The shuffling of mathematics problems improves learning

In most mathematics textbooks, each set of practice problems is comprised almost entirely of problems corresponding to the immediately previous lesson. By contrast, in a small number of textbooks, the practice problems are systematically shuffled so that each practice set includes a variety of problems drawn from many previous lessons. The standard and shuffled formats differ in two critical ways, and each was the focus of an experiment reported here. In Experiment 1, college students learned to solve one kind of problem, and subsequent practice problems were either massed in a single session (as in the standard format) or spaced across multiple sessions (as in the shuffled format). When tested 1 week later, performance was much greater after spaced practice. In Experiment 2, students first learned to solve multiple types of problems, and practice problems were either blocked by type (as in the standard format) or randomly mixed (as in the shuffled format). When tested 1 week later, performance was vastly superior after mixed practice. Thus, the results of both experiments favored the shuffled format over the standard format.     

The effects of teacher collaboration in Grade 9 Applied Mathematics

The current emphasis of many mathematics education reform documents is on the need to change the environment of mathematics classrooms from the transmission of knowledge by the teacher to the transaction of knowledge between the teacher and the students which promotes mathematical investigation and exploration. In this article, we discuss the details of a Collaborative Teacher Inquiry Project which was aimed at increasing the quality of learning of Grade 9 Applied Mathematics, while at the same time, improving professional development opportunities for the teachers. A total of 11 schools participated in this project which spanned over three semesters. Participants included teachers, department heads, curriculum leaders, and administrators. Each school created an implementation team of administrators and teachers to implement collaborative strategies and improve teaching and learning in Grade 9 Applied Mathematics. The main benefit to the participants was that they were able to increase their knowledge and skills through collaboration in six interconnected areas: (a) achieving the goals, (b) student success, (c) professional development, (d) co-planning and co-teaching opportunities, (e) increased communication, and (f) improved technological skills. Bringing in different partners to achieve a common goal was the most challenging aspect of the project.     

An analysis of the relationship between the linear hammer speed and the thrower applied forces during the hammer throw for male and female throwers

The purpose of this study was to investigate the relationship between the cable force and linear hammer speed in the hammer throw and to identify how the magnitude and direction of the cable force affects the fluctuations in linear hammer speed. Five male (height: 1.88 ± 0.06 m; body mass: 106.23 ± 4.83 kg) and five female (height: 1.69 ± 0.05 m; body mass: 101.60 ± 20.92 kg) throwers participated and were required to perform 10 throws each. The hammer's linear velocity and the cable force and its tangential component were calculated via hammer head positional data. As expected, a strong correlation was observed between decreases in the linear hammer speed and decreases in the cable force (normalised for hammer weight). A strong correlation was also found to exist between the angle by which the cable force lags the radius of rotation at its maximum (when tangential force is at its most negative) and the size of the decreases in hammer speed. These findings indicate that the most effective way to minimise the effect of the negative tangential force is to reduce the size of the lag angle.     

Interleaving Helps Students Distinguish among Similar Concepts

When students encounter a set of concepts (or terms or principles) that are similar in some way, they often confuse one with another. For instance, they might mistake one word for another word with a similar spelling (e.g., allusion instead of illusion) or choose the wrong strategy for a mathematics problem because it resembles a different kind of problem. By one proposition explored in this review, these kinds of errors occur more frequently when all exposures to one of the concepts are grouped together. For instance, in most middle school science texts, the questions in each assignment are devoted to the same concept, and this blocking of exposures ensures that students need not learn to distinguish between two similar concepts. In an alternative approach described in this review, exposures to each concept are interleaved with exposures to other concepts, so that a question on one concept is followed by a question on a different concept. In a number of experiments that have compared interleaving and blocking, interleaving produced better scores on final tests of learning. The evidence is limited, though, and ecologically valid studies are needed. Still, a prudent reading of the data suggests that at least a portion of the exposures should be interleaved.     

The issue at a glance

The issue at a glance     

Teachers’ views of the challenges of teaching grade 9 applied mathematics in Toronto schools

Mathematics teachers, mathematics department heads, curriculum leaders, and administrators from 11 schools in four school boards from Toronto, Ontario, Canada, participated in a project to improve the teaching and learning in grade 9 mathematics classrooms. In each of these schools, an implementation team was created, so that at least three teachers from every school could collaborate, in order to improve learning outcomes of their students. This article reports on the challenges identified by teachers when they taught grade 9 applied mathematics. Teachers’ views of challenges fell into five main layers: (a) teacher professional development and pedagogical skills, (b) student learning needs, (c) settlement issues and families’ social and economic background, (d) administrative difficulties and resources, and (e) curricular issues. These challenges were complex and interconnected, demanding special remedial efforts by the administration and teachers. By reflecting on the challenges and practices, these teachers made a long-term strategy to engage in professional development activities to better understand their students’ learning needs and to improve their achievement in provincial tests.     

Emphasising use over attributes in selection of educational software

Rejecting traditional checklist approaches to software selection, this paper discusses an approach emphasising classroom use of software over technical attributes. It proposes a way of thinking about software (the perspectives interactions paradigm) that takes the perspectives of the student, the teacher and the designer and uses interactions between pairs of these perspectives to generate broad questions and more specific issues to be considered when software is being assessed for purchase or classroom use. Some example packages are assessed using the paradigm for several different educational contexts, illustrating that this approach raises issues of classroom interactions and learning processes. These issues go beyond, and are more important for selection decisions than those generally considered with a checklist of software attributes.     

Axiology,the Subject and the Chair

Research in Science Education - This article addresses two gaps in the literature related to science department chairs: the axiological relationship between the chair and science, the subject, and...