However, changes to education are about more than the future lives of our children. Ready access to vast quantities of information, digital tools for collaboration, creativity and communication allow students to engage in spectacular learning experiences and to share that with fellow learners around the world. As knowledge becomes a freely-available resource, rather than a rarified commodity controlled and distributed by the privileged few, the role of teachers has shifted from dispensers of content to empowering agents who guide and stimulate students towards knowledge construction. These changes are being felt in all areas of the curriculum, but in Mathematics tradition and perceptions of what must be taught has slowed progress. What, then, might Mathematics learning look like in the coming years, and what are the essential understandings and dispositions our students will require?
To explore this further I spoke with teachers about their teaching of Mathematics. This revealed a uniform imagining of what Mathematical learning and subsequently teaching should be like. The old standbys of worksheets and rows of algorithms written on the board for students to silently answer are gone. According to Mieke Roodenburg, a Year Five teacher: “We eliminated the use of worksheets and focused on understanding instead of repetition and memory based tasks.”
Perhaps surprisingly, correct answers and unitary approaches to solutions are also gone.
Mieke adds: “I’m always encouraging my students to prove me wrong or to look for multiple answers, so that they understand Mathematics is more than just right and wrong.”
A clear emphasis on Mathematical thinking, rational debate, argument and true individualisation with relevance to the real world use of Mathematics emerged. The word that stood out in each response, one that may seem out of place in traditional Primary Mathematics classes to many adults, was creativity. No longer the sole domain of the arts, creativity is seen as a crucial element across the curriculum and a disposition for students to apply to their Mathematics.
“Activities such as logic puzzles, brain teasers, relays and creative thinking tasks give learners the opportunity to think, have fun and debate their understanding. The changes to the teaching of Mathematics, will shift the perception of Mathematics and in turn, create a love of learning Mathematics,” states Amber Bidwell, a Year Six teacher. Amber is a teacher with a passion for Mathematics and she reveals this to her students who in turn see themselves as successful Mathematicians. She relays the story of a conversation with a student who was being interviewed for entrance to a new school as part of a move overseas. The question “What is your favourite subject?” was asked and the confident response was “Maths, because my teacher loves it, I now love it and she says it’s okay to get things wrong”. Developing students who are engaged, confident and demonstrate a growth mindset towards Mathematics is a goal shared by each teacher interviewed. Melanie Cleary, a Year Four teacher described her use of the “language"As knowledge becomes a freely-available resource, the role of teachers has shifted from dispensers of content to empowering agents." of growth mindsets” in her class and the positive influence this has had.
Traditionally the focus of teaching in Mathematics was on the learning of essential knowledge and processes. For students this approach required the rote learning of a great many facts, in the belief that one day they would need to use these to pass a test or solve complex engineering problems. Since the invention of the pocket calculator, students have questioned the need to know many of these facts and this is an argument only reinforced by our obsession with smartphones. Smartphone-based software today allows even complex algebraic formulas to be solved using the camera, with solutions graphed and explained in near real-time. With these tools, we are beginning to see that what students need is not rote learning of number facts but a deep understanding of Mathematics. Knowing that seven multiplied by eight produces fifty-six is of little value if the concept of multiplication is not understood.
Many students report that Mathematics is too hard. Sixty percent of girls aged twelve in a study by Accenture (McDonagh & Ferguson, 2015) responded that Mathematics (and Science) is too difficult to learn. Confidence levels for boys are only slightly better. One critic of existing Mathematics education is Conrad Wolfram, the founder of Wolfram Research Europe and brother of Stephen Wolfram, founder of Mathematica and Wolfram Alpha. Conrad identifies a problem in how we teach Mathematics:
“Those learning it think it's disconnected, uninteresting and hard. Those trying to employ them think they don't know enough. Governments realise that it's a big deal for our economies, but don't know how to fix it. And teachers are also frustrated.” (Wolfram, 2010)
A personal belief that mastery of a discipline is achievable is crucial to success according to researchers of self-determination theory Ryan and Decci. The ingredients of motivation described by these researchers are mastery, purpose and autonomy and each has relevance to engagement in Mathematics.
