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…

This paper dealt with the design of learning tools, that was the development of learning implementation plan or Rencana Pelaksanaan Pembelajaran (RPP) based on Fun and Easy Math (FEM) approach in the form of a number line model. FEM was an approach in order to teach mathematics effectively to students in a fun and easy way according to the…

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…

The goal of this study was to describe fraction-calculation errors among fourth-grade students and to determine whether error patterns differed as a function of problem type (addition vs. subtraction; like vs. unlike denominators), orientation (horizontal vs. vertical), or mathematics-achievement status (low-, average-, or high-achieving). We…

The goal of the present study was to describe fraction-calculation errors among 4th-grade students and determine whether error patterns differed as a function of problem type (addition vs. subtraction; like vs. unlike denominators), orientation (horizontal vs. vertical), or mathematics-achievement status (low- vs. average- vs. high-achieving). We…

Algorithms and representations have been an important aspect of the work of mathematics, especially for understanding concepts and communicating ideas about concepts and mathematical relationships. They have played a key role in various mathematics standards documents, including the Common Core State Standards for Mathematics. However, there have…

In this case study with Devin (pseudonym), which was part of a larger, constructivist teaching experiment with students identified as having learning difficulties in mathematics, we examine how a fourth grader constructed a dual anticipation involved in monitoring when to start and when to stop the simultaneous count of composite units (numbers…

The Common Core State Standards (2010) involve the demonstration of conceptual knowledge of numbers and operations. For students who struggle with mathematics and have not responded to instruction, it is important that interventions emphasize this understanding. In order to address conceptual understanding of numbers and operations in meeting the…

The maturation of multiplicative thinking is key to student progress in middle school as rational number, ratio, and proportion concepts are encountered. But many students arrive from the intermediate grades and falter in developing this essential disposition. Elementary students have historically learned multiplication and division as operation…

For over a decade, research studies of mathematics education in high-performing countries have pointed to the conclusion that the mathematics curriculum in the United States must become substantially more focused and coherent in order to improve mathematics achievement in this country. To deliver on the promise of common standards, the standards…