Classroom Assessment Techniques 'Reasoning from Evidence' Tasks (Screen 4 of 4)

Variations
The tasks included in this site can be downloaded and used without modification. If you choose to develop your own 'Reasoning from Data' task, you can follow the pattern used in these tools.

Where unsorted data is to be analyzed, simply collect together the raw results from an experimental study in a relevant field, and present these to your students with some background discussion of the reasons why the data were collected and the method of collection. Then allow the students time to develop their own ways of analyzing the data.

Analysis
Student work can be measured against the following criteria:

• can students select appropriate variables for sorting a data set?

• can students select appropriate methods for analyzing a data set?

• can students construct, read and interpret graphical representations of a data set? and,

• can students draw sensible conclusions from a data set?

This generic scoring rubric may be modified and adapted for specific tasks.

Category of performance	Typical response
The student needs significant instruction	Student can begin to organize the data and makes a limited analysis using a single statistic. The student may not have attempted to represent the data in tables or graphs. Only one variable is typically considered.
The student needs some instruction	Student has made an attempt to organize the data and has attempted to represent it and draw conclusions from it. Again, the response may show that only one variable has been considered. The representation used may be inappropriate and the conclusions invalid.
The student's work needs to be revised	Student has selected appropriate variables and methods for sorting, analyzing and representing the data. There may be errors in the calculations and graphs. The student attempts to draw conclusions from the data but these may be flawed.
The student's work meets the essential demands of the task	Student has selected appropriate variables and methods for sorting, analyzing and representing the data. The student has used a variety of analytic tools to interrogate the data set. The conclusions/recommendations follow from and are supported by their analysis of the data

The example below shows how the generic rubric can be modified to fit the 'Emergency 911! Bay City' task:

Category of performance	Typical response
The student needs significant instruction	Students calculate a single statistic (e.g., mean or median response time). They recommend one ambulance service over the other on the basis of a comparison of this single statistic even though the mean difference is only .2 minute, not significant for making a policy recommendation. The analysis of the data ignores all other variables except response time.
The student needs some instruction	Students may calculate measures of center and explore the data with other kinds of analysis (e.g., box plots, stem and leaf plots) but they consider only a single variable - the response times of the two ambulance services. They demonstrate some ability to use their statistical "toolkit" but the analysis is not connected to the real-world context of the problem and the argument is weak.
The student's work needs to be revised	Students select appropriate variables for analyzing the data (e.g., response time in relation to time of call), make appropriate calculations, use appropriate graphical representations, and make a reasonable recommendation based on their analysis. There may be errors in the calculations and in the graphs. However, students do not fully interrogate the data set, thereby not ruling out other possible salient relationships (e.g., response time in relation to day of the call). The recommendations follow from the analysis but the report may lack clarity and thoroughness.
The student's work meets the essential demands of the task	Students select appropriate variables for sorting, analyzing and representing the data. Students consider a number of relationships and use a variety of analytic tools to fully interrogate the data set. Their recommendations follow from and are supported by their analysis of the data.

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Introduction
Description, Purpose, and Limits
Goals, Use, and Instructions
Variations and Analysis
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Tools

Mathematical Thinking CATs || Fault Finding and Fixing || Plausible Estimation
Creating Measures || Convincing and Proving || Reasoning from Evidence