Infinite Powers


Cheery Friday Greetings to our Learning How to Learners!

As a result of interest in our recent email alluding to limits and problems with teaching mathematics using reform approaches, in this week’s email, we’ll focus solely on math.  Next week, back to our usual wide-ranging (hint hint) discussions.

Book of the Week

Infinite Powers: How Calculus Reveals the Secrets of the Universe, by Steven Strogatz. Strogatz is a wonderful writer, and Infinite Powers is a wonderful book about the beauty of calculus. But we hasten to add that you don’t need to know any calculus to enjoy Strogatz’s work. The book begins with a quip that the physicist Richard Feynman made to the novelist Herman Wouk when they were discussing the Manhattan Project. “Wouk was doing research for a big novel he hoped to write about World War II, and he went to Caltech to interview physicists who had worked on the bomb, one of whom was Feynman. After the interview, as they were parting, Feynman asked Wouk if he knew calculus. No, Wouk admitted, he didn’t. ‘You had better learn it,’ said Feynman. ‘It’s the language God talks.’”

So Wouk went on to try—and fail—to learn calculus.  Strogatz continues “It shouldn’t be necessary to endure what Herman Wouk did to learn about this landmark in human history. Calculus is one of humankind’s most inspiring collective achievements. It isn’t necessary to learn how to do calculus to appreciate it, just as it isn’t necessary to learn how to prepare fine cuisine to enjoy eating it. I’m going to try to explain everything we’ll need with the help of pictures, metaphors, and anecdotes. I’ll also walk us through some of the finest equations and proofs ever created, because how could we visit a gallery without seeing its masterpieces? As for Herman Wouk, he is 103 years old as of this writing. I don’t know if he’s learned calculus yet, but if not, this one’s for you, Mr. Wouk.”

This is a timeless book that puts all of calculus into a grand, beautifully written perspective that you’ll enjoy whether you’re a physicist or an English teacher.  Enjoy! 

Math Reform in Need of Dramatic Reform

Our recent email describing problems with reform approaches to teaching mathematics prompted an outpouring of shared parental concern on precisely that topic. Here, for example, is a carefully curated archive of materials critical of Jo Boaler and the highly questionable approaches she, and reform mathematics educators, espouse. It also contains a thoughtful analysis of why these problematic approaches are pursued, despite the obvious challenges they cause for students—particularly disadvantaged students. 

Steve Hollister, an engineer with two master’s degrees in engineering from the University of Michigan who has written over a million lines of code over the past 45 years while growing his successful business, provides an additional helpful view on these issues. Steve writes: 

“I saw two worlds in education for my son who just graduated from college: Kindergarten through 8th grade (K-8), and high school/college. K-8 was all about low expectation full inclusion equity and natural learning ideas. We were told that ‘kids will learn when they are ready.’

“In middle school (7th and 8th grades), things began to change as parents realized that their kids would not be ready for any advanced math and language placement, let alone honors or AP classes, in high school. This was not just a problem with different ideas of learning. It had to do with specific curriculum contents and skills. The low K-8 state test proficiency expectations gave way to the much higher AP/IB expectations. 

“In high school (and college) everything changed and was driven by reality. All the classes my son took were traditional and students completely ignored yearly state Common Core testing results. Life was all about GPA, PSAT, SAT/ACT, AP tests, and extra-curricular activities. I have yet to understand how these two opposite worlds of educational thought exist without public conflict. 

“In high school, students have choice and are separated by willingness and ability, but in K-8, there is no choice in full inclusion, age-tracking academic classes. When I was young, I got to calculus in high school with no help from my parents. But nowadays, my ‘math brain’ son had to have help from us from kindergarten through sixth grade, and all of his STEM-prepared friends had to have the same help outside of school.”

The Deeply Troubled Palo Alto Unified School District

You may (or may not) be surprised to learn that the Palo Alto Unified School District, practically in the shadow of Stanford, is at ground zero of the math wars. This essay, “Why Have American Schools Failed in Closing the Achievement Gap? A Case Study of California’s Palo Alto School District,” provides a description of how, no matter how bad test scores get, reform educators simply dig deeper.  Ultimately, only the advantaged have the resources to pay for the supplemental tutoring needed as a result of current reform approaches to teaching math. As the essay notes: “the rock-bottom test scores of the economically disadvantaged students have never significantly improved over the past decades. This shows that the progressive education model, though boasting ‘higher-order thinking,’ ‘conceptual understanding,’ ‘teamwork,’ or ‘child-centered education,’ deceitfully, devastatingly, and tragically failed these students who relied exclusively on school education.” 

If you share similar problems at your school district, or have any advice or thoughts to share on these challenges, please feel free to share them on the discussion forum here (remember to be logged in to Coursera to access—you can also reach the discussion forum through the general discussion forum tab inside the course).

The Bright Light of the La Ronge Indian Band Schools in Saskatchewan

On the other hand, Liz Barrett, First Nations Outreach & Teacher Support for JUMP Math, BC, SK, YT, NWT and NU, writes that “I continue to believe that one day people will see the light. In my communities across Canada we are focused on mental math fluency and supporting outstanding teaching—so math games have taken on new meaning. I just had to share this video of some wonderful work being done by the La Ronge Indian Band schools in Saskatchewan led by Julius Park and Tammy Robinson. ( Simon Bird is the Ed director.)”

“I am invigorated by the schools in Saskatchewan and am heading back to work with the Standing Buffalo school, led by Eric Honetschlager next month – as a community, they are focused and working hard to ensure math is no longer an accepted  ‘disability’ for any of their students. They are working hard to empower teachers and students to develop a love of all things mathematical. The students and teachers are just wonderful. The Catholic school district of Moose Jaw is also rocking away! It would be wonderful to have a Canadian Math Bee—where by Gr 3 all kids would know the basic math facts and be proud of that!

“Today I am heading off to work in the Yukon this week. My multiplication tables packs are in along with my thermal sleeping bag in case I get stuck on the drive from Whitehorse to Watson lake!”

That’s all for this week. Have a happy week in Learning How to Learn!

Barb, Terry, and the entire Learning How to Learn team

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