Principles for the design of teaching

Abstract

In this introductory article, after some initial discussion of an appropriate approach to mathexnatics as a curriculura subject, we sketch a theory for designing teaching, based on mathematical activity, situations, tasks, and interventions, exposing and resolving cognitive conflicts, changes of structure and context, feedback, reflection and review. We next review the main psychological principles underlying this theory, then consider some examples of teaching designs in the light of the theory. Thus we open the discussion of the theme of this issue, which continues with the fuller discussion of other examples in the remaining articles.Other authors have offered more controversial descriptions, which emphasize the logical aspects. One may recall Russell's "the subject in which we never know what we are talking about, nor whether what we say is true". For the purposes of guiding curriculum construction, we find the positive descriptions more helpful.Education is normally seen as a forward-looking, purposeful activity, the aim of which is to develop pupils' capacities and knowledge so as to equip them

The effect of an historical perspective on prospective teachers’ beliefs in learning mathematics

“…In this regard, prospective teachers' engagement with the material was much higher with those questions that caused cognitive conflict, and they worked harder and thought more on the questions that intrigued them. This perspective is in line with Bell's (1993), who suggested ensuring connectedness, structural transfer across context, feedback, reflection and review, and intensity as successful elements of resolving conflict during the process of discussion.…”

“…A literature review by Fraser (2007) revealed that cognitive conflict can be effective, ineffective, or destructive. Many researchers reported its positive impacts (e.g., Adey and Shayer 1993;Bell 1993;Druyan 1997;Hewson and Hewson 1984;Lee and Kwon 2001;Posner et al 1982). Some scholars, though, found that cognitive conflict failed to lead to desired results (e.g., Niaz 1995;Dreyfus et al 1990;Elizabeth and Galloway 1996).…”

“…There is nothing new with this proposition; Davis (1996) argues that context-rich problems are strongholds for changing views which lead to mathematical achievement and performance. For Bell (1993) as well, problems with such features were found helpful in transferring a given structure to a new context of learning.…”

“…Well-designed discussions open the avenues for reflection and review of ideas. According to Bell (1993), exploring and resolving conflicts through discussion are in themselves reflective activities that promote the development of important schema for future use. It appears that this approach helped the majority of prospective teachers cue in favor of progressive items and against items that favor traditional beliefs in the theme time as evidenced in Table 2 (t 61 = 2.57, p B 0.001) at the end of the intervention program.…”

Gender, Need-Achievement and Assertiveness as Factors of Conceptions about Math among Secondary School Students in Ogun State, Nigeria

“…There are indications that students' conceptions of mathematics and their orientations to study affect the purity of cognitive activity and of learning outcomes (Kloosterman, 2002). Studies such as Bell (1993), Canobi (2005), Hiebert and Carpenter (1992), Mason and Spence (1999) and Yager (1991) showed that students' conceptions of understanding mathematics are important in their success in mathematics. Also, the ways in which learners interpret the context of their mathematical learning and hence the ways they relate to mathematical activities influence their mathematical thinking (Crawford, 1990).…”