Important Things First … And Repeated

Like most faculty, I encounter times in the semester when I have to wonder “how did we get to this point?” — such as when a student in a course like intermediate algebra does not recognize a product versus a sum, or can not recognize a right-triangle distance problem in context.  I could follow the path of blaming previous bad teachers (all of them except me [:)] ), or on students who do not study; there might even be some truth in these explanations.  However, the professional response is to explore how my course enabled these problems to survive until the end of the semester.

I am concluding that we (and I) stop working on ‘basics’ too soon; I (and we) presume that a passing score on an assessment like a chapter test shows that a student has the basics.  However, I suspect that I depend too much on closed-task items on assessments, which enables some students to simulate appropriate knowledge without its presence.  In addition, I am concluding that I need to design classroom interactions to constantly build literacy and analysis of mathematical objects.

People often say ‘mathematics is a language’, and promptly teach mathematics as if it was a set of mainline cultural artifacts.  We can learn much from our colleagues in foreign language instruction, who tend to constantly use basic literacy into all work in a language and to deliberately address the cultural components of the language.  I see most of my student’s basic failures within mathematics to be cultural issues (context, norms) along with language literacy within mathematics.

The implication I see for my own teaching is that classroom time needs to deal with ‘sum or product’ as an issue every day; nothing is more basic than this issue.  In algebraic classes, there is an added layer of work on symbols and syntax which needs a similar focus (sum or product).  I’m also seeing a need to deliberately address reading skills applied to a math textbook, and hope to coordinate these types of efforts.

I am constantly reminded of this notion:  Novices do not automatically see the critical features and structures that experts see without effort.  Our students are capable of more, and can reason mathematically.  We need to deliberately show the features and structures we see, and provide scaffolding for students to become more expert.  We do students no good if they leave a math class in the same novice mode as they started, with some limited problems they can solve.

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