Assessment of Mathematical Competencies and Epistemic Cognition of Preservice Teachers

Abstract

Assessment in higher education requires multifaceted instruments to capture competence structures and development. The construction of a competence model of preservice mathematics teachers’ mathematical abilities and epistemic beliefs allows for comparing different groups at different stages of their studies. We investigated 1st and 4th semester students with respect to their epistemic beliefs on the certainty of mathematical knowledge (assessed by both denotative and connotative judgments) and their mathematical abilities (defined as critical thinking with respect to mathematical problem situations). We show that students’ beliefs change during the first four semesters, and that the level of critical thinking does not depend on belief orientation but goes along with the level of sophistication of the epistemic judgments uttered by the students.

Inductive and deductive justification of knowledge: epistemological beliefs and critical thinking at the beginning of studying mathematics

“…Blömeke, Zlatkin-Troitschanskaia, Kuhn, & Fege, 2013;Baumert & Kunter, 2013), this study focuses not on only one cognitive dimension, that is, beliefs, but also on a second cognitive dimension, that is, an aspect of mathematical ability. We do not measure mathematical ability in terms of assessing success of attending university courses; instead, the use of students' knowledge is captured by drawing on the concept of critical thinking (CT) (Rott, Leuders, & Stahl, 2015).…”

“…In this model, CT is identified within the reflective mind; persons think critically when they engage in hypothetical thinking or when autonomous and algorithmic processes are checked and, if necessary, overridden (Stanovich & Stanovich, 2010)-which fits Jablonka's definition of CT as thinking and reasoning skills, including a disposition for using them. Therefore, we define CT in mathematics as those processes that consciously regulate the algorithmic use of mathematical procedures (Rott et al, 2015).…”

“…Finding correct solutions of such tasks can help identify the disposition of thinking critically. We used this idea to construct a test for mathematical CT (MCT), arguing that such an assessment should reflect discipline-specific processes without requiring higher level mathematics (Rott et al, 2015). For this test, we adapted items from Stanovich, from Frederick (2005) who explicitly mentions the "mathematical content" (Frederick, 2005, p. 37) In previous studies with PST (Rott et al, 2015, Rott & Leuders, 2016a), this MCT test was able to differentiate between different programs of study: the more demanding the mathematics part of the program of studies, the greater the mean scores in the MCT test (PST for upper secondary school scored significantly higher than for lower secondary and primary schools).…”

“…We used this idea to construct a test for mathematical CT (MCT), arguing that such an assessment should reflect discipline-specific processes without requiring higher level mathematics (Rott et al, 2015). For this test, we adapted items from Stanovich, from Frederick (2005) who explicitly mentions the "mathematical content" (Frederick, 2005, p. 37) In previous studies with PST (Rott et al, 2015, Rott & Leuders, 2016a), this MCT test was able to differentiate between different programs of study: the more demanding the mathematics part of the program of studies, the greater the mean scores in the MCT test (PST for upper secondary school scored significantly higher than for lower secondary and primary schools). Additionally, this test supported the differentiation of MEB in position and argumentation by showing that belief position is not correlated to MCT, whereas belief argumentation is significantly positively correlated to MCT (i.e., students who argue sophisticatedly have greater scores in the MCT test; Rott et al, 2015;Rott & Leuders, 2016a).…”

Relevant Content for a Scientific Collaboration in Mathematics and Physics Education Research - A Comparative Content Analysis of Handbooks and Conference Proceedings in Germany and Vietnam

“…Mathematics education in Germany (GM): In mathematics didactics, subject-specific views on mathematics are increasingly being investigated in open questionnaire studies (Rott et al, 2015). Grigutsch et al (1998) were able to identify four factors in the attitude of mathematics teachers towards mathematics in a closed questionnaire format.…”