Constructs
Data Modeling supports the growth of statistical reasoning by engaging middle school students in the construction of data, the invention of statistics, and the development of models of chance, all of which ground inference about data. Construct maps portray conceptual stepping-stones in statistical reasoning, organized by forms of reasoning, such as Conceptions of Statistics and Modeling Variability. Seven curriculum units are tools to support learning. Each unit features classroom activities, formative assessments, and related resources, including teacher-designed extensions to the curriculum units.
Theory of Measurement
1 Identify the object/event to be measured
2 Identify and characterize the attribute of the object to be measured. Direct comparison of attributes.
3 Explain/ Justify/ Demonstrate use of particular properties of a unit of measure.
4 Consider properties of unit in relation to goals of measurement.
5 Coordinate units to constitute a scale.
6 Predict the effects of changes in unit on measure or on scale.
7 Use theory of measurement to solve novel problems.
Data Displays
1 Create or interpret data displays without relating to the goals of the inquiry.
2 Interpret and/or produce data displays as collections of individual cases.
3 Notice or construct groups of similar values.
4 Recognize or apply scale properties to the data.
5 Consider the data in aggregate when interpreting or creating displays.
6 Integrate case with aggregate perspectives.
Meta-Repr. Competence
1 Emerging representational competencies.
2 Elementary representational competencies.
3 Articulate how features of display reveal something about the structure of the data.
4 Simultaneously consider what displays show and hide about the structure of the data.
5 Evaluate trade-offs within or among displays in relation to a particular claim.
Conceptions of Statistics
1 Describe characteristics of distribution informally.
2 Calculate statistics.
3 Consider statistics as measures of qualities of a sample distribution.
4 Consider statistics as measures of qualities of a sample distribution.
Chance
1 Hold an informal view of chance.
2 Develop the concept of trial.
3 Quantify chance as probability and relate it to the structure of a simple event.
4 Empirically examine the relationship between observations and all possible outcomes of repeated events.
5 Develop sample space for aggregate events.
6 Coordinate sample space, probability, and relative frequency for aggregate events.
Modeling of Variability
1 Identify sources of variability.
2 Informally describe the contribution of one or more sources of variability to variability observed in the system.
3 Use a chance device to represent a source of variability or the total variability of the system.
4 Develop emergent models of variability.
5 Judge model fit in light of variability across repeated simulation with the same model.
Informal Inference
1 Base reasoning on personal experience or belief instead of the data.
2 Believe that samples predict but use literal copy as the basis of prediction.
3 Particular cases or values, including sample statistics, guide inference without reference to the likely variability of these values.
4 Make inferences based on emerging understanding of distributional characteristics; expect the shape of the data to remain relatively stable.
5 Base reasoning on regions of distribution that are quantified via proportion or percentage.
6 Consider data in one observation set to comprise a sample distributionally related to other samples or a population.
7 Coordinate ideas about sample-to-sample stability and variation to reason about samples as representing sets from populations.