This study reports a secondary analysis from a randomized control trial study conducted with third graders with mathematics difficulty (MD; N = 75). We used simple linear regression to investigate whether students' performance on a word-problem vocabulary assessment predicted their performance on a measure of word-problem solving. Additionally, we…

The aim of this study was to investigate individual differences in mathematical problem-solving among 3- to 5-year-old children (N = 328; n[subscript 3-year-olds] = 115, n[subscript 4-year-olds] = 167, n[subscript 5-year-olds] = 46). First, we examined the extent to which children in this age group were able to solve open and closed non-routine…

Students' emotions (e.g., enjoyment, boredom) while doing math and their situational interest in mathematics are important for their learning of mathematics, but examinations of teachers' judgments of students' emotions and interest while solving tasks are rare. Moreover, we do not know much about the predictors of teachers' judgments of students'…

Insight into early precursors of proportional reasoning is necessary to further our theoretical understanding of mathematical development and to guide early interventions. Although several researchers have suggested patterning as a possible precursor for proportional reasoning, there is little empirical evidence to support this assumption,…

Individuals solve arithmetic problems in different ways and the strategies they choose are indicators of advanced competencies such as adaptivity and flexibility, and predict mathematical achievement. Understanding the factors that encourage or hinder the selection of different strategies is therefore important for helping individuals to succeed…

This study investigated the extent to which domain-general and domain-specific antecedents contributed to pre-algebra's initial level and growth rate among students who experience word-problem difficulty (WPD). We examined if such a profile differs for English-language learners (ELLs; n = 75) and non-ELLs (n = 55) with WPD. We assessed 130 U.S.…

Prior short-term studies have shown the effectiveness of worked examples and self-explanation prompts in improving elementary students' mathematics knowledge. However, year-long classroom-based interventions have been tested only with older students. The purpose of the current study was to explore the effectiveness of a year-long classroom…

Students often perform arithmetic using rigid problem-solving strategies that involve left-to-right-calculations. However, as students progress from arithmetic to algebra, entrenchment in rigid problem-solving strategies can negatively impact performance as students experience varied problem representations that sometimes conflict with the order…

Background: Creativity requires both divergent and convergent thinking. Previous research established that "divergent" thinking relates to mathematics performance, but generally ignored the role of "convergent" thinking and, hence, leaves it unclear how both might interact when children work on mathematical tasks. This study…

We propose a model delineating the role of control, value, and cognitive disequilibrium in elementary students' experience of emotions during mathematics problem solving. We tested this model across 2 studies. In Study 1, using an explanatory mixed-methods design, 136 students from Grades 3 to 6 worked on a complex mathematics problem appropriate…

In this study, whether the variables of pre-service teachers' reflective thinking related to problem solving, attitude towards mathematical problem solving, metacognitive awareness, mathematical literacy self-efficacy, belief related to mathematical problem solving and problem solving achievements differ according to class level and the prediction…

Background: Adaptive expertise is a highly valued outcome of mathematics curricula. One aspect of adaptive expertise with rational numbers is adaptive rational number knowledge, which refers to the ability to integrate knowledge of numerical characteristics and relations in solving novel tasks. Even among students with strong conceptual and…

The aim of this study was to examine the relationship between mathematics thinking sub-dimensions (higher order thinking, reasoning, mathematical thinking and problem-solving) and critical thinking disposition. In addition, this study investigated whether mathematical thinking sub-dimensions are significant predictors of critical thinking…

This paper provides evidence that a short, fully online, well-constructed diagnostic test based on research literature can give teachers information about their students' thinking and strategies that is sufficiently accurate to use for formative assessment purposes. The example is a test for students beginning to learn to solve equations. The main…

Recent work has demonstrated that having students study worked examples and answer self-explanation prompts as part of their problem-solving practice improves learning on researcher-developed measures of mathematical proficiency. However, little work has been done to date to investigate whether these benefits translate to improvements on the types…