In this paper, we discuss our experience in collaborating with mathematicians to increase their use of active learning pedagogy in a proof-based linear algebra course. The mathematicians we worked with valued using active learning pedagogy to increase student engagement but were reluctant to use active learning pedagogy due to time constraints.…

The capacity for mathematical reasoning, pivotal in grasping core math concepts, directly shapes a student's success in their mathematical studies. This study aimed to detail and analyzed how the search, solve, create, and share (SSCS) instructional framework impacts mathematical reasoning skills within the context of linear equations. We adopted…

'Group work' is a vague description of an instructional activity, because many factors shape its character and effect on students. One important factor is group formation, that is, how groups are formed by the instructor. In this paper, we sought to better understand the variation of group work with respect to group formation by addressing: How do…

In this reflection of teaching, we describe a series of activities that introduce the Taylor series through dynamic visual representations with explicit connections to students' prior learning. Over the past several decades, educators have noted that curricular materials tend to present the Taylor series in a way that students often interpret as…

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…

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…

This study aimed to produce a set of PISA-like mathematics problems content of uncertainty and data using long jump context in Asian Games that were valid, practical and had potential effects on the ability of the students' mathematical literacy. This study used the design research method of development studies type in two stages, preliminary and…

Young children thrive in classrooms that allow them to explore and discover their environment and interests and also support them in this learning. Because children learn best when they are interested and excited, early-childhood educators should offer children play-based, integrated mathematical experiences (NRC 2009). In this article, the…

Students' experiences with statistics and data analysis in middle school are often limited to little more than making and interpreting graphs. Although students may develop fluency in statistical procedures and vocabulary, they frequently lack the skills necessary to apply statistical reasoning in situations other than clear-cut textbook examples.…

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…

This is an exploratory study about engaging students in mathematics learning both inside and outside of the classroom of an introductory proof course. The author utilized the framework of scholarship of teaching and learning as a guide to ensure the research process was carried out systematically. This study was conducted through one cycle of…

Acquaintance with various ways of inculcating concepts in any studied area of knowledge is one of teachers' duties, particularly mathematics teachers. Studies indicate errors and difficulties when inculcating concepts in mathematics and learning them. Many concepts have different meanings in different contexts. Hence, teachers should deal with the…

This article describes an exciting exploration-based activity in which students develop an alternative definition of factor that can help them solve problems like the one presented above. Students work in groups to collect data, analyze the data to make conjectures, and then spend a significant amount of time debating and justifying their…

This article describes how teachers address issues and tensions that students meet in learning division of fractions. First, students must make sense of division of fractions on their own by working individually and in small groups, using concrete or pictorial representations, inventing their own processes, and presenting and justifying their…