Reconsidering Maths as a Creative Discipline

Creativity is at the heart of mathematical practice, with models, images and symbols providing a foundation for solving problems, building empathy and considering others’ points of view. Josh Lury offers some tactics for approaching maths problems while deepening creativity.

‘It sometimes happens that during an arithmetic lesson, when the very atmosphere seems heavy with tedium, a butterfly will flutter into the classroom from out of doors. Then the urchins will all crane their necks and follow its flight with curiosity, as if they saw before them something strange and new and not simply a butterfly.’

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      string(5622) "ResourceNEW SECONDARY SCHOOL CURRICULUMOriginal DocumentThe revised Secondary National Curriculum aims to improve coherence across the curriculum; make better connections between subjects; ensure progression from Key Stage 3 through Key Stage 4; show how schools can integrate the Every Child Matters agenda, and take account of post-14 developments. KeywordsSecondary schools, Key Stage 3, Key Stage 4, curriculum, Every Child MattersSummaryThe new Key Stage 3 curriculum will be phased in over a three-year period. It becomes statutory for Year 7 pupils in September 2008. From September 2009, it will apply to all Year 7 and Year 8 pupils. From September 2010, it will apply across Years 7, 8 and 9. Changes at Key Stage 4 will start in September 2009.Key features of the new curriculum:The programme of study for each subject starts with a statement about the aims of the national curriculum, which are to develop:· Successful learners who enjoy learning, make progress and achieve.· Confident individuals who lead safe and healthy lives.· Responsible citizens who make a positive contribution to society.· All programmes of study take the same format, and identify:· Key concepts that are at the heart of each subject.· Key skills and processes that pupils learn to make progress in the subject.· Range and content that outline the breadth of the subject from which the areas to be studied should be drawn.· Curriculum opportunities that pupils should be given to improve their engagement with the subject.· Most have common elements. For example, all pupils need to develop a critical understanding of communications, the environment and themselves.All 11-14 year old pupils will continue to study all 12 subjects of the National Curriculum. Key changes include:· History: pupils should be able to identify and understand the major events, changes and developments in British, European and world history covering at least the medieval, early modern, industrial and twentieth-century periods.· English: in addition to at least one play by Shakespeare, teachers have lists of contemporary, 20th century and older authors to draw on. Teachers can also look at “multimodal texts” that combine written, aural and visual, for example the combination of words and images in a newspaper or words, images, video clips and sound on a website.· Languages: as well as French, Spanish and German, schools will have more freedom to offer economically useful world languages such as Mandarin and Urdu. Lessons should help children develop intercultural understanding.· Mathematics: described as a creative discipline with an international language.· Citizenship: following Keith Ajegbo’s review, pupils will learn shared British values and study national identity in the UK, including issues such as the legacy of the British Empire.· Geography: a clearer focus on sustainable development, environmental change and world poverty to prepare young people to become global citizens.· Cooking: 11-14 year olds will have an entitlement to cook. They will be taught how to make simple, healthy meals from basic fresh ingredients.· Science: will include study of the ethical and moral implications of science, the effect of drugs, and sexual health. All pupils who reach the required level will be able to study three separate sciences – Physics, Chemistry and Biology – for GCSE by September 2008.· Economic well-being: pupils will be taught essential financial life skills through functional maths and in Personal Social Health and Economic Education. These will include: personal finance, enterprise and financial capability; learning about risk and reward; investment and trade; personal budgeting; mortgages; interest rates; and balancing credit cards.· PE: lessons will combine physical activity with learning how exercise affects fitness and health. Schools will have even more flexibility to run the physical activities that best meet their pupils’ needs.       ActionTimetable for implementationThe new secondary curriculum website will be launched in September. There will then be a three-year period from 2008-2010 for schools to implement the new programmes of study:· Summer 2007: Qualifications and Curriculum Authority curriculum workshops.· Autumn 2007: new programmes of study and curriculum design and development materials available on the QCA website. DCSF national conferences. National College for School Leadership (NCSL) / Specialist Schools and Academies Trust workshops on leading curriculum change.· Spring 2008: Secondary National Strategy network events for English, mathematics, science, and information and communication technology curriculum leaders. Centre for British Teachers Education Trust and subject associations offer support for teachers of the foundation subjects.· Autumn 2008: First teaching of the new secondary curriculum. First teaching of the revised AS and A2 qualifications. First teaching of the specialised Diploma in IT; society, health and development; engineering; creative and media; and construction and the built environment.· Autumn 2009: First teaching of the revised GCSE. First teaching of the specialised Diploma in land-based and environmental; manufacturing; hair and beauty; business administration and finance; and hospitality and catering.· September 2010: First teaching of specialised Diploma in public services; sport and leisure; retail; and travel and tourism.· Summer 2011: First national curriculum tests for the new secondary curriculum at key stage 3. Evaluation of the impact of the new"
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Leadership

