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PISA Equations and Inequalities: Making Mathematics Accessible to All PDF

224 Pages·2016·4.214 MB·English
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PISA PISA Equations and Inequalities Equations and Inequalities MAKING MATHEMATICS ACCESSIBLE TO ALL More than ever, students need to engage with mathematics concepts, think quantitatively MAKING MATHEMATICS ACCESSIBLE TO ALL and analytically, and communicate using mathematics. All these skills are central to a young person’s preparedness to tackle problems that arise at work and in life beyond the classroom. But the reality is that many students are not familiar with basic mathematics concepts and, at school, only practice routine tasks that do not improve their ability to think quantitatively and solve real-life, complex problems. P How can we break this pattern? This report, based on results from PISA 2012, shows that IS A one way forward is to ensure that all students spend more “engaged” time learning core mathematics concepts and solving challenging mathematics tasks. The opportunity to learn E q mathematics content – the time students spend learning mathematics topics and practising u a maths tasks at school – can accurately predict mathematics literacy. Differences in students’ t io familiarity with mathematics concepts explain a substantial share of performance disparities n in PISA between socio-economically advantaged and disadvantaged students. Widening s a access to mathematics content can raise average levels of achievement and, at the same n d time, reduce inequalities in education and in society at large. In e q u Contents a lit Chapter 1. Why access to mathematics matters and how it can be measured ie s Chapter 2. Variations in students’ exposure to and familiarity with mathematics M A Chapter 3. Exposure to mathematics in school and performance in PISA K IN Chapter 4. Opportunity to learn and students’ attitudes towards mathematics G M Chapter 5. A policy strategy to widen opportunities to learn mathematics AT H E M A T IC S A C C E S S IB L E Consult this publication on line at: http://dx.doi.org/10.1787/9789264258495-en TO A This work is published on the OECD iLibrary, which gathers all OECD books, periodicals and LL statistical databases. Visit www.oecd-ilibrary.org and do not hesitate to contact us for more information. Programme for International Student Assessment ISBN 978-92-64-25848-8 98 2016 04 1P Co-funded by the European Union PISA Equations and Inequalities MAkIng MAtheMAtIcS AcceSSIble to All This work is published under the responsibility of the Secretary-General of the OECD. The opinions expressed and the arguments employed herein do not necessarily reflect the official views of the OECD member countries. This document and any map included herein are without prejudice to the status of or sovereignty over any territory, to the delimitation of international frontiers and boundaries and to the name of any territory, city or area. Please cite this publication as: OECD (2016), Equations and Inequalities: Making Mathematics Accessible to All, PISA, OECD Publishing, Paris, http://dx.doi.org/10.1787/9789264258495-en. ISBN 978-92-64-25848-8 (print) ISBN 978-92-64-25849-5 (PDF) Series: PISA ISSN 1990-8539 (print) ISSN 1996-3777 (online) The statistical data for Israel are supplied by and under the responsibility of the relevant Israeli authorities. The use of such data by the OECD is without prejudice to the status of the Golan Heights, East Jerusalem and Israeli settlements in the West Bank under the terms of international law. Photo credits: © Flying Colours Ltd /Getty Images © Jacobs Stock Photography /Kzenon © khoa vu /Flickr /Getty Images © Mel Curtis /Corbis © Shutterstock /Kzenon © Simon Jarratt /Corbis Corrigenda to OECD publications may be found on line at: www.oecd.org/publishing/corrigenda. © OECD 2016 You can copy, download or print OECD content for your own use, and you can include excerpts from OECD publications, databases and multimedia products in your own documents, presentations, blogs, websites and teaching materials, provided that suitable acknowledgement of OECD as source and copyright owner is given. All requests for public or commercial use and translation rights should be submitted to [email protected]. Requests for permission to photocopy portions of this material for public or commercial use shall be addressed directly to the Copyright Clearance Center (CCC) at [email protected] or the Centre français d’exploitation du droit de copie (CFC) at [email protected]. Foreword Pisa has long established that disadvantaged students tend to trail behind their privileged peers in their mathematics achievement – even if the achievement gap varies widely across countries. but that left open the question: to what extent can teachers and schools do something about this? the Pisa report, Equations and Inequalities: Making Mathematics Accessible to All, sheds light on this. While education systems have generally done well in providing equitable access to the quantity of mathematics education – in the sense that disadvantaged students spend about the same time in mathematics classes in school as their advantaged peers – the data show large differences in the quality of learning experiences between social groups. these inequalities result in a waste of talent. While disadvantaged students tend to learn simple facts and figures and are exposed to simple applied mathematics problems, their privileged counterparts experience mathematics instruction that help them think like a mathematician, develop deep conceptual understanding and advanced mathematical