The mathematical egg hunt is a hands-on activity designed to help students understand mathematical relations in an Introduction to Proofs course. This activity gives students the opportunity to practice selecting which ordered pairs do and do not belong to a given relation in a moderately competitive egg hunt. It is designed to be low-stakes, yet…

There have been recent pushes for more active learning in mathematics classrooms, especially at the undergraduate level. To incorporate more active learning, there is a need for tasks that explicitly support this type of instruction, attention to student reasoning and whose ideas are publicly acknowledged, and awareness of differences in students'…

Justification skills should be fostered in teaching mathematics as they are highly related to effectiveness in problem solving. However, pre-service mathematics teachers do not always have the necessary skills in using mathematically convincing language and justifying their solutions. Thus, they should be introduced to a variety of instructional…

Mathematical reasoning ability is the ability to think logically to get a conclusion. This study aims to analyzing the effectiveness of Process Oriented Guided Inquiry Learning (POGIL) with Peer Feedback towards the students' achievement of mathematical reasoning abilities. The population in this study were 7th-grade students in one junior high…

Like many math educators, I have spent much of my career bound to traditional methods of instruction and assessment. In recent years, motivated by a growing understanding that such approaches may not result in equitable or inclusive classroom environments, my teaching philosophy has shifted radically. In this article, I describe how I transformed…

A problem sequence is presented developing the basic properties of the set of natural numbers (including associativity and commutativity of addition and multiplication, among others) from the Peano axioms, with the last portion using von Neumann's construction to provide a model satisfying these axioms. This sequence is appropriate for…

A growing body of mathematics education research points to the importance of fostering students' mathematical creativity in undergraduate mathematics courses. However, there are not many research-based instructional practices that aim to accomplish this task. Our research group has been working to address this issue and created a formative…

Inquiry-based instruction is a student-centered approach to teaching that focuses on active learning (Barron and Darling-Hammond 2008) in which students engage with "tasks that promote reasoning and problem solving" (NCTM 2014). Specifically, such tasks encourage a variety of solution strategies and stimulate use of the NCTM Process…

The purpose of this article is to discuss a Fulbright Evaluation Framework and to analyze findings resulting from implementation of two contextualized measures designed as LEARNING BY DOING in response to achievement expectations from the National Education Ministry in Colombia in three areas. The goal of the Fulbright funded project was to…

This article considers the place of proof, as a mathematical process, in the primary classroom. It describes the struggle the author, a primary school educator, went through with defining what proof is, what the educational goals of proof are, how these educational goals feature implicitly in the primary classroom, and what pedagogical…

It is widely accepted in the mathematics education community that pedagogies oriented toward inquiry are aligned with a constructivist theory of learning, and that these pedagogies effectively support students' learning of mathematics. In order to promote such an orientation, we first separate the idea of inquiry from its conception as a…

The necessity of using inquiry-based learning (IBL) was recently recommended by studies and reports made for the European Commission. Several European projects are devoted to the widespread use of IBL methods. The effects of using IBL are studied worldwide. In the framework of the Seventh Framework Program (FP7) project PRIMAS, a series of…

The author of this paper submits that humans have a natural inquisitiveness; hence, mathematicians (as well as other humans) must be active in learning. Thus, we must commit to conjecture and prove or disprove said conjecture. Ergo, the purpose of the paper is to submit the thesis that learning requires doing; only through inquiry is learning…