Whole-class inquiry (WCI) assessments range from challenging, paper-and-pencil puzzles to lab-based problems that require students to apply their own gathered data to a new scenario; the latter might also require students to perform a lab with new parameters, or to answer a question using data from a previous lab. In this article, the authors…

Solving indeterminate algebraic equations in integers is a classic topic in the mathematics curricula across grades. At the undergraduate level, the study of solutions of non-linear equations of this kind can be motivated by the use of technology. This article shows how the unity of geometric contextualization and spreadsheet-based amplification…

Poor math performance is a major concern leading the current educational reform agenda. Many educational math critics are claiming a math crisis. Researchers and school personnel are trying to resolve this crisis. Some are looking at curriculum-based evaluation (CBE) as a process for solving this problem. CBE and curriculum-based measurement (CBM)…

This article describes one seventh-grade teacher's classroom efforts to integrate traditional exercises from different content areas to form more robust questions that provide genuine problem-solving opportunities for students. These exercises are illustrated by connecting the Pythagorean theorem with a variety of prealgebra topics. Since the…

"Dora the Explorer" is a twenty-three-minute television program for preschoolers viewed by millions every day in many countries. These programs are also marketed as videotapes and DVDs. This seven-year-old Latina, bilingual cartoon character teaches many things by interacting with the young viewers. On every program Dora and friends have to go…

Using sticky notes and number lines, a hands-on activity is shared that anchors initial student thinking about absolute value. The initial point of reference should help students successfully evaluate numeric problems involving absolute value. They should also be able to solve absolute value equations and inequalities that are typically found in…

This article addresses the issues of coaching and assessing. A preservice middle school teacher's unique solution to the Pizza problem was not what the professor expected. The student's solution strategy, based on sequences and a reinvention of Pascal's triangle, is explained in detail. (Contains 8 figures.)

A central theme of the "National Science Education Standards" is teaching science as an inquiry process, allowing students to explore an authentic problem using the tools and skills of the discipline. Research indicates that more active participation by the student, which usually requires higher-order thinking skills, results in deeper learning.…

This guide will help policymakers understand and define the principles behind fusing core subject knowledge and higher-order thinking skills. Recommendations that reflect these principles will help policymakers support 21st century readiness for all students throughout a reauthorized ESEA and other federal legislation.

The author was asked to develop a list of actions that teachers could take to build students' mathematics abilities. Too many students fail to graduate and fail to pass state assessments as a result of weak mathematics skills. Even many students who do graduate leave high school lacking sufficient understanding of mathematics to pass college…

Most principals admit that despite the huge changes that have taken place in the world over the last 50 years, the education that students receive in today's high schools is remarkably similar to the education that was offered their parents. Educators recognize that changes should occur, but the reality of creating change can be overwhelming.…

Much like the shifting landscape in K-12 educational technology, this year's "Technology Counts" issue is changing to address the challenges of covering schools in the digital age. The 2010 report does not issue state report cards or state policy reports. Instead, the report takes a more district- and school-level look at educational…

We introduce some concepts for analyzing proofs, including various structures, and for analyzing undergraduate and beginning graduate mathematics students' proving abilities. We then discuss how the coordination of these two analyses might be used to improve students' ability to construct proofs. For this purpose, we need a richer framework for…

The paper discusses the boundary in the frequency-amplitude plane for boundedness of solutions to the forced spring Duffing type equation x[umlaut] + x + [epsilon]x[cubed] = F cos[omega]t. For fixed initial conditions and for representative fixed values of the parameter [epsilon], the results are reported of a systematic numerical investigation…

Students learn to use linear algebra covered in their first algebra course to design mobiles like those created by artist Alexander Calder. (Contains 17 figures and 2 tables.)