Prospective Mathematics Teachers’ Use of the Symbolic Manipulation Features of a CAS in their Lesson Planning
AbstractAlthough secondary mathematics teachers in the U.S. have been hesitant to make use of the symbolic manipulation features of a computer algebra system (CAS-S) (Braswell et al., 2001) we may now be on the cusp of a shift in teachers’ attitudes towards and consequently their use of this technology. Recently, three secondary mathematics textbooks have become available for U.S. teachers that incorporate CAS-S to varying degrees (Cuoco, 2007; Fey & Hirsch, 2007; Usiskin, 2007). This study had three goals. First, it used a research-based analytical framework (Davis, under review) to examine the use of CAS-S by curriculum developers in one lesson appearing within these three textbooks. Second, the framework was used to analyze the use of CAS-S by ten prospective secondary mathematics teachers (PST) in their lesson plans based upon these textbooks. Third, PST also justified CAS-S in their lesson plans and these explanations were categorized using a combination of open coding and in-vivo coding methods (Strauss & Corbin, 1998) and used as a window into their beliefs about how and when this technology should be used by students.
In the first lesson, textbook developers intended to provide students with the opportunities to solve equations involving quadratic functions using tables, graphs, and CAS-S. In the second lesson, textbook developers asked students to use CAS-S to explore the simplification of symbolic expressions. The majority of the PST followed the textbook developers’ intended use of CAS-S. The textbook developers in the last lesson did not explicitly advocate CAS-S use as students learned how to find the magnitude and direction of complex numbers using paper-and-pencil procedures. In this lesson, the majority of PST were willing to explicitly ask students to use the technology. Across all three lessons PST were willing to incorporate equal to higher levels of CAS-S than the textbook authors. This suggests that the incorporation of this technology in secondary mathematics textbooks has the potential to increase the use of CAS-S by teachers in classrooms.
A theme appearing in one PST’s (Chris) lesson plan was the importance of the strategic use of tools. He saw the CAS-S as a representation on par with a table and graph and wanted students to reflect on the strengths and weaknesses of each of these tools when solving mathematical problems. In the last lesson, Chris was much more concerned that students practice mathematical procedures by hand as this helped them to better understand procedures. Nonetheless, Chris did allow students to use CAS-S when problems involved investigating mathematical ideas. Occasionally, he also asked students to reflect on the pros and cons associated with the use of CAS-S technology. The implications of these results for university level technology courses for prospective teachers will be discussed.