This study used units coordination as a theoretical lens to investigate how whole number and fraction reasoning may be related for preservice teachers at the conclusion of a math methods class. The study contributes quantitative evidence that units coordination provides a common foundation for both mathematical knowledge for teaching whole number…

Teacher knowledge is one of the main factors in the quality of mathematics learning. Many mathematics teachers have difficulty using proportional reasoning. Proportional reasoning is one of the essential aspects of the middle school mathematics curriculum to develop students' mathematical thinking. Teachers should realize that developing…

This research aimed to examine whether the activities related to mental computation strategies had any effect on the development of the second-grade elementary school students' problem-solving (PS) skills. Participants of the study are comprised of 14 children aged 7-8 years and enrolled in the second grade of the elementary school of a village.…

National and state standards in the US have emphasized the importance of solving and posing word problems in students' mathematics learning for decades. Therefore, it is essential for prospective teachers (PTs) to have the mathematical knowledge necessary to teach these skills to their future students. Unfortunately, little research has…

This paper draws on numerous data sources to better understand the shift from additive to multiplicative thinking in years 4 to 9. Research studies that have used the Scaffolding Numeracy in the Middle Years assessment tasks have found that while students can be supported to move through the early and upper zones of the Learning and Assessment…

Students with learning disabilities/difficulties in mathematics often apply ineffective procedures to solve word problems. Given that current mathematics curriculum standards emphasize conceptual understanding in problem solving as well as higher-order thinking and reasoning, the purpose of this study was to evaluate the impact of a model-based…

This observational study used data from 270 second-grade students to investigate the association between students' strategy use for multidigit addition and subtraction and their mathematics achievement. Based on strategies they used during a mathematics interview, students were classified into the following strategy groups: (a) standard algorithm,…

CBM for mathematics assesses growth in accuracy and fluency of basic math skills using content from a student's curriculum. CBM for mathematics can include single-skill measures (SSM), skill-based measures (SBM), and general-outcome measures (GOM). Past research on growth rates in CBM for mathematics has focused on GOMs and has relied on…

Children with mathematical difficulties need to spend more time than typically achieving children on solving even simple equations. Since these tasks already require a larger share of their cognitive resources, additional demands imposed by the need to switch between tasks may lead to a greater decline of performance in children with mathematical…

This paper details an exploratory study of 14 elementary prospective teachers (PTs) solving purposefully crafted, two-digit addition problems. The numbers in each problem were chosen to elicit diverse solution strategies. We coded 95 responses based on the ways the PTs completed the calculation (for example, by referring to the number as…

Developing an understanding of fractions is critical as a significant predictor for the learning progression of advanced domains; however, students face significant challenges in learning fractions because of their unique properties. To systematically approach remediation, this study examined the common error patterns committed by middle-school…

One of the factors associated with the less than positive mathematics performance of American students could be poorly designed textbooks that fail to facilitate the development of critical mathematical ideas. This study examined two reform-based textbooks (Go math! and Investigations) in reference to essential, mathematical big ideas emphasized…

Mathematical writing is one way for primary students to communicate their mathematical thinking. Research in the field of writing has shown that to become an effective teacher of writing, preservice teachers must have experience engaging in the kinds of writing given to their students. The study reported in this paper explored how 27 preservice…

There is a growing awareness that many children are not developing fast and accurate retrieval-based strategies for solving single-digit addition problems. In this study we individually assessed 166 third and fourth grade children to identify a group of children (called accurate-min-counters) who frequently solved simple single-digit addition…

We present results of a grounded analysis of individual interviews in which students play Vector Unknown -- a digital game designed to introduce visualizing vectors, scaling vectors, vector addition, and vector equations, attending to the geometric and algebraic representations of vectors. The game was designed to be used at the beginning of a…