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)


  1. Making progress on my book. Should be available November, 2014

  2. I'm in the final editing stages. Book could be out in January, 2015