Intervention methodology and the quest for the autonomous learner in mathematics Tania Nethercote

Thinking Learning is a natural process. It happens without schools and teachers. If we want to change what people learn we have to intervene in the natural process of learning. What student know and what teachers know influence what schooling is. For schooling to change we have to change what students and teachers know. What teachers and students know will change. How do we promote learning that is appropriate and timely? Who better to be in control of what needs to be learned than the learner. How do they learn to exploit all resources to secure their future?

Research Question If autonomous learning is a desired outcome for students, how do we intervene? With students? With teachers?

Context ASMS - specialist science and mathematics-based school Years 10 and 11 study an interdisciplinary curriculum Curriculum design – constant state of flux – personalised learning opportunities for students. Students need to demonstrate interest in pursuing a mathematics or science based career. Teachers - innovation and research professional learning requirement - expected to provide professional learning opportunities. Physical environment is open plan. Metacognition is a whole school focus.

Method: Case Study of Action Research Student Autonomy (STUDENT ARTEFACTS) Teachers collect student comments that reflect “typical” and “unique positive” and “unique negative perspectives (see diagram). Two collection points, approximately six months apart. Leadership and Management Strategies (TEACHER SURVEY) Teacher survey Reflect on professional learning community – Which factor is most important ? is least important ? is best supported? needs the most improvement? Reflect on thinking skills used – Which thinking skills is most important ? is least important ? is best supported? needs the most support? Unique - Typical Unique + Student reflective comments

Results: Student Autonomy Teacher Selected and Categorised Student Quotes Typical – Student where more likely to After CML 1 Recall past learning environments Talk about resources and strategies they liked After CML 5 Provide substantiated self- evaluation Accept responsibility for enterprise Provide a specific reason or goal linked to strategy

Results: Student Autonomy Teacher Selected and Categorised Student Quotes Unique Positive – Focus on After CML 1 memory understanding organisation After CML 5 flexibility strategic choices seeking help drafting identifying and rectifying misconceptions

Results: Student Autonomy Teacher Selected and Categorised Student Quotes Unique Negative – Focus on After CML 1 time management challenges task relevance After CML 5 desire for extension clearer understanding of requirements

Results: Student Autonomy NoviceExpertExamples/Generalisations Self-regulationReactive Forward thinking Evidence of movement toward expert self-regulation present at every category (below) Goal settingNon-specific Hierarchical (Process goals linked to outcome goals) setting specific study times to combat procrastination at home, planning to do more challenging problems and persisting with different options for solving these before asking for help Effort[haphazard] Planned and strategic considering the CML as a whole, gauging the relative difficulty of different elements and then planning how they should use their time Returning students used their journals to help them quickly revise and then move on with new ideas Self - monitoring Non- systematic Observe effects of strategies used seeking out multiple ideas about knowledge from peers and teacher so as to develop flexible ways of their own design Self assessment Against the performance of others Against personal goals recognising forgotten factual and procedural knowledge meant that different action was warranted thinking through problems by oneself was a skill that an individual needs to develop Performance attribution AbilityStrategy sense of power of having control over their performance by changing and refining what they needed to suit their learning needs TABLE: Example demonstrating movement towards Expert Self-Regulation (Zimmerman. 2002)

Results: Leadership and Management PROFESSIONAL LEARNING COMMUNITY most important COLLABORATION! least important (little consensus - ⅓ Shared Norms) best supported COLLABORATION! needs most improvement (eclectic responses - some Shared Norms featured) THINKING SKILLS FOR INNOVATION most important (diversity of opinion - Collaborative Inquiry, Paying Attention featured) least important IMAGING! best supported COLLABORATIVE INQUIRY! needs most support (diverse comments - Paying Attention featured)

