Page 162 - Children’s mathematical development and learning needs in perspective of teachers’ use of dynamic math interviews

Chapter 5
Table 1 Aspects of Dynamic Math Interviews in Relation to Teachers’ Mathematics Teaching Behavior and Children’s Mathematical Development
T
Mathematics- teaching behavior
1.
2.
3.
4.
5.
6.
7.
8.
T1 T2
1 2.96 3.44
2 3.47 3.67
3 2.86 3.40
4 3.32 3.68
5 3.52 3.68
6 3.31 2.95
7 2.46 2.97
8 2.91 3.31
9 2.85 2.97
10 2.16 3.38
11 3.15 3.48
12 3.57 3.70
13 3.63 3.75
14 3.44 3.30
15 3.33 3.70
16 2.90 2.83
17 2.81 2.73
18 2.96 2.68
19 3.22 3.54
% open %
54.84 19.36 54.00 42.00 59.02 14.06 67.44 2.33 87.50 21.88 56.76 25.23 66.07 23.21 72.09 21.28 64.29 20.00 80.65 40.32 71.74 28.28 75.38 14.29 54.70 54.70 87.32 32.39 50.00 50.00 75.00 6.25 60.20 17.20 71.90 46.15 57.45 25.93
%
47.31 38.00 31.15 48.84 31.25 33.33 35.71 21.11 35.71 12.90 32.61 25.00 15.39 29.58 20.00 45.83 23.66 7.69 51.06
%
10.75 8.00 36.07
20.93 18.75 22.52 23.21 11.70 22.86 16.13 14.49
9.52
8.55 26.76 0.00 33.30 21.51 15.39
8.51
%
>4 times 1-4 1-4
8.06 b 10.00 a,b 1.64 b 11.63 b,e
26.56 - 17.12 a,b,c
3.57 b 37.87 a,b 8.57 b
22.58 b 21.74 a,b 34.52 a,b,e 10.26 b 5.63 b 33.33 b 0.00 b
9.68 a,b,c 10.26 d
0.00 b,c
3 3 4 4 3 4 4 4 4 4 2 3 1 2 3 4 3 4 3 4 4 4 4 4 2 2 3 3 4 4 1 2 3 4 3 4 2 3
Note: T = Teachers, C = Children ; 1: Ratio of open to closed questions used by teacher; 2-5: Proportion of total number of questions with focus on: 2) child’s math experiences, beliefs, and emotions; 3) child’s thinking and problem-solving processes; 4) checking that child knows correct answer; or 5) identification of child’s math needs by actively eliciting child’s voice; 6: Most frequently provided support; 7: Adequacy of responding; 8: Providing a safe and stimulating climate; 9: Teacher summary of child’s educational needs; 10: Scope of the dynamic math interview.
Dynamic math interview 2 stands out in a positive way. This teacher showed a good level of actual mathematics teaching behavior to start with (> 3) with increased scores from T1 to T2. More open than closed questions were asked. There was variation across questions concerned with child’s math experiences, beliefs, and emotions (42%); questions focused on child’s mathematical thinking and problem-solving processes (38%); questions used to check that the child knows the right answer (8%); and questions showing the teacher to involve the child, give the child a voice (10%). This teacher clearly provided support during the dynamic math interview (four times by stimulating the child to write down the steps in thinking, six times by giving verbal support, and two times by clearly structuring the task). Responsiveness, Climate, and Summarizing child’s needs also received high ratings, and the interview was judged to have a wide scope (a). The child’s mathematical development increased from 187 (T1) to 216 (T2) in the experimental condition for math problem-solving and from 69 (T1) to 134 (T2) for arithmetic fluency. Furthermore, the child’s math self-concept and self-efficacy clearly increased and their math anxiety clearly decreased from 27 (T1) to 12 (T2). Among the identified math learning needs were the following: step by step
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