The aim of the present study was to investigate the performance in arithmetic related to achievement levels in reading and mathematics. Basic arithmetical facts and multi-step calculations were examined. The participants were 941 pupils aged 8 (N = 415), 10 (N = 274) and 13 (N = 252) years. The pupils were divided into four groups by standardized…

A fundamental question in developmental science is how brains with and without language compute numbers. Measuring young children's verbal reactions in Spain and Finland, we show that, although there is a general arithmetic ability for small numbers that is shared by monkeys and preverbal infants, the development of such initial knowledge in…

Many students find the leap from arithmetic to algebra a difficult one to make, and current literature suggests that a number of the common misconceptions held by students arise as a result of the methods which teachers use to present algebra. The abstract nature of algebra makes it difficult for students to grasp; students also struggle with the…

In this article, data from a study of the mental computation competence of students in grades 3 to 10 are presented. Students responded to mental computation items, presented orally, that included operations applied to fractions, decimals and percents. The data were analysed using Rasch modelling techniques, and a six-level hierarchy of part-whole…

Preservice elementary school teachers' fragmented understanding of mathematics is widely documented in the research literature. Their understanding of division by 0 is no exception. This article reports on two teacher education tasks and experiences designed to challenge and extend preservice teachers' understanding of division by 0. These tasks…

An influential proposal about aquiring mathematical knowledge is that it entails linking instruction-based concepts to intuitions derived from informal activities. In the case of non-positive numbers, informal knowledge is unlikely to emanate from observing physical objects, because non-positive objects or sets of objects do not exist. However, it…

This document, which was developed to meet the needs of trainers and workers in Australia's automotive industry for learning activities designed to boost auto workers' numeracy skills, contains a total of 33 learning activities organized into 8 sections. The topics covered in the individual sections are as follows: calculators (key words and…

This collection of mathematics word problems was developed by adult learners in the Reach One Program. The first page describes the steps that led to the finished product: having learners work word problems; listing steps for solving word problems; having learners work problems according to these steps; providing a list of key words that indicate…

Learning activities and questioning skills that teachers in Tasmania can use to determine a child's mathematics understanding are presented. Covered topics include division, multiplication, subtraction, addition, sorting and classification, one-to-one correspondence, patterns, ordering, and counting. Included for each topic are the aim, needed…

The objectives and the scope and sequence for the elementary school mathematics program of the Denver Public Schools (Colorado) are presented. The guide begins with a statement of the philosophy and general objectives of the K-12 mathematics program and a discussion of the methods of achieving those objectives. Several important ideas and concepts…

The Skill Acquisition Measures (SAM) were designed by the Lancaster (Pennsylvania) School District as criterion referenced tests for mathematics. This manual consists of copies of the student test forms for level 6, with additional information for the teacher's use. Each of the test items is presented with the correct answers and the criteria for…

In 1989, a study was conducted to examine basic mathematics programs in the California community colleges and to produce specific program recommendations for the mathematics curriculum at Saddleback College. The study involved a number of components, including: (1) a review of the literature on developmental education and basic mathematics…

The Skill Acquisition Measures (SAM) were designed by the Lancaster (Pennsylvania) School District as criterion referenced tests for mathematics. This manual consists of copies of the student test forms for level 2, with additional information for the teacher's use. Each of the test items is presented with the correct answers and the criteria for…

The Skill Acquisition Measures (SAM) were designed by the Lancaster (Pennsylvania) School District as criterion referenced tests for mathematics. This manual consists of copies of the student test forms for level 4, with additional information for the teacher's use. Each of the test items is presented with the correct answers and the criteria for…

These item specifications were developed as a part of the Arkansas "Minimum Performance Testing Program" (MPT). There is one item specification for each instructional objective included in the MPT. The purpose of an item specification is to provide an overview of the general content and format of test items used to measure an…