Mathematics Education

Colloquium

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PEDAGOGICAL AND COGNITIVE FLOW IN MATHEMATICS

 

November 27, 2007

Room 114 at 4:00

 

         This paper is based on partial results of an exploratory study that looked at the potential pedagogical and cognitive flow in secondary school mathematics classes as revealed by 36 public school mathematics teachersŐ choices of activities and problems or exercises they plan to use in a standard mathematics class.  The teachers were given three instruments to complete: a demographics questionnaire, a beliefs questionnaire, and a curriculum questionnaire.  Responses to the curriculum questionnaire, which provided the main data for this part of the study, were analyzed using content analysis methods.  The teachers were asked to select from a list of 10 problems and exercises on the content lesson Equations of a Line typical problems or exercises they would use for each of 6 parts in a normal mathematics class, namely: motivation or introduction to the lesson, demonstration of solving a sample problem, practice exercises, review, assigned homework, in-class assessment.  Using the TIMSS 2003 framework, the researcher classified each problem or exercise as developing low-level skills (Knowing and Solving Routine Problems), mid-level skills (Using Concepts and Solving Routine Problems) and high-level skills (Reasoning).   The cognitive sequence resulting from the choices of problems or exercises for each part of the lesson was categorized based on the potential cognitive response of students: rewarding, challenging, or frustrating.  Descriptions of each category or cognitive response are discussed in detail.

         Results show that 21 of the 36 teachers could potentially develop low-level, low to mid-level, and mid-level skills at best while only 15 could potentially develop mid to high-level and high-level skills at best.  Students could potentially end up frustrated in 20 of the 36 teachersŐ classes while students could potentially feel cognitively rewarded in only 7 of the 36 teachersŐ classes.  Selected teachersŐ explanations for their choices indicate lack of understanding of the cognitive demands of a particular problem or exercise and inadequate pedagogical and content training, among others.  Implications for teacher training are offered and these include the need for introducing a more systematic approach to developing pedagogical content knowledge among mathematics teachers.