The article describes the harmonic mean and explores situations for using it. Activities that involve hands-on practice for students are provided. Students learn to recognize which mean, harmonic or arithmetic, is appropriate.

This note discusses some set equations, using set matrices, i.e. matrices whose entries are sets.

Choosing challenging problems to facilitate student learning of new mathematics is a difficult task so by using open-ended problems with prospective mathematics teachers, the potential solution characteristics were studied. It is shown that considering the conceptual diversity of solutions helps students develop a better sense of different…

Marion Walter, an internationally acclaimed mathematics educator discusses about problem posing, focusing on both the merits of problem posing and techniques to encourage problem posing. She believes that playful attitude toward problem variables is an essential part of an inquiring mind and the more opportunities that learners have, to change a…

This study examined the Root Cause Analysis (RCA) teaching strategy on pre-service primary science teachers and instinct pre-service teachers to apply RCA teaching strategy to science curriculums. RCA Teaching Strategy is to coordinates 5 Why Method and Fishbone Diagram. The participants included 18 pre-service primary science teachers and the…

Problem solving can be thought of in two phases: the first phase is problem formulation and the second solution development. Problem formulation is the process of identifying a problem or opportunity in a situation. Problem Formulation Ability, or PFA, is the ability to perform this process. This research investigated a method to assess PFA and…

Individual teachers have the largest single school effect on student performance. Documented experience also indicates that individual teachers in high-poverty schools can effect rapid, dramatic student learning improvements within their own classrooms. Organization-wide change of a similar magnitude takes a broader effort with daring leadership…

Evidence collected over the last 30 years suggests that effective school leaders significantly influence student learning and other aspects of school performance. Documented experience also indicates that individual leaders in failing organizations in various sectors, including education, can effect rapid, dramatic improvements. School turnaround…

The purpose of this study was to assess algebra and geometric prerequisites skills as incorporated into the Applied Calculus Optimization Problem (ACOP) solution. The difficulties that students encounter in applying algebraic and geometric prerequisites at the early stages of the ACOP solution were identified. The study analyzes errors related to…

This study investigates the role of graphing calculators in multiple representations for knowledge transfer and the omission of oversimplification in complex function graphs. The main aim is to examine whether graphing calculators were used efficiently to see different cases and multiple perspectives among complex function graphs, or whether…

In a study of the types of problems encountered by students that led them to seek assistance, Robins et al. [2006] found that the most common problems were related to trivial mechanics. The students in this study worked by themselves on their programming exercises. This article discusses a replication of the Robins et al. study in which the…

This article reports the findings of two studies focused on the personal and professional values of school administrators. Two themes were employed as general organizers for the research: the influence of personal preference and trans-rational principles on the problem solving actions of school administrators and the value conflicts that…

In the last column we focused (as a primary goal of instruction) on the importance of teaching so that students learn to think their way into and through content. We stressed the need for well-designed daily structures and tactics for fostering deep learning, offering three strategies as examples. In this column, we provide four additional…

The international literature suggests students frequently resort to the use of formulae when solving stoichiometry problems without understanding the concepts. In prior work we identified Thai student alternative conceptions and ability to solve numerical problem for stoichiometry. The results indicate that many Thai students also hold alternative…

This study examined adult age differences on five tests of divergent thinking: associational fluency, expressional fluency, ideational fluency, word fluency, and consequences. Our hypothesis was that young adults ( M = 20.53, n = 60) would score higher than old adults (M = 72.10, n = 60) under standard timed test conditions, but old adults would…