The Wannado* Curriculum - A Math Teacher's Journey to the Dynamic Math 2.0 Classroom - now available!

Now Available at Amazon

“The Wannado* Curriculum: A Math Teacher's Journey to the Dynamic Math 2.0 Classroom” presents glimpses of what 21^st century math teaching and learning could look like if, we truly embrace a student driven, teacher supported, national approach. The flawed NCLB and recent “Race to the Top” reforms are doomed to failure because they depend on a model that stubbornly will not scale, namely having cadres of well-prepared teachers who are experts in their field in every school. False hope continues to support these misguided efforts because of success stories from smaller, more homogenous countries like Finland and cities like Shanghai. Our more diverse, and heterogeneous approach does not lend itself easily to copying their successful(?) platforms. We need our own style that fits our needs better.

In this book, I plan to address this issue head on and explain how we could have a “tipping point” [1] where math achievement dramatically improves without having to resort to “super teachers” in the classroom to save us. Yes, we need good teachers, but to achieve progress in student math learning we need to follow a variety of paths, not just the one set over 100 years ago by the Committee of Ten [2] that outlined the current order of math topics in play today. What I propose is not a new idea. John Dewey and other progressive pioneers (mostly ignored by the mainstream decision makers in proposing solutions) offered it and practiced it successfully in their pockets of influence and notably in places where research studies acknowledged their success. Unfortunately, most reform efforts just tinker around the edges and don’t get at the heart of the problem: Most students find formal math learning boring and unrelated to their everyday life.

Even the top kids who are successful have little choice in how they study mathematics because the path has been set in stone, a path I call the “Royal Road to Calculus” which has its origins in the aforementioned Committee of Ten report.

The question, then, is what can educators, parents, and mentors do to offer alternatives to the current “one size fits all” path so that students will want to go to school not just because they need the necessary credentials and grades, but because they see the content of what they are learning as significant stepping stones to their dreams and ambitions and because they have adults around them who support their visions and provide the opportunities for them to explore the paths that interest them. Everyday math [3] is important but it can be learned in much more creative and empowering ways that enable students to see the value of math in their lives. This book will share examples of how this can be done.
Now available at http://amzn.to/1E4b1RV

*Wannado is the heightened version of “want to do” It’s what kids (and adults?) say when they really, really want to do something.

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[1] Malcolm Gladwell – Tipping Point

[2] Committee of Ten 1893 report

[3] Keith Devlin – Mathematics Education for a New Era. Chapter 3. P. 23

Three Wannado Activities

In the preview to my upcoming book (previous blog) I mentioned that one of the challenges in changing the culture of schools is the difficulty in upgrading the level of teaching abilities. Unfortunately, that is a bit like waiting for superman (or woman) and it's not going to happen anytime soon.  Michael Fullan writes that unless the teachers are motivated to continue to learn and improve their craft not much will change.

"The key to system-wide success is to situate the energy of educators and students as the central driving force. This means aligning the goals of reform and the intrinsic motivation of participants. Intrinsic energy derives from doing something well that is important to you and to those with whom you are working. Thus policies and strategies must generate the very conditions that make intrinsic motivation flourish."*

Motivating teachers to improve their teaching is more likely to happen if the activities they do are intrinsically interesting to students.

An example is “13x7=28” starring Abbott and Costello. (See lesson - student and teacher pages.)

Another example of this is the famous jinx puzzle that I wrote about here.

A third example is to script a sequel to the video Weird Number which I describe in detail here.

In each activity the teacher presents an engaging scenario followed by a hands-on activity or discussion. This leads to some surprise twists or conclusions which are discussed and debriefed at the end of the activity.

*https://michaelfullan.ca/wp-content/uploads/2016/06/13396088160.pdf

Wannado Wannabes

"It is time for a change. We do not have to accept that the school we have always had is what we have to have now. Times have changed. Now everyone goes to school and now we have computers and the internet. The possibilities are endless. The economics of school can be quite different than what they are now. We can let kids learn what they want to in the way that works best for them. We will have happier and better functioning society because of it."

-Roger Schank

When I think back to my high school days what I remember most was playing baseball and basketball on my high school teams. Those were my favorite subjects. They served me well. I continued to play those games until my early 50s when my knees couldn't take the pounding anymore. The other subject that served me well was math. Without that I wouldn't have had the career I had being a math teacher. But math was not something that I would go out of my way to do. I never was interested enough to explore the wonderful math books in the library. If it wasn't for my math crisis in my sophomore year in college when I almost quit majoring in math, I would have never discovered the books in 510-599 section of the library which got me to see that math could be interesting and even empowering. I'm sorry to this day that the traditional math curriculum that I followed didn't allow for excursions to those books that might have fostered a love for math that I really didn't have despite being a straight A student in math.

