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 Naeem Nisar

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 Naeem Nisar

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 Naeem Nisar

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 Naeem Nisar

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 …? Naeem Nisar

Effective questioning Naeem Nisar

by Naeem

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 Naeem Nisar

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. Naeem Nisar

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 Naeem Nisar

Displays Naeem Nisar

Choosing a poster by learners Naeem Nisar

Evaluating mathematical statements: Naeem Nisar

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 Naeem Nisar

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. http://www.nrdc.org.uk/?p=288 R McLeod, B Newmarch ( 2006) Maths4Life: Fractions. NRDC: London D Bouch, C Ness (2007) Maths4Life: Measurement. NRDC: London Naeem Nisar