Page 48 - Children’s mathematical development and learning needs in perspective of teachers’ use of dynamic math interviews

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Chapter 2
Teacher factors
Actual teaching behavior in mathematics lessons. The actual teaching behavior of the teachers in their mathematics lessons was measured using the International Comparative Analysis of Learning and Teaching (ICALT), an observation instrument (Van de Grift, 2007). The ICALT, consisting of seven scales, covers many aspects of teaching behavior and is not math-specific. For purposes of the present study, the instrument was therefore supplemented with an eighth scale specifically addressing the teaching of mathematics (see Appendix A). The ICALT itself involves 32 items addressing six aspects of teaching behavior ranging from lower order teaching behavior to higher order teaching behavior (Van der Lans et al., 2015, 2018): a) safe and stimulating learning climate, b) efficient classroom management, c) quality of instruction, d) activation of children, e) teaching of learning strategies, and f) differentiation/ adaptation of lesson content to meet children’s math learning needs. The seventh scale addresses children’s involvement. The eighth scale addressed math-specific teaching strategies using the following 8 items: a) informal manipulation, b) representations of real objects and situations, c) abstract mental representations (models and diagrams), d) abstract concepts/mental operations, e) connecting these four levels and using these appropriate to the goal of the lesson, pay attention to f) planning, g) solving processes, and h) metacognitive skills. All of the scales used in the present study were found to have reliable Cronbach’s alphas. The internal consistency of the ICALT has been found in the past to be good (α = .82). The internal consistency of the ICALT with the supplemental scales (ICALT+S) used in the present study was similarly found to be good (α = .85).
Mathematical knowledge for teaching. Teachers’ mathematical knowledge for teaching was self-assessed using a questionnaire specifically developed for the present study: the Teachers’ Sense of Mathematical Knowledge for Teaching Questionnaire (TSMKTQ; Kaskens et al., 2016; see Appendix B). Composed of three parts and 38 questions, the following are assessed: a) mathematical skill in the domains of numbers, number relations and operations, proportions and fractions, measurement and geometry (Subject Matter Knowledge); b) ability to follow and analyze children’s thinking including recognition