The purpose of this study is to analyze pre-service elementary teachers' problems in terms of the different meanings of the addition of fractions and to determine the types of errors made in these problems. Data were collected from 83 pre-service elementary teachers in the spring semester of the 2016-2017 academic year by means of a problem posing…

Data from a longitudinal investigation were used to examine the effects of mothers' and teachers' language on children's developing mathematical competencies during the kindergarten year. Specifically, 1) mothers' use of metamemory talk, or references to the process of remembering, and 2) teachers' use of "cognitive processing language"…

The purpose of this study was to investigate how prospective elementary school mathematics teachers and elementary school students' ability to distinguish proportional situations from nonproportional situations differ or are alike. Participants of the study were 319 prospective primary and middle school teachers and 320 elementary school students…

This article contributes to the research literature concerning prospective elementary teachers' mathematical thinking and learning with a focus on flexibility. We present a case study of a prospective elementary teachers' development of flexibility in mental addition and subtraction during a Number and Operations course. Building upon the…

This study examined how six experienced teachers got information about students' knowledge and used that information to adjust their instruction while tutoring the students in addition. Each teacher tutored five simulated students and one live student. (RB)

Presents an activity that engages children in thinking about the results of combining numbers. (ASK)

Presents activities using the Three Pigs to increase students' understanding of addition and subtraction. Argues that addition and subtraction are something that students can view and participate in when using the Three Pigs instead of just the manipulation of numbers. (ASK)

Presents some results of a study on teaching negative numbers. Focuses on the identification of addition and subtraction, the use of the number line, additive problem solving, and the possibility of following several sequences of numerical extensions. Indicates the importance of previous ideas on positive numbers and how these ideas influence the…

Very specific suggestions for teaching subtraction facts using addition are given. Several activities are suggested. (MK)

Presents materials and methods that have been found to be effective in teaching addition and subtraction in specialized schools for the speech- and hearing-impaired. Concludes that there has been considerable success with students learning necessary mathematical skills by completing activities. Contains 11 references. (ASK)

Explores adult adding techniques and ponders whether they have any relevance to working with primary school children. Suggests ways that can help children develop into effective adders. (ASK)

Developing concepts, modeling, and solving problems form the core of essential learning about addition and subtraction. That educators may make the task more difficult than necessary is the thrust of several recent studies. Highlights from these studies (with suggestions for instruction) are presented. (JN)

Presents an activity involving students in a research project with pictures like those commonly found in elementary school mathematics textbooks and workbooks to sharpen student appreciation of the need for standardized methods of data collection. Illustrates that several different interpretations of the operations of addition and subtraction are…

This paper is concerned with the role of meaning and understanding in the acquisition of computational skill in subtraction. Evidence on the syntactic nature of subtraction errors is reviewed, with common "bugs" described. Then, data collected from interviews with four children are summarized in terms of their semantics of concrete…

Fifty Brazilian children aged seven-13 were individually given addition and subtraction exercises. Counting was the preferred procedure, with use of school-taught algorithms limited. Some children decomposed numbers into tens and units and then worked at both levels. They rarely referred to previous results when doing related exercises. (MNS)