All About Models

This semester, I’m taking a course (CEP 902, for those of you in PRIME) called “Psychology of Learning School Subjects.”  I don’t think the following was a goal of the course, but I have come to think of this course as “All About Models,” in an interesting way. Let’s see if I can communicate why!

On the one hand, it seems (reasonably) that we read about models constructed by researchers to explain student learning in each broad topic area: writing, reading, mathematics, physics, science, and engineering. On the other hand, it seems as though in at least some of these areas that students create their own models as part of their learning.

What is a model?

Merriam-Webster says, “a usually small copy of something.” Well, that’s kind of close. But I’m really meaning to say a “scientific model” perhaps. American Heritage Science Dictionary says, “A systematic description of an object or phenomenon that shares important characteristics with the object or phenomenon. Scientific models can be material, visual, mathematical, or computational and are often used in the construction of scientific theories. See also hypothesis, theory.

Good. The latter definition is what I was looking for:

  • systematic
  • description (or representation? or simplification?)
  • “shares important characteristics with the object or phenomenon.”

I think that my model of definition is: a representation of a complex object or phenomenon that reduces the complexity in a way that focuses users’ attention on chosen aspects or features.

We use these types of models in everyday life. For example, maps are models. Depending on your goals, the “important characteristics” may change. Map designers make decisions about what features are important. Here are a few different examples of models / maps / representations of Washington, D.C.:

Can you think of the creator’s goals for each map? Which characteristics are important in each map? How does the focus help the viewer? Are the maps above valid “as maps”? Or should a map of Washington, D.C. always look like this:MapDC-05My point is: there is no “best” or “more correct” model for all time and in every circumstance – a model is always a simplification, which means the creator must always be thoughtful about their goals and how some characteristics support their goals.

Models of Student Learning

A question that keeps coming up in this course is: “Does this model describe every person’s learning? If not, how many models would we need to describe every person’s learning?” I’m not sure I understand the question fully. In my mind, no model can completely describe a person’s learning – because then it would not be a model but would be the thing itself. My perspective on creating models of students’ learning is not accurately describe every student, but as a useful way to think about learning as support for creating better learning opportunities.

Models and Scaffolds in Student Learning

In different subject areas, we have talked about ways students can simplify their task. For example, creating a template to structure your writing or creating an algorithm to structure your problem-solving. These scaffolds can support students in arriving at the finished essay or answer, but can also proceduralize the work. That is, a scaffold can support students but can also block their learning. At what point can the student begin to remove a scaffold? Or is it okay for them to continue using it forever?

Another way of simplifying a task (or reducing complexity) that might be scaffolding but might not be – I’m not sure – is use of models. I’m going to stretch the definition of “model” a little bit, but say that in most fields students can create models to support their learning. In math or science, we talk explicitly about modeling situations. In writing, I mean “model” as an outline for notes or for writing – a small, lightweight  representation of their ideas that can help organize their thoughts around the important characteristics, whatever those may be.

In any case, talking explicitly about how to think critically about those important characteristics should be important. Supporting students in understanding that it isn’t possible to create a model that accounts for every variable or idea can help students develop into more critical consumers or citizens who will ask: “This advertisement or article makes a particular claim and backs it up with data. What choices did they make in the characteristics to keep and the characteristics to lose?”


model. (n.d.). The American Heritage® Science Dictionary. Retrieved September 22, 2015, from website:


Choosing a retirement plan

When I started as an instructor at Minnesota State University, Mankato, I was told to choose between two retirement plans: a pension or an independent retirement account plan (IRAP). I chose the IRAP because I would only work there for 4 years. But, I wondered which I should choose and how would the two plans compare over time? How many years should I work for the pension to be a better choice? How many years would I have to live after retiring? (or does that matter?)

At the time, I remember (I think) that employee contribution for the IRAP was 4.5% on gross income and the university contributed 6.5%, which is amazing.

(Final Average Salary) x (1.9%) x (Years of Service) = monthly pension amount

So, after four years at about $40,000, I would have earned (40000)x(.019)x(4) = $3040 per month.  Okay, wait.  They give an example:

30*54000*(1.9%) = 2565.

But actually that is 25650. So, I’m guessing the formula really is:

(Final Average Salary) x (0.19%) x (Years of Service) = monthly pension amount

So, after four years at about $40,000, I would have earned (40000)x(.0019)x(4) = $304 per month. Huh.  Maybe I chose wrong after all (if this is even close to our formula)

What do you think? Should portability figure in or only the monetary amount? Should I have done the math?