Teaching Math in the 21st Century

A few months ago I was fortunate enough to read Barry Garelick's latest book Teaching Math in the 21st Century (yes, it IS available at Amazon.ca here). Aside from having a wonderful illustration of Mr. Garelick himself on the front cover behind the desk, this book is filled to the brim with a unique kind of wit that only Garelick can deliver. Having read Letters from John Dewey/Letters from Huck Finn awhile back, I was genuinely excited to have a go with his new title.

Inside the front cover.

The forward is written by Ze'ev Wurman, an individual who was heavily involved in the 1997 state standards of mathematics in California, a set of standards which I have heard were very strong (unfortunately they have been since replaced by the new, and lacking, Common Core standards). Wurman sets a wonderful tone for the book by looking at the content knowledge, or lack thereof, of many classroom teachers and their administrators. This is not an attack on our educators, but moreso a serious critique of the "professional training" received. It is as though educational training promotes a culture of ignorance, a system where mathematics teaching is devoid of mathematics and those in the system cannot see their lack of skill.

Just as interesting is Garelick's introduction. He speaks of the man in the sailor's cap who uses common trickery to sell the new standards: "How many of you have solved a quadratic equation, who are not math teachers?", "If all we are doing is teaching algorithms, then we are doing our students a disservice", "We want students to 'think like a mathematician' using the eight math practices", "We are moving away from a way of teaching that didn't work". It all seems rather odd to me, considering that the California standards, to my knowledge, were quite good - how was it that they were not working? I highly doubt the man in the sailor's cap actually had any relevant data.

The book describes Garelick's work as a substitute teacher in two different locations. The first he tells us his stories from his time at a high school. Perhaps my favourite story is that of Grant's Tomb being used to describe radical notation. Garelick describes √2² as asking "Who is buried in Grant's Tomb?" to which his daughter replied "Who is Grant?" Being from Canada, and lacking in American history, I have to admit I was a bit like his daughter - I had to do some research to determine that, in fact, it was Ulysses S. Grant buried in Riverside Park in Manhattan.

At the end of the first section, Garelick writes "I showed up for every class period, taught to the best of my ability, and tried to be consistent." He let's the reader ponder over whether we believe this to be success or failure. I think it is fairly easy to see the success he accomplished in a small amount of time. The students appreciated the time they spent with him, and, in my opinion, they learned something of value.

Elisa's wolf drawing on Garelick's final day.

The second portion of the book follows Garelick's long-term substitute appointment at Lawrence Middle School teaching mathematics. Personally, I would have 'run like the wind' while chatting with the principal about his son's 'deep understanding' of numbers. It makes me wonder if all school administrators are under the same oblivious cloak - falling victim to fancy terms like 'deep understanding' to describe mathematics devoid of mathematics. Do all teachers applying for positions have to jump through these hurdles? How does one escape this culture of ignorance?

The most eye-opening portion of the second half of the book was Garelick's discussion of the new Algebra 1 structure. According to Sally (she appears several times throughout the book) only the elite will be permitted into Algebra 1 in California. The explanation given is that "Common Core is very challenging" and only the truly gifted will have access. To me, it sounded like they were trying to keep students behind to beat them to death with 'conceptual understanding'. Of course, there is the typical jargon regarding more 'problem-solving' and 'critical thinking'. How is keeping highly skilled students behind good for their motivation? If America truly needs more students entering the STEM fields, should we not allow the competent students access to higher mathematics rather than holding them back? Hmm.

Garelick continues describing the culture of ignorance with a beautiful example of the quadratic formula:

"Of course, under Common Core, he might not be required to memorize the quadratic formula, but would have to explain how and why it works."

How a student could be deemed to understand the quadratic formula without knowing it was puzzling.

This is a very valid point: how can we expect students to show 'understanding' of an operation or procedure if they do not know how to perform the computation? A deeper understanding often comes out of a well-developed schema of the subject matter (students have something to draw on). Trying to force understanding leads to inappropriate and incorrect usage (Daisy Christodoulou has written about this here). Seems to me that those who promote the culture of ignorance are devoid of the idea that procedural knowledge promotes schema acquisition which can be drawn upon to build 'deeper understanding'. Trying to build 'deeper understanding' first seems counter-intuitive.

Overall, Garelick's book is a lovely (albeit scary) adventure into the current state of teaching in America in the 21st century. The text is full of just the right amount of humor to mix with the eye-opening stories of Common Core implementation. He does an excellent job describing the culture of ignorance and allowing the reader to ponder his/her beliefs, despite knowing which side of the fence Garelick aligns with. The book comes highly recommended: the students are charming, the stories are memorable, and Garelick is as witty as ever.