Knowledge Quartet’s Unit of Contingency in the Light of Mathematics Content Knowledge

The purpose of this study is to introduce the Contingency unit of Knowledge Quartet, which is a framework used in assessing mathematics student teachers’ subject matter knowledge and pedagogical content knowledge, address its significance and demonstrate examples from its reflections in mathematics lessons. The study initially covers the type of knowledge that teachers should possess and Knowledge Quartet, which enables examining and assessing subject matter knowledge and pedagogical knowledge together. Next, general information was given regarding knowledge units of this model and Contingency unit was detail explained. Finally, the importance of Contingency was mentioned and some examples in classroom setting were discussed. The Knowledge Quartet, which is the model that ensures joint evaluation and development of subject matter knowledge and pedagogical content knowledge of mathematics student teachers consists of the four knowledge units - Foundation, Transformation, Connection and Contingency - and codes affiliated to these knowledge units (Rowland, Turner, Thwaites, Huckstep, 2009). The Contingency, being the focal point of this study, deals with potential events that are almost impossible to predict, which could occur in a class during the learning period, and therefore, the teacher acquires a skill to think for another person during this process (Rowland, Huckstep, Thwaites, 2005). The codes of Contingency are defined as (a) responding to students' ideas, (b) deviation from agenda, (c) teacher insight, and (d) responding to the (un)availability of tools and resources (www.knowledgequartet.org). The fact that mathematics student teachers, who do not have sufficient opportunities to acquire practical experience in the class, will face unanticipated events and that such events would prevail during their first years of education draws to the conclusion that more attention should be given to the Contingency. Sleep and Ball (2009) draw attention to the importance of responding to students' questions and Ball (2003) draws attention to the importance of organizing the in-class discussion process and evaluating the verbal and written responses of students. Schoenfeld (2005) emphasizes the need for the teachers to review their goals at the moment of occurrence of an unanticipated event in the class. It is thought that as mathematics teachers acquire experience, their approach to unanticipated events will become more professional and their reactions will become more positive. The fact that a teacher needs to make an average of 500 decisions during one day spent at school and face situations that require making difficult choices during the decision stage (Doyle, 1986) uncovers the need of providing the teachers and, especially, student teachers with education in regard to possible situations they could encounter. Kula (2011) indicates that certain student teachers are able to overcome certain contingencies during their education, while having troubles with other situations. Therefore, the importance of providing student teachers with knowledge related to contingencies that could be encountered in the class environment is obvious. In this regard, it is thought that identifying the pre-planned situations that could be encountered by mathematics student teachers with no sufficient experience and defining the approach exhibited towards such contingencies would be beneficial in teacher training education. This study will incorporate examples of contingency moments occurring in real class environments and reactions exhibited towards such contingencies. It is thought that through this study, awareness of mathematics student teachers can be made ensured with regards to situations that teachers may encounter and that are almost impossible to plan in advance.