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.

plerudulier

said:Reblogged this on Things I grab, motley collection .

Jose

said:Bravo, Grant. I wish you would write an analogous series of posts for us English teachers, who have a tendency to view an English “course” as an arbitrary sequence of genres and texts, as opposed to “purposefully designed learning in support of clear intellectual goals.” The texts then become vehicles for assessing comprehension of content as opposed to vehicles for inquiry around big ideas and for the demonstration of skills that build on previous ones.

grantwiggins

said:Happy to oblige at some point! The fetish with teaching ‘books’ as opposed to courses is just as bad a problem. And we are losing boys at an alarming rate because teachers are reluctant to deviate from traditional reading lists (and a single book read by all) in too many cases. Did you know that the gender gap in reading is now greater than the reverse gender gap in math? That’s alarming… In our surveys, the boys detest most of the books they are asked to read.

James

said:Hello Mr. Wiggins,

I forwarded your post to my fellow teachers. I received a response that I would like to share with you, as it is one I have heard often from math teachers, on the difficulties of teaching math for learning and real-world application, rather than for coverage. IF you could take a few minutes to read this, and comment on the teachers frustrations, it would be very much appreciated:

“I have just read through that article and I have some questions that I wish an article like that would answer. In my opinion the writer suggests that textbooks are merely a collection of topics with examples of exercises under each and that teachers merely race through a textbook to get to the end. In a sense I agree with this but my problem/concern is that he offers no alternative/answer to what we should be doing instead. For example when I teach algebra, at the end of the unit my students should be able to write equations, manipulate variables and solve for the unknown values. They need to also be able to apply these skills to everyday/real world applications. This I understand but it seems there are so many people out there saying that this is not what we should be teaching our students and that us Maths and Science teachers are in fact wasting students time with our outdated teaching methods. My question is then what should we be teaching them? What am I missing? He offers no answer to that question and every time I read an article like that I feel like I have no idea what I should be doing as a teacher of Maths or Science.

At the end of the day my students need to be able to enter University with the skills and the knowledge that will enable them to complete a Bachelor of Science or Maths and be able to complete lab work and everything else that comes with a University Degree. They need to be prepared to enter the working world. If I dont teach them the content from a textbook then how will they be able to do that? What should I be teaching them? Have I misinterpreted this text?

I just want to know what I am doing wrong and more importantly what I should be doing? Maybe we could have a chat next week because I am desperate to become a better teacher and even more desperate to try to make Maths more interesting for my students but to be completely honest I don’t know how to make algebra anymore interesting. I am already being told that I am working too slowly because I havent completed a certain section of the textbook with my students. I try to spice things up but then I am told (not directly) that I work too slowly. Anyway sorry for my rant but I am just a little stressed at the moment because I do feel the pressure to make Maths and Science a more interesting subject for the students. I just need some help in achieving that.”

Thank you for your time… James

grantwiggins

said:James – this is a common lament of math teachers. Indeed, it has been the most common lament I have faced in 30 years of doing this work. That tells us something right off the bat, doesn’t it? Math teachers are not versed in the training they need to answer a very basic question: how might this work be more meaningful and intriguing intellectually? Nor am i saying that real-world application is the only way. The problem is a lack of big ideas in math teaching as well.

I of course have answered this question many times, in multiple publications – and that illustrates a different problem: many teachers are not well versed in the literature of their field. Understanding by Design has sold over a million copies, in 6 languages; we have provided dozens of sample units in math in our two most recent books. The literature on problem solving based math is vast, and Dan Meyer’s blog has great stuff on this kind of teaching almost every week. Have him look at my 3 posts on the kids of E Tipp Middle School. Etc. At a certain point, people have ot take responsibility for their professional work, I think.

I am going to post a few math units in my next blog entry since this is an endless lament.

BTW: his/her last paragraph is dispiriting – then what is this person being paid to do – just ‘teach’ interest and learning be damned? I would say that there is a basic confusion here about one’s job as a teacher – and that is a common leadership failure, the failure to not be specific about a job description and evaluation based on it (cf. Schooling by Design on What’s My Job?

