Events in learning mathematics: Insights from research in classrooms

In this paper, it is contended that in order to understand individual student's learning in the complexity of the mathematics classroom it is necessary to examine the events that occur before, during, and after learning. To illustrate, the process by which two children each construct new mathematical meanings is examined in this manner. The detailed analyses of each of these events provides insight into the processes by which individual students construct mathematical meanings in classroom settings. The investigation also reveals that the underlying social norms differ from those found in traditional classes, and that this creates different opportunities for learning. It is contended that it is the differences in the norms that have been established in their respective classes that distinguishes between the events in learning for the two children.Preparation of this paper was supported by the National Science Foundation (RED 9254939) and while the author was the Snodgrass Scholar in the School of Education Purdue University. The final draft was completed at the Mathematics Education Research Centre, Oxford University. All opinions are those of the author.     

A follow-up assessment of a second-grade problem-centered mathematics project

Five second-grade classes in two schools participated in a project that was generally compatible with a constructivist theory of knowing. At the end of the school year, the students in these classes and their peers in six non-project classes in the same schools were assigned to ten textbook-based third-grade classes on the basis of reading scores. The two groups of students were compared at the end of the third-grade year on a standardized achievement test and on instruments designed to assess their conceptual development in arithmetic, their personal goals in mathematics, and their beliefs about reasons for success in mathematics. The levels of computation performance on familiar textbook tasks were comparable, but former project students had attained more advanced levels of conceptual understanding. In addition, they held stronger beliefs about the importance of working hard and being interested in mathematics, and about understanding and collaborating. Further, they attributed less importance to conforming to the solution methods of others.     

The Keys to STEM: Australian Year 7 Students’ Attitudes and Intentions Towards Science,Mathematics and Technology Courses

Research in Science Education - Educational researchers have long noted the apparent link between positive student attitudes and a student’s desire to continue their study of particular...     

Multimodal literacy learning opportunities within a grade six classroom literacy curriculum: constraints and enablers

This case study of a grade six classroom literacy curriculum in Ontario, Canada was designed to produce new knowledge of how curricula can promote multimodal literacy learning opportunities for students. With a focus on constraints and enablers, the study found few opportunities for multimodal literacy learning due to standardised assessments, an outcomes-based programmatic curriculum with related standardised report card, and assessment-focused professional learning opportunities. Despite the print-centric nature of the curriculum, however, the study found that students did initiate their own multimodal opportunities. The study has implications for educators across the globe who are interested in expanding students’ literacies.     

Information systems management: The need for a post-modern approach

This paper proposes a post-modern way of thinking about the development and the management of information systems and especially information systems development. The paper proposes a framework for a co-evolutionary or co-creation approach to information systems development and management incorporating all the main stakeholders.     

Faculty Study Groups: Solving “Good Problems” Through Study, Reflection, and Collaboration

We describe the development, implementation, and assessment of a faculty study group program designed to foster teaching as a reflective, collaborative activity within a research university. Conceived within conceptual frameworks that challenge technical/rationalist approaches to faculty development, the program was successful in creating opportunities for faculty of different disciplines, age groups, ranks, and teaching experience to establish productive discourse communities around their own teaching. Our experience shows that such programs require careful thought and planning, which we detail here, and that faculty even in research oriented institutions can be captured by the good problem that teaching represents.     

Building a Unidimensional Test Using Multidimensional Items

This paper demonstrates, both theoretically and empirically, using both simulated and real test data, that sets of items can be selected that meet the unidimensionality assumption of most item response theory models even though they require more than one ability for a correct response. Sets of items that measure the same composite of abilities as defined by multidimensional item response theory are shown to meet the unidimensionality assumption. A method for identifying such item sets is also presented     

A comparison of pretrial and intertriai rewards on runway extinction

In two experiments, rats were trained to run a straight alley for food reward in the goalbox. During subsequent extinction sessions, food rewards were given in the holding cages either immediately pretrial or during the intertriai interval. Pretrial rewards retarded extinction. Importantly, this resistance to extinction was also apparent on nonprefed test trials that occurred either embedded within the daily extinction sessions or at the start of the daily sessions. The results suggest that food reinforcers have a temporary aftereffect that can maintain already conditioned behaviors.