Math on the Brain

On this morning’s run to Priest Point Park, I was thinking of Ms. Z’s Marysville Middle School mathematicians. More specifically, I came up with a real world word problem for them. Maybe a “do not proceed to high school” until passing problem of sorts.

In Olympia, Washington there’s a beautiful little waterfront community called Boston Harbor. Visit it sometime. Rent a kayak, eat an ice cream bar at the marina, meditate on the Puget Sound. BH is 7 miles from downtown Oly. Traveling from BH to town on BH Rd. the first 5 miles are 40mph and the last two are 30mph. However, it just so happens that Thurston County doesn’t patrol North Olympia’s rural roads. Therefore, half the residents, the Rule Followers, do 40 and 30, but for the other half of Deplorables, like myself, the only deterrent is occasional deer on the road (for the record, I do 45 and 35).

On Monday’s run, a van passed me doing approximately 70mph, today a white Volvo wagon doing 65mph (yes, I am a speed estimating savant). Which got me thinking. How much time does a BH driver save on their way to town if they drive 60mph for the 5 miles designated 40mph, and then stuck behind a Rule Follower, 30mph for the last 2 miles?

I’ll wait.

Here’s my peabrain calculation. Sorry in advance to Ms. Z. for my unconventional approach. First, we need to calculate the Law Obiders travel time. As a cyclist that tends to ride around 18-20mph, I know that at 20mph, it takes 3 minutes to travel 1 mile. Therefore, if we double the speed, we can halve the time, so 40mph = 1:30/mile. So multiply 1:30/mile x 5 = 7:30. At 30mph it obviously takes 2 minutes to travel 1 mile, so 4 more minutes, so BH to downtown Oly in 11 minutes, 30 seconds.


Now what about The No Regarders for the Law? 60mph is 1 minute/mile, so 5 minutes. Then our 4 minutes to cover the 2 mile stretch for a grand total of 9 minutes.

Here’s the tricky part, keep your columns straight people! 11:30 – 9:00 equals a grand total savings of 2 minutes and 30 seconds.

Now a message for my BH friends. If you’re so efficient with your time that you never waste two and a half minutes once you get to your destination, go ahead and speed away, just don’t look for any sympathy when your car is totaled by Bambi. Or leave for work 2-3 minutes earlier?

All good math lessons have extensions, so here’s mine for Ms. Z. Based on available government statistics, calculate the increased likelihood of an accident as a result of increasing one’s speed by 20mph. Then take that increased likelihood and calculate the approximate negative effect on the speeding driver’s life expectancy. I’m guessing it’s greater than 2 or 3 minutes.

Class dismissed.


Strange Math

From Bill Gates’s: The Billionaire Book Critic:

Mr. Gates says he reads about 50 books in a year, eschewing digital readers for old-fashioned books on paper. When he is busy with work, he reads about a book or two a week but will consume four or five in the same period while vacationing with family.

Let’s say he works two-thirds of the year or 35 weeks and vacations the other 17.

That would be (35 x 1.5) + (17x 4.5) or 52.5 + 76.5 or 129.

[Related: The Math-Class Paradox.]

Continuous Improvement

A bullshit workplace notion. Midway into artistic or athletic activities, jobs, careers, relationships, life, we plateau. Shortly thereafter, energy ebbs, and our performance erodes.

We improve for a bit, we plateau, we decline.

I observed a good second year math teacher today at the independent middle school. Then we conferenced. After listening to him reflect on the pre-algebra lesson, I listed his many strengths. Then I made a few suggestions. Call on Ben as soon as he puts his head on his desk. Give Robin your marker, take her seat, and have her teach everyone her prime factorization method by illustrating it on the board. Have two more students explain and illustrate their methods and then ask, “Which is most efficient and why?” Let the kite string out a bit and “guide from the side” for awhile. Remember, the educative effect is greater when students do something than when something is done to them.

He told me he likes it when I observe because he’s reminded of effective teaching methods that he has let slip. He’s a good second year teacher who has started to plateau because he’s rarely observed, and rarely gets to observe other, more accomplished teachers.

