Once upon a time Mathematics was easy to teach. A typical lesson would begin with a direction towards a particular page of the text book and would conclude with the ceremonial marking of the answers. This process was repeated over and over, year after year and in the end students would be able to repeat the required method with a satisfactory degree of accuracy. Understanding was not a requirement and as such the teacher needed to know only a little more than the student or perhaps only have ready access to the answer page. But times change and today Mathematics is an area of study that requires a deeper level of understanding from both the student and the teacher. This change is the result of numerous factors each demanding a rethink of our pedagogy for mathematics and has led to calls for specialist teachers and professional development for teachers of mathematics in Primary schools.
Increasingly Science, Technology, Engineering and Mathematics (STEM) are viewed as focus areas for national growth and the emergence of an innovation driven economy. Most recently in response to the Australian Federal Government’s ‘Innovation & Science Agenda’ the Office of the Chief Scientist released a paper that specifically calls for enhanced teaching in Mathematics. 'Mathematics is central. Student success in STEM is dependent upon an understanding of mathematics and the ability to apply it.’ (OCS 2015 p4) This paper points to research that shows teacher education candidates have ‘either a poor mathematical background, or significant gaps in their mathematical knowledge’ and 'displayed significant levels of ‘mathematics anxiety’ (OCS 2015 p3). This finding is backed by primary principals who report 51% of graduates ‘could not teach mathematics to a reasonable level’ (OCS 2015 p4). While at a secondary level students encounter specialists in Mathematics and Science, research shows that students make choices about their career pathway during their primary years (Broadley 2015). The lack of exposure to teachers who are confident in the delivery of Mathematics education or who are not passionate about the subject is likely to hamper continued study in STEM fields. Beliefs about the level of ability required to cope with Mathematics or STEM courses at more advanced levels of study plays a role here and anxiety about the content is transferred from teacher to student (McDonagh & Ferguson 2015).
In response to this deficit the Office of the Chief Scientist (2015) calls for a three pronged attack; increase the prestige of teachers by lifting entry requirements for teacher education along with the provision of specialist teacher support and enhanced professional development programmes for pre-service and existing teachers. The report looks to the practice of high performing systems such as Singapore that provides 100 hours of professional development to its teachers every year. Importantly the report identifies the role for Principals in driving STEM innovation; ‘Change begins at the top, requiring an understanding from principals that STEM is vital; that teachers require time to master it, and to collaborate; and that progress can be achieved and ought to be expected through a whole-of-school approach.’ Such commitment to change needs to be built upon a clear understanding of what quality age appropriate pedagogy for STEM and in particular Mathematics is and within existing systems this knowledge is rare. While teaching in Science, Technology and Engineering may be largely absent from Primary Schools, Mathematics teaching is well entrenched and occupies a significant part of any school’s timetabled learning. Bringing about change in the practices utilised will require a shift in thinking about the nature of mathematics not just more of the same. In many instances our current approach to mathematics is deeply flawed.
One critic of existing mathematics education is Conrad Wolfram the founder of Wolfram Research Europe and brother of Stephen Wolfram, maker of Mathematica and Wolfram Alpha. It is a family with maths running through its veins. 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 realize that it's a big deal for our economies, but don't know how to fix it. And teachers are also frustrated'. (Wolfram 2010) The problem comes from the underlying beliefs about what mathematics education should be about and the disconnect between this and maths outside of schools. Mathematics education in schools is comprised of 'dumbed-down problems, lots of calculating, mostly by hand.’ (Wolfram 2010) In the real world according to Wolfram maths is very popular but it is used by people for a purpose, not pure mathematics and not the calculation heavy model of schools. The short answer is to move away from a desire to make the simple aspects of mathematics hard by preventing the use of tools that do this part of mathematics very well. Teach a mathematics that leverages the power of computers and in doing so shift the focus onto the mathematical thinking that is essential for deep understanding and real world applications. As Wolfram puts it 'Stop teaching calculating. Start teaching math’. (Wolfram 2010)
What this means is that we should be spending more time on developing the ability to ask mathematical questions, more time on checking that a mathematical solution is viable and relevant to the problem and then spending more time on making sense of the answer. Between the asking of mathematical questions and making sense of the result lies calculations but Wolfram is emphatic that this step should not occupy the 80% of maths learning presently devoted to it. The use of computers and calculators in mathematics education has always been contentious. Most students of mathematics will at some point argue that they should be permitted to use calculators in their lessons. Hand calculation is believed to enhance the recall and understanding of mathematical concepts but perhaps we are focusing on the wrong concepts. Empowered by computers and calculators we should expect students to engage effectively with Mathematics at a deeper level with greater levels of real world application than is enabled by repetition of algorithms or manipulations of arcane formulae. To what end do we labour table-facts at the expense of engagement with a mathematics that is genuinely relevant and of use within a STEM context?
Beyond shifting our focus from teaching calculations to teaching maths is a world of new possibilities for the learning of mathematics through emerging technology. Mathematics is essential to STEM as it plays a role in all disciplines but it is in the integration of mathematical learning with the other disciplines that new opportunities emerge. Taking mathematical thinking and combining it with robotics, computer coding and engineering brings new layers of meaning and engagement. A child solving a problem within a robotics project will be forced to apply mathematical thinking but is unlikely to identify the task as boring or irrelevant as it is immediately relevant to the task. An example of this can be seen when students are given the task of programming a SPHERO robot. SPHERO is a small acrylic ball that uses a combination of motors and gyros to move from place to place. It can be controlled directly from a smart-phone or programmed to follow coded instructions. An engaging challenge for students that SPHERO makes possible is programing it to complete a maze. This engages students in calculations of speed, distance, time, angles and acceleration. The device provides immediate feedback and students are able to quickly test multiple iterations of their code. In a collaborative environment ideas and learning are shared and students quickly fine tune their programmes.
Increasingly schools are experimenting with ‘Making’ and with this, further opportunities for mathematical thinking emerge. Through projects that incorporate traditional timber crafts, 3D printing, small scale manufacturing, electronics and computing the world of making presents boundless new challenges for educators. In this sort of environment mathematical learning is one of the tools to be mastered and its relevance is inescapable. This is the sort of environment that all students need access to but it is an environment that is still uncommon in Primary schools and one that challenges teacher abilities. As schools begin to pursue new options in this sphere great care must be taken to support teachers as they move their teaching into these new domains. Without the relevant pedagogical content knowledge ‘Makerspaces' are likely to be little more than extra-curricular add-ons with only tenuous connections to the real curriculum.
What is needed is an ongoing conversation around what Mathematics education could and should look like. Conrad Wolfram poses questions about the teaching of Mathematics that should be considered in this conversation; 'Why are we teaching people math? What's the point of teaching people math? And in particular, why are we teaching them math in general?’ In seeking answers to these questions we may better understand what it is about Mathematics that makes it worth learning and with that answer in mind a clear vision for what it means to 'learn' mathematics might emerge.
by Nigel Coutts
Kate Broadley (2015) Entrenched gendered pathways in science, technology, engineering and mathematics: Engaging girls through collaborative career development Australian Journal of Career Development Vol 24 (1) 27-38
McDonagh, M. & Ferguson, T. (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
Roslyn Prinsley and Ewan Johnston (2015) Transforming STEM Teaching In Australian Primary Schools - Office of the Chief Scientist
Conrad Wolfram (2010) Teaching kids real maths with computers. TED Talk