The premise of this book is enticingly simple . It presents two solutions to two prevalent problems in education . The first is the vast amount of content required to be taught because of various state standards, and how one can thread that maze and “teach for understanding .” That is, how can educators get students to apply what they’ve learned to new and unfamiliar problems? The second is the diverse nature of today’s classrooms, the result of heterogeneous grouping of students of different abilities . How does an educator differentiate instruction to accommodate such diversity in a single classroom?
I read this book in a math teaching methods class a few years ago . One event in that class stands out regarding this textbook . In a chapter on assessing understanding, a chart presents examples of “Inauthentic versus Authentic Work” (p . 68) . For example, “Solve contrived problems” is listed as inauthentic; “Solve ‘real world’ prob- lems” is listed as authentic . The black-and-white nature of the dis- tinctions on the chart bothered me, so when the teacher asked if we had any comments, I said that calling certain practices “inauthentic” is not only pejorative but misleading . Since the chart listed “Practice decontextualized skills” as inauthentic and “Interpret literature” as authentic, I asked the teacher, “Do you really think that learning to read is an inauthentic skill?”
She replied that she didn’t really know about issues related to reading . Keeping it on the math level, I then asked why the authors automatically assumed that a word problem that might be contrived didn’t involve “authentic” mathematical concepts . She answered with a blank stare and the words “Let’s move on .”
That incident remains in my mind because it is emblematic of the educational doctrine that pervades schools of education as well as this book . The doctrine holds that mastery of facts and attaining procedural fluency in subjects like mathematics amounts to mind- numbing “drill and kill” exercises that ultimately stifle creativity and critical thinking . It also embodies the belief that critical thinking skills can be taught .
In a discussion of what constitutes “understanding,” the authors state that a student’s ability to apply what he or she has learned does not necessarily represent understanding . “When we call for an appli- cation we do not mean a mechanical response or mindless ‘plug-in’ of a memorized formula . Rather, we ask students to transfer–to use what they know in a new situation” (p . 67) . In terms of math and other subjects that involve attaining procedural fluency, employing worked examples as scaffolding for tackling more-complex prob- lems is not something that these authors see as leading to any kind of understanding . That a mastery of fundamentals provides the foun- dation for the creativity they seek is lost in their quest to get stu- dents performing authentic work from the start