Roger is right. Schools should allow students to study things that interest them; to follow what I call a wannado curriculum. I'm sure we would have a lot of wannado wannabes in schools everywhere.

I'm writing about my path to the Wannado Curriculum in my forthcoming book titled "The Wannado Curriculum - A Math Teacher's journey to the Dynamic Math 2.0 Classroom"

More from the Wannado Curriculum (Book in Progress)

Click to see Youtube video

The Weird Number

Back in 1970 I saw an animated film that changed my perspective on teaching fractions. It was called The Weird Number. (1) Here’s a piece of narration from the movie:

“My story concerns a strange event that took place in a little town nestled in the mountains.  A little town inhabited only by natural [counting] numbers, but whenever the townspeople gathered together rumors were exchanged; rumors that other numbers lived in the dark woods beyond the mountains but no one could imagine a number that wasn’t a natural number so no one believed the rumor.”  

So starts the story of the Weird Number a delightful excursion into a fantasy world of a town inhabited by natural numbers. Two citizens of this town 9 the baker and 736 the sheriff play key roles in the development of the story.

The narrator continues:

“Now one thing that never happens in this town is robberies.  This is because the thief is easily identified since the number of items stolen is always the same as the number of the thief.  For example, if 4 stole something, he would steal 4 of that particular item so he would be easily identified.  Therefore, there were never any robberies. But one day there was a robbery.  9 who was the baker rushed over to the sheriffs office to tell him about the robbery. ‘What was stolen?’ the sheriff asked 9.  “Just a little piece of bread.” replied 9.  ‘One piece of bread?’ said 763.  ‘I can’t believe it.  One is the mayor.  He would never steal.’

‘No, no,’ said 9, ‘not one piece of bread, a little piece of bread.’

‘Not one piece of bread, but a piece,’ said 763.  “What kind of nonsense is that?’”

Actually this makes a lot of sense once you understand who the thief was.  It turned out to be 2/3 a number totally unknown to the residents of this town. The sheriff organized a posse to catch the thief, but 2/3 was a clever escape artist because he was a master of disguise.  When the posse discovered his location in a barn, he stepped out wearing his 4/6 disguise and told his pursuers that he had no idea where 2/3 was. In the meantime the posse learns from 4/6 a trick that all whole numbers are capable of since they are also masters of disguise. For example, One, the sheriff could become 2/2, 3/3, 4/4 etc. Five could become 15/3 and so on.

Soon after 4/6 left them, 763 realized that 2/3 and 4/6 were one and the same number.  So he continued to pursue him.  But 2/3 was always clever enough to take on a new form (in this case 18/27) to outwit the sheriff.

After the whole numbers realized their ability to transform into other forms numbers in fractional form became common site on the town square.  Even 2/3 was not afraid to hangout in town, albeit in a different form. (2)

The movie ends with this cliffhanger that inspires a wannado followup.

The fractions and whole numbers are sitting around at tables in a pub pleased as punch that they were all members of the same number family when they learned of rumors that were other kinds of numbers living in the dark woods beyond the mountains.  Numbers that could not be written as a natural number on top and natural number on the bottom.  But no one paid any attention to that. The movie ends with a flash of lightening in the window followed by “The End” splashed on the screen.

After I saw this movie for the first time I was hoping for a sequel, but it never materialized as far as I know. So who or what were these mysterious non-rational (irrational) numbers?

Here’s a suggested activity/project for your class: Have your students create a video sequel about this mysterious number. 

What kind of story line could you have?  Here’s a suggestion. Start off with this:

“It’s a stormy day on the sea off the coast of Greece.  The year is around 520 BC.  A man, fighting for his life, is heaved over the side of a boat and plummets into the open sea to die.  His crime?  Stealing the crown jewels?  Murdering the King?  Nope. He was telling the world a mathematical secret. The secret of the dangerous ratio. This was the fate of Hippasus, a follower of Pythagoras who was forced to walk the plank and drown as a punishment for this crime. it’s difficult to imagine what a stir it created when it was first proposed! The Pythagoreans just couldn’t imagine that there was no ratio that equaled the length of the diagonal of a 1 unit square. The value was the square root of 2 – an irrational number. So they wanted to keep it a secret. Thus Hippasus who knew otherwise was doomed to his fate. (3)

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1.    Xerox, 1970. The Weird Number. Video. 

