieldCode="AR" term="%22Creager%2C+Mark%22">Creager, Mark</searchLink><br /><searchLink fieldCode="AR" term="%22Eker%2C+Ayfer%22">Eker, Ayfer</searchLink>
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  Data: <searchLink fieldCode="SO" term="%22Mathematical+Thinking+and+Learning%3A+An+International+Journal%22"><i>Mathematical Thinking and Learning: An International Journal</i></searchLink>. 2021 23(2):95-124.
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  Data: Routledge. Available from: Taylor & Francis, Ltd. 530 Walnut Street Suite 850, Philadelphia, PA 19106. Tel: 800-354-1420; Tel: 215-625-8900; Fax: 215-207-0050; Web site: http://www.tandf.co.uk/journals
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  Data: Y
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  Data: 30
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  Label: Publication Date
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  Data: 2021
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  Data: National Science Foundation (NSF), Division of Research on Learning in Formal and Informal Settings (DRL)
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  Data: <searchLink fieldCode="EL" term="%22Junior+High+Schools%22">Junior High Schools</searchLink><br /><searchLink fieldCode="EL" term="%22Middle+Schools%22">Middle Schools</searchLink><br /><searchLink fieldCode="EL" term="%22Secondary+Education%22">Secondary Education</searchLink>
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  Data: <searchLink fieldCode="DE" term="%22Mathematics+Instruction%22">Mathematics Instruction</searchLink><br /><searchLink fieldCode="DE" term="%22Teaching+Methods%22">Teaching Methods</searchLink><br /><searchLink fieldCode="DE" term="%22Individualized+Instruction%22">Individualized Instruction</searchLink><br /><searchLink fieldCode="DE" term="%22Thinking+Skills%22">Thinking Skills</searchLink><br /><searchLink fieldCode="DE" term="%22Middle+School+Students%22">Middle School Students</searchLink><br /><searchLink fieldCode="DE" term="%22Decision+Making%22">Decision Making</searchLink><br /><searchLink fieldCode="DE" term="%22Small+Group+Instruction%22">Small Group Instruction</searchLink><br /><searchLink fieldCode="DE" term="%22Multiplication%22">Multiplication</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+Concepts%22">Mathematical Concepts</searchLink><br /><searchLink fieldCode="DE" term="%22Concept+Formation%22">Concept Formation</searchLink><br /><searchLink fieldCode="DE" term="%22Algebra%22">Algebra</searchLink><br /><searchLink fieldCode="DE" term="%22Fractions%22">Fractions</searchLink><br /><searchLink fieldCode="DE" term="%22Worksheets%22">Worksheets</searchLink>
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  Data: 10.1080/10986065.2020.1731656
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  Data: 1098-6065
– Name: Abstract
  Label: Abstract
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  Data: Three iterative, 18-episode design experiments were conducted after school with groups of 6-9 middle school students to understand how to differentiate mathematics instruction. Prior research on differentiating instruction (DI) and hypothetical learning trajectories guided the instruction. As the experiments proceeded, this definition of DI emerged: proactively tailoring instruction to students' mathematical thinking while developing a cohesive classroom community. Analysis of 10 episodes across experiments yielded five teaching practices that facilitated DI: using research-based knowledge of students' mathematical thinking, providing purposeful choices and different pathways, inquiring responsively during group work, attending to small group functioning, and conducting whole class discussions across different thinkers. The latter three practices, at times, impeded DI. This study is a case of using second-order models of students' mathematical thinking to differentiate instruction, and it reveals that inquiring into research-based knowledge and inquiring responsively into students' thinking are at the heart of differentiating mathematics instruction.
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  Data: EJ1292407
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