1. ALM 25th London Boundaries and bridges: adults learning mathematics in a fractured world How effective questioning and discussion can help to remove misconceptions in the adult mathematics classroom
Naeem Nisar
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2. Effective questioning
Questioning cycle
Initial assessment : what questions do we need to ask a potential learner to find out his/her motivation? e.g. intrinsic motivation, extrinsic motivation and instrumental motivation
Teaching and Learning:
checking understanding: how do we make sure a potential learner has understood?
use of non-verbal communication, in combination with speaking and listening: use of facial expression, eye contact, positioning and movements etc.
Formative & summative assessment i.e. to assess learning
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3. Effective questioning at IAG stage
Targeted questions to learners:
Learners’ back ground
Learning history i.e. method of learning maths ( standards/ non standard)
Numeracy/maths level
ESOL / literacy level
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4. Develop effective questioning
Established norm of numeracy tutors is to ask questions to test the ability of learners to recall facts and procedures e.g. closed questions
Questions to promote open higher level reflective thinking, such as ability to apply , synthesise or explain e.g. open questions invite a range of responses
Ample time for the learners to think before offering help or moving on to ask a second learner e.g. 3-5 second rule depending upon a learner’s ability
Effective prompts
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5. Effective questioning
Multiple wh-questions
What do we need… .?
Why do people use ….?
When do we use… ?
What does it mean?
How accurately….?
What is the difference between….?
Have you used in your country…?
Do you use …in your daily life …?
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6. Effective questioning
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7. by Naeem

8. Expose and discuss common misconceptions
Expose common mistakes and misconceptions e.g encourage learners to share information on the whiteboard; using mini white board etc.
Challenge and discuss i.e. expose learners’ existing way of thinking followed by group discussion
encourages learners to read problem solving tasks and discuss in pairs/groups before going on to find solutions
Conflict resolved through reflective discussion set a framework or environment for cross-cultural discussion about the topics to help classroom learners identify errors and to remove misconceptions, focusing on methods, rather than ‘answers’
the facilitator (not traditional teacher) to make sure to find out the solution and it will lead to more permanent learning
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9. Emphasise methods rather than answers
obtaining a correct answer rather than learning a powerful method e.g. completing exercise/ homework, not focusing on an idea
differentiated tasks e.g. limit number of questions
pair/group work discussing various methods on doing a question
critical thinking after solving a question e.g. if…; making questions ; using same approach/method with numbers; same structure with different words
develop culture of paperless learning: fewer worksheets; more discussion, games, collaborative tasks etc.
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10. Conducive learning environment for discussion
Seating arrangement i.e. café style so learners can move around
Stimulus i.e. new kind of questions from everyone
Use poster to stimulate thinking i.e. displays and encourage learners working together to create posters that connect ideas together
Dos for learners:
talk one at a time
share ideas and listen to each other
make sure people listen to you
follow on
challenge
respect each other’s opinions
share responsibility
enjoy mistakes and try to agree in the end
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11. Displays
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12. Choosing a poster by learners
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13. Evaluating mathematical statements:
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14. From ‘transmission’ to challenging to ‘challenging’ teaching
A ‘Transmission’ view: short term
‘Connected’; ‘challenging’ view: longer-term learning
mathematics is an interconnected body of ideas and reasoning processes, and learning is a collective activity in which learners are challenged and arrive at understanding through discussion.
Key role of effective questioning and discussion, which cater well for spiky profile— a ‘pragmatic eclecticism’ to enhance learning
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15. References:
Swan M (2005), Improving Learning in Mathematics: Challenge and strategies, Success for All, Department for Education and Skills: London.
Hudson. C (2006) Maths4Life: Pathfinder report. NRDC: London.
R McLeod, B Newmarch ( 2006) Maths4Life: Fractions. NRDC: London
D Bouch, C Ness (2007) Maths4Life: Measurement. NRDC: London
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