The teachers interviewed are each making efforts to enhance their students’ perception of Mathematics. “Showing passion for the subject, taking risks with the ideas being taught and learned, connecting with mathematicians outside of schools, allowing students to take charge of where to next and continuous learning and development as a teacher” are the essential elements for innovative teaching and learning of Mathematics, according to Amber Bidwell.
These sentiments are echoed by Jo Robinson, also a Year Six teacher: “Innovative teaching and learning in Mathematics demands an environment where students are encouraged to question, to think, to create, to be curious, to discover, to take risks, to have arguments and to debate while being supported non-judgmentally through the process.”
Looking beyond the teaching of Mathematics to assessment, an always important messaging system that influences our perception of what learning matters most. Melanie Cleary indicates that: “Assessments need to change to show the rate of a student’s growth and how creatively and critically a student can think.”
If we aim to shift the mathematical thinking we value in our students then traditional tests with clearly defined right or wrong answers will not serve our needs. Creativity guru and educational thought leader Ken Robinson addressed this challenge when speaking at EduTech Brisbane in 2014. He described a conversation with a professor of Mathematics that focused on the criteria used for assessing Doctoral theses. The answer revealed an emphasis on the aesthetic qualities of the thesis; is the solution elegant or is it overly complex. Each of the teachers interviewed described strategies they used to create learning scenarios that allowed students to think creatively, to follow multiple pathways towards a solution, and to even take on the role of problem finders as they explored the real world application of Mathematics. It was through this type of learning that they assessed their students’ understandings.
No discussion of Mathematics today can avoid mentioning the explosion of STEM or STEAM approaches. The integration of Mathematics with Science, technology, Engineering and Art offers new opportunities for the inclusion of richly relevant learning. Recently we have had students in Year Six use Sphero robots to explore aspects of two-dimensional shape and measurement. In a unit of inquiry titled ‘Great Cities of the World’, students explore three-dimensional shape, scale and architectural drawing as they design and make models of famous buildings. In each instance the clear relevance and purpose of the task to the students ensures that when challenges are encountered and plans fail they are motivated to push on and find a solution. This style of relevant, integrated task builds resilience as students discover, that through persistence, they can overcome challenges. Similar opportunities for integration exist with the humanities and the real world application of statistics is one aspect of mathematics which deserves greater exploration and emphasis within the curriculum according to educational thought leader David Perkins.
Despite fears of a decline in Mathematics "Since the invention of the pocket calculator, students have questioned the need to know many of these facts."and a failure of educational systems to keep pace with the demand for highly competent mathematicians, there is good evidence that teachers are finding ways to ensure students are engaged and challenged. Sharing stories of success and building collaborative connections between teachers with a passion for Mathematics and those who find it a challenge to teach will speed this process of innovation. If our goal is a generation of students who can confidently apply mathematical thinking to the solution of real-world problems, then we need to look to those who are already innovating towards this end for inspiration.
David Perkins. (2014) Future Wise: Educating our children for a changing world. Joey Bass; San Francisco
Molly McDonagh & Timothy Ferguson. (2015) Accenture finds more than half of 12-year-old girls in the UK and Ireland believe STEM subjects are too difficult to learn. Accenture Accessed online 1.11.2015 https://newsroom.accenture.com/news/accenture-finds-more-than-half-of-12-year-old-girls-in-the-uk-and-ireland-believe-stem-subjects-are-too-difficult-to-learn.htm
Richard Ryan & Edward Deci. (2000). Self-determination theory and the facilitation of intrinsic motivation, social development, and well-being. American Psychologist, 55(1), 68-78.
Conrad Wolfram. (2010) Teaching kids real maths with computers. TED Talk http://www.ted.com/talks/conrad_wolfram_teaching_kids_real_math_with_computers#t-36648
How do you engage students with Maths? Let us know below.