Page 153 - Children’s mathematical development and learning needs in perspective of teachers’ use of dynamic math interviews

Dynamic math interviews to identify children’s math learning needs
lessons (7 scales). The first six observational scales address less complex to more complex teaching behaviors: providing a safe and stimulating learning climate; efficient classroom management; clarity of instruction; activating learning; teaching of learning strategies, and differentiation and adaptation of lesson. The seventh scale assesses children’s involvement. Given that the ICALT is not math-specific, a supplemental eighth scale (S) for mathematics teaching strategies in particular was created (see Appendix A).
The eight items for the math-specific scale were developed by the first author in consultation with the co-authors for purposes of the present study. The items were based upon the levels of action as identified by Gal’perin (1978) and the model of problem-solving model of Polya (1957): 1) informal manipulation, 2) depiction of concrete mathematical actions and situations, 3) depiction of abstract models and diagrams, and 4) formal/abstract mathematical operations, 5) understand the problem and making connections between the previous four levels and using these connections to support lesson goals, 6) devise a plan, 7) carry out the plan/problem-solving process, and 8) check and interpret (see Appendix A). The internal consistency of the 8 scales considered together was good (α > 0.89). This was also the case for the individual scales (α > 0.85). The scoring for each of the 40 observational items was done along a 4-point Likert scale ranging from 1 (= predominantly weak) to 4 (= predominantly strong) and conducted by two independent mathematics teaching experts (the first author and a second observer, who were both trained and certified to use the ICALT). The inter-rater reliability was found to be good (α = 0.86).
Children’s mathematics achievement, beliefs, and emotions
Mathematical problem-solving. The first measure of mathematics achievement consisted of the criterion-based standardized Dutch national tests commonly administered at the middle and end of each school year to monitor student progress (Cito; Janssen et al., 2005). The tests present mathematical problems in variety of manners from several domains: using only mathematical notation or various combinations of text, pictures, and mathematical notation. The internal reliability in the present study was good (year 1 α = 0.87; year 2 α = 0.81).
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