This article examines the benefits and teaching procedures resulting from a classroom activity in student problem posing. The benefits included an enhancement of student reasoning and reflection and a heightened level of engagement. "Principles and Standards for School Mathematics" indicates that one of the critical requirements for successful…

Musicians practice to build endurance, flexibility, and dexterity. They practice to maintain good performance, to sight-read better, to memorize, and simply, to enjoy music making. There are other motivations for practice, but one, more than others, is a catalyst for consequential change in musical development--practicing to solve performance…

The National Science Education Standards (NSES; National Research Council [NRC], 1996) include Science and Technology as one of the eight categories of content standards. The science and technology standards establish connections between the natural and designed worlds and provide students with opportunities to develop decision-making abilities.…

This study investigated the differential effects of two problem-solving instructional approaches--schema-based instruction (SBI) and general strategy instruction (GSI)--on the mathematical word problem-solving performance of 22 middle school students who had learning disabilities or were at risk for mathematics failure. Results indicated that the…

The students need not compute dependent values required in making line graphs but to teach the students the usage of graphing calculator to plot, calculating and graph linear equations, which are best suited to real world data. In this initial learning process, the teacher should give minimum support to the students in arriving at a solution as…

Students should be encouraged to focus on a big mathematical idea and to look for connections between problems and solution strategies. This unified view suggests that the students are developing computational fluency with fractions.

Teaching methods often promote fact gathering and memorization rather than the use of those facts to solve complex, realistic problems. Students easily memorize basic facts, steps and procedures, repeating them flawlessly from memory when asked. The problem, however, lies in teaching students how to use these facts and procedures creatively in…

We show that there is a link between a standard calculus problem of finding the best view of a painting and special tangent lines to the graphs of exponential functions. Surprisingly, the exponential function with the "best view" is not the one with the base "e." A similar link is established for families of functions obtained by composing…

From the start of the year, the author's goal is to teach his students to be metacognitive thinkers. This means that they will think about what they are doing during each step of the inquiry process. The author uses a variety of methods to enculturate students into using the thinking processes and developing the dispositions necessary for them to…

This article illustrates the fact that unless tempered by algebraic reasoning, a graphing calculator can lead one to erroneous conclusions. It also demonstrates that some problems can be solved by combining technology with algebra.

The theme of the 38th meeting of the International Group for the Psychology of Mathematics Education (PME 38) and the 36th meeting of the North American Chapter of the Psychology of Mathematics Education (PME-NA 36) was "Mathematics Education at the Edge." Academically, the theme provides opportunities to highlight and examine…

In efforts aimed at acquainting learners with "how to learn" skills rather than static content knowledge, more student centric instructional approaches are being increasingly adopted in informing curriculum design and delivery. Technology-rich problem solving environments offer great promise in scaffolding and facilitating…

In most teacher education courses, instructional strategies are merely listed and explained. Students rarely have the opportunity to see these strategies in use until they become student teachers. What better way to teach secondary instructional strategies to pre-service teachers than by modeling these strategies using teacher education content?…

Despite the challenges inherent in adopting problem-based learning (PBL) in the middle school classroom, successful PBL teachers are able to find suitable solutions. In this exploratory study we examined the perceptions and practices of five successful middle school PBL teachers regarding the specific difficulties encountered with PBL and the…

How can teachers learn what they need to know? Every community of educators, regardless of field or specialization, can benefit from being well informed about current research findings. A considerable amount of mathematics education research exists to inform teachers and administrators about teaching and learning mathematics. Research can show…