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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