Thursday, June 30, 2016

Achieving Mediocrity and what to do about it

This comic reminded me of my days teaching math at Brooklyn Friends School (BFS) in the late 1970s when I offered every student an opportunity to get an "A" if they were willing to do what was necessary to achieve it. I was always surprised by how few of my "C" students would take me up on it. Today I know why. It's because I was "selling" a product that those students didn't really care about but were forced to "buy." For Curtis a "C" is good enough for a subject that he feels he is terrible at and doesn't think is worth the effort. Kids want to achieve success, but they are not willing to work hard at something they think they can't be sucessful at. 

Math becomes more engaging for students if it is embedded and integral to the to the goal of the activity but not the main focus. For example, games or challenges can motivate students to learn basic skills where without the game context learning the skills would be a bore.
Since math is an arena where context matters, solving contrived math problems is not engaging enough for most students. So we as teachers do the best we can to make traditional problem solving as interesting as possible.

Let's say our goal is have students know something about graphing linear equations. In the flipped classroom model, the teacher could assign students  Salman Khan's presentation of the skill (albeit rather sloppily) on video. Then in class the teacher could have a handout ready with a bunch of linear equations on one side of the paper and corresponding coordinate axes next to it. (I downloaded this piece from 
The solutions are provided so students can check them and then move on to the next lesson. Very high tech, Right? Yes, but overall boring and pointless. Most students don't really care enough to even ask "What's the point?" because they know it will be on the next test/quiz.

An alternative method is to use the computer program Green Globs. Here drawing lines has a purpose. They blow up globs! Students are presented with an array of 13 globs randomly distributed on a coordinate axis. The goal is to get the highest score by exploding all the globs using algebraic functions in this example we can stick to just linear equations which produce straight lines.
Below is a game in progress. The first shot y = -2 hit two globs that have y values equal to -2. And since the scoring doubles for each additional glob I hit with one shot, I get 3 points (1 for the first and 2 for the second glob.)
 I can do the same with x = - 4 and get 2 more globs for a score total of 6. To get more points I would shoot a line that slopes downward from left to right. For example, y=-x+5 gets me 3 globs which is 7 (1+2+4) points.
Upon reflection I can see that I could probably get 4 globs instead of 3 by tweaking the previous equation. If I make the slope -.8 the line hits all 4 globs which increases my score from 7 to 15 points since the 4th glob was worth 8 points for a total of 21 points. (Watch this explanation in more detail here.)
(To give students some intuition about slopes and Y intercepts they could watch Salman's demonstration of developing intution in getting lines to go through points.)

Notice that the focus is on blowing up globs, not on the math. However the math is needed for the student to succeed. And the better he or she knows the math the higher the score. And students really do "wanna*" get a higher score.

We need new curriculum that will make the math intrinsically interesting for students where the focus is outside the math. I call these wannado activities because the students are motivated intrinsically. They love the game and they want to learn the math to be successful which is within their reach. 

Many wannado activities are already out there. You can start to move your curriculum in that direction by trying out existing activities. I will be sharing examples in future blog entries.

Wannado Activities
There are 3 steps:
1. Set the stage for the learning of the math. Announce a game or challenge or puzzle or whatever else is instrinsically interesting to your class. It will vary from class to class. But from my experience there are strategies that are universally motivating to students.
2. Do the activity. Here students shoot globs. The teacher helps them to improve their skills by practicing certain strategies that can get them better results.
3. Debrief the activity. Ask the students to demonstrate what they have learned. 

Here is a detailed account on introducing Green Globs.

Currently Green Globs is available from David Kibbey at

*I began to distinguish between "want to do" and "wanna do" after a student who was told he was not allowed to use the computer said "But I really, REALLY wanna use it." (circa 1981)

Saturday, June 13, 2015

The Motivation Equation

The heart and soul of student learning is intrinsic motivation. And no one does a better job of describing this phenomenon than Kathleen Cushman in her refreshingly short and web-based book "The Motivation Equation" which is available to read online or download for free.

The table of contents gives you a nice snapshot of what the book contains. Here are the chapter titles:

Preface. In which we meet Ned Cephalus, his teachers, and their learning scientist friends
Introducing the Motivation Equation. In which we consider what learners value and their expectations of success
Chapter 1. Make sure we’re okay. In which teachers make it safe to risk a try
Chapter 2. See that it matters. In which students discover a reason to care
Chapter 3. Keep it active! In which fun, play, and surprise create a culture of curiosity
Chapter 4. Get us to stretch. In which students see in different ways and reach beyond their grasp
Chapter 5. Act like a coach. In which teachers guide practice and reinforce new skills
Chapter 6. Ask us to use it. In which students explain, teach, present, and perform what they learn
Chapter 7. Give us time to reflect. In which students think back on their learning and growth
Chapter 8. Have us make plans. In which students figure out where to go next
Appendix 1. Teachers and their lessons. In which teachers use a protocol to study learner motivation
Appendix 2. Resources. In which we offer practical resources for teachers

If you only have time for one chapter read Introducing the Motivation Equation (linked above) to experience what this is all about.

Though I loved the book, it is not easy for a teacher to implement given the constraints of a typical classroom. But its definitely a worthwhile goal on the road to the Wannado curriculum*.

*In my book, I define “wannado” as an excited form of “want to do.” For example, I wanted to do my math homework, fearing the consequences of not doing it, whereas I always would wannado (play) baseball in whatever form it appeared. The same for having to do something. “Haftado” is an extreme, distasteful form of “have to do.”

“Instead of making kids learn math, let’s make math kids will learn.”

Sunday, June 7, 2015

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.

Tuesday, April 21, 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.

Monday, March 23, 2015

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.

Tuesday, March 10, 2015

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 21st century math teaching and learning could look like if, we truly embrace a student driven, teacher supported, national approach. The flawed NCLB and current “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

*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

Saturday, December 27, 2014

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

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

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.