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 QuestionIf 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 -
Typi
cal
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 QuotesUnique 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 Novice Expert Examples/Generalisations
Self-regulation Reactive Forward thinking
• Evidence of movement toward expert self-regulation present at every category (below)
Goal setting Non-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
Ability Strategy • 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 ManagementPROFESSIONAL LEARNINGCOMMUNITYmost important
COLLABORATION!least important (little consensus
- ⅓ Shared Norms)best supported
COLLABORATION! needs most improvement
(eclectic responses - some Shared Norms featured)
THINKING SKILLS FOR INNOVATIONmost 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?
.
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