Through the lenses of statistical investigations and cognitive demands, we examined bivariate data tasks offered in US high school mathematics textbook series--a popular representative of three curriculum types: traditional, integrated, and hybrid. We developed a framework grounded in literature of association topics for the inclusion and…

This study explored a diagnostic assessment method that emphasized the cognitive process of algebra learning. The study utilized a design and a theory-driven model to examine the content knowledge. Using the theory driven model, the thinking skills of algebra learning was also examined. A Bayesian network model was applied to represent the theory…

The purpose is to improve insights and educational results by applying analytic methods. The focus is on the mathematics applied to learn from the kind of data available to most classes such as final examination marks or homework grades. The sample is 249 students learning introductory college statistics. The result is a predictive model for…

The purpose of this quantitative causal-comparative research was to examine if and to what extent there were differences in students' cognitive load and the subsequent academic performance based on block bell schedule and traditional bell schedule for freshmen in Algebra 1 in the Southwestern United States. This study included students from two…

The aim of this study is to analyse how mathematical problem solving is represented in mathematical textbooks for Swedish upper secondary school. The analysis comprises dominating Swedish textbook series, and relates to uncovering (a) the quantity of tasks that are actually mathematical problems, (b) their location in the chapter, (c) their…

In an experiment, secondary students from Australia and Malaysia (n = 130) were randomly assigned to one of three approaches (equation, unitary, unitary-pictorial) to learn how to solve challenging percentage-change problems. In line with the differential types of cognitive load associated with the three approaches, the unitary-approach group…

In the context of a generic harmonic oscillator, we investigated students' accuracy in determining the period, frequency, and angular frequency from mathematical and graphical representations. In a series of studies including interviews, free response tests, and multiple-choice tests developed in an iterative process, we assessed students in both…

At the start of mathematics education children are often presented with addition and subtraction problems in the form of pictures. They are asked to solve the problems by filling in corresponding number sentences. One type of problem concerns the representation of an increase or a decrease in a depicted amount. A decrease is, however, more…

This quasi-treatment study, using a non-equivalent group design, explored how a set of animations related to various concepts in algebra impacted students' ability to learn as measured by changes in quiz and test scores. The concepts that were investigated were addition and subtraction of rational expressions, solving equations involving rational…

Mathematics has been widely recognized as being challenging for most students. In this study, an online formative peer-tutoring approach was proposed to cope with this problem, and an online learning system was developed accordingly. To evaluate the effectiveness of the proposed approach, an experiment was conducted to explore its effects on…

Difficulties in mathematics learning are a multi-faceted issue and the role of language in it is crucial. Language of mathematics includes mathematics text, discourse in classroom and language used in evaluation situations with its specific verbal, symbolic expressions, structure and function. Ambiguity arising from the difference between formal…

In this paper we report on the outcomes of two surveys carried out in higher education institutions of Ireland; one of students attending first-year undergraduate non-specialist mathematics modules and another of their lecturers. The surveys aimed to identify the topics that these students found difficult, whether they had most difficulty with the…

Online adaptive tutoring systems are increasingly being used in classrooms as a way to provide guided learning for students. Such tutors have the potential to provide tailored feedback based on specific student needs and misunderstandings. Bayesian knowledge tracing (BKT) is used to model student knowledge when knowledge is assumed to be changing…

Within mathematics teaching, ways to help students resolve proportional reasoning problems remains a topical issue. This study sought to investigate how a simple innovative procedure could be introduced to enhance skill acquisition. In two classroom-based experiments, 12-year-old students were asked to solve proportional reasoning mathematics…

During the last reform, Slovakia has reduced geometry in curriculum in primary mathematics education. Pre-school education schools devote more time to geometry in curriculum, but this is not mandatory for all the children. In the primary schools, teachers devote very little lessons time to this problem. These lessons are mainly focused on…