A number of math teachers have complained either directly or indirectly recently that I have offered criticisms but no solutions to the problem of poorly-designed math courses, especially at the secondary level. For example:
“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…. It seems there are so many people out there saying that this is not what we should be teaching our students and that us Math teachers are in fact wasting students time with our outdated teaching methods.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.
“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?
Leaving aside the fact that I have indeed offered numerous resources under the Understanding by Design name (including many math units such as this one: Algebra Unit – before and after) over many years, let me offer a short list of print and web sources for problems, assessments, and pedagogical advice on teaching mathematics more meaningfully that every secondary math teacher ought to have in their library (or at least know about). Math teachers and supervisors: please post others and I’ll add them to this list. I am also building a Storify page of tweets that propose such sites.
The first go-to resource is Dan Meyer’s video, blog and his open-source collection of problems. The second go-to site is the archive of Car Talk Puzzlers. Here’s my favorite, and make sure to read all the follow-up posts and listen to the next week’s radio show). Here’s my next favorite, and the great kids from E Tipp MS had fun with it.
Another helpful source is from the United Kingdom (and has served as a partner to Common Core developers) – the Shell Center.
I contributed to a big volume for MAA on Quantitative Literacy (my article begins on p. 121) and you can find many examples not only in my article but in those of others in the volume.
NCTM publishes resources under the Illuminations banner. Here are lessons in algebra.
To build courses around worthy performance tasks, the series entitled Balanced Assessment, edited by Judah Schwartz, is excellent. (You can find free resources from it here.) Good tasks, good rubrics, and samples of student work. There are books for middle school, high school, and advanced high school.
The 20 year-old book from NCTM entitled Teaching and Assessing Problem Solving is probably the best of it s kind, a great mix of theory and practice, filled with helpful examples. A newer NCTM book, Teaching Mathematics Through Problem Solving, is equally helpful.
An edited volume entitled Real-World Problems for Secondary School Mathematics Students has lots of great examples from different countries.
One of the better textbooks in math is by Harold Jacobs called Geometry: Seeing, Doing, Understanding.
Beyond Formulas in Mathematics and Teaching is a bit text heavy but provides a solid perspective on such an aim. For a more general text on the meaning of mathematics, highly readable and usable with HS students, nothing beats Morris Kline’s old book Mathematics in Western Culture.
And as I have noted numerous times in this blog, arguably the best course ever designed, from the 1930’s, was Harold Fawcett’s course later written up as an NCTM Yearbook, and republished 20 years ago. And surely the most seminal and vital book in a math teacher’s library is Polya’s classic How To Solve It. Here is a great old video of Polya at work. Stick with it: there is a dramatic conclusion to the inquiry.
A blunt postscript: All of these resources are not new. I find it a bit depressing that so many math teachers such as the ones I quoted above are seemingly unaware of the materials that are available to ensure better engagement and outcomes in mathematics. BTW, it is ONLY math teachers who routinely make complaints in high numbers (such as the ones up above) that they lack resources to develop better courses, instruction, and assessment. At a certain point, I simply must say: isn’t it your professional obligation to know about these resources rather than vent at me for not providing more resources?
Please also note the comment posted by Rose in which she identifies many great resources (as well as provides important stories related to my main point).