Resumen de Pre-service mathematics teachers’ knowledge of functions: a mixed methods sequential explanatory study
Edgar John Sintema
It is common knowledge that teachers cannot teach students and help them learn and comprehend concepts they themselves do not understand. Thus, the purpose of this mixed methods sequential explanatory study was to examine knowledge held by pre-service secondary mathematics teachers in the topic of functions. The study attempted to characterize the depth of their subject-matter and pedagogical content knowledge of the concept of a function. In the first phase (quantitative) of the study, the investigation focused on categorizing pre-service teachers based on their level of knowledge of the concept of a function. In particular, the grouping was based on their Mathematical Pedagogical Content Knowledge perceptions, Common Content Knowledge, Specialized Content Knowledge, and Knowledge of Content and Students related to their knowledge of the concept of a function.
To accomplish the first phase of the study, data were collected using two surveys: a functions survey and the pedagogical content knowedge survey (N = 150). A two-step cluster analysis procedure was performed to categorize participants into groups based on the common content knowledge, specialized content knowledge, and knowledge of content and students. This technique was chosen because of its potential effectiveness in the context of this study to group participants based on their knowledge features provided by data from the surveys. Pre-service teachers‟ responses to survey items were also analysed using descriptive statistics for each cluster. A one-way multivariate analysis of variance was also performed to compare participants‟ knowledge between the two clusters. A follow-up discriminant function analysis identified one variable which best predicted the group membership: common content knowledge.
In the second phase (qualitative), three cases were selected, two from Cluster 1 and one from Cluster 2 using a typical response and maximum variation principle for in-depth examination. Data for this phase were collected from multiple sources: Vignettes, functions survey, semi-structured interviews, lesson plans and the classroom teaching activity. Data were analysed for each case and across cases for an in-depth understanding of participants‟ knowledge of the concept of a function.
The integration of results from the quantitative and qualitative phases was done during the discussion and interpretation stage of the entire outcome of the investigation based on the findings of the two phases, it was concluded that pre-service teachers who participated in this study had insufficient knowledge of the concept of a function. Policy implications were suggested for the Ministriy of General Education and that of Higher Education.