Secondary National Curriculum

19 Jul 2007

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      string(4228) "theboy begins to move when the message is received.In contrast to conventional Logo, a powerful aspect of Scratch is that itis object-oriented so that sprites, like the boy and the girl, are treated asindependent objects but can communicate with each other through the sendingand receiving of messages. Parallel processing means that sprites and othersobjects might run actions simultaneously whenever triggered. These featuresadd enormous narrative expression.For me, this example demonstrates memorably the sense in whichmathematics in the form of programming can be used to create fantasy orexpress ideas more normally than the domain of art, poetry and music. Whatimpressed me was that this student found programming to be a means ofexpression, a hallmark of making mathematics phenomenal.Figure 3: Scratch screenshot11Volume3.2nCreativeTeaching&LearningFocuson: MathsComing later…In the forthcoming articles I will set out in more detail key aspects of makingmathematics phenomenal. In the second article, I shall focus on how usingmathematics can lead to understanding mathematics, challenging theapparent orthodoxy that learners need first to learn the skills and proceduresbefore they are able to apply them. Even in the programming example, wecan see how some students may have been using the fd and rt commandsbefore having a complete understanding of distance and angle. Or using theinput 😡 in the procedure before understanding algebra.In the third article, I shall discuss the importance of designing tasks thatare seen as purposeful by the students and lead to an experientially-basedsense of how mathematics can ‘get stuff done’. I have commented aboveon how the students may, for the first time, have sensed how algebra mightbe used to create a street of houses with varied sizes.In the fourth article, I shall focus on one specific design principle, wherebyoffering control of their own activity might provide the student with insightsinto powerful mathematical representations. The Logo example offers turtlegraphics as a representation of geometry but at the same time providescommands that control activity to create the geometric pictures andanimations.In the final article, the focus will be on the interface between mathematicsand other aspects of human activity. The Scratch example shows howmathematics can create artistic, poetic and musical experiences. In thisarticle, I shall explore how, by engaging with social decision-making, studentsmay begin to map out the territory of mathematics to appreciate the scopeand limitations of the discipline.Overall, my intention is that the reader will understand that the projectof making mathematics phenomenal is essentially a design challenge. Myexamples will draw on digital technology but I will not be making the argumentthat technology alone offers the solution. On the contrary, technologywithout principled pedagogic design is likely to disengage students byhiding the mathematizing process that can be so creative and enjoyable.The components of making mathematics phenomenal that I will introducein the next four articles are not exhaustive but they are illustrative of howthe carefully designed use of technology could be one important ingredientin the challenge ahead.David Pratt is a Professor of Mathematics at Institute of Education,University of London. d.pratt@ioe.ac.ukKnowledge trails1) Can you be creative in maths? – Laying down the conditions that help tomake maths considered as a creative subject.http://library.teachingtimes.com/articles/can-you-be-creative-in-maths.htm2) What’s this got to do with maths? – Reporting on a secondary schoolproject that raised its achievements in maths using drama.http://library.teachingtimes.com/articles/whats-this-got-to-do-with-maths.htm3) Maths adventures – An alternative to computer-based mathematical gameshas caused children to ‘hug each other in excitement’. We find out why.http://library.teachingtimes.com/articles/ctl-1-4_maths-adventure.htmReferencesPapert, S. (1982). Mindstorms: Children, Computers and Powerful Ideas. London:Harvester Press."
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Creative Teaching & Learning

