Teachers are regularly asked to use data to inform their instruction. In the past, teachers examined student work in isolation. Now, however, teachers increasingly have dedicated meeting times. So how can teachers collaboratively examine student work and use their findings to improve instruction? In this article, a team of teachers at Hilltop…

This mixed-method, qualitative/quantitative study examined (a) how a constructivist-based intervention (CBI) effected adults' learning of unit fractions and performance on whole-number (WN) or unit fraction (FR) comparisons and (b) brain circuitry implicated (fMRI) when processing these comparisons. The CBI used unit-iteration based activities to…

Examples and explanations are inherent elements of mathematics learning and teaching. This study explores the relationship between examples and explanations given for the same concept. Results indicated that for the concept of parity, fifth grade students offer different explanations for different examples. However, for the concept of equivalent…

One of the challenges in learning fractions is understanding how and why a fraction can have multiple interpretations. As presented in one textbook, a fraction is "a symbol, such as 2/3, 5/1, or 8/5, used to name a part of a whole, a part of a set, a location on a number line, or a division of whole numbers" (Charles et al. 2012, p.…

This paper investigates how the selected three East Asian countries--Japan, Korea, and Taiwan-- introduce and develop ideas related to fractions and fraction addition and subtraction compared to the Common Core State Standards of Mathematics and EngageNY. Looking at curricular approaches used across countries can provide a better picture of what…

This study investigated how pre-service teachers' fractional concepts are related to solving problems involving advanced fractional knowledge. 96 Participants took a written test including three fractions questions about fraction concept, fraction comparison, and multiplicative relationship involving fraction quantities and composite units. The…

The 3 purposes of this study were to: (a) describe fraction ordering errors among at-risk 4th-grade students; (b) assess the effect of part-whole understanding and accuracy of fraction magnitude estimation on the probability of committing errors; and (c) examine the effect of students' ability to explain comparing problems on the probability of…

This study used a multiple probe across participants design to examine the effects of a model drawing strategy (MDS) intervention package on fraction comparing and ordering word problem-solving performance of three Grade 4 students. MDS is a form of cognitive strategy instruction for teaching word problem solving that includes explicit instruction…

Previous research on preservice teachers' understanding of fractions and algebra has focused on one or the other. To extend this research, we examined 85 undergraduate elementary education majors and middle school mathematics education majors' solutions and solution paths (i.e., the ways or methods in which preservice teachers solve word problems)…

The three purposes of this study were to (a) describe fraction ordering errors among at-risk fourth grade students, (b) assess the effect of part-whole understanding and accuracy of fraction magnitude estimation on the probability of committing errors, and (c) examine the effect of students' ability to explain comparing problems on the probability…

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…

The purpose of this study was to explore the relationship between instructional modality used for teaching fractions and third- and fourth-grade students' responses and strategies to open-response fraction items. The participants were 155 third-grade and 200 fourth-grade students from 17 public school classrooms. Students within each class were…

The aim of this study was to investigate primary student teachers' perspectives of the teaching of fractions, i.e. their PCK of fractions. The research design used for the study was a descriptive survey method. As data collection instrument, we conducted a questionnaire composing of 14 open and closed-ended questions. The questionnaire was…

Proportional reasoning involves thinking about parts and wholes (i.e., about fractional quantities). Yet, research on proportional reasoning and fraction learning has proceeded separately. This study assessed proportional reasoning and formal fraction knowledge in 8- to 10-year-olds. Participants (N = 52) saw combinations of cherry juice and water…

The ubiquity of the subject of percentages in our everyday life demands that math teachers and pre-service math teachers demonstrate a profound knowledge and thorough understanding of the concept of percentages. This work, which originated from one specific lesson in an 8th grade math class, studies the conceptual understanding and problem-solving…