Day 165 (of 187) reflections on the maths after reading Pi of Life by @mathgarden – not just down the rabbits hole, but starting to dig new tunnels! Bonus thanks to Paul Lockhart @cbrownLmath @joboaler
I don’t think it is possible to write about Pi of Life without linking it back to Paul Lockhart Mathematicians Lament… the books are so closely aligned in mindsets that they compliment each other without even trying… and I don’t think it can be “reviewed” in a traditional sense as it is so awesome in scope and sequence in its approach to move mindsets and shift paradigms about the maths. Essentially, there are reasons that so many people would rather have a root canal than do math…. much of the education of the maths has been about memorizing formulas to link in and not about the stories that help better understand why we are doing what we do in math.
I’ve regularly questioned why “we” do such a good job differentiating our reading and writing lessons and classes, but math continues to be a struggle with staying on pace with the chapters in a textbook… we do a good job with centres, but it always seems that math work is… different, but not always differentiated….
So when I had the one-two punch of Lockhart and then Singh’s books….it’s hard to look at our math practice the same… and yet even I will plead guilty as we are doing our district math assessment, if we change our paradigm practice, how will we do on those assessments…. and then remind myself of the “class that didn’t do math until grade six” and by grade seven were caught up… https://www.psychologytoday.com/us/blog/freedom-learn/201003/when-less-is-more-the-case-teaching-less-math-in-school
Anyways, on to Pi of Life – a great play on words of one of my favourite novels where what you read may or may not be what is actually going on… but more importantly focuses on the importance of story… and math understanding needs good stories, not ones that deal with slices of pizza or trains colliding etc…
But spoiler– I think this is one of the key books to read if you are dissatisfied with attitudes and actions (or lack thereof) around numerical literacy.
Some key takeaways
Math needs to be more than a “paint by numbers” approach that would not be acceptable as an art program (even if the finished product can look pretty cool as my cousin has shown as she does them as a self regulation strategy).
We need to slow down. The very notion of Zero didn’t exist forever, so why do we not spend more time talking about that. Or is it more about “moving on”… in which case why not emphasizing + – x / skills only via calculator since that is the most efficient methodology (though my kids at home remain impressed by how quickly I tabulate score on Ticket to Ride – in my head…. using “friends of ten” 7&6 = 3, so is 8&5….)
We explore letters and words. We take the time to look at vowels, consonants and rhymes. We play with them. Why do we not play with numbers. Looking at odds, evens and primes. Playing with patterns.
There was a misunderstanding about proof with math – too often it’s a+b=c Q.E.D. quod erat demonstrandum. It is correct. Nothing to see here. Move along. When the reality is that there can be a lot of ambiguity- especially with rich questions….heck it took 300 pages for mathematicians Russell & North to prove 1+1=2. And in elementary we just make assumptions we know better?
After all: inert education is not only beneficial; it is dangerous
When we look at big numbers (beyond what the mind can be comfortable with) it is nice to have a reminder from Lockhart: Mathematics is the music of reason. To do mathematics is to engage in an act of discovery and conjecture, intuition and inspiration; to be in a state of confusion – not because it makes no sense to you, but because you gave it since and you still don’t understand what your creation is up to you; do you have a breakthrough idea; to be frustrated as an artist; to be on another one but I’m almost painful duty; to be alive, dammit
And then there is infinity. No spoilers here. But…wow….
And there are the wonders – why does dividing by zero make something undefined (as a secondary student we geeking had jokes and discussions about this oddity) much like the error message by trying to get the square root of a negative number…and using imaginary numbers…and fractals…which may be the theme of an upcoming Mr Landy Classroom Takeover…..
And secretly “we” like maths. There is a reason why Sudoku exploded in popularity. Patterns and logic in games started shifting changed the traditional mindset of: I’d rather ____ than do math.
We need to spark the happiness of mathematics that we catch glimpses of
And “the magnificent seven” of math problems are fabulous – spoiler: the 24 problem is great: using 1, 3, 4, and 6 (exactly once) and then any combo of operations + – x /
Easy: 14 = 6 + 4 + 3 + 1
1 = (6-3) / (4-1)
If my class tomorrow solves 24 = ??? I will bring in a treat.
Then there is the power of probability. My favourite game for this is Deal or No Deal – love doing this as a group activity for when we should “cash out”. And possibly one of the most important areas to study (why one lotto ticket is just as good “odds” as 20….) the reality of actuaries and life insurance (essentially don’t buy… though my family experience says otherwise, but for reasons that defy “probability”)
In other words: value lost (cost) + value gain (possible winnings) x probability = sucky math aka Expected Value
There is similar math that says “no” to other things such as extended warranties. The math in Singh’s boom is simply mesmerizing. I could have read this book faster than I did, but I did not want to. As he says, sometimes slowing down is amazing – with math as well as others.
Speaking of time and flow (referenced nicely in the book), how often in math do we spend ti e exploring a math problem. I’ll admit my evolution shifted from a variety of questions on 11×14 paper (in all directions) to one question and exploring multiple ways to solve it.
Math is not a subject without room to wonder – not everything has been solved, and sometimes things we think are always right…aren’t. Even 2+2 can equal 5…..
I’ll admit that while I am a #westcoastbias guy, with my daughter at school in Waterloo, I am tempted to go to Toronto to see the math store: The Right Angle…
Why is it that librarians (two of us that have conspired a bit) love maths later in our careers – come for the books, stay for the numbers (and I don’t mean Dewey’s Decimal System)?
Mathematics can’t be taught as a delivery system – there needs to be creative and individual attention – not the dreaded “it’s Thursday so we must be on page 42”
And I love that there are references in the book to elements such as the ultimate answer (from Hitchikers Guide to the Galaxy)
Why is the book called “Catch-22” – because the number “fits” no other reason. Not a military regulation, but the rhythm of the digits.
There are interesting things in pop culture around the number 37.
What is your favourite number? Why? Are odd numbers funnier than even ones?
Why do we rely on base 10s for things like forecasts (30% chance of rain when really it is likely 27..or 34…)
Long division or wrong division…? 4280/64 or 64/4280?
Page 142 has the “Singh Rule” and I’ll note that again, the digits 42 appear….
Why do we spend time on mnemonics like Bedmas and SOHCAHTOA instead of exploring why and understanding the rules, not just “knowing” rules to use in given conditions?
I also agree with Mr Singh on the use of tools – I’m okay with multiplications leading to “close enough” (precision comes with practice) – and if using sin, before the calculator is used for precision, hopefully those working on the skill will know the sin of 61 degrees (which is 87%) – a ballpark of mote than 50% – not less….
Overall, Pi of Life did what I think was intended: confirmed that it is possible for math to be “happy” and doing math. And bring happiness to students doing math. It fills me with wonders and questions about what “we” are doing with the maths, and fills me with worries about those who want to emphasize a “back to basics/drill and kill” mindset to do well on standardized tests. But with the maths, I prefer the brain synthesizing over memorizing.
Looking forward to exploring Math Recess!