Kara Jeanne Johnson

said:Mr. Wiggins. You do an excellent job of criticizing. You do an excellent job of laying out broad theoretical outlines for curricular development. I’ve got to agree with much of what you say, even though I find your writing and presentational style offensive and highly combative. What I find lacking in your rants are specifics. What types of “broad questions” would you suggest to stimulate the interest of hormone driven 14-year old boys? or incredibly self-conscious 14-year old girls many of whom lack basic computational skills, the ability to read critically or who are afraid to take chances or to explore into areas in which they are not familiar, yet who are required to sit in my Algebra I class? Those would be questions that I could actually use and not get fired? That would be at a school full of upper middle class kids where the department chair tells me to “be sure they have the skills” Honestly! I’m open to suggestions – but so far, you’re long on rhetoric and really short on solutions. Do you have any concrete suggestions I can use?

grantwiggins

said:Kara: In 4 books by the title of Understanding by Design and under the newest title Essential Questions you will receive many answers to your questions. I apologize if my style seems combative. My aim is simple: I ask teachers to confront honestly problems that they have often failed to face in the service of kids. School need not be as boring or off-putting as it is. Google on Essential Questions: Doorways to Understanding, and download the first chapter of the book from the ASCD website and see if that doesn’t give you some direction. Happy to help you once you do some reading.

gasstationwithoutpumps

said:I disagree with one claim: “the textbook doesn’t identify any priorities or through lines that unite all the chapters”. A good textbook does do those things—of course, there are a lot of very bad textbooks on the market, just as there are many bad courses being taught.

A good textbook is not an encyclopedia or a dictionary, but a carefully crafted tour through selected material. It defines a course in precisely the way that you are asking teachers to do (and generally has an explanation of this structure).

If the textbooks you are helping create are goalless resources, then you are not creating textbooks but reference manuals. Perhaps you need to look into the differences.

It is true that a reference manual can have a bigger market than a good textbook, because many different courses can use a reference manual (with a lot of effort on the part of the teacher to order and pare away the stuff that is not relevant to their course). That doesn’t mean that all textbooks should be reference manuals.

As for your complaint that most algebra courses are terribly designed—I agree, and most of the algebra textbooks are of no help, being designed as badly written reference manuals. I think that pushing for better textbooks would be of more help than asking teachers to ignore the books and make up their own courses. You’ve been working for 10 years to try to structure better math courses. Can you capture some of that thinking in a math textbook, or does every teacher have to struggle with curriculum design for 10 years? (With half of STEM teachers quitting within 5 years, that is a recipe for disaster.)

grantwiggins

said:Well, the discouraging part is that of all my recommendations, the 2 math textbook editors took the fewest of my suggestions. They felt that the market was not ready for such a sweeping change. Sigh. I heard the same argument 30 years ago when Ted Sizer and I visited two publishers to ask for similar changes.

However, there is truth in their lament: in all three cases, I have seen wonderful books that were put out that didn’t sell at all and were retired. So, this is a longstanding chicken-egg problem that may hopefully change in an era of digital texts.

BTW: I think you unwittingly underscore my point by describing a textbook as a ‘carefully crafted tour through selected material’. That is precisely the problem: it focuses on material, not learning; it focuses on coherent ‘coverage’ rather than coherent learning via purposeful engagement and the long-term aim of transfer – arguably two key goals.

gasstationwithoutpumps

said:Yeah, I became aware of my poor choice of phrases about half an hour after posting the comment. I have to admit that I have not followed a textbook in any of my university courses for about 15 or 20 years, because I can never find one that teaches the material I want to teach with the order and emphasis that I want. My most recent course design started from the goal of creating engineering thinking (which spent some time defining for myself), created labs with strong design components, and then figured out what theory was needed to support the design tasks. I was unable to find a textbook that supported the course, as they all had massive theory dumps and little or no design until the end. I think that my course design method is fairly consistent with your suggestions, so we are not in major disagreement.

