Research Ideas
Do the math workshops
Mathematics (funded by SSHRC + Fields)
- Infinity in my hand (gr. 3: fractions, infinity, limit)
- Making 10 (gr. 3-4: patterning, linear functions)
- How to fence a pen (gr. 2-4: area, perimeter, optimization)
- Where parallel lines meet (gr. 2: geometry of a sphere)
- Probability race (gr. 2-4: probability with dice)
- Odds and evens (gr. 2, 7: growth patterns, odds, evens)
- Low floor, high ceiling (big ideas for young mathematicians)
- I don't like math anymore (I love it now! - math-for-teachers)
- Math performance (what did you do in math today?)
- Research performance (arts-informed research dissemination)
- How big is a billion? (gr. 3: Fermi questions, social justice)
- Math trains (gr. 1-4: growth patterns, slope, linear functions)
- Math waves (gr. 3-4: patterning, trigonometry)
- Cough, cough (gr. 4: pollution, social justice)
- Eating plastic (gr. 3-4: the great plastic dump, social justice)
- Refraction action (gr. 2-3: refraction)
- Will it float, will it sink? (gr. 2-3: density, buoyancy)
- Gravity's pull (gr. 2-3: gravity, density)
- Never met a happy bully (bullying and breaking the silence)
- The lizard in your brain (violence in the media)
Feedback
"These videos are wonderful. I noticed the eager participation of the learners. They did not appear intimidated and shared so willingly. They were jumping in to express their learning. I appreciated the excited voices of the children in the background. The spontaneity is contagious. I am impressed with the eagerness, willingness and fun these students are experiencing. Really, in math? I love it!"
"Thank you very much for these video resources on "Making 10". I really like this problem. It is a totally different approach to teaching math. I will pass these resources on to our teacher candidates."
The Pleasure of Making 10
In grades 3 and 4, students solve missing number equations, like 3 + __ = 12 and __ + 5 = 8. When solving such simple, unrelated problems, students do not have opportunities to experience the beauty of math patterns and relationships. How might we provide a better mathematical experience for students?
One approach is to engage students with problems such as __ + __ = 10 and __ + __ < 10. Students get lots of practice solving missing number problems. But they also get lots of practice exploring patterns and representing relationships. The videos below show how this was done in two grade 3/4 classrooms.
Resources to support this activity
Materials
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1 - Making 10
1.a - How it unfolded in the classroom
| Students roll a number cube to determine the first number in the equation __ + __ = 10, and they calculate the missing number. They organize their data and look for patterns. They also plot the pairs of numbers on a grid and notice that the points line up! They repeat this for other equations, such as __ + __ = 8 and __ + __ = 5. They notice that the graphs are parallel! Is there a way to design an equation so that its graph points in a different direction, or curves? |
1.b - Using children's literature
 Children's literature helps students make emotional connections with math ideas, through the characters in the story. Stories are also easy to remember and help anchor student learning. In the Making 10 story used in these activities, Wolf offers Hoodie a mathematical surprise. Like the grade 3/4 students, Hoodie realizes that the points of missing number equations like __ + __ = 8 and __ + __ = 5 "line up" and "they are parallel". So she ponders, "I wonder whether I can make equations whose points line up in a different direction, or fit a curve?" |
1.c - A student's explanation
| Children are much more capable mathematically than we typically assume. A problem with our education thinking is that we have not sufficiently questioned Piaget's ideas of what children can and cannot do. Egan (2002, p. 105) notes that "Piaget's ideas and overall approach absolutely dominate in education. ... "Development" in education is discussed and taught, in my experience and informal surveys, almost exclusively in Piagetian terms." Papert (1980, p. 7) challenges the idea of Piaget's developmental stages and suggests the problem is not in children's minds but in the "culture" of schooling. As Ginsburg (2002) notes, although mathematics is big, children's minds are bigger. |
2 - Making less than 10
2.a - How it unfolded in the classroom
| Missing number equations and inequations like __ + __ = 10 and __ + __ < 10 are low floor representations of x + y = 10 and x + y < 10, which students typically study in grades 9 and 10. When we design learning activities with a low mathematical floor and a high mathematical ceiling, (a) we develop ways of engaging a wider audience with cool math ideas that at the moment lay trapped in specific grades, and (b) we offer young students opportunities to experience the beauty and pleasure of complex math relationships. |
2.b - Classroom action #1
| How many solutions are there to __ + __ < 10? How would you know that you have them all? |
2.c - Classroom action #2
| Is there an infinite number of solutions to __ + __ < 10? |
3 - Songs of celebration and collective knowledge
3.a - "More homework like this": how it was written
| Our society has "boxed" mathematics either as something we do in school or as something done by mathematicians. In our project classrooms students develop arts-based communication skills for sharing their math stories with a wider audience. In this classroom, comments by parents on the math shared by students were used to write the song "More homework like this." This song was shared at the Math and Science Performance Festival. |
3.b - "More homework like this": student performance
if you roll a die and you get 2 roll the die and make 10 try changing the sum one number goes up if you change the operation it's amazing that they're learning |
my daughter learned it fast what a good teacher she would be the math came from a story this was a great time for me my daughter learned that math it's amazing that they're learning |
Grade 3/4 students perform their song "More homework like this ." |
3.c - "More homework like this": music video
| A re-performance of the song, "More homework like this". Produced by Marlene Frederick (UWO). |
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3.d - "I'm from math ": student lyrics used to create song
| Poetry is one method we use to help students express their learning. Using George Ella Lyon's poem "Where I'm from", students write stanzas about (a) what they learned and (b) how they felt. Their stanzas were used to write the song "I'm from math." This song was shared at the Math and Science Performance Festival. |
3.e - "I'm from math ": student performance
I'm from math I'm from making equations Finding number pairs I'm from making graphs I'm from ordered pairs I'm from math |
I'm from number pairs 0, 0, 0, 1 I'm from patterns But with negative numbers I'm from math I'm from math |
Grade 3/4 students perform their song "I'm from math ." |
4 - Seeing "The pleasure of making 10" through art
4.a - Let's paint a math story!
Below is an artistic representation of "The pleasure of making 10." Artistically rendered by Ann Langeman (Faculty of Education, UWO). Designed by George Gadanidis. Download the poster for printing.
References
- Egan, K. (2002). Getting it wrong from the beginning. Our progressive inheritance from Herbert Spencer, John Dewey, and Jean Piaget. New Haven: Yale University Press.
- Ginsburg, H. G. (2002). Little children, big mathematics: Learning and teaching in the pre-school. Proceedings of the 26th Conference of the International Group for the Psychology of Mathematics Education (Vol.1, pp. 3-14) University of East Anglia: PME.
- Papert, S. (1980). Mindstorms: Children, Computers, and Powerful Ideas. New York: Basic Books.