SBG – Assessments Based on Cognitive Principles

1. SBG assessment and reading

Whether this is a general phenomenon or it applies only to our school I don’t know, but my experience is that students do not like to read. At the lower levels, this means students have trouble with (and sometimes do not even attempt to solve) word problems. At the higher levels, the disinclination to read results in relying exclusively on class notes and on examples worked out in class.

Because I agree wholeheartedly with Willingham’s idea that one of the best ways to accumulate factual knowledge is by reading (see previous post), I plan to build a reading component in the assessment/reassessment process.

As part of the homework there will be assignments such as “Summarize the main ideas in section 2.3”.  (In AP Statistics, asking for written summaries of textual material has the added benefit of preparing students for the free response part of the exam.)

Assessment can then take the form of: “In this section two measures of spread of distributions are discussed. For spread around the median, the textbook suggests that you should use the ______ and for spread around the mean you should use the ________”.  I think it is important to include wording such as “the textbook suggests” to signal to the students they should have opened the book.  In addition, to reinforce the importance of the text, reading the appropriate material will be one of the pre-requisites for reassessment.

What are the potential downsides?  (a) Too much to read and/or (b) Students will copy from the textbook or “Google it”.  I don’t think either of these are too objectionable. For summaries, it is easy to skim the paragraph and look for key words. One can detect copying rather easily, especially if it circulates on Facebook and multiple cherubs access it before they hand it in.

2.  SBG assessment and connecting factual knowledge

Willingham talks about chunking – the notion that factual knowledge is easier to remember if facts are connected in some way, if they form a single idea.  He argues that lists or drill have only limited use, may produce boredom and, when used exclusively, will preclude the joy of discovery.

For example, in AP Statistics we may depict distributions as box plots, histograms, stem plots etc. Each one of these depictions has its own vocabulary and definitions – IQR, bins, stems, etc. But the main idea is not the depiction, but to characterize the center, shape and spread of the distribution.

For example, some questions can be definition oriented – such as “What is the IQR for the distribution depicted in the box plot below?”

We can achieve a deeper assessment by using the following question instead: “Given the histogram below, if this distribution were plotted as a box plot, what would be the IQR?” (No graphing calculator)

I would argue that the second question is better at making the student understand not only what is the IQR and how to compute it, but also that the various graphs are just different ways of depicting the same distribution.

3. SBG Assessment and Critical Thinking

Frankly, I find this idea the most difficult to implement. Willingham argues that students have the necessary background knowledge to carry out critical thinking tasks in assignments. However, in AP Stats, I always find myself under time pressures – not only is the exam a month earlier than the end of the school year, but I also want to leave three weeks of cumulative review. Where to find the time for acquiring sufficient background knowledge before asking some critical thinking questions?

Perhaps one way is to make all the quizzes cumulative, and when we revisit a topic, say the third time, then the questions can become critical thinking questions. Any other ideas?


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