1 / 2017-03-03 10:41:55

A Prospective Teacher's Knowledges in Fraction Teaching

Fraction is a difficult concept for most of the students, and teachers’ knowledges are important factors to affect students’ mathematics learning. Thus, the issue of teachers’ knowledges in fraction teaching becomes more critical. It is also found that some prospective teachers are not sure how to appropriately interpret the mathematics textbook and design plan in teacher education programs. Therefore, the purpose of this study is to explore a prospective teacher’s knowledges in fraction teaching. Depaepe, Verschaffel, and Kelchtermans (2013) made a systematic review of the way PCK is conceptualized in mathematics educational research and found that even though most authors refer to Shulman (1986) when they define PCK, there is no consensus in the literature about the components covered by it. Even so, grasping teaching materials and promoting students’ learning are two main aspects in this study to explore a prospective teacher’s knowledges in fraction teaching.
The data of this study was collected from a prospective teacher, Priscilla; the method used is in-depth interview, and the interview problems include posing problems and interpreting textbook about some fraction units.
Here are some discoveries of this study. First, Priscilla’s design of main problems doesn’t always meet the teaching goals of textbook. For example, the textbook uses hands-on activities to teach equal-sharing concept, but Priscilla uses graphic representation first. The textbook offers many problems with different equal-partition graphics and hopes that students can find equivalent fractions through observing those graphics, but Priscilla’s problem posing uses purely mathematical symbols, like
, after one word problem. Second, when students can’t understand the meaning of the problems in textbook, Priscilla may help them by direct explanation and questioning, assisting after listening to their explanation of the problem meaning, and providing real life examples in relation to the problem. Third, when students meet difficulties in solving problems in textbook, she may help them by asking them to do actual operation, assisting the identification of fraction terms via living language and teaching tools, reviewing prior knowledge, and using graphic representation.

References
Depaepe, F., Verschaffel, L., & Kelchtermans, G. (2013). Pedagogical content knowledge: A systematic review of the way in which the concept has pervaded mathematics educational research. Teaching and Teacher Education, 34, 12–25.
Shulman, L. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14.