Page 156 - Children’s mathematical development and learning needs in perspective of teachers’ use of dynamic math interviews

Chapter 5
5. Questions to identify math learning needs by actively eliciting ‘student’s voice’. By posing questions with a solution-focused character the teacher can help the child begin moving towards solutions and future regarding mathematics learning. Have you ever had great math help? What did the person who gave you that do? What do you need to reach your next math learning goal? are examples of questions that elicit student’s voice. Also increasing waiting time after posing a question can maximise the chances of gaining insight into the child’s own thinking, the child’s ideas, the promotion of commitment, and increased ownership. The percentage of the total number of questions posed is counted and should be at least 10% for the dynamic math interview to be judged adequate.
6. Support given. The teacher can provide support during a dynamic math interview. We distinguished: a) stimulating the child to write down steps in thinking, b) verbal support (e.g., hints), c) verbal support provided by notes by the teacher, d) material support (e.g., manipulate with imitation money), e) use of concrete representations of abstract models, f ) use of representations of concrete mathematical actions and situations, g) clear structuring of problem/task, h) reduction of complexity, i) demonstration, and j) modelling. Support provided 4 times or more is indicated as most frequently provided support. Most important is that the support be appropriate.
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. This requires extensive mathematical knowledge. Adequate responding requires: insight into possible misunderstandings, provision of not only clear but also complete support, correct interpretation of child’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 between 1 (= to a very small extent) and 4 (= to a very large extent), with a score > 3 indicating adequacy.
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. This aspect of the dynamic math interview is assigned a score between 1 (= to a very small extent) and 4 (= to a very large extent), with a score > 3 indicating adequacy.
9. Teacher summary of educational 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 child is also fostered. Summary of math learning needs assigned a score of 0 (= not) or between 1 (= to a very small extent) and 4 (= to a very large extent), with a score > 3 indicating adequacy.
10. Scope of the dynamic math interview. A beneficial dynamic math interview must address various aspects of a child’s mathematical development: thinking and problem-solving abilities; math-related experiences, beliefs, and emotions; and active involvement in the identification what they need for successful mathematics achievement. We distinguished five types of dynamic math interview scope, with the widest (a) being most preferred: a) teacher focus on child’s mathematical thinking and problem-solving; math experiences, beliefs, and emotions; and active involvement in identification of needs; b) teacher focus on mathematics achievement; math experiences, beliefs, and emotions; c) teacher focus on math experiences, beliefs, and emotions; active involvement in identification of needs; d) teacher focus on mathematics achievement; active involvement in identification of needs; and e) focus solely on mathematics achievement.
Figure 2 Analytic Framework 154