In one of my previous posts I wrote about the use of children’s literature to encourage rich mathematical investigations and improve student engagement with mathematics. One of my favourite books, Math Curse by John Szieska and Lane Smith, is described in the blog post as a great way to engage reluctant learners. Even better, Math Curse encourages children (and their teachers) to see the mathematics that is embedded in every aspect of our lives. In this post I am going to share some student work from a Grade 3 classroom. In this classroom, the teacher read the book to the students before challenging them create their own class maths curse. The children took their own photographs, and working in small groups, they came up with a range of mathematical problems and investigations, which they then gave to other groups to solve.
Here are some of the photos with their accompanying questions:
- If one of the beyblades spins for 2 minutes and 31 seconds and the other one spins for 1 minute and 39 seconds what is the difference between the two times?
- If one of the beyblades spins for 1 minute and 1 second and another spins for 78 seconds, which beyblade spun for the longest and by how long?
- If there are 31 people in the class (10 boys and 21 girls) and all of them have hair that is 30cm long. Half of the boys cut 10cm off their hair, the other half cut 20cm off their hair. How long is the classes hair now altogether? How long was it before? How much hair has been cut altogether?
- Check your friend’s hair. Estimate how long it is when it is out, how long it is when it is in a ponytail, and how long it is when it is in a braid. List some different ways you could check if your estimate is accurate? What are the potential problems with your methods?
- I’m 9 years old. I had really long hair for 6 years, then I cut it. How long did I have short hair for?
- I have 5 friends that are girls and 2 friends that are boys. All 5 girls have hair length of 50cm. The boys both have different lengths of hair. The 1st boy has 30cm of hair, the second has 25cm of hair. What is the difference between the 1st boy and the girls and the 2nd boy and the girls?
- Write down the dates of important celebrations. If you add all the dates together, what is the value of their numbers?
- How many days are there in 6 years?
- If everyone’s birthday occurred every three years (starting the year you are born) what years would your birthday fall on?
- If Lisa and Jane went on a holiday every 2 months, how many holidays could they take in a year?
- If you could rearrange the seasons, what months would you choose to be Spring? Why?
- What is the most popular letter in the days of the months?
- Why do you think there are 4 seasons in a year?
From Problem Solving to Problem Posing
What is the purpose of getting students to write mathematical problems? First of all, the problems give us good insight into whether students recognise mathematical situations, and whether they understand where, how, and what mathematics is applied in day to day situations. An added bonus is that the students are highly engaged because they have ownership of the mathematics they are generating, the topics they choose are of interest to them, and stereotypical perceptions of school mathematics are disrupted.
The students who wrote the examples above completed a structured written reflection following the sequence of designing and solving each others’ maths curses. Here are some of reflection prompts and a sample of responses:
What did you enjoy about today’s learning?
“working with my team”
“working at the problems for a long time and then finally getting them after a long, hard discussion”
“solving questions that my friends wrote”
“I felt challenged and I learnt more about what maths is”
“working with my group, choosing our own questions and learning something new”
“I liked the chess card the best because we had to solve it together and use problem solving”
“having a go at tricky questions even if i got them wrong”
Did you learn anything new?
“how to work things out in different ways”
“working in groups helps you learn more skills”
“not every question uses just one skill like addition, division, multiplication or subtraction”
“when I am challenged I learn more”
“Maths is not always easy”
“how to work together”
“Everyone in the group has different responses so we needed proof to figure out the right one”
What surprised you about this task?
“It surprised me how hard my own questions were”
“I didn’t know that we could come up with so many interesting questions”
“I got a shock! We had to research to solve some problems, Adam even taught me how to add a different way”
“I got some questions wrong “
“It was hard but if we put our brains into gear we could figure it out”
“I was able to play while doing maths”
Using activities such as this provides multiple benefits for students. Contextualising the mathematics using students’ interests highlights the relevance of the curriculum, improves student engagement, and makes mathematics meaningful, fun and engaging!