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Preparing prospective secondary teachers to teach mathematical reasoning and proof: the case of the role of examples in proving
Mathematics teacher education programs in the United States are charged with preparing prospective secondary teachers (PSTs) to teach reasoning and...
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Mathematical Knowledge for Teaching Proof: Comparing Secondary Teachers, Pre-Service Secondary Teachers, and Undergraduate Majors
The calls for reasoning and proof to have a prominent place in secondary mathematics classrooms raise the question of knowledge that teachers need to...
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Undergraduate students’ attitudes towards mathematical proving in an introduction to proof course
In this study, we investigated undergraduate mathematics students’ ( N = 267) attitudes towards proving. The students were taking an...
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Using the proof assistant Lean in undergraduate mathematics classrooms
In this paper we develop a case for introducing a new teaching tool to undergraduate mathematics. Lean is an interactive theorem prover that...
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Transitioning to proof via writing scripts on the rules of a new discourse
Coming from the commognitive standpoint, we consider proof-based mathematics as a distinct discourse, the transition to which requires special rules...
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Generating mathematical knowledge in the classroom through proof, refutation, and abductive reasoning
Proving and refuting are fundamental aspects of mathematical practice that are intertwined in mathematical activity in which conjectures and proofs...
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The Flow of a Proof - Capturing the Elusive Whole
We propose the ‘flow of a proof’ as a construct that relates to the balance lecturers achieve in their presentation between the proof as a whole and...
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The role of epistemic emotions in undergraduate students’ proof construction
Proofs as epistemic tools are central to mathematical practice, as they establish and provide explanations for the validity of mathematical...
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Teaching practices that support revising definition drafts to adhere to mathematical norms
Definitions play an integral role in mathematics and mathematics classes. Yet, expectations for definitions and how they are intended to operate,...
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“This cannot be”—refutation feedback and its potential affordances for proof comprehension
Professors in proof-based mathematics courses often intend that the feedback they provide on students’ flawed proofs will promote proof...
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From Collaborative Construction, Through Whole-Class Presentation, to a Posteriori Reflection: Proof Progression in a Topology Classroom
Coming from a social perspective, we introduce a classroom organizational frame, where students’ proofs progress from collaborative construction in...
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Proof in the Context of Tertiary Mathematics: Undergraduate Inquiry-Based Learning in Abstract Algebra as a Precursor to Mathematical Proof
This chapter examines how mathematical proof and its precursors are utilized and developed through an inquiry-based learning (IBL) abstract algebra...
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Instructions and recipes in mathematical proofs
In mathematics education research, proofs are often conceptualized as sequences of mathematical assertions. We argue that this ignores proofs that...
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Proof and proving in school and university mathematics education research: a systematic review
This systematic review aims to provide a complementary to existing synopses of the state-of-the-art of mathematics education research on proof and proving...
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Lessons Learned About Incorporating High-Leverage Teaching Practices in the Undergraduate Proof Classroom to Promote Authentic and Equitable Participation
In recent years, professional organizations in the United States have suggested undergraduate mathematics shift away from pure lecture format....
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Investigating a teacher-perspective on pedagogical mathematical practices: possibilities for using mathematical practice to develop pedagogy in mathematical coursework
One of the challenges of university mathematics courses in secondary teacher preparation is incorporating pedagogical discussions. The focus in a...
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Strongly didactic contracts and mathematical work
This paper describes how the notion of the strongly didactic contract can serve to characterize the teaching adopted to implement a task in...
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Meta-mathematical aspects of definitions
The notion of definition is a central building block of mathematics. In addition to specific definitions, it is desirable that students learn about...
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Assessing Proof Reading Comprehension Using Summaries
In this paper, we explore the role of mathematical proof summaries as a tool for capturing students’ reading comprehension of a given proof. We...
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Comprehension of argumentation in mathematical text: what is the role of interest?
This article describes the research design and findings from a use-inspired study of online text-based mathematics resources. We sought to understand...
