International Approaches to Professional Development for Mathematics Teachers

Chapter 5: Secondary Teachers’ Professional Development through the Exploration of School Mathematics

88 Chapter 5 Secondary Teachers’ Professional Development through the Exploration of School Mathematics Jérôme Proulx Introduction In this chapter, I report on a professional development initiative set up for secondary mathematics teachers (see Proulx, 2007). Six teachers (Carole, Carl, Eric, Lana, Linda, and Gina) participated in the project with the intention to revitalize and improve their mathematics teaching practices. The teachers generally thought that their mathematical knowledge was too focused on procedural knowledge and that this orientation had an important impact on their teaching practices. Some of them expressed the following: “Why is it that we are not able to solve by reasoning? ... It is because we have not been educated to reason in mathematics. Me, I did copy, paste, repeat, and let’s go, ... and I had 95% in mathematics!” (Carole); “I never understood why it worked. ... When students ask me why, I simply say that this is how it is!” (Lana). This situation with regard to secondary mathematics teachers is not new, and important critiques have been raised about the mathematical preparation of school teachers. Indeed, studies point to difficulties that secondary teachers have experienced with aspects of the mathematics that they teach. Studies by Ball (1990) and Bryan (1999) have illustrated that, though the secondary mathematics teachers whom they studied made few if any mistakes in their usage of mathematical procedures, they experienced significant difficulties in providing sound meanings and explanations for the mathematical rationales underlying these procedures. Other Secondary Teachers’ Professional Development || 89 studies have highlighted difficulties of a different order concerning their unfamiliarity with the meanings of concepts and solving processes (e.g., definitions, conjectures, relationships within concepts). Even (1993) and Hitt-Espinosa (1998) have observed that many teachers possess an “old” definition of a function as a continuous graph, preventing them from recognizing or accepting alternative drawings as representing a function and leading them to transform or treat discrete functions as continuous. Also, Schmidt and Bednarz (1997) and Van Dooren, Verschaffel, and Onghena (2003) have reported on secondary teachers’ ease with algebraic solutions but difficulties in appreciating arithmetical procedures as valid solutions to algebraic problems. Despite criticism that these types of studies present a “deficit model” of teacher knowledge, and are not generalizable to all teachers, they nevertheless offer us significant and insightful information for informing our teacher education practices. The issue appears to be not about what teachers know or do not know but about what these findings tell us about what we could or should offer teachers as mathematical experiences in teacher education initiatives. Learning from Studies of Teachers’ Knowledge: Rethinking Mathematical Experiences One issue that arises from these studies concerns the significance of investing efforts in teachers’ development of mathematical knowledge in teacher education practices. However, as Cooney and Wiegel (2003) explain, one needs to clarify what sorts of mathematics one is talking about. Clearly, the issue is not about academic mathematics,1 since the underlined difficulties relate to school mathematics knowledge, and academic mathematics simply appears too far removed from the mathematics teaching practices of teachers.2 The issue therefore appears to concern school mathematics knowledge. This can appear counterintuitive since secondary teachers are considered specialists who know their subject well and thus do not require additional education in mathematics.3 But the situation is more subtle than a “know/don’t know” issue. What we see from these studies is that teachers do know a lot of/about mathematics. Indeed, they have had great success in their student careers and have been teaching mathematics for a number of years. Hence, even if it is reported in some studies that teachers have procedural knowledge or focus too 90 || Professional Development of Mathematics Teachers heavily on algebra, this mathematical knowledge is an important part of what they need to know in mathematics. This knowledge can be further developed, as with any knowledge, but does not need to be discarded or erased or seen negatively as “bad knowledge”; secondary teachers need not to “unlearn” what they know but to continue learning about mathematics . Additionally, secondary teachers, for the most part, have a good relationship with mathematics (academically and emotionally). As Cooney and Wiegel (2003) explain, they enjoy doing mathematics and investing themselves in its study. Mathematics is often seen as part of their lives and receives a privileged status: indeed, they decided to pursue a career in teaching mathematics! Thus, mathematics appears as a privileged point of entry...