Background/purpose: Investigation into the misconceptions of preschool students in mathematics and their differences between the ages of 4-5 and 5-6 years old helps form appropriate developmental mathematics teaching programs. However, although several studies have been conducted examining preschoolers' previous knowledge and misconceptions about…

This paper presents an analysis of fractions errors displayed by learners due to deficient mastery of prerequisite concepts. Fractions continue to pose a critical challenge for learners. Fractions can be a tricky concept for learners although they often use the concept of sharing in their daily lives. 30 purposefully sampled learners participated…

A robust understanding of place value is essential. Using a problem-based approach set within meaningful contexts, students' attention may be drawn to the multiplicative structure of place value. By using quotitive division problems through a concrete-representational-abstract lesson structure, this study showed a powerful strengthening of Year 3…

Purpose: The purpose of this descriptive study is to investigate why some elementary children have difficulties mastering addition and subtraction calculation tasks. Design/methodology/approach: The researchers have examined error types in addition and subtraction calculation made by 697 Portuguese students in elementary grades. Each student…

Students with physical and health disabilities struggle with basic mathematical concepts. The purpose of this research study was to increase the students' mathematical computation skills through implementing new strategies and/or methods. The strategies implemented with the students was utilizing the ten-frame tiles and technology with the purpose…

The Common Core State Standards for Mathematics (CCSSI 2010) expect second grade students to "fluently add and subtract within 20 using mental strategies" (2.OA.B.2). Most children begin with number word sequences and counting approximations and then develop greater skill with counting. But do all teachers really understand how this…

This study investigated the promotion of children's understanding and acquisition of arithmetic concepts and the effects of inhibitory skills. Children in Grades 3, 4, and 5 solved two sets of three-term addition and subtraction problems (e.g., 3 + 24 - 24, 3 + 24 - 22) and completed an inhibition task. Half of the participants received a…

This paper argues for teaching pre-service teachers about remediation strategies for learners who encounter problems in mathematics in the early grades. The premise is that all teachers should be equipped with theory-based practical knowledge to support learning. A few teaching sessions to develop the concepts that underlie the mathematical…

Mastering single-digit arithmetic during school years is commonly thought to depend upon an increasing reliance on verbally memorized facts. An alternative model, however, posits that fluency in single-digit arithmetic might also be achieved via the increasing use of efficient calculation procedures. To test between these hypotheses, we used a…

Little research has focused on an informal understanding of subtractive negation (e.g., 3 - 3 = 0) and subtractive identity (e.g., 3 - 0 = 3). Previous research indicates that preschoolers may have a fragile (i.e., unreliable or localized) understanding of the addition-subtraction inverse principle (e.g., 2 + 1 - 1 = 2). Recognition of a small…

Action research (AR) is defined by Macintyre to be: "an investigation, where, as a result of rigorous self-appraisal of current practice, the researcher focuses on a problem,or a topic or an issue which needs to be explained, and on the basis of information, plans, implements, then evaluates an action then draws conclusions on the basis of…

Understanding conceptual relationships is an important aspect of learning arithmetic. Most studies of arithmetic, however, do not distinguish between children's understanding of a concept and their ability to identify situations in which it might be relevant. We compared 8- to 9-year-old children's use of a computational shortcut based on the…

This article describes a multisensory method for teaching students how to multiply and divide as well as add and subtract integers. The author uses sidewalk chalk and the underlying concept of integers to physically and mentally engage students in understanding the concepts of integers, making connections, and developing computational fluency.…

Examined whether 5- and 6-year-olds understand that addition and subtraction cancel each other and whether this understanding is based on identity or quantity of addend and subtrahend. Found that children used inversion principle. Six- to eight-year-olds also used inversion and decomposition to solve a + b - (B+1) problems. Concluded that…

The primary objective of this study was to provide an experimental model of children's representations of addition and subtraction concepts viewed as constructed schemes. How children with different counting schemes differ in their addition and subtraction concepts and how the types of problems children solve correlate with the addition and…