"There is no one way"

Friday, December 13, 2013

Algebra: Themes, Tools, Concepts and the Common Core

Way back in the early 90's, I co-authored the textbook Algebra: Themes, Tools, Concepts (ATTC) with Anita Wah. It failed to become a best-seller, in part because while the lessons work well with students, the book is not very easy for teachers to manage. Still it's a good book. We have continued to use different parts of it in different classes at the Urban School of San Francisco, where I used to work. Moreover, the book pioneered some lessons that have been widely emulated elsewhere. (For example: the Lab Gear approach to algebra manipulatives has directly inspired the College Preparatory Mathematics Algebra 1 manipulatives strand; the geoboard approach to the Pythagorean theorem appears in a "formative assessment" unit from the Shell Centre; the McNuggets problem has become ubiquitous.)

When it first came out, the book was under virulent attack by some traditionalists, but it was vindicated by an independent blind study conducted by University of California professors, comparing it with the classic Dolciani text. The study showed it to be more effective with students who scored in the bottom two-thirds in a pretest, and no less effective with the top scorers.

Twenty years have passed since we wrote the book. You might think that it has been completely forgotten, but you'd be wrong! I recently received this message from Tyler Hasnam, a public school teacher in Utah:
This is my second year using ATTC in my classroom and I love it.  I have long been trying to “escape from the textbook,” and when our district switched over to the new Common Core I found it a blessing that textbook companies where behind in the game.  That is, until I had to actually plan out how I would fill every single day of the school year.  It was at that time that I was introduced to this wonderful book.  This is not a traditional textbook.  It is not a collection of isolated math algorithms with an example followed by endless repetition. There are not story problems, but story lessons.  There are not "think about it" problems thrown in as an afterthought, but the whole book makes students think.  
The book naturally aligns to the practice standards of the new Common Core and is one of the few truly “integrated” math textbooks out there.  The lessons are great for helping students make connections while at the same time introducing them to the rigor of mathematics.  The manipulatives and other tools used throughout the book help students comprehend topics that I have seen them struggle with in the past.  Never have I had a group of students so fluent in topics such as radicals and completing the square as those with whom I used this book.  Even the quadratic formula took on a personal feel as we walked through lesson 14.05
The fact that ATTC works well in a Common Core oriented classroom is not an accident. The use of themes is very much in line with the Common Core emphasis on modeling. The use of tools is explicitly endorsed in the Mathematical Practice standards. And the ultimate goal of concepts (rather than simply facility with memorized algorithms) is of course consistent with overall thrust of the CCSS, with its emphasis on reasoning and sense-making.

ATTC is available for free download. Check it out!


PS: I got more ATTC fan mail.

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