This paper reports on the first part of a multiphase research project that seeks to identify and address the difficulties encountered by physics students when studying differential equations. Differential equations are used extensively by undergraduate physics students, particularly in the advanced modules of their degree. It is, therefore,…

Originally written 30 years ago, this paper is an analysis of the central challenge of schooling--that of engaging fully the powers of students' minds in classroom learning. This challenge maintains its relevance today. The work of engaging what John Dewey referred to as students' "inner attention" becomes the focus of an investigation…

Physics educators today face two major challenges: supporting the acquisition of a solid base of conceptual knowledge and reducing the persisting gender gap. In the present quasi-experimental study, we investigated the potential of physics instruction that is enriched with evidence-based cognitively activating methods, such as inventing with…

This descriptive case study approach with multiple cases and an interrupted time-series design used quantitative and qualitative data to answer two research questions: 1) What changes occur over time in the problem-solving strategies, text-reading accuracy, and phonological knowledge of struggling readers in response to targeted instruction in an…

Over the past few decades there has been increased interest in how students and teachers think and learn about negative numbers from a variety of perspectives. In particular, there has been debate about when integers should be taught and how to teach them to best support students' learning. This book brings together recent work from researchers to…

Research shows that U.S. students continue to lag behind in science and mathematics internationally (Fleischman, Hopstock, Pelczar, & Shelley, 2010; Provasnik et al., 2012). A recent study found there is a direct link between students' mastery of academic subjects and their ability to collaboratively problem solve, a critical 21st century…

Using memorized rules and algorithms without coherence and understanding is a perennial problem for teachers and students especially in the teaching and learning of fraction operations. I present data in which prospective middle school teachers explain a commonly used rule for fraction division--keep-change-flip. I argue that using both strip…

An action learning process was used at a large Midwestern business college ("LMBC") to promote greater use of active learning approaches in the classroom. At an all-college gathering, faculty received instruction and encouragement in the use of the case method in their respective classes. Faculty were subsequently surveyed about their…

Many teachers are using the Five Practices model to guide them in orchestrating whole-class mathematics discussions that focus on understanding: (1) anticipate an array of possible student-generated solution strategies to a mathematical task before implementing the lesson; (2) monitor students' work as they grapple with the task; (3) select a…

This article reports on a project that used a game-creation tool to introduce middle-school students ages 10 to 13 to problem-solving strategies similar to those in computer science through the lens of studio-based design arts. Drawing on historic paradigms in design pedagogy and contemporary educational approaches in the digital arts to teach…

In response to a desire to strengthen the economy, educational settings are emphasizing science, technology, engineering, and mathematics (STEM) curriculum and programs. Yet, because of the narrow approach to STEM, educational leaders continue to call for a more balanced approach to teaching and learning, which includes the arts, design, and…

When dividing one fraction by a second fraction, invert, that is, flip the second fraction, then multiply it by the first fraction. To multiply fractions, simply multiply across the denominators, and multiply across the numerators to get the resultant fraction. So by inverting the division of fractions it is turned into an easy multiplication of…

The desire to persuade students to avoid strictly memorizing formulas is a recurring theme throughout discussions of curriculum and problem solving. In combinatorics, a branch of discrete mathematics, problems can be easy to write--identify a few categories, add a few restrictions, specify an outcome--yet extremely challenging to solve. A lesson…

When a second-grade class struggled to make sense of the algorithms for multidigit addition and subtraction, attitude and morale were down, and student discourse was at an all-time low. When daily mathematics class started, the teacher was hearing an overall class moan. The instructed needed to turn it around, to find a way to help excite and…

You read in the paper this morning that people who take multivitamins have fewer heart attacks and are less likely to get cancer than people who don't. Does this information make you more likely to want to take multivitamins? To truly prepare students for life, schools need to teach them the critical thinking skills they need to answer questions…