Research has found that students, particularly those in middle school and high school, believe that their participation in mathematics classrooms includes listening to teachers explaining, working in textbooks, and solving exercise problems quickly (Franke, Kazemi, and Battey 2007). In this article, the authors describe a classroom vignette and…

Studies of mathematics teacher preparation frequently lament the divide between the more theoretically based university methods course and the practically grounded classroom field experience. In many instances, attempts to mediate this gap involve creating hybrid or third spaces, which seek to dissipate the differences in knowledge status as…

Improving student learning is the primary goal of every teacher of algebra. Teachers seek strategies to help all students learn important algebra content and develop mathematical practices. The new Institute of Education Sciences[IES] practice guide, "Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students"…

Erroneous examples--step-by-step problem solutions with one or more errors for students to find and fix--hold great potential to help students learn. In this study, which is a replication of a prior study (Adams et al. 2014), but with a much larger population (390 vs. 208), middle school students learned about decimals either by working with…

Background: The interactive nature of the teaching process is built on a social relationship between teachers and students. Conflicts in the relationship between students and teachers may occur for a several reasons. Effective and constructive management of conflict can decrease its negative effects on the learning environment, students, and…

In the Winter, 2015, issue of the "College Quarterly," Donovan McFarlane provided some guidelines for the use of case studies in college teaching based in part on his own experience and in part on the published literature. This was not the first time that case-based teaching was the focus of work in the "College Quarterly."…

Threshold concepts, student learning and curriculum are constructs within a learning and teaching discourse foregrounded by Meyer and Land. In this paper, we introduce a conceptual model that integrates these three constructs and identifies desired outcomes at the intersects: namely the processes of (1) ways of thinking and practising, (2)…

The article describes the development of a new approach to teach molecular biology to undergraduate biology students. The 34 students who participated in this research belonged to the first period of the Biological Sciences teaching course of the Instituto Federal Goiano at Urutaí Campus, Brazil. They were registered in Cell Biology in the first…

"Low threshold, high ceiling" tasks are accessible to diverse learners; invite a wide range of approaches; and hold the potential to further challenge, strengthen, and extend everyone's mathematical reasoning. In this article, the authors present a family of Brick Pyramid problems as examples of "low threshold, high ceiling"…

Many teachers of required secondary school mathematics classes are introducing statistics and probability topics traditionally relegated to college or AP Statistics courses. As a result, they need guidance in preparing lesson plans and orchestrating effective classroom discussions. In this article, the authors will describe the students' learning…

Intelligent tutoring and personalization are considered as the two most important factors in the research of learning systems and environments. An effective tool that can be used to improve problem-solving ability is an Intelligent Tutoring System which is capable of mimicking a human tutor's actions in implementing a one-to-one personalized and…

Reaction workup can be a complex problem for those facing novel synthesis of difficult compounds for the first time. Workup problem solving by systematic thinking should be inculcated as mid-graduate-level is reached. A structured approach is proposed, building decision tree flowcharts to analyze challenges, and an exemplar flowchart is presented…

Principal Component Analysis (PCA) is a highly useful topic within an introductory Linear Algebra course, especially since it can be used to incorporate a number of applied projects. This method represents an essential application and extension of the Spectral Theorem and is commonly used within a variety of fields, including statistics,…

Attention to the core practices of teaching necessitates core pedagogies in teacher preparation. This article outlines the diffusion of one such pedagogy from medical to teacher education. The concept of clinical simulations is outlined through the lens of "signature pedagogies" and their uncertain, engaging, formative qualities.…

Holidays and seasonal activities provide excitement and a change of pace for teachers and students alike. They also offer perfect backdrops for mathematical tasks that can be related to other topics and themes in the classroom. "Problem Solving in All Seasons, Prekindergarten-Grade 2" delivers thirty-two appealing, real-world situations,…