In my 100th blog post I complained about the course called ‘algebra’. Some commenters misunderstood the complaint. Though I said a few times in the article that my critique was not about the content called algebra but the aimless march through stuff that makes up almost every algebra course in existence, some thought I was bashing the value of the content. Not so. Another commenter said: you might have ranted, then, about many history courses! Indeed I could have – and have done so multiple times in my career.

The issue, then, is not ‘algebra’ or ‘history’ but what we mean by ‘course of study’. I am claiming that to be a valid course, there has to be more than just a list of valued stuff that we cover – even if that list seems vital to me, the teacher. Rather, a course must seem coherent and meaningful from the learner’s perspective. There must be a narrative, if you will; there must be a throughline; there must be engaging and stimulating inquiries and performances that provide direction, priorities, and incentives.

Notice that I haven’t merely defined a course. What I have just done is identify some criteria by which any so-called ‘course’ can be designed and critiqued. And such criteria are vital: I know from 35 years at this work that very few teachers ever self-assess a course as a course against explicit criteria – with unfortunate consequences. They may tweak lessons and even units but they rarely dispassionately critique the design of the entire course against criteria such as mine; or receive feedback against criteria about their design.

The problem of the (misuse of the) textbook

Next time I will say a bit more about my criteria, but we can’t ignore the other lurking issue in this discussion: ‘coverage’, i.e. teachers marching through the pages in a textbook.  I wish to claim that defining a course as a tour through the textbook, page by page, is simply not a course by ANY valid set of criteria. A textbook is merely a collection of topics, with exercises and text under each topic. The textbook does not know your personal or school priorities; the textbook does not know your students; the textbook doesn’t identify any priorities or through lines that unite all the chapters, etc. So, a march through a book is a non-design. It would be like learning English through a page by page tour of the dictionary and grammar book; it would be like learning history by reading through the Encyclopedia page by page.

It doesn’t matter how good the textbook is. My critique is not a critique of textbooks. (I have worked on over a half-dozen for Pearson, to infuse UbD). My critique is the use of books. A text – be it an algebra textbook or Catcher in the Rye – is a resource in support of clear and learning-focused goals. Goals cannot be supplied by a text; they are supplied by purposeful teachers.

Here are some simple prompts that a teacher who has really thought through the course as a course should be able to answer:

  • By the end of the year students should be able to…. and grasp that…
  • The course builds toward…
  • The recurring big ideas about which we will go into depth are…
  • The following chapters and sequence support my goal of…
  • Given my long-term priority goals, the assessments need to determine if students can…
  • Given my goals, the following activities need to build insight and incentive…
  • If I have been successful, students will be able to transfer their learning to… and avoid such common misconceptions and habits as…

So, even before spelling out the meaning of and rationale for my course criteria, you should be able to realize from these prompts why almost all algebra courses are complete failures as courses – i.e. purposefully designed learning in support of clear intellectual goals. No, almost every algebra course (and, yes, history and science course) is a mere march through a textbook, page by page. Rarely do explicit overarching goals and priorities inform the sequence, the activities, assessments, and choice of topics. Most importantly, the assessments almost never require students to synthesize learning across many chapters and transfer their understandings and skills to priority performance tasks. And it is therefore no accident that students uniformly find HS math to be their most boring and difficult course, as our student surveys show.

In my follow-up post I will say more about the criteria mentioned above as well as walk the talk: I’ll share some design work that my colleagues and I have done over a 10 year  period to build better HS math courses. Here’s a hint: if we want understanding instead of mere dutiful learning, we must begin in a very different place than almost every math course I have ever seen. We have to begin with giving the learners intellectual reasons and incentives for taking such a course. And, thus, we have to justify both the content and the overall direction of the course.

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