Results: Leadership and Management Innovation in mathematics education requires teachers to work collaboratively Collaboration is supported by de- privatization of practise, time to meet and talk and teacher empowerment. Neither collaboration nor innovation is easy Risks are easier to take as part of a group Working collaboratively places different often contrasting and conflicting stressors on different individuals Leaders address needs of individual teachers Meetings structure allow sand encourages learning, sharing, conversation, writing and debate. Observations, beliefs and ideas need to be heard and valued. Shared norms and values are an asymptotic aspiration Norms and values in a constant and irregular state of flux School vision and teacher well-being is a juggle Need to help individuals find their own autonomy within team planning Different preferences about thinking for innovation used metacogntively Least important might thinking skills - possible potential for growth ?( links between imaging and the development of conceptual knowledge)

Conclusions Students can learn to be more self-directed. Self-direction is learnt different ways and at different rates for different students. Scaffolding thinking and metacognition supports self-directedness. Goals for self-regulation need to be explicit Collaboration is essential for innovation Improvement needs to be ongoing Norms and values are in a constant state of flux Future needs are far too eclectic to trust a single prescribed methodology Metacognition allows teachers (and students) to become more strategic and flexible Teachers and students need metacognitive knowledge to co-create learning environments Further investigation – What is the relationship between self-directedness and self-differentiation? – What are appropriate professional learning opportunities for teachers?.

References Atkin, D. J., An Outline of Integral Learning. [Online] Available at: pdf [Accessed 14 June 2012]. Autism Assocation of South Australia, Making Sense of the Seven Senses. 1st ed. Adelaide: Autism SA. Dweck, C., Mindset. [Online] Available at: [Accessed 3 August 2012]. Gardner, H., Multiple Intelligences. New York: Basic Books. Hargreaves, D. (., Personalising learning - 4. London: Specialist Schools Trust. Harmony Education Center, n.d. NSRF Materials. [Online] Available at: [Accessed 5 September 2012]. Harpaz, Y., Winter Teaching and Learning in a Community of Thinking. Journal of Curriculum and Supervision, 20(2), pp Karthwohl, D. R., A Revision of Bloom's Taxonomy: An Overview. Theory into Practice, 41(Autumn), pp Kilpatrick, J., Swafford, J. & Findell, B., Adding it up: Helping children learn mathematics., Washington DC: National Academy Press. Kranowitz, C. S., The Out-of-Sync Child: Recognizing and Coping with Sensory Processing Disorder. 2nd ed. United States: Perigee. Livingston, J. A., Metacognition: An Overview. [Online] Available at: [Accessed 18 June 2012]. Nethercote, T., Fostering metacognition in the classroom. [Online] Available at: gb/resources/Pages/olc/papers/fosteringmetacognitionin.aspx [Accessed 14 June 2012]. Paris, S. G. A. L. R.,., Becoming reflective students and teachers with portfolios and authentic assessment.Psychology in the classroom: A series on applied educational psychology.. Paris, Scott G. Ayres, Linda R., (1994). Becoming reflective students and teachers with portfolios and authentic assessment.Psychology in the classroom: A series on applied educational psychology., (pp ). Washington, DC, US: American Psychological ed. Washington, DC: American Psychological. Perry, C., Learning in Style. Cheltenham: Hawker Brownlow Education. Silverman, L., Visual Spatial Resource. [Online] Available at: [Accessed ]. South Australia Department of Education and Children's Services, South Australian teacing for effective learning framework guid: a resource for developing quality teaching and learning in South Australia, Adelaide: Curriculum Services. Sullivan, P., Teaching Mathematics: Using research-informed strategies, Camberwell: Australian Council for Educational Research. Williams, M. S. & Shellenberger, S., An Introduction to "How Does Your Engine Run?" The Alert Program for Self Regulation. 1st ed. Nebraska: TherapyWork Inc. Zimmerman, B. J., Becoming a self-regulated learner: An overview. Theory into Practice, 41 Spring, pp

Address: Australian Science & Mathematics School Flinders University Sturt Road, Bedford Park South Australia 5042 Telephone: Facsimile: South Australian Department for Education and Child Development T/A South Australian Government Schools CRICOS provider number 00018A