Conclusions from the Wannado (Math) Curriculum (a recently published book written by Ihor Charischak)

It’s entirely possible to fall in love with mathematics if the context is
right, like the “perfect storm,” where all the elements come together.
Beyond the day-to-day usefulness of math, mathematics can be
dynamic, fascinating, and empowering. Intrinsic motivation should drive learning. The math curriculum should be open-ended and allow for student and teacher creative flairs. There is a place for teachers and students to be partners in their learning enterprise, so that creating stories can bring a new life to what students would otherwise say is boring.

Weaving other subjects into the teaching of math is an incredibly powerful way to engage student imagination and help them to see math’s relevance to the real world. It’s fine to be able to solve an algebraic equation, but if students have no idea what it’s used for […], then what’s the point? Without a context, it’s just “mental gymnastics.” You don’t have to go far to see the math in history, science, music, and art. The list is endless.

Currently, story-based learning adventures are not part of most math curriculums. The focus remains on the “haftado” curriculum (e.g., passing through all the gates on the "royal road to calculus," where rewards are mostly extrinsic). However, one can invent—or better yet, reinvent—mathematics. The shift from a “haftado” to a “wannado” curriculum does not need to deprive students of the basic skills they need to be successful. Rather, it provides the perfect context for understanding the relevancy of those skills and the motivation to learn them. If kids “wannado” the projects, they will learn whatever hard stuff they encounter in order to accomplish their project’s goals … just as they do when they play video games. We, as a math community, need to develop alternative routes for students with unique needs and skills. Technology opens the door for a whole host of alternatives. To keep the focus on math, it is imperative that technology be integral to the curriculum, rather than integrated. This is a subtle but important distinction because technology-based microworlds empower students to focus on getting to know powerful mathematical ideas seamlessly. I firmly believe that technology can transform teaching and learning environments and help students achieve beyond what is possible without it.

Excerpt from "The Wannado Curriculum A Math Teacher's Journey to the Math 2.0 Classroom" by Ihor Charischak (2015)

MTBoS and other NCTM conference adventures

"We are math teachers who share what we've learned, cause we don't want our classes to suck the energy from students. Professional development among friends, not just colleagues. Fun! Immediately useful! Interesting!" So starts the description of MTBoS a 

The chart

refreshing new movement in the NCTM world. Armed with a table in the exhibit hall at the annual NCTM meeting in Boston this fledgling group of young social network activist teachers are slowly yet exponentially changing the face of math education. At least that's how it appeared to me every time I passed the booth and could barely squeeze in to say hello to the latest facilitator (of which there were many) at the booth. Led by Tina Cardone's enthusiasm the MTBoS booth was the best place to visit. What did they have to offer? Lot's of free stuff that members created and shared passionately with visitors. "Do you tweet? Do you blog?" If no was the answer then newbie visitors were given a 5 minute overview of the advantages of these socially viable venues. I'm sure many "joined" the movement and signed their names on the chart with their new twitter handles.

At the MTBoS booth

Tonight MTBoS will be doing a webinar having participants share their experiences at the conference. Click here for details.

I hope to "see" you there!

More NCTM conference adventures in my next blog entry.

The Wannado* Curriculum: A Math Teacher's Journey to the Dynamic Math 2.0 Classroom

Ihor Charischak

In his new book Ihor Charischak describes the dynamic classroom as a place where the interaction between teacher and students produces engagement and learning. Success depends on what the teacher does, how it fits in with the needs of the students, and the quality and utilization of resources. In The Wannado* Curriculum, Charischak tells how he turned his vision of a dynamic Math 2.0 classroom into a reality. Part memoir, part teaching tool, the Wannado Curriculum offers insight into helping teachers establish a context for creating their own "wannado" curriculum, a project-based approach where the context makes the content interesting to students. The book:

• describes how growing up as an immigrant in America impacted his learning
• tells how he discovered the secret to working with unmotivated students 
• Explores the idea that alternative ways of teaching and learning are the keys to powerful, dynamic teaching and learning that motivates students 
• discusses his experiences in a private, child-centered school, where he used computers to practice the teaching and learning he was excited about 
• relays how the real-life game of craps inspired a reluctant student to ask questions about the mathematical intricacies of the game 
• brings to life his experiences with computers in teaching math 
• details his vision of the dynamic math classroom 
• introduces Math 2.0, a powerful environment that uses mathematics software and collaborative Web 2.0 tools in a dynamic classroom setting 

The Wannado Curriculum presents glimpses of what twenty-first century math teaching and learning could look like if a student-driven and teacher-supported method was universally embraced.

More information about the Wannado Curriculum is available here.

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

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.

---

[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)

________________

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