This article outlines a problem-centered approach to the topic of canonical matrix forms in a second linear algebra course. In this approach, abstract theory, including such topics as eigenvalues, generalized eigenspaces, invariant subspaces, independent subspaces, nilpotency, and cyclic spaces, is developed in response to the patterns discovered…

Proportional reasoning as the capacity to compare situations in relative (multiplicative) rather than absolute (additive) terms is an important outcome of primary school mathematics. Research suggests that students tend to see comparative situations in additive rather than multiplicative terms and this thinking can influence their capacity for…

This essay is an account of student civic engagement in action. It stresses the vital role of environments in which students learn to be civic actors. The student experiences recorded in this account point toward a form of campus politics that places students in a role of coworker and cocreator, where they must negotiate differences and…

Students with mathematics learning disabilities have a weak understanding of mathematical concepts that underlie success in Algebra I, such as ratios and proportional reasoning. In this study, researchers used a multiple baseline across participants design to evaluate the effects of a intervention based on a instructional trajectory of how…

We describe a range of practical activities that allows students to investigate the properties and applications of magnets. The activities can be used in isolation or used together to build a rounded understanding of the subject area. The activities include simple demonstrations using common or inexpensive equipment, hands-on experiments for small…

The Common Core State Standards for Mathematics (CCSSI 2010) asks students in as early as fourth grade to solve word problems using equations with variables. Equations studied at this level generate a single solution, such as the equation x + 10 = 25. For students in fifth grade, the Common Core standard for algebraic thinking expects them to…

Applying mathematics to real problems is increasingly emphasized in school education; however, it is often complained that many students are not able to solve mathematical problems embedded in contexts. In order to solve story problems, a transition from a textual description to a mathematical notation has to be found, intra-mathematical…

The purpose of this study was to investigate the influence of goal specificity and scaffolding on the programming performance and self-regulation of elementary students engaged in learning game design. This study recruited 232 students for the experimental activities. Two levels of goal specificity were employed: specific and nonspecific.…

Little is known about how students learn the basic ideas of ring theory. While the literature addressing student learning of group theory is certainly relevant, the concepts of zero-divisor and, more generally, elements with no multiplicative inverse are among those for which group theory has no analogue. In order to better understand how students…

There is widespread agreement that further research is needed in order to identify afterschool program characteristics useful for understanding why some programs are more successful than others. The bulk of recommendations put forth by researchers, practitioners and policy makers focus on observable characteristics of the afterschool setting as a…

Collaborative learning has been shown to be beneficial for older students, but there has not been much research to show if these results transfer to elementary school students. In addition, collaborative and individual modes of instruction may be better for acquiring different types of knowledge. Collaborative Intelligent Tutoring Systems (ITS)…

In a society that is becoming more dynamic, complex, and diverse, the ability to solve ill-structured problems has become an increasingly critical skill. Emerging adults are at a critical life stage that is an ideal time to develop the skills needed to solve ill-structured problems (ISPs) as they are transitioning to adult roles and starting to…

This paper explores the group dynamics among three groups of students involved in collaborative learning in mathematical modelling activities. It reports how group dynamics were established and their influence on the students' mathematical problem-solving endeavours. Through video analyses, discourse structures were identified to suggest the…

Kayla was a 15 years old girl with Down syndrome attending a special education school in Indonesia. A modification of Wright et al.'s (2006) approach to assessment documented her number knowledge and arithmetical strategies. This paper discusses the assessment process and the results focusing on her ability to solve number problems. Results show…

This paper reports findings from a classroom based study with 5 year old children in their first term of school. A data modelling activity contextualised by a picture story book was used to present a prediction problem. A data table with numerical data values provided for three consecutive days of rubbish collection was provided, with a fourth day…