Proposes methods to teach the more difficult concepts of linear algebra. Examines features of the Linear Algebra Curriculum Study Group Core Syllabus, and presents problems from the core syllabus that utilize the mathematical process skills of making conjectures, proving the results, and communicating the results to colleagues. Presents five…

Children with autism have special characteristics (such as communication problems, lack of common sense, and resistance to change) that present a challenge in gaining access to Great Britain's National Curriculum. Possible problem-solving approaches include creating a thinking environment, teaching cognitive strategies, and developing…

Presented are classroom-tested examples of instructional materials (courseware) for ordinary differential equations using the software package PHASER. All of the examples include in-class demonstration techniques and commentaries for instructor use, student homework and laboratory exercises, and suggestions for in-class examination questions. (JJK)

This article describes a training program, Self-Regulation Empowerment Program (SREP), that school professionals can use to empower adolescent students to engage in more positive, self-motivating cycles of learning. It is a two-part approach whereby self-regulated learning coaches (SRC) (a) use microanalytic assessment procedures to assess…

Working together and exchanging ideas is inherent in interactive learning. The focus of interactive learning is on what learners believe is important to learn, the various processes learners use to learn and how learners use learning in other settings and situations. Active learning processes that promote reflection, writing, demonstrations,…

Norms govern the criteria by which students decide what is good and what is not good, and align their learning trajectories accordingly.We found that the high-school students' norm is to produce working, but not necessarily error-free, programs and to argue for their correctness solely on the basis of a few executions. Therefore, they prefer…

This study reports on the algebraic generalisation strategies used by two fifth grade students along with the factors that appeared to influence these strategies. These students were examined over 18 instructional sessions using a teaching experiment methodology. The results highlighted the complex factors that appeared to influence student…

A qualitative study documented the use of reflection-in-action by adult educators in problematic situations. Its focus was to investigate the mental processes involved in problem solving. Since individuals engage problem situations from a personal conceptualization that is unobservable, qualitative interviewing was used to provide respondents with…

This study investigated the effectiveness of a schema strategy on the addition and subtraction word problem solving performance of four sixth and seventh grade students with learning disabilities. Students were taught to map features of the word problem onto problem schemata diagrams, first for one-step problems and then for two-step problems. A…

Metacognition is considered by most educationists to be an element necessary for many cognitive learning tasks. In general, within problem solving tasks, procedural, factual, and conceptual knowledge, by themselves, are insufficient for successful task completion. To be successful, the problem solver must usually demonstrate higher level cognitive…

This paper reports a study to address two questions concerning children's understanding of average: How do children construct and interpret representativeness within the context of data sets? and How do children think about the mean as a particular mathematical definition and relationship? Twenty-one students (seven each of 4th, 6th, and 8th…

This resource guide represents the first comprehensive guide to the innovative practices of accelerated schools. It is designed to be used by a wide variety of participants as a supplement for training, as well as for discussion and guidance in the move to transform schools nationwide. Eleven chapters include detailed descriptions of the…

Progress is reported on research conducted in school settings to investigate methods to help students--especially at-risk students--to acquire and use knowledge to solve problems. The methods incorporate principles of learning and instruction derived from basic research on cognition. Specifically, the research involves using microcomputer and…

Use of metacognitive strategies, creative problem solving, and creative thinking techniques in intermediate grade writing instruction can promote students' thinking and creativity. Metacognitive strategies can help students attack the writing task in an orderly fashion. Answering specific questions for descriptive, expository, narrative, or…

The cognitivist view of composition suggests that if students are supplied with a set of writing strategies, they will learn to think in more complex and powerful ways, observing their own ideas and writing from another person's viewpoint. On the other hand, some social critics argue that composition teachers need to help their students enter into…