According to our approach to mathematics education, the optimal aim of the teaching of mathematics is to assist students in achieving efficient mathematical work. But, what does efficient exactly mean in that case? And how can teachers reach this objective? The model of Mathematical Working Spaces with its three dimensions--semiotic, instrumental,…

Learning how to give effective feedback can be a difficult task for teacher leaders. This is especially true for what is called "hard feedback"--that is, feedback that challenges the teacher's practice and therefore may cause some level of professional discomfort. Educators at the University of Pittsburgh's Institute for Learning have…

A major goal of education is to help learners store information in long-term memory and use that information on later occasions to effectively solve problems (Vockell 2010). Therefore, this author began to use the Rubik's cube to help students learn to problem solve. There is something special about this colorful three-dimensional puzzle that…

Child psychologist Peg Dawson explains that some students who appear to be lazy simply lack the executive skills they need to stay organized and get their work done. She tells the story of Josh, a student with attention problems whose academic performance started plummeting in middle school. With the help of a coach, Josh learned to manage his…

Central Auditory Processing (CAP) difficulties have attained increasing recognition leading to escalating rates of referrals for evaluation. Recognition of the association between (Central) Auditory Processing Disorder ((C)APD) and language, learning, and literacy difficulties has resulted in increased referrals and detection in school-aged…

Starting from a situated cognition perspective, this paper reports on the activity of 9th grade students who are interpreting the shape of a graph arising from the motion of a bouncing ball. In an unfamiliar context, informed by previous knowledge of similar experiments, the obstacle of understanding why the graph does not start from the origin is…

To probe beyond declarative knowledge about real numbers in secondary school, the authors interviewed students in Grades 9, 10 and 12. The main question seems to be whether the length of a decimal expansion is "indefinite" or "infinite." It blurs the mental representation of rational numbers as well. (Contains 3 footnotes.) [For complete…

In this paper, we suggest that case-based resources, which are used for assisting cognition during problem solving, can be structured around the work of narratives in social cultural psychology. Theories and other research methods have proposed structures within narratives and stories which may be useful to the design of case-based resources.…