This study analysed the different types of arithmetic knowledge that young children utilise when solving a multiple-step addition task. The focus of the research was on the procedural and conceptual changes that occur as children develop their overall problem solving approach. Combining qualitative case study with a micro-genetic approach,…

This article gives an elementary proof of the famous identity [image omitted]. Using nothing more than freshman calculus, the present proof is far simpler than many existing ones. This result also leads directly to Euler's and Neville's identities, as well as the identity [image omitted].

Many adults who need an understanding of statistical concepts have limited mathematical skills. They need a teaching approach that includes as little mathematical context as possible. Iterative participatory qualitative research (action research) was used to develop a statistical literacy course for adult learners informed by teaching in…

The purpose of this study was to determine if a typical third-grade boy and fifth-grade girl and a boy with learning disabilities could benefit from the combined use of Direct Instruction (DI) flashcard and math racetrack procedures in an after-school program. The dependent variable was accuracy and fluency of saying basic multiplication facts. A…

The article contains general information about the use of specialized mathematics software in the preparation of math teachers. The authors indicate the reasons to study the mathematics software. In particular, they analyze the possibility of presenting basic mathematical courses using mathematical computer tools from both a teacher and a student,…

Recent calls have been made to enhance and extend the statistical experiences of K-12 students. However, to ensure that such goals are met, teachers also need to develop deep conceptual understanding and pedagogical content knowledge that are essential to statistical thinking and reasoning. In this regard, over the past two decades, leading…

Students' different learning performance on mathematical problem solving across contexts has attracted a number of researchers' interest. The study investigates the spatial orientation ability of primary school students in an outdoor situation, where six pairs of grade six students are asked to coordinate themselves physically in terms of given…

Research Findings: In each of 16 public school classrooms serving multiethnic low-income neighborhoods, 2 first graders were assigned to be taught patterning, 2 to be taught reading, 2 to be taught mathematics, and 2 to be taught social studies for 15-min sessions 3 days per week for 6 months. Assignment within each classroom was randomized. The…

By some estimates, students lose an average of 2.6 months of learning during summer break, roughly one quarter of the time spent in school. To combat this problem, the school under study implemented a summer math program that was thematically linked to the Boston Red Sox baseball team. Hundreds of students have participated in the program, but the…

The authors' purpose was to determine the effects of computer-based practice and conceptual interventions on computational fluency and word-problem solving of fourth- and fifth-grade students with mathematics difficulties. A randomized pretest-posttest control group design found that students assigned to the computer-based practice intervention…

For cell-like upper semicontinuous (usc) decompositions "G" of finite dimensional manifolds "M", the decomposition space "M/G" turns out to be an ANR provided "M/G" is finite dimensional ([Dav07], page 129). Furthermore, if "M/G" is finite dimensional and has the Disjoint Disks Property (DDP), then "M/G" is homeomorphic to "M" ([Dav07], page 181).…

Many students confuse the standard deviation and standard error of the mean and are unsure which, if either, to use in presenting data. In this article, we endeavour to address these questions and cover some related ambiguities about these quantities.

In this article, we consider the concept of rhotrices and present one-sided system of the form R[subscript n]x = b, where R[subscript n] is an n-dimensional rhotrix, x the unknown n-dimensional rhotrix vector and b the right-hand-side rhotrix vector.

A base for linear recursive sequences, such as the sequence of Fibonacci numbers, is defined within the framework of the sum of the digits of a number. Examples of bases of a number of such sequences are then outlined, and a Mobius strip is also used to illustrate the effects diagrammatically.

In this study, we show how to construct a function from the set N of natural numbers that explicitly counts the set Q[superscript +] of all positive rational numbers using a very intuitive approach. The function has the appeal of Cantor's function and it has the advantage that any high school student can understand the main idea at a glance…