This report focuses on key elements of teaching occurring during intensive, one-to-one instruction with 3rd- and 4th-graders. The study involves six cases in all, each consisting of video records of up to eight lessons, each of 30-45 minutes' duration, resulting in the analysis of about 33 hours of video data. A resulting framework of four stages…

The Fibonacci series has been studied since it was first described by Leonardo of Pisa--Fibonacci--in 1202. It begins with the sequence 1, 1, 2, 3, 5, 8... Each succeeding number is the sum of the previous two. In number theory courses, students are introduced to the concept of modulo arithmetic, sometimes called "clock" arithmetic. In modulo…

Finding the sum of a series in the form of a closed expression has always been a challenging problem in analysis. The paper presents an elementary method for summation of series with terms generated by functions satisfying subtraction identities.

This study determined the working memory (WM) components (executive, phonological short-term memory [STM], and visual-spatial sketchpad) that best predicted mathematical word problem-solving accuracy in elementary schoolchildren (N = 392). The battery of tests administered to assess mediators between WM and problem-solving included measures of…

Studies reveal that students as well as teachers have difficulties in understanding and learning of decimals. The purpose of this study is to investigate students' as well as pre-service teachers' solution strategies when solving a question that involves an estimation task for the value of a decimal number on the number line. We also examined the…

This study is intended to investigate student's achievement capability among two families i.e. Low and High income families and designed for primary level learners. A Reading, Arithmetic and Writing (RAW) Achievement test that was developed as a part of another research study (Tamim Ahmed Khan, 2015) was adopted for this study. Both English medium…

Understanding of base 10 and place value are important foundational math concepts that are associated with higher use of decomposition strategies and higher accuracy on addition problems (Laski, Ermakova, & Vasilyeva, 2014; Fuson, 1990; Fuson & Briars, 1990; National Research Council, 2001). The current study examined base-10 knowledge,…

Several cognitive deficits associated with reading and mathematics problems have been identified. However, only few studies assessed the impact of these variables in children with combined problems in reading and arithmetics, and none of these studies included children with low IQ. This longitudinal study was designed to assess the impact of…

The present study describes the usage of strategies of symbolic representation during teaching introduction of decimal system in primary school in Mexico. Our research is based on Activity Theory conception of teaching-learning process and of gradual introduction of scientific concepts in school age. The method includes symbolic external…

Must two triangles with equal areas and equal perimeters also be congruent? This question was introduced in "Mathematics Teacher" ("MT")by Rosenberg, Spillane, and Wulf in their article "Heron Triangles and Moduli Spaces" (2008), which also described the authors' subsequent investigation of a particular moduli…

This study explored the effectiveness of external representations presented together with compare word problems, and whether such effectiveness was moderated by working memory. Participants were 49 secondary school students. Each participant solved 48 problems presented in 4 presentation types that included 2 difficulty treatments (number of steps…

The purpose of this study was to determine the constructs measured by the WISC-IV and the consistency of measurement across large normative and clinical samples. Competing higher order four- and five-factor models were analyzed using the WISC-IV normative sample and clinical subjects. The four-factor solution is the model published with the test…

This article presents a number of carefully selected activities for the mathematics classroom in the early grades. The motivation for their selection is the development of concepts rather than the learning of the procedural skills of arithmetic. As the teacher is faced with a great heterogeneity of children starting school, the concrete learning…

Mrs. Fisher's class was learning about arithmetic functions by pretending to operate real-world "function machines" (Reeves 2006). Functions are a unifying mathematics topic, and a great deal of emphasis is placed on understanding them in prekindergarten through grade 12 (Kilpatrick and Izsák 2008). In its Algebra Content Standard, the…

Action observation (AO) and movement imagery (MI) have been reported to share similar neural networks. This study investigated the congruency between AO and MI using the eye gaze metrics, dwell time and fixation number. A simple reach-grasp-place arm movement was observed and, in a second condition, imagined where the movement was presented from…