Page 233 - Children’s mathematical development and learning needs in perspective of teachers’ use of dynamic math interviews

aforementioned suggestions for the support that teachers can provide. Some of the suggestions have been developed by Gal’perin (1978) on the basis of Vygotksy’s action theory and thus entail four levels of action: 1. informal mathematics and informal procedures; 2: representation of concrete mathematical actions and situations; 3: representation of abstract models; 4: formal mathematical operations. Other suggestions for supporting children are: the clear structuring of problems/ tasks, giving verbal hints, reducing complexity, and modelling (Van Luit, 2019). Most important is that the support be appropriate and within the child’s so-called zone of proximal development.
7. Adequate responding. When a teacher responds to what a child says or does, they must do this in a manner which allows the child to take advantage of their response (Empson and Jacobs, 2008; Lee and Johnston-Wilder, 2013). This requires extensive mathematical knowledge for teaching (e.g. Hill et al., 2008). Adequate responding requires: insight into possible misunderstandings, provision of not only clear but also complete support, correct interpret of children’s mathematical statements, determination of appropriate support and effective timing of the support. On the basis of this information, adequacy of responding can be assigned a score of 1 (= to a very small extent) to 4 (= to a very large extent).
8. Creation of safe and stimulating climate. Particularly for the conduct of a productive dynamic math interview, several conditions must be met: creation of a sufficiently warm and relaxed atmosphere, showing of respect, starting with a mathematical problem on which the child is likely to succeed, encouraging verbalisations, sincerity, and supportive remarks (Delfos, 2001; Ginsburg, 1997). Tell me everything you can about what you are thinking. The correctness of the answer does not matter to me. I want to know how you are trying to solve the problem. This of the dynamic math interview is assigned a score between 1 (= to a very small extent) and 4 (= to a very large extent).
9. Teacher summary of math learning needs. When the teacher succinctly reproduces what lies at the core of the child’s needs, using the child’s own words, this shows that the teacher has been listening carefully. It also allows the teacher to check their understanding of the child’s math learning needs and goals. Co-responsibility on the parts of the teacher and the child is also fostered (Bannink, 2010; Delfos, 2001). Summary of math learning needs assigned a score of 0 (= not) to 1 (= to a very small extent) to 4 (= to a very large extent).
10. Scope of the dynamic math interview. A beneficial dynamic math interview must address various aspects of a child’s mathematical development; the child’s thinking and problem-solving abilities; the child’s math experiences, beliefs, and emotions; and active involvement of the child in the identification what is needed for successful mathematical development (e.g., Black et al., 2004; Delfos, 2001; Ginsburg, 1997). We distinguished five types of scope, with the widest being most preferred. A teacher can focus on the child’s mathematical thinking and problem-solving; the child’s math experiences, beliefs, and emotions; and actively involving the child in the identification of their math learning needs (a). The teacher can focus on the child’s mathematics achievement and the child’s math experiences, beliefs, and emotions (b). The teacher can focus on the child’s math experiences, beliefs, and emotions and the active involvement of the child in identifying their math learning needs (with no attention to mathematics achievement) (c). The teacher can focus on child’s mathematics achievement and on active involvement of the child in identifying their math learning needs (with no attention to math experiences, beliefs, and emotions) (d). And finally, the teacher can focus solely on mathematics achievement (e).
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