Tun Apiwattanakorn
Australian Science and Mathematics School (ASMS)
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Developing a positive disposition towards mathematics can help transform what is too often regarded as an academic chore into what should be an exciting and rewarding journey of discovery: fostering curiosity, resilience, and a passion for problem-solving. Why is it that learning and teaching maths is such a discouraging undertaking for so many and what can be done to improve the classroom experience? In the following case study, I explain how we teach and learn maths at ASMS.
Background Knowledge
At ASMS, we teach and learn in an interdisciplinary setting. The example provided (entitled ‘Terra Knowing’) is part of our Central Studies Programme undertaken by a combination of Years 10 and 11 students of varying abilities and interests.
The following topic, ‘quadratics and Other Polynomials’, was run in two blocks of five sessions of 100 minutes each.
In the first block, we:
- Introduced quadratic functions (their characteristics and applications)
- Taught/recapped expansion and factorisation (distributive laws, common factors, special identities and their applications)
- Introduced various ‘forms’ of quadratics (standard, vertex, factored forms and conversion between the forms)
- Covered how to solve quadratic equations (factoring, completing the square, quadratic formula and graphical solutions)
Students were given a number of worksheets to practise and by the end of the unit, they were assessed by means of a timed test with/without provided formula sheets.
Generally speaking, the outcome was as we had expected: namely, students’ grades were normally distributed. However, student feedback was not uniformly positive.
Many students felt that this kind of assessment provided only a snapshot of their learning.
On the other hand, teachers felt it provided a useful measure of students’ current skills and proficiency. I refer to this kind of assessment as the traditional maths learning cycle (see the diagram below).
Learning maths at ASMS involves asking our students to explore and critique their personal learning experience. They are asked to make connections, to see if they can transfer their knowledge to different settings and to exercise what we call Student Agency.
In the second block, students were exposed to project-based learning (Folio/Investigation). We asked students to reflect upon and provide us with Evidence of their Learning (EoL). To this end, staff provide students with a scaffold of skills we consider to be relevant parameters.
Students are given various activities to explore (using Desmos/GeoGebra) and encouraged to build up skills relevant to their final project which is submitted in the form of a Folio together with their EoL.
After five sessions, students are required to produce a work of art using Desmos/GeoGebra based on one of three options: metaphor as an image (a); a company logo (b); or a culturally appropriate image (c) which relates to their Terra Knowing topic framework. Below are some examples of student work produced after weeks of learning.
Figure 3. Examples of Student Work
General Impressions
All students were fully engaged with their learning as they felt free to exercise student agency in terms of personal choice. Moreover, students were encouraged to support one another and therefore willing to share the various tips and techniques they acquired along the way.
Overall observation: all students were fully engaged with their learning as they exercised student agency through free choice. Students supported each other and willingly shared tips and techniques they acquired along the way. Despite the assessment being due in the last week of school, we achieved a 100% submission rate and overall students were happy with their learning experience.
The question arises: should we adopt the traditional teach-and-test approach or the more open-ended appeal to student agency? Each has its own pros and cons. Perhaps a blend of both? Regardless of approach, the fundamental question remains: how best to measure achievement?
In doing so, why not make the subject of our assessment (i.e. the students themselves) partners in the assessment process? Who better to know how much they have learnt, what skills they have acquired, and whether or not they are able to apply that knowledge and those skills to new situations and changed circumstances?
I am not saying that one approach is better than the other. Both approaches have advantages and disadvantages. It is a matter of balancing how we measure our students’ success, particularly in terms of their own perception of how they learn and how they apply the skills they have developed to different circumstances.
