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Pupil interviews - Fractions (Research-based or theoretical models-…
Pupil interviews - Fractions
Pupil interviews methodology
Interview process
1 p145-146+150 (audio)
5 p5
Wait time
5 p13
Reliant on listening skills
1 p143+146
Chn may not think out loud
1 p149
Example questions/prompts to elicit understanding
5 p5+6+13
Fraction tasks
Fraction pairs - 5 p12
Cognitive demand levels of tasks
6 (HC) p345+346+348-349
10 p312 (relating to each fractions construct)
12 p22, 26
13 p80
Multiple group problems (division)
14 p85 + 89
15 (throughout)
Different representations of same fraction
17 p3
17 p9,10,11,12+14
Misleading features
18 p137
20 p141
21 p416 (see also p420)
23 p17-20
17 p13
Conclusion
Knowledge of chn's mathematical thinking improves effectiveness of teaching
1 p142+143
Combined with teachers' subject content knowledge
1 p142+143
2 p20-21
3 p25
5 p3
3 p1
Better than traditional written tests
5 p4
Identifies indiv differences and progress
5 p10
5 p13
Teaching is about listening as well as telling
3 p2
Disincentives
3 p2
3 p35
Combats negative associations
4 p8
Can combat rigid stereotypes/preconceptions of chn
3 p25
Research-based or theoretical models- GENERAL
Mathematical thinking
Varies by topic
1 p142
Continually evolving
1 p143
Is observable, coherent etc.
1 p143
Misconceptions
Intuitive rules theory
4 p3
Knowledge vs misconceptions
4 p4
Relational vs instructional knowledge
4 p5-6
Conceptual vs procedural knowledge
4 p6
13 p61-62
Stages towards reaching conceptual knowledge
13 p63
Algorithmic, formal & intuitive knowledge
4 p7
Knowing to act
4 p7
Defn of mathematical understanding
11 p127
13 p62
Research-based or theoretical models- FRACTIONS
Knowledge vs misconceptions
4 p4
Using untaught knowledge to problem solve
5 p12
Gap thinking
5 p12
21 p414+421
22 p129
Chn don't have enough life experience of fraction situations
14 p89
15 p64
19 p4-5
Fractions are a multi-faceted construct
10 p293-5 + 309-310
Part-whole
10 p296
12 p20-23
Equipartioning different shapes
12 p26
Equipartioning shapes that are already partioned
12 p27-28
Reconstitution
12 p28
12 p30
13 p64
Big halves, small halves
15 p49
Leftover strategy
15 p57-60+63
17 p10
21 p415
22 p129+134
Reference point strategy
15 p59
17 p10
21 p415
22 p129+134
17 p2
Ratio
10 p297
Operator
10 p298
17 p7
Quotient
10 p 299
12 p26-27
19 p5,8,10,11,17,22,26
Measure
10 p 299
11 p128
12 p29+30
13 p64
13 p64
15 p49+54+64
17 p4+6
19 p8-9
22 p128
More useful than decimals for relational reasoning
11 p127+129 + 141
Bi-dimensional (vs unidimensional decimals)
Visual representations, fractions notation and language
11 p143
12 p23
12 p32
14 p85
16 p5
17 p6+9
20 p153-155
22 p134
Confusing position terminology with fraction terminology
12 p31
Fraction equivalence
13 p65
15 p61
19 p8,9
Comparisons of fractions
13 p65
whole number dominance
15 p63
22 p130
Addition of fractions
13 p66
Procedural vs conceptual
13 p66-67 +74-78
Direct modelling
14 p86-87
Using fraction relationships
14 p86
Proportional reasoning
17 p4
19 p5+27
22 p134
Multiplication & division
17 p2
Rationale
Quiet achievers
5 p11
Fractions are difficult to learn
10 p 293
11 p128
12 p19
Success with fractions predicts future mathematical success
11 p129
Ethics
7
8