Evaluation of teacher candidates' knowledge about vectors

In this study, level of understanding and misconceptions of math teacher candidates were revealed on concepts of vector quantities, vector addition, subtraction, scalar and vector product. Accordingly, only 12.12% of the teacher candidates were able to fully express vectors equal in magnitudes. We found that a significant proportion of math teacher candidates had serious conceptual confusion related to the representation of vector magnitude for the first question. This problem was obtained from Nguyen & Meltzer (2003). They found that 63%-87% of students were able to answer the problem correctly. It can be decided that the reason of serious difference is due to the fact that the representation of vector magnitude is given with brackets in the question by Nguyen & Meltzer (2003). For the question about vector addition, teacher candidates graphically opted addition through the triangle law. It was generally observed with misconceptions in partial understanding that students had difficulties while identifying resultant vector, and either reverse-identifying or not even identifying the resultant vector direction. Küçüközer (2009) reports that 44% of students from the programme of primary school teacher education give a correct response to vector addition question. This result is smaller than the 77.27% correct response in our study. Another comparison we may make is to the results reported by Küçüközer on the alternative conceptions involving vector addition. Küçüközer emphasize that 25% of students has alternative conceptions, while the responses of math teacher candidates on misunderstanding level were 7.58% for this paper. For the question regarding vector subtraction, teacher candidates provided correct answers with the rate of 65.15%. It was also observed that the success rate of 77.27% by the teacher candidates in two-dimensional vector addition was higher when compared to the results of studies by Flores et al. (2004), Knight (1995), Küçüközer (2009) and Nguyen & Meltzer (2003). For male teacher candidates, the success rates in vector properties with full understanding are lower than female teacher candidates.It can be said that the results are in accordance with some studies (Flores et al., 2004; Knight, 1995; Küçüközer, 2009; Nguyen & Meltzer, 2003).

In this study, it was expected from participants to assign the results the scalar and vector product through three open-ended questions designed by researchers. Zavala & Barniol designed different opened-ended questions to investigate the difficulties on the calculation and misconceptions in the interpretation of the dot and cross products. In addition, we investigated both knowledge level and gender factor on these two products. As a result, it was observed that the mathematics teacher candidates showed a little success in vector and scalar products (1.51% and 6.06%, respectively). The success rate of math teacher candidates in this study is observed to be significantly lower when compared to the study about vector products conducted by Zavala & Barniol (2010). Female teacher candidates have more misconceptions with dot and vector products than male teacher candidates, but they have smaller rate with non-encodable or unanswered. Teaching techniques and educational materials should be developed to eliminate teacher candidates' failure in vector properties and operations and a better understanding of the concept.