This study established an online game-based assessment to explore third and fourth graders' performance of computational estimation in addition and subtraction. Students' computational estimation strategies could be automatically recorded and classified in this assessment, and the Higher-Order DINA model was used as a measurement model in order to…

The purpose of this study was to examine the effects of "Understand and Solve!" Strategy on change problems including change of a one-step addition and subtraction of children with mild intellectual disabilities and whether they maintained their achievements 3, 5, and 8 weeks after the intervention. Moreover, the effects of the…

Knowledge representations that result from practicing problem solving can be expected to differ from knowledge representations that emerge from explicit verbalizing of principles and rules. We examined the degree to which the two types of learning improve problem-solving knowledge and verbal explanation knowledge in classroom instruction. We…

Strategy flexibility, adaptivity, and the use of clever shortcut strategies are of major importance in current primary school mathematics education worldwide. However, empirical results show that primary school students use such shortcut strategies rather infrequently. The aims of the present study were to analyze the extent to which Dutch sixth…

In a cross-sectional study, 160 students in Grades 2, 4, 7, and 11 were interviewed about their reasoning when solving integer addition and subtraction open-number-sentence problems. We applied our previously developed framework for 5 Ways of Reasoning (WoRs) to our data set to describe patterns within and across participant groups. Our analysis…

This chapter focuses on the interaction of two first graders as they attempt to make sense of a particular instructional context for learning negative numbers. The context is one where they move an elevator to a building's floors above and below ground in order to model integer addition and subtraction problems. In particular, the focus of the…

According to numerous studies (Barrouillet & Camos 2002; Brousseau 1988; Chevallard 1988; Riley et al. 1984; Schubauer-Leoni & Ntamakiliro, "Revue Des Sciences de L'éducation," 20(1): 87-113, 1994; Vergnaud 1982; Xin, "The Journal of Educational Research," 100(6):347-360, 2007), a combination of many factors, including…

A mathematical mnemonic is a visual cue or verbal strategy that is used to aid initial memorisation and recall of a mathematical concept or procedure. Used wisely, mathematical mnemonics can benefit students' performance and understanding. Explorations into how mathematical mnemonics work can also offer students opportunities to engage in proof…

This article investigates how students in third grade learn to reason on multiplication when they first encounter that concept in the classroom context. By analysing the data from 24 classrooms focused on teaching and learning multiplication, the article aims at contributing to the research and conceptualisations about how students learn to…

A considerable number of children rely on counting to solve single-digit addition problems when they are expected to use accurate retrieval-based strategies. There are different reasons why this may be so. Children may use inefficient counting strategies, produce errors when applying backup strategies or lack sufficient confidence to just state…

The aim of the study is to investigate the effects of using computer for developing arithmetical skills of students with mathematics learning difficulty (MLD). The study was carried out with pre-test - post-test single subject research design. The participants of the study consist of a girl and two boys who attend 3rd grade at elementary school.…

Mathematical relationships are crucial elements to consider for learning mathematics. However, too often students pay more attention to the calculations to be done rather than the reasons for doing them. Relying on the relational paradigm to support elementary school students, we proposed two specially designed tasks to help students recognize and…

We investigate thirty-three second and fifth-grade students' solution strategies on integer addition problems before and after analyzing contrasting cases with integer addition and participating in a lesson on integers. The students took a pretest, participated in two small group sessions and a short lesson, and took a posttest. Even though the…

Measuring computational fluency, an aspect of procedural fluency, is complex. Many attempts to measure this construct have emphasised accuracy and efficiency at the expense of flexibility and appropriate strategy choice. Efforts to account for these latter constructs through assessing children's computational reasoning using structured interviews…

Many general and special education teachers teach mathematics word problems by defining problems as a single operation and linking key words to specific operations. Unfortunately, teaching students to approach word problems in these ways discourages mathematical reasoning and frequently produces incorrect answers. This article lists eight common…