Teaching and learning functional mathematics Fiona Allan fiona.m.allan@gmail.com

Teaching functional mathematics Aims of today: To think about the needs of students studying Functional Mathematics To reflect on approaches to teaching and learning which are appropriate for these students To explore some of resources/activities which can be used with these students fiona.m.allan@gmail.com

Teaching functional mathematics http://www.youtube.com/watch?v=ZPMRA4yFeeM http://en.wikipedia.org/wiki/Tom_Lehrer fiona.m.allan@gmail.com

Teaching functional mathematics Work in a group Write down EVERYTHING you know about triangles Everyone must take part You have ten minutes fiona.m.allan@gmail.com

Teaching functional mathematics “There are two aspects to low attainment in mathematics: not knowing enough mathematics and not knowing how to learn mathematics.” Deep Progress in Mathematics 2003 http://oro.open.ac.uk/22808/ Deep Progress in Mathematics - The Improving Attainment in Mathematics Project Watson, Anne; De Geest, Els and Prestage, Stephanie (2003). Deep Progress in Mathematics - The Improving Attainment in Mathematics Project. Oxford, UK: University of Oxford, Department of educational studies. fiona.m.allan@gmail.com

Teaching functional mathematics “All students can think hard about mathematics and thus do better at mathematics” Deep Progress in Mathematics 2003 Deep Progress in Mathematics - The Improving Attainment in Mathematics Project Watson, Anne; De Geest, Els and Prestage, Stephanie (2003). Deep Progress in Mathematics - The Improving Attainment in Mathematics Project. Oxford, UK: University of Oxford, Department of educational studies. fiona.m.allan@gmail.com

Teaching functional mathematics Compare these shapes. In what ways are they the same? In what ways are they different? fiona.m.allan@gmail.com

Teaching functional mathematics “The only way to avoid the formation of entrenched misconceptions is through discussion and interaction. A trouble shared, in mathematical discourse, may become a problem solved.” Wood 1988 Wood, D. (1988) How Children Think and Learn, Oxford fiona.m.allan@gmail.com

Teaching functional mathematics Take it in turns to choose a card Decide whether the statement on the card is true, false or if you are not sure whether it is true or false. Explain your answer to the others in your group. If you not agree with what someone says, say so! http://www.nationalstemcentre.org.uk/elibrary/maths/collection/282/improving-learning-in-mathematics http://www.nationalstemcentre.org.uk/elibrary/maths/collection/485/mostly-number-materials http://www.nationalstemcentre.org.uk/elibrary/maths/resource/1966/evaluating-directed-number-statements-n9 fiona.m.allan@gmail.com

Teaching functional mathematics Reflect on your discussion Has anyone learnt anything? If so, how did this happen? What was good about the activity? fiona.m.allan@gmail.com

Teaching functional mathematics “When you explain something to someone else then you really understand it.” A-level Maths student “When you really understand something, you don’t need to revise - you’ve got it for life!” GCSE Maths student fiona.m.allan@gmail.com

Teaching functional mathematics Find the errors in this bill Explain to the others in the group your reasoning http://www.nuffieldfoundation.org/fsmqs http://www.nuffieldfoundation.org/fsmqs/fsmq-teaching-resources http://www.nuffieldfoundation.org/fsmqs/level-1-money-management#spot%20the%20errors fiona.m.allan@gmail.com

Teaching functional mathematics http://www.nationalstemcentre.org.uk/elibrary/maths/collection/282/improving-learning-in-mathematics http://www.nationalstemcentre.org.uk/elibrary/resource/997/learner-learner-discussion (first video only) http://www.nationalstemcentre.org.uk/elibrary/resource/997/learner-learner-discussion (first video only) fiona.m.allan@gmail.com

Teaching functional mathematics Teaching is more effective when it: Builds on the knowledge learners already have Exposes and discusses common misconceptions Uses higher-order questions https://www.ncetm.org.uk/public/files/309231/Mathematics+Matters+Final+Report.pdf https://www.ncetm.org.uk/resources/mm_values_principles https://www.ncetm.org.uk/resources/4685 https://www.ncetm.org.uk/public/files/274681/NCETM+Mathematics+Summary.pdf fiona.m.allan@gmail.com

Teaching functional mathematics Makes appropriate use of whole class interactive teaching, individual work and cooperative small group work Encourages reasoning rather than ‘answer getting’ Uses rich, collaborative tasks Creates connections between topics https://www.ncetm.org.uk/public/files/274681/NCETM+Mathematics+Summary.pdf fiona.m.allan@gmail.com

