Kathleen (Kate) Melhuish
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    • Laying the groundwork: The grounding metaphors that build quotient groups
    • Humanizing Proof-based Mathematics Instruction Through Experiences Reading Rich Proofs and Mathematician Stories
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    • Whose experiences are we capturing? A critical reflection on classroom observation measures
    • Adapting the Proof of Lagrange's Theorem into a Sequence of Group-Work Tasks
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    • Lessons Learned about Incorporating High-Leverage Teaching Practices in the Undergraduate Proof Classroom to Promote Authentic and Equitable Participation
    • Students' Techniques for Approaching Defining Properties of Functions
    • Using Extant Proofs in the Classroom: A Comprehension Activity Structure
    • Why ask why? An analysis of teachers’ why-questions in elementary and middle grade mathematics classrooms
    • Examining the concept of inverse: Theory-building via a standalone literature review
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    • Teaching routines and student-centered mathematics instruction: The essential role of conferring to understand student thinking and reasoning
    • The Role of the Partitioning and Coset Algorithm Quotient Group Partial Meanings in Comprehending the First Isomorphism Theorem and Its Proof
    • Can We Engage Students in Authentic Mathematical Activity While Embracing Critical Pedagogy? A Commentary on the Tensions between Disciplinary Activity and Critical Education
    • Collegiate mathematics teaching in proof-based courses: What we now know and what we have yet to learn
    • Comparing student proofs to explore a structural property in abstract algebra
    • Operationalizing authentic mathematical proof activity using disciplinary tools
    • The Efficacy of Research-Based 'Mathematics for All' Professional Development
    • Dual Measures of Mathematical Modeling for Engineering and Other STEM Undergraduates
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    • Two replication studies of the relationships between mathematical knowledge for teaching, mathematical quality of instruction, and student achievement
    • Abstract algebra students’ evoked concept images for functions and homomorphisms
    • Building mathematics self-efficacy of STEM undergraduates through mathematical modelling.
    • Division Is Pretty Much Just Multiplication
    • Elementary School Teachers' Noticing of Essential Mathematical Reasoning Forms: Justification and Generalization
    • Group Theory Students' Perceptions of Binary Operation
    • Inquiry and Gender Inequity in the Undergraduate Mathematics Classroom
    • Leveraging Variation of Historical Number Systems to Build Understanding of the Base-Ten Place-Value System
    • The Group Theory Concept Assessment: A Tool for Measuring Conceptual Understanding in Introductory Group Theory
    • The Student Discourse Observation Tool: Supporting Teachers in Noticing Justifying and Generalizing
    • When Students Prove a Theorem without Explicitly Using a Necessary Condition: Digging into a Subtle Problem from Practice
    • Reframing Replication Studies as Studies of Generalizability: A Response to Critiques of the Nature and Necessity of Replication
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    • Multiplication by 10 base-5: Making Sense of Place Value Structure Through an Alternate Base
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    • NSF: STructuring Equitable Pariticipation in Undergraduate Proof (STEP UP)
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NSF: Orchestrating Discussions Around Proof (ODAP)

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The ODAP project focused on promoting students’ authentic discussions and engagement in proof activity within abstract algebra courses.

Abstract Algebra Proof Design-Based Research
Kathleen (Kate) Melhuish
Authors
Kathleen (Kate) Melhuish
Mathematics Education Professor
← NSF: Generating a Research-Informed Transition to a Mathematical Proof Curriculum Jan 1, 0001
NSF: STructuring Equitable Pariticipation in Undergraduate Proof (STEP UP) Jan 1, 0001 →

© 2025 Kathleen Melhuish. This work is licensed under CC BY NC ND 4.0

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