reasoning skills. these differences matter, because greater exposure to pure mathematics tasks and concepts has a strong relationship with higher performance in Pisa, and the data suggest that exposing all students to challenging problems and conceptual knowledge in mathematics classes can have a large impact on performance. in addition, the relationship between the content covered during mathematics instruction at school and the socio-economic profile of students and schools is stronger in countries that track students early into different study programmes, that have larger percentages of students in selective schools, and that transfer less-able students to other schools. on the one hand, the findings from this report are disappointing, in the sense that they show that mathematics education often reinforces, rather than moderates, inequalities in education. on the other hand, they show that high-quality mathematics education, and thus education policy and practice, are an essential part of the solution to redressing social inequality. Policy makers can develop more ambitious and coherent mathematics standards that cover core mathematical ideas in depth, increase connections between topics and align instructional systems with these standards. they can also reduce tracking and stratification and/or moderate their effects. teachers can help students acquire higher-order mathematics knowledge and skills by replacing routine tasks with challenging open problems, support positive attitudes towards 3 equations and inequalities: making mathematics accessible to all © OECD 2016 FOREWORD mathematics, provide students with multiple opportunities to learn key concepts at different levels of difficulty, and offer tailored support to struggling students. Parents’ expectations and attitudes towards mathematics matter too. and we can all do much better in monitoring and analysing not just students’ learning outcomes, but students’ opportunity to learn. Andreas Schleicher director for education and skills 4 © OECD 2016 equations and inequalities: making mathematics accessible to all Acknowledgements this report is the product of a collaboration among the countries participating in Pisa and the oecd secretariat. the report was prepared by mario Piacentini and chiara monticone, with contributions from Judit Pál and bonaventura Pacileo, and edited by marilyn achiron. andreas schleicher, montserrat gomendio, Yuri belfali, miyako ikeda, Francesco avvisati, Francesca borgonovi, alfonso echazarra, tue halgreen, Richard lee, daniel salinas, Javier suarez-alvarez and Pablo Zoido from the oecd secretariat, as well as William schmidt, provided valuable feedback at various stages of the report. marika boiron, Rose bolognini, claire chetcuti, Juliet evans, hélène guillou, dario laudati and giannina Rech provided statistical, editorial and administrative support. the development of the report was steered by the Pisa governing board, which is chaired by lorna bertrand (united kingdom). the report was generously supported by the european commission.1 1. this document has been co-funded by the european union. the opinions expressed and arguments employed herein do not necessarily reflect the official views of the european union. 5 equations and inequalities: making mathematics accessible to all © OECD 2016 Table of Contents ExEcutivE Summary ..............................................................................................................................................................13 rEadEr’S GuidE ...........................................................................................................................................................................31 ChApTEr 1 Why accESS to mathEmaticS mattErS  and hoW it can bE mEaSurEd....................................................................................................................................35 the importance of mathematics skills in everyday life .........................................................................................38 the relationship between mathematics knowledge and mathematical literacy .................................42 the concept of opportunity to learn .................................................................................................................................44 measuring opportunity to learn in PiSa .........................................................................................................................47 Questions used to measure opportunity to learn in PiSa 2012 ...................................................................62 Exposure to pure and applied mathematics .................................................................................................................62 Familiarity with mathematics .................................................................................................................................................63 Students’ exposure to different kinds of mathematics problems ...................................................................63 ChApTEr 2 variationS in StudEntS’ ExPoSurE to and Familiarity With mathEmaticS .................................................................................................................................71 variations in access to mathematics content within countries ......................................................................73 individual student characteristics and access to mathematics content ....................................................81 gender differences in opportunity to learn mathematics ......................................................................81 