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The Wisdom of the Crowd

Inspired by this segment of the BBC’s series, The Code, I recently tried replicating the jelly bean experiment during my school’s science fair.

 

I filled an old pickle jar with jelly beans and put it on display as students, teachers and parents explored the science fair. All science fair visitors were invited to estimate the number of jelly beans in the jar for a chance to win all the jelly beans. Meanwhile, I collected the estimates to determine whether the average estimate approached the actual number as more and more people participated.

In order to streamline the data collection, I had students enter their estimate in a google form. The estimates were automatically collected in a spreadsheet that I could analyze. It only took a few minutes to graph the results:

Jelly Bean Graph

The display was a popular exhibit at the science fair and appealed to both elementary and secondary students, as well as parent visitors. As it turned out, the three best estimates all came from elementary students. I just presented the results at the elementary school assembly and it was a big hit. It was great to be able to present scientific evidence that two heads (or many heads) are better than one!

Would you like to give this a try at your school? Here’s a sample Google Form that you can use to get started.

Team Problem-Solving

My grade 8 students just spent 40 minutes working on this problem:

A circle with a area = pi is tangent to the x and y axes of a grid. What is the distance from the centre of the circle to the origin?

Other than defining “tangent” for them, I didn’t give them any other hints. They were able to solve the problem using the knowledge that they have just acquired about Pythagorean Theorem, along with their prior knowledge of x-y co-ordinates and the area of circles. The class is a mixed-ability class (as all math classes are at my school), but I had grouped students in similar-ability groups for this activity. As a watched students working on the problem, I was impressed with a few things… Continue reading

Productive Collaborative Relationships in Math Class

The longer I teach math, the more I find myself teaching students how to learn math while I teach math itself. Whether it’s a developmental stage, or the product of the routines they’ve had in previous years, students often go through the motions of practice assignments as if they’re for my benefit, rather than their own. When individual students have this attitude, they tend to rush through work just to get it done, rather than taking the time to make sure that they’ve mastered the skills. I’ve written about this before and you can read about it in detail here.

In addition to developing habits for effective practice on an individual level, I’ve noticed that students also need guidance when it comes to working collaboratively. An ecologist at heart, I started classifying the collaborative pairings that I observed in my class as either parasitic, altruistic or mutualistic. Some students ask for help right away. Of those students, some are even strategic in their choice of who and how to ask, and manage to get the work done for them, just like parasites. Other students, the altruists, are always willing to help but sometimes spend so much time helping others that they don’t have time to get to more challenging material. Only a few students have learned how to ask for help and provide help in ways that are mutually beneficial.

I brought this up with my students the other day and asked them to suggest some strategies that would make collaboration as productive as possible for everyone.

They decided (with a bit of help), that they needed to…

  • Try each question on their own for at least 2 minutes before asking for help.
  • If they receive help, they then need to “pay it forward” by helping someone else with that topic.
  • When they’re helping others, they can explain what to do, but they can’t just give away the answer.

I’ve posted this in the classroom as a reminder:

collaborative partnerships

This is already making a difference. I’m optimistic that with regular reminders, students will internalize these habits and become more independent as mathematicians and as learners.