While teaching in New York City public schools, the author began planning collaboratively with a team of mathematics teachers. Collaborative planning enabled them to consider a range of issues that may not have emerged had they been planning independently. In this article, the author first describes their work through excerpts of conversations…

This teacher research study explores the changes in early childhood teacher candidates' perceptions of how children construct and represent knowledge following repeated exposure to "The Wonder of Learning: the Hundred Languages of Children" exhibit. When the renowned exhibit from Reggio Emilia was housed on the study participants' campus for 6…

Statistics is the art and science of gathering, analyzing, and making conclusions from data. However, many people do not fully understand how to interpret statistical results and conclusions. Placing students in a collaborative environment involving project-based learning may enable them to overcome misconceptions of probability and enhance the…

This article uses "fibbin" (Fibonacci poems) as an instructional strategy to teaching reading and writing across the curriculum. It describes fibbin from a historical and mathematical perspective and discusses it as an adaptation of the famous Fibonacci sequence to teaching content area material (e.g. science, math, and social studies). This…

Many students find it difficult to engage with mathematical concepts. As a relatively new class of learning tools, visualization tools may be able to promote higher levels of engagement with mathematical concepts. Often, development of new tools may outpace empirical evaluations of the effectiveness of these tools, especially in educational…

This What Works Clearinghouse (WWC) review focuses on mathematics interventions for high school students in grades 9-12 designed to impact student achievement, including curriculum-based interventions, instructional techniques, and products designed to deliver content and monitor student progress. Systematic reviews of evidence in this topic area…

This study examined whether college students are better able to apply knowledge of simple mathematical concepts when they are taught the concepts using abstract symbols or concrete examples. The research described in this article is consistent with What Works Clearinghouse (WWC) evidence standards. Strengths: The study is a well implemented…

Flexible knowledge, knowing multiple approaches for solving problems, is a hallmark of expertise in mathematics. Frequently, the author writes, students memorize only one method of solving a certain kind of problem, without understanding what they are doing, why a given strategy works, and whether there are alternative solution methods. Comparison…

A student's conceptual learning is facilitated by a harmonious method of learning. In teacher-directed strategy lessons, there is little guarantee that a method permits students to reach an "ideal" understanding. In the investigative classroom, the learning experience is rigidly structured, leaving students the unenviable responsibility to…

A complex technology-based problem in visualization and computation for students in calculus is presented. Strategies are shown for its solution and the opportunities for students to put together sequences of concepts and skills to build for success are highlighted. The problem itself involves placing an object under water in order to actually see…

We solve two problems that arise when constructing picture frames using only a table saw. First, to cut a cove running the length of a board (given the width of the cove and the angle the cove makes with the face of the board) we calculate the height of the blade and the angle the board should be turned as it is passed over the blade. Second, to…

When students learn mathematics, they tend to understand and remember the mathematical processes that they find practical and relevant. It is not surprising then that "Principles and Standards for School Mathematics" (NCTM 2000) encourages teachers to help students discover the relevance of mathematics in their daily lives. To help young people…

In this article, we consider some generalizations of Fibonacci numbers. We consider k-Fibonacci numbers (that follow the recurrence rule F[subscript k,n + 2] = kF[subscript k,n + 1] + F[subscript k,n]), the (k, l)-Fibonacci numbers (that follow the recurrence rule F[subscript k,n + 2] = kF[subscript k,n + 1] + lF[subscript k,n]), and the Fibonacci…

The mechanics of breathing has always been a difficult topic for some medical and graduate students. The subject is very quantitative and contains a number of concepts that some students have trouble with, including physical principles such as pressure, flow, volume, resistance, elasticity, and compliance. Apparently, present-day students find the…

New methods of teaching linear algebra in the undergraduate curriculum have attracted much interest lately. Most of this work is focused on evaluating and discussing the integration of special computer software into the Linear Algebra curriculum. In this article, I discuss my approach on introducing the concept of eigenvectors and eigenvalues,…