Making maths phenomenal - The case for programming

14 Aug 2012

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      string(4076) "than the domain of art, poetry and music. What impressed mewas that this student found programming to be a means of expression, a hallmark ofmaking mathematics phenomenal.44Vol 4.2School Leadership Todaywww.teachingtimes.comLeadingLearningMathemathics Coming later…This article is the first in a series on ‘Making Mathematics Phenomenal’ which will bepublished in Creative Teaching and Learning. In the second article, I shall focus on howusing mathematics can lead to understanding mathematics, challenging the apparentorthodoxy that learners need first to learn the skills and procedures before they are ableto apply them. Even in the programming example, we can see how some students mayhave been using the fd and rt commands before having a complete understanding ofdistance and angle. Or using the input 😡 in the procedure before understanding algebra.In the third article, I shall discuss the importance of designing tasks that are seenas purposeful by the students and lead to an experientially-based sense of howmathematics can ‘get stuff done’. I have commented above on how the students mayfor the first time have sensed how algebra might be used to create a street of houseswith varied sizes.In the fourth article, I shall focus on one specific design principle, wherebyoffering control of their own activity might provide the student with insights intopowerful mathematical representations. The Logo example offers turtle graphics asa representation of geometry but at the same time provides commands that controlactivity to create the geometric pictures and animations.In the final article, the focus will be on the interface between mathematics andother aspects of human activity. The Scratch example shows how mathematics cancreate artistic, poetic and musical experiences. In this article, I shall explore how, byengaging with social decision-making, students may begin to map out the territory ofmathematics to appreciate the scope and limitations of the discipline.Overall, my intention is that the reader will understand that the project of makingmathematics phenomenal is essentially a design challenge. My examples will drawon digital technology but I will not be making the argument that technology aloneoffers the solution. On the contrary, technology without principled pedagogic designis likely to disengage students by hiding the mathematizing process that can be socreative and enjoyable. The components of making mathematics phenomenal, thatI will introduce in the next four articles, are not exhaustive but they are illustrative ofhow the carefully designed use of technology could be one important ingredient in thechallenge ahead.Dave Pratt is a Professor of Mathematics Education at Institute of Education,University of London. d.pratt@ioe.ac.ukThe complete series on ‘Making mathematics phenomenal’ will be publishedin Creative Teaching and Learning. For more details, visit: http://www.teachingtimes.com/publications/creative-teaching-and-learning.htmKnowledge trails1) Pupils, maths and motivation – Maths can be a tricky subject toteach in an inspiring way, but a new university–led project is capturingchildren’s interest using technology and famous speakers.http://library.teachingtimes.com/articles/pupils-maths-and-motivation.htm2) Maxed out on maths – Schools are entering more and more studentsfor GCSE maths before they turn 16. A new report suggests the practicecould be doing more harm than goodhttp://library.teachingtimes.com/articles/maxedoutonmaths.htm3) What’s this got to do with maths? – How one secondary schoolimplemented a project to raise achievement in maths using drama.http://library.teachingtimes.com/articles/whats-this-got-to-do-with-maths.htmArticle available in Creative Teaching and Learning on the ProfessionalLearning Community (access by subscription).FurtherinformationPapert, S. (1982).Mindstorms:Children,Computers andPowerful Ideas.London: HarvesterPress.mai"
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Leadership

Mathematics can be phenomenal!

30 Oct 2012

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      string(4551) "Is creativity a skill that can be taught? Creative Partnerships are about encouraging pupils to be innovative and to develop the ability to solve problems in all areas of the curriculum, from maths to technology. Despite initial criticisms that it encourages ‘loose discipline’ or undermines the essential skills of numeracy and literacy, new research definitively proves that such partnerships change young lives for the better.In 1999 a government report entitled All Our Futures: Creativity, Culture and Education discussed the importance of promoting creativity and culture both in and out of school.Marking the 10th anniversary of the publication, a new report has confirmed that Creative Partnerships, the Government’s flagship creative learning programme which resulted from All Our Futures, is changing the lives of young people and having a real impact on their aspirations, achievements, skills and life chances.The Creative Partnerships: Changing Young Lives report – published by new organisation Creativity, Culture and Education (CCE), which manages Creative Partnerships nationally – shows how involvement in the programme has improved GCSE results, cut truancy, helped to engage families in education and had a positive impact on the economy.According to research from the independent National Foundation for Educational Research (NFER), which covered 13,000 young people, pupils who have taken part in Creative Partnerships’ programmes have often outperformed others who have not been involved. The NFER research found many of the differences were relatively small but it did conclude that the results of the study suggested that Creative Partnerships is contributing to better attainment. In particular, it found that young people who have attended Creative Partnerships activities made, on average, the equivalent of 2.5 grades better progress in GCSE than similar young people in other schools. The NFER evidence also suggests the Creative Partnerships programmes have been associated with an educationally significant reduction in absence in primary schools.Figures published by the DCSF show that the total absence rate in primary schools in 2006-07 was just over 5 per cent and that the rate has generally been declining in recent years. Participation in Creative Partnerships was shown to be associated with an educationally significant reduction in total absence in primary schools and this reduction continued over a period of years as Creative Partnerships became more established in these schools.Total absence rates in schools that had been participating in Creative Partnerships for five years were almost one percentage point lower than in otherwise comparable schools with no history of involvement with Creative Partnerships. Ofsted also monitored the programmes and found significant improvements in writing and speaking in a majority of schools it visited.The evidence so far seems to back the view that putting a real emphasis on creative and cultural education in schools has broad benefits. However, there is still a long way to go before creativity is seen as fundamental to teaching and learning in schools. And getting all schools to take this route will continue to be difficult when the accountability measures that determine the success or failure of schools continue to emphasise short-term improvements in formal qualifications.While SATs still dominate the final years of primary school, success and failure will continue to be based on formal tests, which means headteachers will continue to be inclined to place the school’s position in the league tables or its Ofsted rating ahead of promoting creativity. However, the new report suggests that a focus on creativity in schools need not be at the expense of achievement in the basics – in fact, as we have seen, it shows that exam results and attendance improve.The problem is that there are no formal indicators that reflect pupils’ creativity. One solution to this may be to use the new School Report Cards to include an achievement score in creative and cultural education.The Changing Young Lives report is a compilation of independent research reports and case studies investigating the impact of Creative Partnerships. It is available for download at  www. creativitycultureeducation.org/research-impact/showcaseresearch.Taken from School Leadership Today.Subscribe"
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Leadership

Creative Partnerships

17 Sep 2009