Generating, collecting, and analyzing data is an essential practice in the science classroom (NRC 2012). Taking this data and using it to craft an explanation that demonstrates understanding of content is another essential practice. But both practices can be challenging, and students often require teacher support to succeed. Accordingly, the…

We present a synthesis of findings from constructivist teaching experiments regarding six schemes children construct for reasoning multiplicatively and tasks to promote them. We provide a task-generating platform game, depictions of each scheme, and supporting tasks. Tasks must be distinguished from children's thinking, and learning situations…

Children's learning of early number bonds is a significant issue in South African schools because evidence shows that flexible and efficient (fluent and reasoned) knowledge of number bonds to 20 correlates with success at the end of primary schooling, yet the evidence is that many South African students are over-reliant on inefficient counting…

A review of the research literature indicated that there were probable orders in which students develop understandings and skills for calculating with percentages. Such calculations might include using models to represent percentages, knowing fraction equivalents, selection of strategies to solve problems and determination of percentage change. To…

This note points out that realized compound yield (RCY) has a similar concept from capital budgeting; namely, modified internal rate of return. Recognizing this relationship makes it easier to teach the concept and allows students to easily compute RCY using a financial calculator.

The multiplicative principle is the tool allowing the counting of groups that can be described by a sequence of events. An event is a subset of sample space, i.e. a collection of possible outcomes, which may be equal to or smaller than the sample space as a whole. It is important that students understand this basic principle early on and know how…

Mathematical elegance is illustrated by strikingly parallel versions of the product and quotient rules of basic calculus, with some applications. Corresponding rules for second derivatives are given: the product rule is familiar, but the quotient rule is less so.

This paper presents a new algorithm called competency-based guided-learning algorithm (CBGLA), which can be applied on adaptively guiding e-learning. Computational process analysis and mathematical derivation of competency-based learning (CBL) were used to develop the CBGLA. The proposed algorithm could generate an effective adaptively guiding…

"Let's Count" is an early mathematics program that has been designed by The Smith Family and the authors to assist educators in early childhood contexts in socially disadvantaged areas of Australia to work in partnership with parents and other family members to promote positive mathematical experiences for young children (3-5 years). A…

Math games bring out kids' natural love of numbers. Yet in the waning days of school, students can't wait for that final bell to ring. Each summer, most students lose about two months of mathematical computation skills. So how do teachers keep their students focused on math up till the end? Before sending them off for the summer, get them hooked…

Ofsted was asked to provide evidence of effective practice in the teaching of early arithmetic, its report entitled; "Good practice in primary mathematics: evidence from 20 successful schools," was published in November 2011. Did this report pass you by? Unfortunately, as with many other reports not blessed with a "high…

This article describes a follow-up analysis of findings from a randomized study that tested the efficacy of a blended version of Enhanced Anchored Instruction (EAI) designed to improve both the computation and problem-solving performances of middle school students with disabilities. The goals of the secondary analysis were to track overall error…

The purpose of the present study was to examine factors that influence strategic flexibility in computational estimation for Chinese- and Canadian-educated adults. Strategic flexibility was operationalized as the percentage of trials on which participants chose the problem-based procedure that best balanced proximity to the correct answer with…

Soroban abacus training is called as mental arithmetic training in our country. It is known for mental arithmetic to increase the ability of four mode operations. Besides this, how is the situation for the students which are having Soroban abacus training in the terms of problem solving abilities, creativity, development of concepts, attraction…

Arecent episode of "MythBusters" (Williams, 2013) involved a series of "battles of the sexes" to examine myths and urban legends about things that men are supposedly better (or worse) at doing than women. Some of the processes that were used on the show to investigate these myths, along with the data they generated, can be used…