GCSE re-sits: develop your practice (Level 5 module) maths Session - - PowerPoint PPT Presentation

GCSE re-sits: develop your practice (Level 5 module) maths

Session 6 – Improving learning in mathematics Julia Smith June/July 2020

SESSION OBJECTIVES

Improving Learning In Mathematics

EDUCATION AND TRAINING FOUNDATION Slide 3

LEARNING OUTCOMES

Can you …

Use active learning strategies and connected, challenging teaching methods to improve learning in GCSE maths? Facilitate learners’ mathematical reasoning and ability to explain and use mathematical language, methods and ideas? Use co-operative small group work to facilitate discussion and create a supportive and encouraging atmosphere in the learning environment? Use rich collaborative tasks to develop transferable higher-order thinking and problem- solving skills? Use technology appropriately to promote learner engagement, motivation and success in mathematics teaching and learning?

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MOST COMMON TEACHING METHODS

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LEAST COMMON TEACHING METHODS

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• Developed by the DfES Standards Unit in

response to the Smith report (2004).

• Initially aimed at the Post-16 sector (GCSE maths

re-sits and ‘A’ Level) but was also made available to schools from 2006.

• No longer available in hard copy but available
• nline at The National STEM Centre

IMPROVING LEARNING IN MATHEMATICS

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• From ‘passive’ to ‘active’ learning.
• From ‘transmission’ to ‘connected,

challenging’ teaching.

• From ‘teacher centred’ to ‘learner centred’

practices.

IMPROVING LEARNING IN MATHEMATICS

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PRINCIPLES FOR EFFECTIVE TEACHING

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• 1. Build on the knowledge learners bring to sessions.
• 2. Expose and discuss common misconceptions.
• 3. Develop effective questioning.
• 4. Use cooperative small group work.
• 5. Emphasise methods rather than answers.
• 6. Use rich collaborative tasks.
• 7. Create connections between mathematical topics.
• 8. Use technology in appropriate ways

PRINCIPLES FOR EFFECTIVE TEACHING

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Do you agree with the principle? What are the advantages of implementing this principle? What would implementation look like in practice? What are the difficulties in implementing this principle?

PRINCIPLES FOR EFFECTIVE TEACHING

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• These are the principles that underpin the approaches

contained in Improving Learning in Mathematics.

• We’ll look at them in more depth in this and future

sessions.

IMPROVING LEARNING IN MATHEMATICS

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DISCUSSION IN MATHEMATICS

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WHY IS DISCUSSION RARE IN MATHS?

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WHAT KIND OF TALK IS MOST USEFUL?

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PROBLEM SOLVING

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How many different sets of 5 positive whole numbers with a mean of 4, median of 3, mode of 3 and range of 5 can you find?

• An example of the ‘doing’ and ‘undoing’ processes in

mathematics.

• The problem ‘creator’ would take five numbers and

calculate the mean, median, mode and range.

• The problem ‘solver’ then has to find the five numbers

from the information given

PROBLEM CREATING AND SOLVING

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CREATING PROBLEMS: DOING AND UNDOING PROCESSES

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• Most learners will have been taught rules for solving

equations e.g.

– ‘change the side, change the sign’ – ‘always do the same to both sides’.

• When used without understanding such rules can result in

many errors.

• ‘Do the same to both sides’ is the more meaningful method

but there are difficulties

– How to change both sides so that equality is preserved. – Knowing

CREATING AND SOLVING EQUATIONS

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• Creating

Think of a number x = 4 Multiply by 3 3x = 12 Add 5 3x + 5 = 17 Multiply by 2 2(3x + 5) = 34

CREATING AND SOLVING EQUATIONS

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• Solving

Solve the equation 2(3x + 5) = 34 – This equation tells the story of ‘a day in the life of ‘x’). – What happened first? How do you know? – Then what? – What was the last thing that happened? How do you know? – Can you reverse the process to find x?

CREATING AND SOLVING EQUATIONS

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• Create an equation by starting with a number then using

the step by step method.

• Check that your equation works by substituting the original

value in the equation.

• Swap equations with the person next to you and try to

solve their equation.

• How does this approach help you to understand the

methods for solving a linear equation?

CREATING AND SOLVING EQUATIONS

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RICH TASKS

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– are accessible and extendable; – allow learners to make decisions; – involve learners in testing, proving, explaining, reflecting, interpreting; – promote discussion and communication; – encourage originality and invention; – encourage ‘what if?’ and ‘what if not?’ questions; – are enjoyable and contain the opportunity for surprise.

