Fraction and decimal arithmetic are crucial for later mathematics achievement and for ability to succeed in many professions. Unfortunately, these capabilities pose large difficulties for many children and adults, and students' proficiency in them has shown little sign of improvement over the past three decades. To summarize what is known about…

This research targets children's informal strategies and knowledge of fractions by examining their ability to create, interpret, and connect representations in doing and communicating mathematics when solving fractions tasks. Our research group followed a constant comparative method to analyze clinical interviews of children in grades 2-6 solving…

Background: Students' ability to construct and coordinate units has been found to have far-reaching implications for their ability to develop sophisticated understandings of key middle-grade mathematical topics such as fractions, ratios, proportions, and algebra, topics that form the base of understanding for most STEM-related fields. Most of the…

All students should have opportunities to develop their ability to reason mathematically. Gersten and Chard (1999) support this stance with respect to students with learning disabilities: "Even if students are not automatic with basic facts, they still should be engaged in activities that promote the development of number sense and…

Prior research shows that multiple representations can enhance learning, provided that students make connections among them. We hypothesized that support for connection making is most effective in enhancing learning of domain knowledge if it helps students both in making sense of these connections and in becoming perceptually fluent in making…

Prior research shows that multiple representations can enhance learning, provided that students make connections among them. We hypothesized that support for connection making is most effective in enhancing learning of domain knowledge if it helps students both in making sense of these connections and in becoming perceptually fluent in making…

To what degree can multilingual students profit from bilingual teaching approaches, even when they lack experience in the academic or technical register in their home languages? This study explores this research question in a mixed methods design for a German/Turkish bilingual intervention aimed at fostering conceptual understanding of fractions…

The movie "Frozen" took the world by storm and this global popularity of the movie and its music can be harnessed by teachers of mathematics. This article builds on the "frozen fractal" lyric from "Let It Go" to incorporate fractal geometry into primary mathematics classrooms.

Fractions are known to be difficult to learn and difficult to teach, yet they are vital for students to have access to further mathematical concepts. This article uses evidence to support teachers employing teaching methods that focus on the conceptual understanding of the magnitude of fractions.

The ability to reason about numbers in relative terms is essential for quantitative literacy, which is necessary for studying academic disciplines and for critical citizenship. However, the ability to reason with proportions is known to be difficult to learn and to take a long time to develop. To determine how well higher education applicants can…

Students in the United States continue to struggle with fraction mastery despite the fact that understanding fractions is essential for further progress in mathematics (NAEP, 2008). This research project investigated the potential of using high-press mathematical discourse (Kazemi & Stipek, 2008) to investigate fourth graders' emerging…

Tangible user interfaces (TUIs) are frequently used to teach children abstract concepts, in science and mathematics. TUIs offer a natural and immediate form of interaction that promotes active and hands-on engagement and allows for exploration and reflection. Tangible objects are representational artifacts in their essence, and they increase the…

The increasing use of educational technologies in classrooms is producing vast amounts of process data that capture rich information about learning as it unfolds. The field of educational data mining has made great progress in using log data to build models that improve instruction and advance the science of learning. Thus far, however, the…

Traditionally, "z" is assumed to be a complex number and the roots are usually determined by using de Moivre's theorem adapted for fractional indices. The roots are represented in the Argand plane by points that lie equally pitched around a circle of unit radius. The "n"-th roots of unity always include the real number 1, and…

This study investigates how 20 prospective elementary teachers make connections among children's multiple mathematical knowledge bases in their thinking about assessing children's understanding of fractions. The researcher facilitated concept-mapping tasks to examine the ways the prospective teachers linked concepts related to children's lives and…