21st Century Learning in Mathematics
According to the CareersNZ , there are seven essential skills, qualities and attitudes which employers are looking for: Positive attitude, Communication, Teamwork, Self-management, Thinking skills, Willingness to learn and Resilience. How can we prepare our young people for a world which is changing so quickly, that many of the jobs which are currently around may no longer exist in 20 years’ time? Although there is merit in learning subject-based facts, this is no longer going to adequately prepare our students for their futures.
The importance of developing the whole person is supported by our school’s six touchstones of Family, Scholarship, Truth, Service, Prayer and Joy. Along similar lines, the 6Cs of 21st century learning (Communication, Collaboration, Critical Thinking, Creativity, Citizenship and Character) reinforce the idea that schools need to change their approach in order to offer students what they need for an ever-changing future. According to Carol Dweck, a Stanford University Professor of Psychology and author of the million-copy bestseller, ‘Mindset’, “[young people] have to be prepared to take on new challenges successively throughout their lives. They have to be prepared to re-train, they have to be prepared for all kinds of things. We don’t even know what they have to be prepared for yet! So I am concerned that our education systems are not preparing for that … we focus on high stakes testing and teaching to the test, learning for the test, memorising, [but] we know that’s not what the future of work is.”
This year, in the Mathematics Faculty at Aquinas College, we have been redesigning our units in Year 9 in particular, in order to encourage deeper thinking and understanding. We still have lessons where some concepts are explicitly taught when needed, but this is now supported by giving students problems which they solve in small groups (usually groups of three). The problems allow students to select a variety of strategies to solve them. Students in Year 9 have been developing their communication and collaboration skills, and they enthusiastically share their thinking with the other groups during the reporting back time. We have found having the class split into two large groups (15 students problem solving and 15 students doing book work) has been a very successful strategy. They are much more willing to share their ideas with others when the group is smaller. This also means that students are doing group problem solving every second period at most. When doing book work, the teacher is available to help, but learners are expected to take responsibility for their learning by reading the notes and examples in their workbooks, checking their answers, and seeking help from others when needed.
Justifying and questioning are two important elements which are reinforced in each maths lesson. When students give their answers, they need to be able to explain their thinking so that others can understand. When students don’t agree with what has been said, or they don’t understand what has been said, they are encouraged to ask questions of the student presenting their idea. Although this is quite a new way of doing things, we are very pleased with the progress students are making.
Below is an example of a question given to the Year 9 class during the Probability topic:
Students have to first decide whether an ice cream with a Lemon and Strawberry scoop of ice cream is the same as an ice cream with a Strawberry and Lemon scoop of ice cream. In this way, they are encouraged to state any assumptions they are making (an Excellence skill in NCEA Level 1). All groups solved this question within 10 minutes, so they were asked how many different ice creams could be made with the six flavours if there were three scoops. (Problems which are broad can easily be extended.) The first day, the five groups worked on this question without reaching a final solution. On the second day (when the other half of the class tackled the same problem), three of the five groups tried different strategies and came up with the same answer. This time, they were asked to report back to the whole class so that everyone could benefit from their understanding. This problem was a challenging one, but the students rose to the occasion. By showing their thinking clearly on the board and explaining what they noticed, everyone in the room was able to see how they solved the problem.
In a similar way, teachers of Year 7 and 8 classes have been introducing problem solving into their lessons. It is vital that students experience mathematics as a subject which we use in every aspect of our lives and not just something which is a huge list of rules to follow in order to answer questions in a book or a test. In this way, it is our hope that students gain a deeper understanding and appreciation of mathematics, and that they have the flexibility and confidence to work together to tackle unfamiliar problems. After all, these are the skills they will need for the workforce in a few years’ time.
Boaler, J. (2015). The elephant in the classroom: Helping children learn and love maths. Souvenir Press.
Boaler, J. (2015). Mathematical mindsets: Unleashing students’ potential through creative math, inspiring messages and innovative teaching. John Wiley & Sons.