As part of an integrative learning experience at the end of a sophomore Calculus II course at the United States Military Academy, this project served as a multidisciplinary problem-solving exercise that explored the connections among mathematics, biology, and other fields of study. During a seven-lesson block of instruction, this module was…

For more than one hundred years teachers have paddled beside the great ocean of mathematical adventure. Between them they have taught millions of young people. A few have dived in and kept swimming, some have lingered on the shore playing in pools, but most have dipped their toes in and run like heck in the other direction never to return. There…

Can middle-grades students determine which of two rectangular prisms has a larger volume? Can they do so without using a formula? Geometry, and particularly the concept of volume, is important in many subjects, such as physics and chemistry. Students greatly enhance their mathematics knowledge when they make generalizations and construct arguments…

For many students, geometry is the first course in which mathematical proof takes center stage. To help ease students into writing proofs, the author tries to create lessons and activities throughout the year that challenge students to prove their own conjectures by using tools learned in previous mathematics courses. Teachers cannot get all…

A multiple-probe-across-problem-sets (tasks) design was used to evaluate the effects of the Detect, Practice, and Repair (DPR) on multiplication-fact fluency development in seven third-grade students nominated by their teacher as needing remediation. DPR is a multicomponent intervention and begins with a group-administered, metronome-paced…

Problems are an important instrument for teachers to mediate physics content and for learners to adopt this content. This collection of problems is not only suited to traditional teaching and learning in lectures or student labs, but also to all kinds of new ways of teaching and learning, such as self-study, long-distance teaching,…

This article draws on data from a three-year Australian Research Council-funded study that examined the ways in which young children become numerate in the twenty-first century. We were interested in the authentic problem-solving contexts that we believe are required to create meaningful learning. This being so, our basic tenet was that such…

"Help! I'm stuck!" How many times have you heard a student make a similar plea? What do you consider when deciding how to respond? What reasoning is most productive? As part of a large research project, the authors explored these questions with 131 prospective and practicing teachers and found patterns in their reasoning. They began their project…

During the early childhood years, children learn to interact with one another in ways that are positive and successful. Researchers stress the importance of positive peer relationships in childhood and later life. The absence of positive social interactions in childhood is linked to negative consequences later in life, such as withdrawal,…

To improve student success in mathematics, the use of research-based interventions is necessary to help secondary students with learning disabilities (LD) access the algebra curriculum. The authors provide an overview of the following research-based approaches: explicit instruction, graduated instructional sequence, technology, and graphic…

Although mathematics is visual language of symbols and numbers it is also expressed and explained through written and spoken words. For students to excel in mathematics, they must recognize, comprehend and apply the requisite vocabulary. Thus, vocabulary instruction is as critical in content areas as it is in language arts. It is especially…

Although substantial attention has been directed toward building the psychometric evidence base for academic assessment methods (e.g., state mastery tests, curriculum-based measurement), similar examination of behavior assessment methods has been comparatively limited, particularly with regard to assessment purposes most desirable within…

Digital video is used to capture and assess a wide range of everyday classroom teaching practices. Generally, these applications are informal in nature and considered either risk-free or risk-neutral by teachers. Increasingly, however, captured video can be scrutinized and assessed by "others" to determine the presence and/or quality of specific…

When we use technology to teach mathematics, we hope to focus on the mathematics, restricting the computer software systems to providing support for our pedagogy. It is a matter of common experience, however, that students can become distracted or frustrated by the quirks of the particular software system being used. Here, experience using the…

A pretest-posttest cluster-randomized trial involving 31 middle schools and 335 students with disabilities tested the effects of combining explicit and anchored instruction on fraction computation and problem solving. Results of standardized and researcher-developed tests showed that students who were taught with the blended units outscored…