Early years mathematics textbooks are support material for teachers and learners as they contain visual representations which communicate and clarify mathematical concepts. In this paper, we report on the types and functions of visual representations of multiplication and division in South African early years mathematics textbooks. There seems to…

The Akita approach is the guideline in learning that responds to rapid changes in the 21st century. This research aimed to determine the effectiveness of learning management based on the Akita approach in accordance with the criteria efficiency of 75/75 and to explore the index of effectiveness of learning management pursuant to the Akita…

Background: In several countries, children's math skills have been declining at an alarming rate in recent years and decades, and one of the explanations for this alarming situation is that children have difficulties in establishing the relations between arithmetical operations. Aim: In order to address this question, our goal was to determine the…

Developing multiplicative reasoning is an important milestone for elementary school students, which influences their learning of later mathematical concepts (Hackenberg and Tillema 2009). For children to conceptually understand multiplication, one should move beyond merely counting by ones to dealing with composites (twos, fives, etc.) and other…

Mathematics educators and researchers have advocated for the use of manipulatives to teach mathematics for decades. The purpose of this article is to provide illustrative uses of a readily available manipulative rather than a complete list. From an Australian perspective, Pop-it fidget toys can be used across the mathematics curriculum. This paper…

Visual representations and manipulatives are a highly advocated mathematical tool for the teaching and learning of multiplication and division. Although there is some prior research on elementary teachers' general use of manipulatives and visual representations, there is little to no specific focus on use of such representations on a specific…

Mathematics teacher professional-development (PD) programs based on Cognitively Guided Instruction (CGI) have been developed and implemented with tens of thousands of elementary mathematics teachers worldwide since the 1980s. Starting with a focus on addition and subtraction on whole numbers in the first CGI PD program, the content of these…

This study aimed to create a constructivist learning environment wherein third-grade students talk to problem solve, which is different from traditional approaches to math learning. The study focused on the group talk and discussions to understand the students' actions and interactions during the process of problem-solving. Fifteen students and…

This paper is a report on the results of a 3-year teaching experiment conducted in Ithaca, New York, introducing students to the concepts of multiplication, division, and ratio as a trio, and to ratio and proportion in a project-based curriculum with heterogeneous grouping. Fractions were introduced as a subset of ratio and proportion. The paper…

This book reports on young students' strategies, the ways they construct knowledge, and how to support such development over time. Focus is placed on how to develop an understanding of multiplication and division in grades 3-5. The book describes and illustrates what it means to do and learn mathematics, provides strategies to help teachers turn…

Describes an informal research activity in which third grade students invent their own algorithms for multidigit multiplication and division. Discusses teaching implications and action research ideas. (ASK)

The purpose of this study was to compare instruction in multiplication and division by means of manipulative materials and pupil discovery to instruction using abstract and semi-concrete materials combined with teacher explanation and exposition. The effect of the two methods on pupils' attitude and achievement also was compared. Ten classrooms…

Following instructions provided in the teacher's manual, the SCOPE Mathematics Achievement Test booklet for grade 3 presents 11 mathematical concepts. Testing items include: skip counting by 2's, 5's, and 10's to 100, 3's to 30, and 4's to 40; writing number words to 20; identifying and naming 100's, 10's, and 1's in three-digit numerals; reading…

The SCOPE Mathematics Achievement Test booklet for grade 3-s contains the same testing items as the test booklet for grade 3. This booklet is more suitable for the more mature student; therefore, directions have been written to permit the student to take the test with little or no teacher direction. (ERB)

Presents an instructional strategy for teaching how to solve word problems and understand the operations involved. Describes the acquisition method of the part-whole relationships of problem situations. Provides some samples of the instructional strategy used and classroom test results. Lists nine references. (YP)