It is fairly well recognized among (at least) secondary and college-level mathematics teachers that the problems in essentially every major published textbook can now be found online — with answers. This is even true for some “typical” or “classic” problems that teachers might assign outside of the book. Given this situation, it behooves us as mathematics teachers to think about how to use this situation to our advantage — or, minimally, not allow it to hinder students’ learning.
Particularly, we should be thinking carefully about how to use mathematics class time to assess students’ understanding (formally or informally) so that we are sure that we know best how to support each student. Further, homework assignments could be more focused on providing explanations about concepts or problems — for example, “The answer to #10 is XYZ. Use a diagram and two to three sentences to explain why this makes sense.” Or, “Charlie Brown made the following error in solving problem 6… tell what you think Charlie was thinking as he did this, and explain why this is incorrect and what he should have done.” Of course, this also means that during class, we need to focus on both skill and concept development so that all students — not just the “verbal” few — gain experience answering these kinds of questions.
Moreover, this kind of work fits perfectly with what the Common Core State Standards — especially the Standards for Mathematical Practice — say students should be doing in mathematics. Another perspective: if technology provides us with more information than ever before, we should be helping students learn how to apply and use this information. Times are changing!
