Preparing children to be successful in mathematics begins with what they learn before they reach 1st grade. Math knowledge in prekindergarten and kindergarten predicts school achievement in math and in other topics, such as reading. Indeed, early math knowledge is one of the strongest predictors of math grades in high school, high school…

A critical aspect of intervention research is investigating the active ingredients that underlie intensive interventions and their theories of change. This study explored the rate of instructional interactions within treatment groups to determine whether they offered explanatory power of an empirically validated Tier 2 kindergarten mathematics…

A web-based two-tier test (WTTT-NS) which combined the advantages of traditional written tests and interviews in assessing number sense was developed and applied to assess students' answers and reasons for the questions. In addition, students' major misconceptions can be detected. A total of 1,248 sixth graders in Taiwan were selected to…

With the adoption of the Common Core State Standards for Mathematics (CCSSM), many teachers are changing their classroom structure from teacher-directed to student-centered. When the author began designing and using problem-based tasks she saw a drastic improvement in student engagement and problem-solving skills. The author describes the Cake…

The focus of this study is the relationship between students' performance in mental calculation and the strategies they use when solving three-digit mental addition problems. The sample comprises 78 4th grade students (40 boys and 38 girls). Their mean age was 10 years and 4 months. The main novelties of the current research include (1)…

Although low performers should invest more time and effort in their studies, they seldom do. One reason is because they often feel that they get no return on their investment: more studying does not automatically lead to better marks in school. But with the right kind of in-school support, including creative and engaging mathematics-related…

This paper reports on a study that examines the effects of problem context on students' performance. The performance of 151 Year 10 students on six mathematical problems was compared with the performance on fifteen variants with more and less context familiarity (CF) and engagement (CE) across levels of context use (LCU). The latter explanatory…

As part of a project exploring various aspects of teachers' choice and use of challenging mathematics tasks, we sought some responses from students on their preferences for the difficulty of tasks on which they might work and also on the ways of working. Despite the common finding that teachers are reluctant to pose challenges to their students…

This paper focuses on children's number fact knowledge from a study that explored the impact of using multiplication and division contexts for developing number understanding with 34 five- and six-year-old children from diverse cultural and linguistic backgrounds. After a series of focused lessons, children's knowledge of number facts, including…

The study of function transformations helps students understand the function concept which is a basic and main concept in mathematics, but this study is problematic to school students as well as college students, especially when transformations are performed on non-basic functions. The current research tried to facilitate grade 9 students'…

The widespread concern about mathematics achievement has drawn extensive research attention to what skills predict later academic achievement. There is clear and consistent evidence that math achievement at school entry is the strongest predictor of later school success and educational attainment. Early childhood math achievement can thus have…

This article presents an Exponential Growth Learning Trajectory (EGLT), a trajectory identifying and characterizing middle grade students' initial and developing understanding of exponential growth as a result of an instructional emphasis on covariation. The EGLT explicates students' thinking and learning over time in relation to a set of tasks…

In early childhood settings narratives that capture children's learning as they go about their day-to-day activities are promoted as a powerful assessment tool. However, in the New Zealand context there is increasing concern that learning stories currently downplay domain knowledge. Data from teacher interviews and samples of learning stories…

Research findings have established that students often struggle with mathematical symbols including common misconceptions for literal symbolic representations of variables but provide little evidence of when or how these misconceptions arise. This article reports findings from a study of grade 4-6 students' conception(s) for various…

Mathematics-related beliefs play an important role in the willingness to engage in academic activities in mathematics education. Such beliefs might not be consistent with the beliefs students hold about context problems that require sufficient mathematical knowledge and the application of such knowledge to various real-life situations. This study…