We explore prospective elementary-school teachers' attempts to provide signs and symbols with mathematical meaning in a case involving non-integers as numerator or denominator. The data comprises 33 responses to a task inquiring about the existence of numbers between 1/6 and 1/7, in which the participants were asked to compose a hypothetical…

This study aims to investigate the non-algebraic solution strategies that prospective mathematics teachers use to solve word problems and their thought process while they were solving the problems. A total of 76 prospective mathematics teachers were asked to solve two word problems without using algebraic solutions and, then, clinical interviews…

Potential benefits of providing elementary school students experiences with coding robots are well-documented. These include building skill sets related to logical thinking, problem solving, persistence, collaboration, and communication (Harrell 2015). The authors embrace the value of coding in helping elementary school students develop these…

Competence in fractions is important in achieving advanced mathematics such as algebra and calculus. To foster students' understanding of fractions, intervention studies have found number lines to be an effective representational tool. Yet, it is unclear whether or not number lines are equally effective regardless of the ways in which they are…

This study examined the performance of sixth graders in Hong Kong on a number sense three-tier test (NSTTT) and identified their possible misconceptions about number sense. The NSTTT comprises a content tier, which assesses the content knowledge of number sense; a reason tier, which assesses the reasons for the first-tier responses; and a…

The present study is a part of design research in local instructional theory in a pre-algebraic lesson using the Realistic Mathematics Education (RME) approach. The article will focus on recommendations for the type of pre-algebra class that supports elementary school students' algebraic thinking. As design research study, it followed the three…

Informal strategies reflecting the representation of a situation described in an arithmetic word problem mediate students' solving processes. When the informal strategies are inefficient, teaching students to make way for more efficient ways to find the solution is an important educational issue in mathematics. The current paper presents a…

Normative discourse about probability requires shared meanings for disciplinary vocabulary. Previous research indicates that students' meanings for probability vocabulary often differ from those of mathematicians, creating a need to attend to developing students' use of language. Current standards documents conflict in their recommendations about…

We make a "prima facie" case for identifying a single pathway in the learning of Hindu-Arabic numerical symbols and discuss why this ability may be a critical gateway concept in developing mathematical competencies. A representative sample of English and Scottish children was assessed using a number symbol identification paradigm in the…

The purpose of this study is to reveal the concept definitions and examples of pre-service elementary mathematics teachers regarding sets. In this context, students' formal definitions, personal definitions and examples in sets were investigated. Concept of equal sets, subsets, union, intersection, compliment, and difference were considered as…

"Fraction Face-Off!" is a supplemental math program designed to support fourth-grade students who need assistance solving fraction problems. Teachers use program materials with individual students or small groups to promote understanding of the magnitude of fractions, to compare two fractions, to put three fractions in order, and to…

"Fraction Face-Off!" is a supplemental math program designed to support fourth-grade students who need assistance solving fraction problems. Teachers use program materials with individual students or small groups to promote understanding of the magnitude of fractions, to compare two fractions, to put three fractions in order, and to…

"Fraction Face-Off!" is a supplemental math program designed to support fourth-grade students who need assistance solving fraction problems. Teachers use program materials with individual students or small groups to promote understanding of the magnitude of fractions, to compare two fractions, to put three fractions in order, and to…

This study aims to understand the instructional interactions that foster students' generalizing. By analysing video-recorded lessons from 13 different Grade 3 classrooms in which an early algebra intervention was implemented, activities related to generalizing and students' generalizing activities were identified, and the nature of the…

The New York State Education Department (NYSED) has a partnership with Questar Assessment Inc. (Questar) for the development of the 2020 Grades 3-8 Mathematics Tests. Teachers from across the State work with NYSED in a variety of activities to ensure the validity and reliability of the New York State Testing Program (NYSTP). The 2020 Grades 3-5…