Discussion of model-eliciting activities (MEAs)
1) Look at Departing on time (MEA) prior to discussion
2) What is the history of MEAs
a) Purpose of MEAs: mainly to research student thinking (pg 605) as well as teaching and
assessment (pg. 632)
b) Synonyms: You might also see MEAs referred to as thought revealing activities or case studies
3) What is a mathematical model? Page 611…third paragraph (continued on page 612)
a) What does it mean to mathematize? Page 593…last sentence of text
b) What does it mean to express, test, and revise and how does this process fit into mathematical
problem solving? Page 598…first full paragraph
c) What’s the value of doing MEAs (students get to actually do mathematics and perceive it as a
real discipline rather than a set of isolated tasks/rules). Dick Lesh provides a basketball analogy
for this description.
4) What are the components of a MEA?
a) Newspaper article
b) Warm-up or readiness questions
c) Data table, diagram, or other mathematical information
5) Are there any disclaimers of MEAs
a) These are not the only type of thought revealing activities that exist
b) These tasks are realistic, but authors of the activities are not intending to define real life
c) These tasks, though they have some connection to performance assessment, are not intended
to be performance assessment activities per se. Further, they are often used as an introduction
to a concept as opposed to a culminating activity/assessment.
d) MEAs are not to be mixed up with traditional conceptions of applied problem solving (pg. 604)
6) What design principles exist for MEAs?
a) Model construction principle: Simply stated, each MEA written must demand of the student that
a mathematical model is constructed to explain the mathematical phenomenon (sing) or
phenomena (pl). The developed model should have immediate utility and future utility
b) Reality principle (aka the meaningfulness principle): Each MEA should demand that students try
to make sense of a mathematical situation.
c) Self-assessment principle: Each MEA should have some component that enables students to
determine whether or not their response is logical. One question often posed to assess this
principle is, “Will students know when they’re finished with the problem?”
d) Construct documentation principle: Each MEA must demand that students document their
work. This documentation should closely detail their thinking (especially their mathematizing of
e) Construct shareability and reusability principle: Each MEA must have the construction of a
model for it to be an MEA. Moreover, the model should meet the demands of the immediate
problem, and as models go, should be able to be used in subsequent, similar mathematical
situations. Therefore each model should satisfy an immediate and long-range need.
f) Effective prototype principle: Each MEA should leave some residue (as Skemp, 1982 referred to
it) for future mathematical situations. The construct shareability and reusability principle
demanded that the model is transferrable to future situations. The effective prototype principle
demands that mathematical concepts learned may be applied to future, non-identical,
7) What questions exist about MEAs?
a) What role should teachers play when students are working on MEAs?
b) How can teachers afford to spend several class periods on a single problem solving situation?
c) How can students be expected to create mathematical models that took advanced
mathematicians several centuries to create?
8) Who is currently using MEAs?
a) University of Minnesota Engineering: http://www.tc.umn.edu/~catalst/materials
b) University of Minnesota Statistics: http://serc.carleton.edu/sp/library/mea/examples.html
c) Purdue University Engineering:
d) Purdue University Education:
e) Indiana University Education: http://crlt.indiana.edu/research/csk.html
9) What questions do you have?