Many U.S. students possess only a weak knowledge of fraction arithmetic. I hypothesize that textbooks are a critical reason for students' poor performance on fraction arithmetic. This is not because of what textbooks contain but rather because of what they lack. Distributions of fraction arithmetic problems in textbooks are imbalanced, with…

The aim of the study reported on here was to assess the impact of differentiated instruction in terms of mathematics achievement and the attitudes of secondary school learners to reveal their views on differentiated instruction. The study was designed according to a mixed method design in which both quantitative and qualitative methods were used.…

Background: Digital game-based learning is gaining increased attention from both researchers and educators for improving mathematics instruction. However, the evidence for game-based learning is mixed and research with rigorous research design and analyses are limited. Objective: Here, in a pre-registered randomized controlled study, we…

The aim of this longitudinal study was to examine the differences between high- and low-performing students' development of fraction proficiency over a school year and to investigate how those differences were related to instruction in fractions versus instruction in other mathematics topics. The data for this study were drawn from a group of (n =…

In this study, our team observed sixth grade teachers as they taught fractions to students in their mathematics intervention classes to see whether they were including motivational-supportive messages within the framework of Situated Expectancy-Value Theory. Messages in the intervention lessons and teacher transcripts were explored and analyzed,…

One way to emphasize students' strengths when reasoning verbally is through number talks. During a number talk, a teacher facilitates a 5- to 15-minute conversation during which students have the opportunity to engage in mental mathematics and verbally explain and justify their reasoning regarding how they make sense of numerical computations.…

In this paper, we have tried to clearly explain the meaning of fractions and operations with fractions. Also, we have tried to illustrate with some examples how to apply the rules of operations with fractional numbers, giving different practical techniques through different figures, visualization methods, and concretizing problems. The paper…

Identifying the knowledge resources teachers productively and unproductively draw upon can provide a means by which to create support structures to develop a more robust understanding of the content. To provide more informed grade-level support structures in teacher education programs, this study examined the knowledge resources 20 secondary…

Educational technologies in mathematics typically focus on fostering either procedural knowledge by means of structured tasks or, less often, conceptual knowledge by means of exploratory tasks. However, both types of knowledge are needed for complete domain knowledge that persists over time and supports subsequent learning. We investigated in two…

Research suggests teachers have positive motivational and emotional orientations regarding statistics but little statistical knowledge. How does this fit together? Since teachers' professional competence in statistics has not been well explored, we asked 88 in-service mathematics teachers about their orientations regarding teaching statistics and…

To test the hypothesis that a higher tendency to "s"pontaneously "f"ocus "o"n "m"ultiplicative "r"elations (SFOR) leads to improvements in rational number knowledge via more exact estimation of fractional quantities, we presented sixth graders (n = 112) with fraction number line estimations and a…

This research aimed to develop a valid and reliable test to be used to detect sixth grade students' misconceptions and errors regarding the subject of fractions. A misconception diagnostic test has been developed that includes the concept of fractions, different representations of fractions, ordering and comparing fractions, equivalence of…

This study presents an extension of the validity argument for the PCK-Fractions measure. PCK-Fractions is designed to assess the effectiveness of professional experiences in facilitating teachers' pedagogical content knowledge (PCK) for children's fraction reasoning in grades 3-5. We examined data across 101 participants from two Midwest…

The main purpose of this study is to assess pre-service and public elementary mathematics school teachers' conceptual understanding and computational abilities of fractions. 20 pre-service mathematics teachers and 24 in-service mathematics teachers participated in this study. In-service teachers were divided into two categories; one for teachers…

The present study uses a short, computerized task to investigate individual differences among middle school students in terms of the intuitions and strategies that they use to compare fractions. To tap into their intuitions about fractions, students were presented with pairs of fractions on the screen for a limited time of 10 s. Fraction pairs to…