One of the threads that runs through the CCSS is the need for more rigor in math education. The Algebra II textbook reviewed here (Glencoe/McGraw Hill) responds to this need by introducing “H.O.T.” problems in each section. H.O.T. stands for higher order thinking skills and, like the rest of this book, these problems are a huge disappointment.

Consider the following example. In the section on logarithms and logarithmic functions, one such “H.O.T.” problem is an error analysis. Given that

which is the correct next step:

Frankly, I think this is an insult to the students (and to math) to call this high-order thinking. What kind of standards do we establish if we label a definition as high order thinking?

Unfortunately, this mislabeling of definitions as high-order thinking is widespread. I looked at random at Error Analysis/Critique H.O.T. problems in the sections on function composition, graphing exponential functions and multiplying and dividing rational expressions. In all of these sections, what should be definitions are labeled as higher-order thinking problems.

There is no way one can call this book “informed by other top performing countries” as the CCSS wishes. Just to stay with logs, here is first an example from a foreign high school collection of problems and second, a less difficult one, from an older US high school textbook:

Solve the system for x and y:

Show that

Why is it that we don’t think our students can do these kinds of problems? Why don’t the authors put in truly higher-order thinking problems in their book? Where is the CCSS rigor?

All in all, this book is a travesty of the Common Core standards. One can only hope that other publishers will do a much better job.

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