Teaching functional mathematics Uses resources, including technology, in creative and appropriate ways Confronts difficulties rather than seeks to avoid or pre-empt them Develops mathematical language through communicative activities Recognises both what has been learned and also how it has been learned https://www.ncetm.org.uk/public/files/274681/NCETM+Mathematics+Summary.pdf fiona.m.allan@gmail.com

Teaching functional mathematics Today we are going to look at: Building on the knowledge that learners already have Exposes and discusses common misconceptions Uses higher order questions fiona.m.allan@gmail.com

Teaching functional mathematics Sort the shapes in any way you want Now sort them again Write down all the ways you have sorted them http://www.nationalstemcentre.org.uk/elibrary/maths/collection/282/improving-learning-in-mathematics http://www.nationalstemcentre.org.uk/elibrary/maths/collection/291/teaching-activities-and-materials http://www.nationalstemcentre.org.uk/elibrary/maths/collection/492/mostly-shape-and-space-materials http://www.nationalstemcentre.org.uk/dl/c979f9755b6816a4a7a3c3338145ac97de635ec4/6442-SS1.pdf fiona.m.allan@gmail.com

Teaching functional mathematics Divide your flip chart paper into 3 columns Write 5, 12 and 24 at the top of the columns Under each number write down all the facts that make it different or the same as the other two numbers fiona.m.allan@gmail.com

Teaching functional mathematics http://www.nationalstemcentre.org.uk/elibrary/maths/collection/282/improving-learning-in-mathematics http://www.nationalstemcentre.org.uk/elibrary/resource/1000/using-misconceptions http://www.nationalstemcentre.org.uk/elibrary/resource/1000/using-misconceptions fiona.m.allan@gmail.com

Teaching functional mathematics Write down all the mathematical misconceptions that learners bring with them to college fiona.m.allan@gmail.com

Teaching functional mathematics Learners have worked enthusiastically with the tutors, and motivation, attendance and achievement have increased. Attendance in the classes taking part is 90% compared to 78% for those not taking part The pass rate for GCSE Mock has increased to 77% in the classes taking part, compared to a College pass rate of 52% in 2009/2010. In an AS Level mock exam learners achieved an average of 1.57 grades higher than the grades predicted by their GCSE scores. North Hertfordshire College ‘Teaching is more effective when it uses higher-order questions’ Professional development opportunities for mathematics teachers in Post-16 colleges (https://www.ncetm.org.uk/resources/32452) North Hertfordshire College ‘Teaching is more effective when it uses higher-order questions (https://www.ncetm.org.uk/resources/32529) fiona.m.allan@gmail.com

Teaching functional mathematics Open questioning Lay out the fraction cards in front of you Please don’t mix up the sets! fiona.m.allan@gmail.com

Teaching functional mathematics Teaching functional maths http://tlp.excellencegateway.org.uk/tlp/xcurricula/learning-mathematics-context.html http://tlp.excellencegateway.org.uk/tlp/xcurricula/learning-mathematics-context.html fiona.m.allan@gmail.com

Teaching functional mathematics http://tlp.excellencegateway.org.uk/tlp/xcurricula/lmic/ http://tlp.excellencegateway.org.uk/tlp/xcurricula/lmic/ fiona.m.allan@gmail.com

Teaching functional mathematics http://tlp.excellencegateway.org.uk/tlp/xcurricula/lmic/ fiona.m.allan@gmail.com

Teaching functional mathematics http://tlp.excellencegateway.org.uk/tlp/xcurricula/lmic/sessions/index.html http://tlp.excellencegateway.org.uk/tlp/xcurricula/lmic/assets/documents/2175_11_orderofoperations6a_o.pdf fiona.m.allan@gmail.com

Teaching functional mathematics http://tlp.excellencegateway.org.uk/tlp/xcurricula/lmic/assets/documents/2175_16_mathsinworkplace_o.pdf http://tlp.excellencegateway.org.uk/tlp/xcurricula/lmic/assets/documents/2175_16_mathsinworkplace_o.pdf fiona.m.allan@gmail.com

