A considerable number of children rely on counting to solve single-digit addition problems when they are expected to use accurate retrieval-based strategies. There are different reasons why this may be so. Children may use inefficient counting strategies, produce errors when applying backup strategies or lack sufficient confidence to just state…

We have been incrementally adding data-driven methods into the Deep Thought logic tutor for the purpose of creating a fully data-driven intelligent tutoring system. Our previous research has shown that the addition of data-driven hints, worked examples, and problem assignment can improve student performance and retention in the tutor. In this…

This study responded to a national call to improve the outcomes in mathematics in the Grade 12 matriculation examination in South Africa by reporting learners' perceptions of the introduction of computer-assisted learning in their mathematics classrooms. Three Grade 12 mathematics classes in a peri-urban school in South Africa were visited over a…

Designers of interactive learning environments with a focus on word problem solving usually have to compromise between the amount of resolution paths that a user is allowed to follow and the quality of the feedback provided. We have built an intelligent tutoring system (ITS) that is able to both track the user's actions and provide adequate…

In this study, I examined the relation between various construct relevant and irrelevant variables and a math problem solving assessment. I used independent performance measures representing the variables of mathematics content knowledge, general ability, and reading fluency. Non-performance variables included gender, socioeconomic status,…

In the literature, problem-posing abilities are reported to be an important aspect/indicator of creativity in mathematics. The importance of problem-posing activities in mathematics is emphasized in educational documents in many countries, including the USA and China. This study was aimed at exploring high school students' creativity in…

This paper explored variation of strategy use in pattern generalization across different generalization types and across grade level. A test was designed to assess students' strategy use in pattern generalization tasks. The test was given to a sample of 1232 students from grades 4 to 11 from five schools in Lebanon. The findings of this study…

The authors completed a narrative review of studies of mathematics interventions from 1996 to 2010 for helping elementary school students with difficulties in mathematics solve word problems. Key instructional components supported by research are teaching cognitive and metacognitive skills; schema-based instruction focusing on semantic analysis,…

The study investigated the effects of Solve-Reflect-Pose Strategy (SRP) on pre-service mathematics teachers' algebraic knowledge for teaching in Nigeria. A pre-test-post-test quasi experimental design was employed. Intact classes were used and in all, 182 pre-service mathematics teachers' participated in the study (92 in the experimental group…

Pivot Professional Learning, in consultation with the Australian Association of Mathematics Teachers, summarises their study into the characteristics of Australian mathematics teachers. The study reinforced that Australia has many excellent teachers of mathematics, but can improve by sharing excellent teaching practices of its expert teachers…

The 2I/E model is an extension of Marsh's (1986) classical internal/external frame of reference (I/E) model. Whereas the classical I/E model describes the formation of academic self-concept by the joint operation of social (external) and dimensional (internal) comparisons, the 2I/E model integrates temporal comparisons as an additional internal…

Communicating their thinking in mathematics is challenging for young children. This research studied the change in six-year old students' oral and written solution explanations before and after six problem-based mathematics lessons that focused on developing conceptual understanding of adding or subtracting a 2-digit number and a multiple of ten.…

The use of active learning techniques in engineering classrooms has been limited despite substantial evidence supporting their efficacy in helping students construct problem-solving expertise. A blended classroom, which combines online and in-class learning, was employed in a Chemical Engineering Computation class to address instructional…

How many ways may one climb an even number of stairs so that left and right legs are exercised equally, that is, both legs take the same number of strides, take the same number of total stairs, and take strides of either 1 or 2 stairs at a time? We characterize the solution with a difference equation and find its generating function.

Ratio, rate, and proportion are central ideas in the Common Core State Standards (CCSS) for middle-grades mathematics (CCSSI 2010). These ideas closely connect to themes in earlier grades (pattern building, multiplicative reasoning, rational number concepts) and are the foundation for understanding linear functions as well as many high school…