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
LEARNING OUTCOMES Use active learning Facilitate learners’ strategies and mathematical reasoning connected, challenging and ability to explain teaching methods to and use mathematical improve learning in language, methods and GCSE maths? ideas? Use rich collaborative tasks to develop Can you transferable higher-order … thinking and problem- solving skills? Use co-operative small Use technology group work to facilitate appropriately to promote discussion and create a learner engagement, supportive and motivation and success in encouraging atmosphere mathematics teaching and in the learning learning? environment? EDUCATION AND TRAINING FOUNDATION Slide 3
MOST COMMON TEACHING METHODS 4 Delivered by ccConsultancy for the Education and Training Foundation
LEAST COMMON TEACHING METHODS 5 Delivered by ccConsultancy for the Education and Training Foundation
IMPROVING LEARNING IN MATHEMATICS • 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 online at The National STEM Centre 6 Delivered by ccConsultancy for the Education and Training Foundation
IMPROVING LEARNING IN MATHEMATICS • From ‘passive’ to ‘active’ learning. • From ‘transmission’ to ‘connected, challenging’ teaching. • From ‘teacher centred’ to ‘learner centred’ practices. 7 Delivered by ccConsultancy for the Education and Training Foundation
PRINCIPLES FOR EFFECTIVE TEACHING
PRINCIPLES FOR EFFECTIVE TEACHING 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 9 Delivered by ccConsultancy for the Education and Training Foundation
PRINCIPLES FOR EFFECTIVE TEACHING 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? 10 Delivered by ccConsultancy for the Education and Training Foundation
IMPROVING LEARNING IN MATHEMATICS • 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. 11 Delivered by ccConsultancy for the Education and Training Foundation
02 DISCUSSION IN MATHEMATICS
WHY IS DISCUSSION RARE IN MATHS? 13 Delivered by ccConsultancy for the Education and Training Foundation
WHAT KIND OF TALK IS MOST USEFUL? 14 Delivered by ccConsultancy for the Education and Training Foundation
03 PROBLEM SOLVING
PROBLEM CREATING AND SOLVING 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 16 Delivered by ccConsultancy for the Education and Training Foundation
CREATING PROBLEMS: DOING AND UNDOING PROCESSES 17 Delivered by ccConsultancy for the Education and Training Foundation
CREATING AND SOLVING EQUATIONS • 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 18 Delivered by ccConsultancy for the Education and Training Foundation
CREATING AND SOLVING EQUATIONS • Creating Think of a number x = 4 Multiply by 3 3x = 12 Add 5 3x + 5 = 17 Multiply by 2 2(3x + 5) = 34 19 Delivered by ccConsultancy for the Education and Training Foundation
CREATING AND SOLVING EQUATIONS • Solving Solve the equation 2(3 x + 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 ? 20 Delivered by ccConsultancy for the Education and Training Foundation
CREATING AND SOLVING EQUATIONS • 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? 21 Delivered by ccConsultancy for the Education and Training Foundation
04 RICH TASKS
RICH TASKS – 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 23 Delivered by ccConsultancy for the Education and Training Foundation
“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] 24 Delivered by ccConsultancy for the Education and Training Foundation
RICH TASKS • 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. 25 Delivered by ccConsultancy for the Education and Training Foundation
05 THINKING SKILLS
BLOOM’S TAXONOMY • 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)? 27 Delivered by ccConsultancy for the Education and Training Foundation
ASSESSMENT OBJECTIVES 28 Delivered by ccConsultancy for the Education and Training Foundation
06 USING TECHNOLOGY
USING TECHNOLOGY IN APPROPRIATE WAYS • ‘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) 30 Delivered by ccConsultancy for the Education and Training Foundation
DIGITAL TECHNOLOGY 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 31 Delivered by ccConsultancy for the Education and Training Foundation
SAMR MODEL 32 Delivered by ccConsultancy for the Education and Training Foundation
ANALYSIS OF DIGITAL RESOURCES • 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? 33 Delivered by ccConsultancy for the Education and Training Foundation
Review of the day
Summary • What are the most important issues arising from this session? • How will you apply this in your teaching & learning? 35 Delivered by ccConsultancy for the Education and Training Foundation
36 Delivered by ccConsultancy for the Education and Training Foundation
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