Figures
1.1Proportion of students at each level of the emergent numeracy profile in 1999 for years 5 to 9 (n = 1315, 1318, 1467, 1484, & 1276 respectively).13
1.2A short task and scoring rubric used in the snmy project (20032006).16
1.3Proportion of students by laf zone and year level, 2004 (n = 3169).17
1.4Proportion of students by laf zone, rmf-p project (n = 1732).22
3.1A bar marked vertically into 3 equal parts, with two of the thirds (pink) marked into 1/5th.68
4.1Benchmark percents LT from the Math-Mapper 6-8 learning map.82
4.2The top half of a student report.84
4.3The heat maps (teacher reports) for the three constructs in the cluster finding key percent relationships. The levels are listed vertically, with increasing difficulty, and the students, based on performance, are ordered from left to right. Student identifiers can be toggled on or off for confidentiality.84
4.4Compound-bar display of proportion correct/incorrect for tested LT levels (L) of construct A, distinguished by district (D1, D2), class section type (regular, accelerated), and grade (6, 7). Each of the five sets of bars corresponds to the cumulative results from all class sections of indicated type. Error bars indicate 1 S.E.90
4.5Compound-bar display of proportion correct/incorrect for tested LT levels (L) of construct B. Information is displayed as in Figure 4.4.91
4.6Compound-bar display of proportion correct/incorrect for tested LT levels (L) of construct C. Information is displayed as in Figure 4.4.92
4.7Item 695, level 1, construct Percents as Amount per Hundred. Correct responses are indicated next to the [1] on right side.93
4.8Item 1294, level 4, construct A (Percent as Amounts per 100).93
4.9Item 698, level 5, construct B (Benchmark percents).94
4.10Item 1292, level 2, construct C (Percents as combinations of other percents).95
5.1Three items from the Algebra Tile Task (atilp).107
5.2Variable map for statistical reasoning items from MR1 and MR2 data (n = 1570).112
5.3Items addressing aspects of angles, gang1 and gang2.114
5.4Geometric reasoning items by difficulty with scoring Rubrics, based on MR1 data, February 2017 (n = 769).117
5.5Geometric reasoning items by difficulty with scoring Rubrics, based on MR1 & MR2 data, June 2017 (n = 1570).119
6.1Sample assessment task on balancing equations and associated rubrics.139
6.2Sample assessment task for function and associated rubrics.140
6.3Sample responses to ahab3.141
6.4Map of the responses to the algebra items following Rasch analysis.142
7.1Framework for developing geometric reasoning.161
7.2Reasoning items on visualising three-dimensional objects.170
7.3Examples of students reasoning on gnet4.172
7.4An activity contributing to student experiences across zones 25.175
8.1The lung disease problem (Batanero, Estepa, Godino, & Green, 1996).197
8.2Initial suggestions for the lung disease problem.198
8.3The importance of an argument.199
9.1Boxplot of the four derived factors by year level.215
Tables
1.1Emergent numeracy profile (Siemon, Virgona, & Corneille, 2001).12
1.2The elaborated laf for zone 3.19
1.3Alignment between snmy materials and masters (2013) design principles for a learning assessment system.24
2.1Goals of curriculum research (adapted from Clements, 2007).42
2.2Categories and phases of the curriculum research framework (crf) (adapted from Clements, 2007).43
3.1The three-part scheme inferred to underlie counting-all.64
3.2The 7-step, cyclic process that constitutes student-adaptive pedagogy.66
4.1Demographics for collaborating school districts.88
5.1Scoring rubrics for three items from the Algebra Tile Task (atilp).109
5.2Scoring Rubrics for gang1 and gang2 used in MR1.115
5.3Fit values for gang1 and gang2 at MR1.115
5.4Amended scoring rubrics for gang1 and gang2.116
5.5Fit values for gang1 and gang2 at MR2.116
5.6Scoring rubrics and rich description for Zone 1 of the learning progression for geometric reasoning.120
5.7Scoring rubrics and rich description for Zone 1 of the learning progression for geometric reasoning.121
6.1Initial hypothetical learning progression.135
6.2Zones in the learning progression for algebraic reasoning.143
6.3Example of teaching advice for a particular zone of the learning progression for algebraic reasoning.146
6.4Example of how mountain range challenge can be utilised across zones to support mixed ability teaching.148
7.1Hypothetical geometric learning progression.167
7.2Results for gnet3 and gnet4.171
7.3Geometric learning progression and broad descriptions of behaviours in each zone.173
8.1Question addressing variation in distribution.186
8.2Questions addressing variation in expectation and randomness, and variation in inference.187
8.3Overview of the statistical reasoning learning progression.189
8.4Distribution of students across zones by year level.190
8.5Descriptor and teaching advice for Zone 5.195
9.1Rotated factor matrix (varimax rotation).211
10.1Rotated factor matrix (varimax rotation).226

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