Ahmed, A. (1987) Better mathematics: a curriculum development study. London: HMSO

RICH TASKS

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“Current research evidence indicates that students who are given opportunities to work on their problem solving enjoy the subject more, are more confident and are more likely to continue studying mathematics, or mathematics related subjects, beyond 16. Most importantly, there is also evidence that they do better in standard tests such as GCSEs and A-levels”.

Hewson, S. (2011) What Is a Mathematically Rich Task? [available at http://nrich.maths.org/6299]

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• Rich tasks can enable pupils to:

– step into them even when the route to a solution is unclear, getting started and exploring is made accessible to pupils of wide ranging abilities; – pose as well as solve problems, make conjectures; – work at a range of levels; – extend knowledge or apply knowledge in new contexts; – allow for different methods; – have opportunities to broaden their problem-solving skills; – deepen and broaden mathematical content knowledge; – have potential to reveal underlying principles or make connections between areas of mathematics; – include intriguing contexts; – have opportunities to observe other people being mathematical or see the role of mathematics within cultural settings.

RICH TASKS

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THINKING SKILLS

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• Think of a recent lesson.
• What level of thinking were you expecting of

your learners?

• How are you developing the

Higher Order Thinking Skills (HOTS)?

BLOOM’S TAXONOMY

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ASSESSMENT OBJECTIVES

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USING TECHNOLOGY

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• ‘Technology has become part and parcel of

everyday life almost without people recognising it.’

Nick Boles, Minister of State for Skills and Equalities, FELTAG Progress Report (Feb 2015)

USING TECHNOLOGY IN APPROPRIATE WAYS

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How are you using digital technology to change your delivery? JISC & AOC Review – webinars FELTAG; purpose to ‘nudge’ the sector Content creation + collaborative learning + blended and distance learning + study skills support

DIGITAL TECHNOLOGY

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SAMR MODEL

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• Technology and pedagogy
• Use the SAMR model to evaluate two digital

resources

– Where on the SAMR scale would you place the resource? – In what way is it different from a traditional activity of this sort? – What might be the benefits or drawbacks?

ANALYSIS OF DIGITAL RESOURCES

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Review of the day

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• What are the most important issues arising

from this session?

• How will you apply this in your teaching &

learning?

Summary

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Delivered by ccConsultancy for the Education and Training Foundation

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• Recommended reading

– Swan, M. (2005) Improving Learning in Mathematics: Challenges and Strategies. London: DfES. [available from https://www.stem.org.uk/elibrary/resource/26057/improving-learning- in-mathematics-challenges-and-strategies ]. – FELTAG (2014) Further Education Learning Technology Action Group: Recommendations [available at http://feltag.org.uk/wp- content/uploads/2012/01/FELTAG-REPORT-FINAL.pdf].

FOLLOW-UP ACTIVITIES

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• Watch the videos at

https://www.stem.org.uk/elibrary/collection/2936/thinking-about- discussion

• Consider how you would instigate a discussion session with

learners.

• Good starting points might be Improving Learning in

Mathematics sessions A4, N2, S2 or SS4 [available at https://www.stem.org.uk/elibrary/collection/2938/teaching- activities-and-materials]. Follow-up activities

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• Department for Business, Innovation and Skills (2015) An update on progress since

the publication of the Further Education Learning Technologies Action Group (FELTAG). [available at https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/4050 01/BIS_15_71_FELTAG_progress_report.pdf].

• Griffin, P. (2009) What makes a rich task? [available at

http://www.atm.org.uk/write/MediaUploads/Journals/MT212/Non-Member/ATM- MT212-32-34.pdf].

• Mercer, N. (2000) Words and Minds: How we use language to think together.

London: Routledge.

• Puentedura, R. R. (2006). Transformation, technology, and education [available at

http://hippasus.com/resources/tte/].

FURTHER READING (FOR THOSE PURSUING ACCREDITATION)

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• In preparation for each of our courses we ask that you reflect upon your
• wn professional progress and development in relation to the Education

and Training Foundation's Professional Standards for FE Teachers.

• You may have also completed the ETF Professional Standards self-

assessment Tool: Professional Standards - Self Assessment.

• You may now wish to revisit the Professional Standards:

– has your learning today supported your progression in relation to the professional standards?

• has your learning today encouraged you to explore other areas of

professional and/ or personal development as they relate to the professional standards? An opportunity for reflection: Engaging with the ETF’s Professional Standards

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ETFOUNDATION.CO.UK

THANK YOU ANY QUESTIONS?

JULIA SMITH TESSMATHS1@GMAIL.COM