Go to Collaborative Learning Go to FLAG Home Go to Search
Go to Learning Through Technology Go to Site Map
Go to Who We Are
Go to College Level One Home
Go to Introduction Go to Assessment Primer Go to Matching CATs to Goals Go to Classroom Assessment Techniques Go To Tools Go to Resources

Go to CATs overview
Go to Attitude survey
Go to ConcepTests
Go to Concept mapping
Go to Conceptual diagnostic tests
Go to Interviews
Go to Mathematical thinking
Go to Fault finding and fixing CAT
Go to Plausible estimation CAT
Go to Creating measures CAT
Go to Convincing and proving CAT
Go to Reasoning from evidence CAT
Go to Performance assessment
Go to Portfolios
Go to Scoring rubrics
Go to Student assessment of learning gains (SALG)
Go to Weekly reports

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

Go to previous page

Classroom Assessment Techniques
'Creating Measures' Tasks

(Screen 2 of 4)
Go to next page

"Creating Measures" tasks consist of a series of questions that require students formally and quantitatively to define a measure of some concept. The concepts are ones of which students are intuitively aware, but which they have probably never attempted to describe mathematically. For example, students are asked to consider how they would define and quantify such concepts as "
squareness," "sharpness," or "compactness." Usually, there are no formally correct and universally agreed-upon answers to such questions, but some definitions are clearly more useful than others. Students are required to not only come up with a measure of the concept, but also to evaluate how well that measure works as a mathematical description of a concept.

To offer one example, let us consider the problem of finding a measure for the "squareness" of a rectangle. One candidate might be: "the difference between the longest and shortest sides." This may seem sensible at first glance as it gives a measure of zero for squares and a larger measure as the difference between the two dimensions of the rectangle increases. One problem is, however, that the measure depends on the units used for measurement. A second related problem is that two mathematically similar rectangles will give a different value for the measure. Clearly a measure that does not depend upon the dimensions of the object would be better, such as "longest side/shortest side."

Example of "Creating Measures" Task

"Steep-ness" of Staircases
This problem gives you the chance to
  • criticize a given measure for the concept of 'steep-ness;'
  • invent your own ways of measuring this concept; and
  • examine the advantages and disadvantages of different methods.
Image showing 6 different sets of stairs with different sized steps.


Without measuring anything, put the above staircases in order of steep-ness.

  1. Someone has suggested that a good measure of 'steep-ness' is to calculate the difference Height of step - length of step for each staircase. Use this definition to put the staircases in order of steep-ness. Show all your work.
  2. Using your results, give reasons why Height of step - length of step may not be a suitable measure for "steep-ness".
  3. Invent a better way of measuring "steep-ness". Describe your method carefully.
  4. Place the staircases in order of "steep-ness" using your method. Show all your work.
  5. Do you think your measure is a good way of measuring "steep-ness"? Explain your reasoning carefully.
  6. Describe a different way of measuring "steep-ness".
  7. Compare the two methods you invented. Which is best? Why?

Thus "creating a measure" in most cases involves combining collections of measurements in new ways and considering the dimensionality of the result.

Assessment Purposes
There are three assessment purposes:

"Creating Measures" tasks are meant to measure the students' ability to "mathematize" a concept, or their ability to define a numerical measure of a concept, as well as evaluate the usefulness of that measure. This is important in that students can see that measures used to model phenomena in science are socially agreed-upon notions that exist primarily because of their usefulness. For most tasks, little mathematical technique is required and so these tasks do not assess algebraic techniques.

Go to previous page Go to next page

Tell me more about this technique:

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

Got to the top of the page.

Introduction || Assessment Primer || Matching Goals to CATs || CATs || Tools || Resources

Search || Who We Are || Site Map || Meet the CL-1 Team || WebMaster || Copyright || Download
College Level One (CL-1) Home || Collaborative Learning || FLAG || Learning Through Technology || NISE