The Boiling Water Problem – Assessment on Functions

Boiling Water – 2 Cups – Full from Andrew Shauver on Vimeo.


Our transition to the common core has forced me to reconsider how I assess what student know and how much they understand.

A fairly standard content expectation from the Michigan Merit Curriculum might read, “Students will be able to identify what family a function belongs to and can analyze transformations to the parent function that will yield…” you get the idea.

A lot of questions come up in my mind when I think about assessing that standard. The first is how am I going to assess it? The second one is how can we make that knowledge useful to the students. The answer to the second question is the input, if the output is to be meaningful learning. The answer to the first question is the basis for how I design the situation that leads to the learning.

So, I submit for internet scrutiny the video above. I asked the following questions.

What is a possible independent variable? What would be the dependent variable? Do your choices create a function? Why or why not? If so, what family does your function best fit in? What would the parent function be? What transformation happened?

I found that there are ALL SORTS of misconceptions about variables, functions, parent functions, transformations.

I also found that the students are pretty good at crafting an argument using a formal math definition as support. They wrote pretty coherently as a group, although some were resistant to write with depth. That is nothing new, I’m afraid.

Ordinarily this type of thing would be an end of the unit project. I’m trying to use it as an exploration that is instructive and provides a chance for collaboration, flexibility, and individuality. Plus the fact that it serves as a formative assessment doesn’t hurt.


Feel free to load the comments with suggestions, constructive critiques, alternatives, and other ideas.


2 thoughts on “The Boiling Water Problem – Assessment on Functions

  1. Something tricky about all this is that to “identify essential variables” (per the request of the CCSS) students need to be presented with an environment rich with variables – both essential and inessential. But those inessential variables can’t fully overwhelm the essential or students won’t be able to identify them. This puts a large burden on the part of the task designer and, in your case and my case, the video producer. Your camera here isn’t focused on the temperature gauge and the light on it is dim, which will make it hard for students to identify it as essential and then to further identify which family it belongs to.

    This is all so much easier if we just give students a table of values, but there we’ve already identified too much. This is tough, satisfying work.

    • It is tough. If I had my druthers in this specific case, I would borrow a science lab for a day and have the students trying different situations.
      This type of inquiry goes better live and not on video. That’s how you really open a discussion on variables. Put the entire problem in their hands. Data collection, design, modeling, representations, what to repeat, on and on.

      But when video has to do, it is tough work to try to make a video that supports the learning properly, especially since I have proficiency with exactly zero video editing software. And I often won’t learn a video’s (or other created problem’s) shortcomings in the production until I unleash it onto a class.

      But I agree with you. Satisfying. It is work that I don’t often have to try very hard to convince myself to do. My students have learned to be patient. I get a sense that they appreciate the effort.

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