2.    A professor of math education used the Weird Number video as a motivator for a lesson development assignment for his students. Here’s what they came up with. http://edu320.blogspot.com/2006/09/weird-number.html

3.    Read more about the Hippasus story in Brian Clegg’s “A Dangerous Ratio” http://nrich.maths.org/2671

My First Days of Teaching - 1967

My first day in front of a room filled with kids scared the hell out of me, but I kept my confident veneer. As a first year teacher, I was assigned 5 classes – three Algebra I and and two General Math. When I asked for advice about teaching the general math classes I was told to give them busy work. The textbook we used was at least 10 years old, and there wasn’t much in it that my students could relate to. Sometimes I pretended to be doing something important at my desk so I would let them chat away the “study” period that I had given them.  Fortunately, it never came back to haunt me, although I did feel guilty about it. What was the matter with me?  I wasn’t sure which was more boring  - teaching them or watching them learn. A couple of them reminded me of the girls who used to sit in the back of the room with the sweathogs in the Welcome Back, Kotter TV show.  Why was I so irresponsible? Because I really didn’t know what to do with them.  So I chickened out and hid behind busy work pretending it was important.

Another memorable moment with that class was having my life threatened by one of the students. I had to throw him out of class for talking back to me. No curse words were uttered, but his intense defiance not only scared me, but also put a serious dent in my façade of being in charge.

The algebra classes, on the other hand, were a joy in comparison. The students were motivated. About 35 years later I heard from a couple of them thanking me for making it interesting for them. (Thank you, Internet.) I appreciated it.  Better late than never.  I still plan to visit one of the students in California. OMG, he’s in his 50s.

The Stock Market Game
So three/fifths of my day was fine, but the other two/fifths of general math classes was boring for both my students and me.  I really didn’t know it, but we had an unspoken compromise, a kind of truce where we agreed that if they didn’t act out and looked busy, I wouldn’t bother them or try to make them think. They had collectively given up on math long before they even got to me.  I knew I wouldn’t be able to do this forever. I could stand it for just so long.  Something had to give.

Then I got a break. On one of my caffeine energized mornings in the spring of 1968, I  read about how well the stock market was doing.  It seemed that any stocks in those early 1960s carrying the name “tronics” became “highflyers.”  The electronics sector was responsible for a two year bull market after President Johnson’s State of the Union address on January 10, 1967.  Despite my math background the electronics field held little interest for me nor did I have much interest in the stock market. It wouldn’t be until 1970 that I’d spend $70 on my first calculator.  But I was intrigued by how the mainframe (whatever that was) seemed to be rocket propelling the stock market.

I was still thinking about the stock market when I discovered a stock market game in a department store. I thought it would interesting to try it with my general math classes. At this point, I had nothing to lose.  I just wanted another way to get through the day with those general math students.

Okay – despite how this sounds – like something scripted in a movie – It really did happen.   I bought the board game and we played it. It was a hit!  Even the principal stopped by my room to see what all the ruckus was about. He just stood there dumbfounded not sure what to make of it. My “sweathogs” were having fun doing something educational.  Kids engaged in buying and selling stocks. Now, fast forward 50 years and I’m playing the same game with a group of distracted 6th graders. But I’m getting ahead of myself. I’ll return to Stocks and Bonds in Chapter 12.

We had fun and my students were doing math willingly because they wanted to not only to win the game but doing math made sense to them. I had stumbled upon something so pedagogically important that it would never forget it: sustained willing engagement.

Excerpt - The Wannado Curriculum - in press (due date: Nov. 2014)

Why can't math textbooks be more engaging reading for students or is that an oxymoron?

Curriculum of prestigious private K-8 school

Aritstotle Academy, a chartered school in Utah, uses the wonderful book byJoy Hakim “A history of US” for history and social studies and Delta modules for science. But in math students are forced to do Glencoe Math which reads like a recipe for Minestrone soup. I’m surprised that Aristotle Academy doesn’t use at least one of Joy Hakim’s science books. (See http://www.joyhakim.com.) For math Ivar Ekeland's The Cat in Numberland is not only interesting to kids, but contains some real math worth considering. But then something would have to give from Glencoe Math's maze of topics which of course are way more important than a silly book about cats. (Really?)

 Since textbooks are written by committee and need to cover all the bases for all the stakeholders involved, adopting a creatively written textbook is a long shot at best. Finding one is not easy either. Julie Brennan over at http://livingmath.net has many good ones to recommend. Her audience is mostly homeschoolers, but good alternative schools will benefit their students by exploring her list.

Think Math - Wonderful video that begs an important question

http://youtu.be/oD8-8uoS5nA

Watch this video. It's truly wonderful. Yes, we need to get kids to think about math. But what math? Rick's example showing the dynamics of generating a sine curve is great, but will all kids appreciate it and do we need to have every student appreciate math at the level that I and other math teachers appreciate it? We always get stuck in thinking as a teacher and what we think is wonderful but not always what the student wants to do. The "Wanna Do" curriculum is what I endorse. Students get to explore math in a way that makes sense to them. Sine curves evolving from a point spinning on circles is wonderful fodder for Youtube so that like minded students and mostly teachers appreciate. I would have chosen a different example that would resonate with more students. and adults. (To be continued.)