Source: Journal of Mathematics Teacher Education, 13(1):49–71, (February, 2010).
(Reviewed by the Portal Tam)
Although growing numbers of secondary school mathematics teachers and students use calculators to study graphs, they mainly rely on paper-and-pencil when manipulating algebraic symbols. However, the Computer Algebra Systems (CAS) on computers or handheld calculators create new possibilities for teaching and learning algebraic manipulation.
This study aimed to investigate the views of prospective teachers on the use of advanced calculators with CAS in algebra instruction.
The research questions of this study are:
• What are prospective teachers’ views of CAS in algebra instruction?
• What are prospective teachers’ views of the three possible ways of using CAS in algebra
instruction—black box, white box, and SMG?
• What kinds of roles do prospective teachers assign to black box, white box, and SMG?
Participants in this study were secondary prospective mathematics teachers at a university in Ankara, Turkey. Prospective teachers were enrolled in the newly reconstructed five-year teacher education program. Twenty-seven prospective teachers, 15 in their fourth-year (12 female, 3 male) and 12 in their fifth-year (10 female, 2 male), participated in this study.
The students in this study had no prior experience with CAS until the methods courses in their teacher education program. They experienced some graphing activities with the advanced calculators in their methods courses. However, they did not know about the CAS feature of the advanced calculators until this study. Their views were based on the experiences they had in their teacher education program.
Data collection methods
An open-ended questionnaire and group interviews revealed prospective teachers’ views and beliefs about when and why they prefer three possible uses of CAS— black box, white box, or Symbolic Math Guide (SMG).
The main results of this study demonstrated that 59% of the prospective teachers did not believe that advanced calculators would be beneficial in algebra instruction before the demonstration of the possible uses of CAS. However, after their brief experience with different uses of CAS, some participants reconsidered their beliefs. The prospective teachers mainly preferred the white box methods and especially SMG to the black box method. The participants suggested that while the black box method could be used after students mastered the skills, the general white box method and SMG could be used to teach symbolic manipulation.
The author suggests that prospective teachers should be provided with environments where they can experience and discuss these technologies in order to make informed decisions. As the participants in this study without knowing other possible uses of CAS, teachers could think negatively about the advanced calculators with CAS as a black box.
It is also crucial to note that this short experience influenced the participants’ views greatly on the possible instructional uses of CAS—nearly half of the participants reconsidered their view of CAS. This result emphasizes the importance of teacher education programs in producing teachers who are willing and able to use CAS effectively in their teaching.
The author also claims that helping prospective teachers to face their views and defend them in group interviews might help them to reconsider their views. This could be done through reflective experiences using something new (such as CAS) or reacting to something they have read.