Resources for high school teachers about APOS theory

Question

As far as I can find, the major resources available to the layteacher about APOS (Action, Process, Object, Schema) theory refer to "undergraduate" concepts such as group theory and vector spaces (such as here).

I am interested in whether people have implemented or investigated APOS theory at the high school or lower-undergraduate level, and whether there are resources for the high school math teacher that can be used concretely, for example, to design a unit. So far I have found this book, but this seems unnecessarily technical to reach a larger audience of teachers.

For example, when I described APOS theory to my coworkers, they immediately connected to it and it helped them understand the struggles that their students were facing in particular problems, such as transitioning from seeing "sine and cosine" as "find the ratio between pairs of sides" to "functions." However I was unable to find good reading for them that referenced mathematics that they used frequently.

There are certainly individual papers using APOS theory at the pre-college level. For example, you mention functions and there is the paper High school students' understanding of the function concept (pdf) by Dubinksy and Wilson (JMB, 2013). As to resources for high school math teachers: not of which I am aware; good question, +1. — Benjamin Dickman, Aug 23 '17 at 20:52

score 3 · Accepted Answer · answered Jan 26 '20 at 21:57

As Benjamin Dickman, I am also not aware of any texts or other resources aimed directly at high-school (or earlier) teachers, but there are a number of APOS oriented studies at these levels that should be accessible and may contain some concrete ideas on structuring e.g. lesson plans.

Here is a small selection of texts that you and your colleagues may find interesting:

I. Arnon, P. Nesher, R. Nirenburg Where do Fractions Encounter their Equivalents? – Can this Encounter Take Place in Elementary-School?, International Journal of Computers for Mathematical Learning, 6 (2), 2001.
E. Dubinsky, R. Wilson, High school students' understanding of the function concept, Journal of Mathematical Behavior, 32 (1), 2013.
E. Dubinsky, K. Weller, I. Arnon, Preservice Teachers’ Understanding of the Relation Between a Fraction or Integer and Its Decimal Expansion, Canadian Journal of Science, Mathematics and Technology Education, 9 (1), 2009.
K. F. Hollebrands, High school students’ understandings of geometric transformations in the context of a technological environment, Journal of Mathematical Behavior, 22 (1), 2013.
T. Tossavainen, Who can solve $2x=1$? An analysis of cognitive load related to learning linear equation solving, The Mathematics Enthusiast, 6 (3), 2009.

This is very good: I can imagine using any of these studies to initiate a conversation and productive discussion about the topic. — Opal E, Jan 27 '20 at 00:54

Resources for high school teachers about APOS theory

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