When homeschooling my son, though, in material that I was not an expert in, I found that following a good textbook made for a much better course than I could have created on my own. (There are some good textbooks in first-year calculus-based physics, for example.)

You might want to look at the Art of Problem Solving math textbooks. They are not for all students, but by carefully defining their market and not trying to sell to all of Texas, they have managed to put together some very good texts.

grantwiggins

said:I shall check them out immediately! Thanks for the tip.

Marilyn J. Hollman

said:When James Moffett published his second book in the very early 70’s, literacy teachers had a mission and a narrative. You couldn’t NOT answer your prompt-questions.

I have worked with many practicing teachers who seem to have difficulty understanding this.

ghewgley (@ghewgley)

said:I agree with your thoughts so much. I honestly believe that we as teachers, administrators, and academia do a horrible job of actually knowing/explaining why courses are offered in the first place. It all seems to boil down to, “Because you’ll need it later.” Huh? I am actually shocked that students follow along as much as they do (I’m not sure if that is a good thing or a bad thing) in their school careers. I don’t think adults could make it through school now as they would constantly be asking, “Why do I need to know this? It’s a waste of time as I am a …”. I almost wonder if some sort of definition of “to be used later” could be blended in to the standards, or at least added as a part of the curriculum. Maybe a section should be added to each course: “Why should you take this course? Here’s how you will use this in your lifetime. Here are the fields that will require this course.”

Why do students need to learn about The Catcher in the Rye? How is it going to help them later in life? What about most high school math classes? Why should a student study trig? What are they going to do with it? Why can’t those be explained and students/parents given more input as to what the student might actually need. Working at CERN – need lots of math. Driving a bulldozer – basic math. Why are we so afraid of individualizing education more and more? We have a standards bar, but it is currently set at one height. Why? Jobs do not all require the same amount of knowledge in every field. We raise the bar in math and reading, but we get rid of the bar for arts, social studies, music, PE, etc. Why? A well defined course could help students/parents choose a path that is best for them.

There are many good reasons to learn almost anything: what are they, why should a student do it, and why are we teaching it?

grantwiggins

said:I have long felt that Standards should NOT be written only by the people who teach in the area in question. There should be a second pass by a group of professionals in all fields to critique the standards proposed by those people in the field who will naturally advocate for it. That’s one reason why I think the common core math standards (and most state standards) are a big failure: every person wants their pet topic in there.

My favorite story of all time – true, too – happened to me in a workshop that included both local educators and state ed. people. I was lamenting the failure of some standards to be justified in just this way, and I gave the example of a history standard that require knowledge of a relatively obscure Chinese dynasty. An immediate objection came from a man as to its importance. I find out later who the man is: the social studies director for the state, it was his insertion, and it just happened to be his dissertation topic.

JupiterMom

said:I agree. Completely. The only issue I take is that your conclusion is so sweeping. How do you know how many classrooms teach by “walking through the textbook”? I’m sure you’ll inform about that though in subsequent blogs. Right?

I’d like to add to your list of guidelines- a successful course will include a goal/plan/target of how to increase independent study and mastery by the student. Students should be encouraged to learn and to be responsible for that. There are methods to encourage this process and we need more of that also. But, thank you! I am tired of instructors who teach as the textbook goes. Yikes!

grantwiggins

said:Completely agree on independence, as I have often written in these blogs. An oversight not to mention it. Thanks – will add it in the next part.

centerfortransformationau

said:Grant,

I have used your research and transformed my practice in K-12. I now share your knowledge with Pre-service and in-service educators. Thank you for your tireless work and dedication to our profession. Your message is getting through and student learning enhanced because of your work. You have many soldiers in the field!

Keep posting, speaking and clarifying. Change is slow but happening.

Dr. Andria Stokes

grantwiggins

said:Thanks!! Slow, indeed, but as long as it is happening we’ll keep fighting the good fight.