Resources Don’t reinvent the wheel! fiona.m.allan@gmail.com

Let’s explore some resources! fiona.m.allan@gmail.com

http://www.ncetm.org.uk fiona.m.allan@gmail.com

Essentials collection https://www.ncetm.org.uk/resources/35530 https://www.ncetm.org.uk/resources/36089 fiona.m.allan@gmail.com

https://www.ncetm.org.uk/resources/11329 https://www.ncetm.org.uk/resources/11329 fiona.m.allan@gmail.com

https://www.ncetm.org.uk/resources/8045 https://www.ncetm.org.uk/resources/34033 fiona.m.allan@gmail.com

https://www.ncetm.org.uk/self-evaluation/ https://www.ncetm.org.uk/self-evaluation/ fiona.m.allan@gmail.com

https://www.ncetm.org.uk/self-evaluation/ https://www.ncetm.org.uk/self-evaluation/assess/102 https://www.ncetm.org.uk/self-evaluation/assess/102 fiona.m.allan@gmail.com

https://www.ncetm.org.uk/self-evaluation/assess/102 fiona.m.allan@gmail.com

https://www.ncetm.org.uk/self-evaluation/summary/101/102#topOfNextSteps https://www.ncetm.org.uk/self-evaluation/summary/101/102#topOfNextSteps fiona.m.allan@gmail.com

https://www.ncetm.org.uk/resources/38830 https://www.ncetm.org.uk/resources/38830 fiona.m.allan@gmail.com

https://www.ncetm.org.uk/community/10445 https://www.ncetm.org.uk/community/10445 fiona.m.allan@gmail.com

http://www. nationalstemcentre. org. uk/elibrary/maths/search http://www.nationalstemcentre.org.uk/elibrary/maths/search?term=mathematical+moments&order=score&filter=C http://www.nationalstemcentre.org.uk/elibrary/maths/collection/758/lsis-mathematics http://www.nationalstemcentre.org.uk/elibrary/maths/collection/1503/number http://www.nationalstemcentre.org.uk/elibrary/maths/resource/7171/fractions-decimals-and-percentages http://www.nationalstemcentre.org.uk/dl/721249ae5168317de5f3bcd593dff244354765d9/22207-Decimals%20Percentages%20and%20Money.pdf fiona.m.allan@gmail.com

http://www. nationalstemcentre. org. uk/elibrary/maths/search http://www.nationalstemcentre.org.uk/elibrary/maths/search?term=mathematical+moments&order=score&filter=C http://www.nationalstemcentre.org.uk/elibrary/maths/collection/758/lsis-mathematics http://www.nationalstemcentre.org.uk/elibrary/maths/collection/1503/number http://www.nationalstemcentre.org.uk/elibrary/maths/resource/7171/fractions-decimals-and-percentages http://www.nationalstemcentre.org.uk/dl/0d3855e4015a69af923eebe265a385d93f16e928/22212-Percentages%20Encouraging%20Reasoning.pd fiona.m.allan@gmail.com

http://www. nationalstemcentre. org http://www.nationalstemcentre.org.uk/elibrary/maths/collection/282/improving-learning-in-mathematics http://www.nationalstemcentre.org.uk/elibrary/maths/resource/1967/developing-an-exam-question-number-n10 http://www.nationalstemcentre.org.uk/elibrary/maths/collection/282/improving-learning-in-mathematics fiona.m.allan@gmail.com

http://archive.excellencegateway.org.uk/page.aspx?o=201311 fiona.m.allan@gmail.com

Preparing to teach students resitting GCSE Mathematics https://www.ncetm.org.uk/resources/38838 Preparing to teach students resitting GCSE Mathematics Resources and CPD for those working with students resitting GCSE Mathematics Tarsia Resources   fiona.m.allan@gmail.com

http://www.ofsted.gov.uk/resources/good-practice-resource-functional-skills-dv8-training-ltd fiona.m.allan@gmail.com

Teaching functional mathematics www.ncetm.org.uk www.nuffieldfoundation.org/applying-mathematical-processes www.nuffieldfoundation.org/fsmqs archive.excellencegateway.org.uk/pdf/TandLMathematicsHT281107.pdf www.nationalstemcentre.org.uk/elibrary/maths/search?order=score www.skillsworkshop.org/numeracy fiona.m.allan@gmail.com

Teaching functional mathematics What are you going to do tomorrow? Join Resitting GCSE Mathematics community What are you going to do next week? What are you going to do before the end of term? fiona.m.allan@gmail.com

Teaching functional mathematics Aims of today: To think about the needs of students studying Functional Mathematics To reflect on approaches to teaching and learning which are appropriate for these students To explore some of resources/activities which can be used with these students fiona.m.allan@gmail.com

Teaching functional mathematics http://www.youtube.com/watch?v=2VZbWJIndlQ http://en.wikipedia.org/wiki/Tom_Lehrer fiona.m.allan@gmail.com