Bird's Eye Summary/alx

Bird's Eye Summary
Contributors	Christian Köppe, Ralph Niels, Robert Holwerda, Lars Tijsma, Niek Van Diepen, Koen Van Turnhout, René Bakker
Last modification	June 6, 2017
Source	Köppe, Niels, Holwerda, Tijsma, Van Diepen, Van Turnhout, and Bakker (in press 2015); Köppe et al. (2016)
Pattern formats	OPR Alexandrian
Usability
Learning domain
Stakeholders

You have just been discussing student’s solutions to a particular homework assignment, applying Use Student Solutions (Use Student Solutions) and possibly also Add Value Beyond Feedback (Add Value Beyond Feedback), Compare Solutions (Compare Solutions), or Generalized Feedback (Generalized Feedback). Much has been shown and said in a short time, at different levels of abstraction.

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Students will find it difficult to extract the main points of the discussion from everything that has been said. Because the session in class will move swiftly to other topics, students may find it hard to retain the “takehome message" from this particular part of the session.

Basing a sizeable part of the classroom session on the discussion of a series of homework assignments creates a more segmented treatment of the subject matter than, for example, a well prepared, long(ish) lecture might be. There is less opportunity for a narrative arc that ends with a clear statement of the overall conclusions. And, if the teacher isn’t careful about it, less attention is spent on integrating the different sub-subjects with one another, and with the overarching theme(s) of the session.

An interesting and effective discussion of a single homework assignment involves a lot of insights, examples, generalization and/or comparisons. Because time is, of course, limited, the information-density of the discussion tends to be somewhat higher in these flipped classroom sessions. All the while, the student is cognitively busy, integrating the insights presented with his/her previous mental model of the subject matter. More so, probably, than in traditional lectures, because he/she has already spent quite some mental energy on the subject matter while doing his preparation and assignments. In this situation, students may find it more difficult to distill the important statements or concepts than in a traditional lecture.

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Therefore: End each segment in the session (e.g. each discussion of a single homework assignment) with a very brief summary of the main points. Use this moment to connect the important point of the current segment with the points of previous segments.

Just a few sentences is usually enough for this purpose. Reiterating the main points, or explicitly restating the “take-home message", of this current topic of discussion, has some benefits to the students:

—It allows the student to perform a mental double check: “Did I understand this correctly?"

—It helps students who have difficulty in separating main points from side-issues.

—Knowing that a summary will follow the discussion, it may allow the student to spend more cognitive effort on integrating the new insights with pre-existing knowledge and earlier experiences.

—It signals the end of the current segment, adding to the perception of structure and progress in the session.

This moment of summary is also an excellent opportunity to integrate the subtopics of the different segments by referring briefly to them. This helps restore the student’s overview of the relations between all the different concepts of the session. It also aids in the retention of earlier “take-home messages".

If possible, one can refer to subtopics that will appear in upcoming segments, providing a bit of a “preview" of the rest of the session. Referring to the topic of the immediately succeeding segment allows you to provide a comfortable segue into the next part of the session.

One session in the programming course “Scripting for Designers" at HAN University of Applied Sciences is dedicated to the topic of different data types in programming languages (such as text, yes/no values and different kinds of numbers). At one point in the homework assignments, students are asked to write a program that repeatedly adds the number 0.1 to itself, and prints the results. Students will observe that the first few results (0.1, 0.2, 0.3, 0.4, ...) are as expected, but after about eight rounds, the result acquires some unexpected numeric “residue": the program shows values like 0.800000000003405.

In the classroom discussion of this experiment, the teacher explains that this is because computers store numeric values in a binary notation (as opposed to the decimal notation that we humans are used to). The value 1/10 has, in binary notation, an infinite sequence of digits after the dot (similar to the way the value 1/3 has an infinite sequence of 3’s after the dot in decimal notation). This forces the computer to round the number to fit in a typical memory cell. This rounding is very subtle, and only becomes apparent after about 8 additions in our experiment.

After this explanation (spiced with some more examples of unexpected behavior of numbers in computer programs), the discussion is terminated by stating the take-home message: In typical programming languages, numbers with decimals after the dot are slightly unreliable. Do not assume exactness of results.

This summary tells the students that they don’t have to understand or remember any intricacies of binary notation that were demonstrated. It’s the unreliability that matters.

Finally, the summary refers to an earlier discussion of the reasons why most programming languages require programmers to choose between two numeric types: whole numbers, and numbers with fractions. The current segment just added another reason: the type of whole numbers is reliable, whereas numbers with fractions aren’t.