Snowballing for Questions
A couple of observations at this point. This took a period. Groups left their questions and the pictures behind when they rotated. So new groups that arrived could read all the previous groups questions. By the time the 4th and 5th groups arrived to each station / theme, most questions had been asked and the behaviour wasn't great. Also there were lots of silly and inappropriate questions. I wonder how many of these questions might have been escalated into conflict between student and teacher in a different format?
In retrospect, I think I would generate the questions over 5 days at the start of those 5 periods. Also I would not allow groups to see other groups questions. Live and learn.
Snowballing to Categorize the Questions into the Curriculum of our Course
At the start of the second period groups then started at their original station / theme and categorized the questions into the curriculum headings for the course. Groups then snowballed to all 5 stations / themes until they had categorized the questions into the curriculum headings. This forced groups to discard irrelevant or inappropriate questions.
Here are a few samples (Of course the sheets were colour coded based on the colour of their group):
When is it better to go to Overwijk's carnival? McLaurin 's Carnival? (Linear relations and intersections of lines)
How far does the bean bag go? (Quadratics)
What is the maximum height of the bean bag toss? (Quadratics)
How much space does the Skee Ball machine take up? (Volume)
What is the angle of incline of the beanbag boards? Skee ball machine? (Trigonometry)
What is the volume of the snowman? (Volume)
What is the volume of snow in the backyard? (Volume)
What is the maximum height of the snowball throw? (Quadratics)
How far does the snowball land from where it was thrown? (Quadratics)
What is the height of the doorway in the igloo? (Quadratics)
What is the length of the outside of the igloo? (Sum of Squares)
What is the width of the igloo? ( Sum of Squares)
What is the angle of incline of the side of the igloo? (Trigonometry)
What is the surface area of the igloo? (Surface Area)
What is the height of each pillar? (Similar Triangles)
What is the Height of the parabolic bridge? (Quadratics)
What is the length of the wire? (Sum of Squares or Trigonometry)
What is the angle between the wire and the bridge? (Trigonometry)
What is the angle between the two wires? (Trigonometry)
Swimming Pool theme
What is the Volume of the pool? (Volume)
What is the surface area of the thatch hut? (Sum of Squares and Surface Area)
What is the height of the pool ladder? (Sum of Squares or Trigonometry)
What is the angle of the poll ladder? (Trigonometry)
What is the maximum height of the dive? (Quadratics)
What is the length (height) of the ramp? (Sum of Squares or Trigonometry or Similar Triangles)
What is the volume of the ramp? (Volume)
What is the depth of the parabola? (Quadratics)
What is the height of each board along the ramp? (Similar Triangles)
How high does the skateboarder jump? (Quadratics)
What is the difference in height of the skateboarder and the skateboard? ( Quadratics)
A Day Break
The class then took a day break from this activity. This gave me time to create the pictures with the appropriate data for each group for each theme so that the groups could answer their best three questions per theme. For some photos I did not add data because there were people in the pictures that the students could use to create a scale.
This should give you the idea:
A couple of observations:
1) Since this basically covered most of the curriculum in our course, as I observed students working on solutions, it was obvious where students had weaknesses.
2) The collaboration and engagement during this time was great. Not sure why? Because they made the questions?
3) Some of the questions were difficult. This caused some frustration.
¨ Did you connect math to the problem?
¨ Can you apply any of the math covered in class to this problem?
¨ Did you translate the problem into math?
¨ Have you use as many ways as you can (e.g. table of values, graphs, equations, diagrams, words, numbers)?
¨ Do you have all the tools you need? (e.g. graphing calculator, grid paper, measuring tools, formula sheets, etc.)
¨ Do you have a plan?
¨ Does your math make sense?
¨ Have you read over your work?
¨ Does your answer make sense?
¨ Can you explain how you know your answer makes sense?
¨ Is there another way you could have approached this problem?
¨ Could someone else understand your work?
¨ Are you able to clearly explain your work to someone else?
¨ Have you used units correctly?
¨ Have you used symbols correctly?
¨ Have you used math terms you learned in class?
¨ Did you write concluding statements, highlighting your answer?
On the back of their best work I asked them to rank the curriculum from 1 - what they were best at to 6 - what they were weakest at. The six curriculum areas were Sum of Squares, Surface area / Volume of 3D figures, Similar Triangles, Trigonometry, Linear relations, Quadratic Relations.