In the modern world information has become the new power. An increasing amount of efforts are being made to gather data, resources being allocated, time being invested and tools being developed. Data collection is no longer a myth; however, it remains a great challenge to create value out of the enormous data that is being collected. Data modeling…

This paper examines correspondences and disjunctions within a national curriculum and between various aspects of its delivery, and how these align with the mathematical needs of the workplace. This is investigated in the context of the New Zealand school mathematics curriculum; the Numeracy Development Project; the senior school assessment regime,…

Euler's method for solving initial value problems is an excellent vehicle for observing the relationship between discretization error and rounding error in numerical computation. Reductions in stepsize, in order to decrease discretization error, necessarily increase the number of steps and so introduce additional rounding error. The problem is…

The well-known Stolz-Cesaro lemma is due to the mathematicians Ernesto Cesaro (1859-1906) and Otto Stolz (1842-1905). The aim of this article is to give new forms of Stolz-Cesaro lemma involving the limit [image omitted].

A standard example used in introductory combinatoric courses is to count the number of five-card poker hands possible from a straight deck of 52 distinct cards. A more interesting problem is to count the number of distinct hands possible from a Pinochle deck in which there are multiple, but obviously limited, copies of each type of card (two…

There is a remarkable difference between formal knowledge and true understanding of the subject. While the former helps students earn top grades, the latter is crucial to the solution of real-world problems. An excellent example is the computation of capacitance, with which some students have difficulty. Also, most textbooks limit problem analysis…

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…

This paper provides a critical examination of the current state and future possibility of formal cognitive theory for insight problem solving and its associated "aha!" experience. Insight problems are contrasted with move problems, which have been formally defined and studied extensively by cognitive psychologists since the pioneering…

Two 12-question estimation instruments were designed to compare the differences of estimating strategies used by the 8th-graders when solving contextual and numerical problems. Both instruments are parallel, meaning that the numbers used in both instruments are the same; however, they were presented differently. One hundred and ninety-eight…

Research on toddlers' mathematical knowledge is sparse. Studies on children's mathematical competencies before school age have mostly focused on older children. Few of the previous studies have included large groups of toddlers, few have been conducted in natural settings, and few have been directed at a broad field of mathematical knowledge. The…

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 longitudinal study aimed to investigate the extent to which primary school text comprehension predicts mathematical word problem-solving skills in secondary school among Finnish students. The participants were 224 fourth graders (9-10 years old at the baseline). The children's text-reading fluency, text comprehension and basic calculation…

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…

In the middle years of school, it is important that mathematics is challenging, engaging and focuses on worthwhile mathematics. In this article, Anne Roche describes a lesson that seemed to have all three of these characteristics, as students grappled with issues of scale to create a fun run, given a range of challenging mathematical constraints.…