immigrant students’ familiarity with mathematics concepts .................................................................83 attendance at pre-primary education and familiarity with mathematics .....................................85 Parents’ preferences, school selectivity and opportunity to learn mathematics ....................................................................................................................................................................87 Equity in opportunity to learn and sorting students .............................................................................................90 Vertical stratification through grade repetition ...............................................................................................92 horizontal stratification between and within schools and programmes .....................................94 selection through transfers ........................................................................................................................................104 how equity in opportunity to learn is related to teaching resources and practices ...................108 7 equations and inequalities: making mathematics accessible to all © OECD 2016 Table of ConTenTs ChaptEr 3 ExposurE to MathEMatics in school and pErforMancE in pisa �������123 Mathematics curricula and performance on different content areas of pisa �����������������������������������125 Variations in opportunity to learn and performance in mathematics �����������������������������������������������������133 Variations in time spent learning ��������������������������������������������������������������������������������������������������������������������������133 Variations in exposure to and familiarity with mathematics ���������������������������������������������������������������136 the links between opportunity to learn, mathematics literacy and socio-economic status ����������������������������������������������������������������������������������������������������������������������������������151 Examples of pisa mathematics units�������������������������������������������������������������������������������������������������������������������������������158 ChaptEr 4 opportunity to lEarn and studEnts’ attitudEs towards MathEMatics �����������������������������������������������������������������������������������������������������������������������165 how students’ motivation and self-beliefs vary across countries and subgroups of students �����������������������������������������������������������������������������������������������������������������������������169 relationships between opportunity to learn and attitudes towards mathematics ��������������������������175 exposure to pure mathematics, familiarity with mathematics and students’ attitudes towards mathematics ������������������������������������������������������������������������������������������������������������������������������������������������������175 exposure to applied mathematics and students’ attitudes towards mathematics �����������������180 mathematics assessments and anxiety ��������������������������������������������������������������������������������������������������������������180 Mediating factors between exposure to mathematics and attitudes towards mathematics ����������182 the benefits and possible shortcomings of hard-working and well-prepared peers ����������������������������������������������������������������������������������������������������������������������������������������������182 Parental involvement and children’s mathematics anxiety �������������������������������������������������������������������186 teachers’ practices and attitudes towards mathematics �������������������������������������������������������������������������190 developing knowledge of and engagement with mathematics at the same time����������������������������195 ChaptEr 5 a policy stratEgy to widEn opportunitiEs to lEarn MathEMatics �����������������������������������������������������������������������������������������������������������201 develop coherent standards, frameworks and instruction material for all students ��������������������202 help students acquire mathematics skills beyond content knowledge �������������������������������������������������205 reduce the impact of tracking on equity in exposure to mathematics �������������������������������������������������������������������������������������������������������������������������������������������������������������������������������207 learn how to handle heterogeneity in the classroom ����������������������������������������������������������������������������������������208 teach heterogeneous classes effectively �����������������������������������������������������������������������������������������������������������209 offer greater and individualised support to struggling students ������������������������������������������������������209 support positive attitudes towards mathematics through innovations in curricula and teaching �������������������������������������������������������������������������������������������������������������������������������������������������������210 Monitor and analyse opportunities to learn ������������������������������������������������������������������������������������������������������������211 aNNEX a list of tablEs aVailablE on linE ��������������������������������������������������������������������������������������������������217 8 © OECD 2016 equations and inequalities: making mathematics accessible to all

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