A small number of the very best teachers, artists, athletes, and people continue improving considerably longer than their peers by seeking out expert, critical feedback; by investing progressively more time and energy; and by surrounding themselves by other positive, hardworking people, who are trending upwards.

And the wisest teachers, artists, athletes, and people have a sixth sense for both when they’ve plateaued and when their performance has begun to decline. And then the wisest, most selfless, most financially secure of them, step aside to provide the next generation opportunities to improve, plateau, and decline.

Adolescent Literacy

Felt nostalgic for Europe I guess and took the train to PDX for a workshop on adolescent literacy. I WANT to be a train person, but Amtrak is making it hard. It’s bad enough the train takes longer than driving. My Squeeze and I planned on eating an early dinner in the big city and then returning on the 6:15p. Workshop ended an hour early and so we decided to take the 4:20p and eat at home. Headed to the iMax at 3:40p. At the train station we learned the 4:20p was delayed about an hour.

Long story short, it never arrived, something about a tree on the track. Instead of a romantic dinner, we took a walk and then sat in front of the station reading in the setting sun eating pistachios. The 6:15p originates in PDX so it would have to leave on time. . . right? Longer story shorter, we walked off the train at 7:40p, exactly four hours after leaving the hotel for home. Something about a broken brake line they couldn’t fix. The man sitting in front of us asked if we wanted a lift home, he was bailing on the train, taking the iMax to his car in Clakamass. He had a morning business meeting in Seattle. What a life, or at least, nightsaver.

But I digress.

Stanford research prof was the main presenter. Excellent researcher I’m sure, but how can I put this nicely, his presentation skills were not as well developed. Here’s what Dr. Stanford Expert and his co-presenter, a much better teacher from The U of Utah, recommended.

1. Strengthen adolescent reading fluency, vocab, and comprehension through scientifically researched (read quasi-experimental and other quantitative studies) teaching strategies that have been proven to be effective including explicit vocabulary instruction and classroom discussion of texts.

2. Explicit instruction involves three steps: I do it (modeling). We do it (guided practice). You do it (independent practice). If teaching a complex literacy skill like summarizing, the three steps may take an entire week. Teachers inevitably rush the steps.

3. There are three elements to classroom discussion of texts: 1) efferent (the who, what, where, and why of what was read. . . what did the writer say); 2) analysis and interpretation; and 3) evaluation. . . how did you feel about it, how convincing was the argument or engaging/illuminating the narrative. Research suggests teachers slight part one which low achieving students benefit the most from. Dr. SE made it clear he had “absolutely no interest” in evaluation/students’ opinions.

It was alternatingly interesting and exasperating. Throughout the day there was no discussion of the purposes of literacy; there wasn’t a single reference to digital, electronic, or multimedia texts; nor was there a single reference to the societal curriculum. Nevermind that adolescents are in school 22-23% of the time and outside it 77-78%.

Here’s an alternative, admittedly less scientific, more sociological perspective.

Immerse children and young adults in rich literary environments for long periods of time. Surround them by interesting reading material. Unplug more and read in front of them. Talk about what you’re reading. Demonstrate a love of reading in your daily life. Repeat year after year.

Here’s a related math literacy, or “numeracy” example. One Sunday morning, when seventeen was two or three, she crawled into bed and snuggled in between mom and dad. Dad started counting. “One.” She squeaked, “two.” And thus began Sunday morning math. Overtime, we counted by twos, threes, fours, whatever we felt like. We never called it multiplication. My hunch that my daughter’s success in math is in part explained by those Sunday mornings would not impress Dr. SE one bit.

I was impressed with how candidate Obama talked eloquently about parents being their childrens’ first and most important teachers. I wonder why he’s abandoned the Bully Pulpit.

The teachers and school leaders in the workshop politely and passively accepted the “literacy and numeracy as a teacher-centered science” way of thinking as if there are no alternatives. Few probably realized with that paradigm comes a narrow emphasis on technical skills, test scores, and national economic competitiveness.

Research and what happens in school matters, but magic can happen when young people are immersed in rich literary environments where word and number play are daily activities.