This study aimed to create a constructivist learning environment wherein third-grade students talk to problem solve, which is different from traditional approaches to math learning. The study focused on the group talk and discussions to understand the students' actions and interactions during the process of problem-solving. Fifteen students and…

To better understand the role that ways of reasoning play in students' success on integer addition and subtraction problems, we examined the relationship between students' flexible use of ways of reasoning and their performance on integers open number sentences. Within groups of students in 3 participant groups--39 2nd and 4th graders who had…

This study investigated the promotion of children's understanding and acquisition of arithmetic concepts and the effects of inhibitory skills. Children in Grades 3, 4, and 5 solved two sets of three-term addition and subtraction problems (e.g., 3 + 24 - 24, 3 + 24 - 22) and completed an inhibition task. Half of the participants received a…

The purpose of this study was to better understand how students with learning disabilities, including those who struggle specifically with mathematics, engage with fraction computation. In particular, we examined error patterns, the influence of like and unlike denominators on these patterns, and correct solution methods. Although skill-related…

Over the last two decades, students in Singapore consistently scored above students from other nations on the Trends in International Mathematics and Science Study (TIMSS; Provasnik et al., 2012). In contrast, students in the United States have not performed as well on international and national mathematics assessments and students with…

The purpose of this study is to determine how Finnish pupils' problem-solving skills develop from the 3rd to 5th grade. As research data, we use one non-standard problem from pre- and post-test material from a three-year follow-up study, in the area of Helsinki, Finland. The problems in both tests consisted of four questions related to each other.…

An adapted alternating treatments design was used to compare the effects of class-wide applications of Taped Problems (TP) and Cover, Copy, and Compare (CCC) procedures designed to enhance subtraction fact fluency in an intact third-grade classroom. During the TP procedure, a tape provided an auditory prompt (i.e., the problem), followed by a…

During the winter of 2011, the author faced an instructional dilemma: Should she teach the concept of adding and subtracting fractions with unlike denominators using a "quick trick" for the sake of staying on schedule, or should she try something different in hopes that her students would gain understanding through their own methods? The latter…

In considering mathematics problem solving as a model-eliciting activity (Lesh & Doerr, 2003; Lesh & Harel, 2003; Lesh & Zawojewski, 2008), it is important to know "what" students are modeling for the problems: situations or solutions. This study investigated Grade 3 students' mathematization process by examining how they modeled different…

In a first experiment, adults were asked to solve one-digit additions, subtractions and multiplications. When the sign appeared 150 ms before the operands, addition and subtraction were solved faster than when the sign and the operands appeared simultaneously on screen. This priming effect was not observed for multiplication problems. A second…

The basis of this intervention study is a distinction between numerical calculus and relational calculus. The former refers to numerical calculations and the latter to the analysis of the quantitative relations in mathematical problems. The inverse relation between addition and subtraction is relevant to both kinds of calculus, but so far research…

This study investigates the relationship between skills that underpin mathematical word problems and those that underpin numerical operations, such as addition, subtraction, division and multiplication. Sixty children aged 6-7 years were tested on measures of mathematical ability, reading accuracy, reading comprehension, verbal intelligence and…

Pat was a 19-year-old attending a Special School for the Intellectually Disabled in Indonesia. She was interviewed by the first author regarding her mental calculation strategies when solving 1- and 2-digit addition and subtraction problems. Results indicate that she was able to see ten as a unit composed of ten ones and was facile in using…

This article describes how teachers address issues and tensions that students meet in learning division of fractions. First, students must make sense of division of fractions on their own by working individually and in small groups, using concrete or pictorial representations, inventing their own processes, and presenting and justifying their…

Previous research has consistently shown that the left parietal cortex is critical for numerical processing, but the role of the right parietal lobe has been much less clear. This study used the intraoperative cortical electrical stimulation approach to investigate neural dissociation in the right parietal cortex for subtraction and…