Teaching strategies Cognitive activation Lessons drawn Classroom climate Students’ attitudes Memorisation Pure & applied maths Control Socio-economic status Elaboration strategies Ten Questions for Mathematics Teachers ... and how PISA can help answer them PISA Ten Questions for Mathematics Teachers ... and how PISA can help answer them 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), Ten Questions for Mathematics Teachers ... and how PISA can help answer them, PISA, OECD Publishing, Paris, http://dx.doi.or /10.1787/9789264265387-en. ISBN 978-9264-26537-0 (print) ISBN 978-9264-26538-7 (online) Series: PISA ISSN 1990-85 39 (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. Latvia was not an OECD member at the time of preparation of this publication. Accordingly, Latvia is not included in the OECD average. 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 info@ copyright.com or the Centre français d’exploitation du droit de copie (CFC) at [email protected]. A TEACHER’S GUIDE TO MATHEMATICS TEACHING AND LEARNING . 3 A teacher’s guide to mathematics teaching and learning Every three years, a sample of 15-year-old students around the world sits an assessment, known as PISA, that aims to measure how well their education system has prepared them for life after compulsory schooling. PISA stands for the Programme for International Student Assessment. The assessment, which is managed by the OECD, in partnership with national centres and leading experts from around the world, is conducted in over 70 countries and economies. It covers mathematics, science and reading. PISA develops tests that are not directly linked to the school curriculum; they assess the extent to which students can apply their knowledge and skills to real-life problems. In 2012, the assessment focused on mathematics. The results provide a comparison of what 15-year-old students in each participating country can or cannot do when asked to apply their understanding of mathematical concepts related to such areas as quantity, uncertainty, space or change. As part of PISA 2012, students also completed a background questionnaire, in which they provided information about themselves, their homes and schools, and their experiences at school and in mathematics classes in particular. It is from these data that PISA analysts are able to understand what factors might influence student achievement in mathematics. While many national centres and governments try to ensure that the schools and teachers participating in the assessments get constructive feedback based on PISA results, most of the key messages published in the PISA reports don’t make it back to the classroom, to the teachers who are preparing their country’s students every day. Until now. 4 . TEN QUESTIONS FOR MATHEMATICS TEACHERS USING PISA TO SUPPORT MATHEMATICS TEACHERS The PISA student background questionnaire sought information about students’ experiences in their mathematics classes, including their learning strategies and the teaching practices they said their teachers used. This information, coupled with students’ results on the mathematics assessment, allow us to examine how certain teaching and learning strategies are related to student performance in mathematics. We can then delve deeper into the student background data to look at the relationships between other student characteristics, such as students’ gender, socio-economic status, their attitudes toward mathematics and their career aspirations, to ascertain whether these characteristics might be related to teaching and learning strategies or performance. PISA data also make it possible to see how the curriculum is implemented in mathematics classes around the world, and to examine whether the way mathematics classes are structured varies depending on the kinds of students being taught or the abilities of those students. This report takes the findings from these analyses and organises them into ten questions, listed below, that discuss what we know about mathematics teaching and learning around the world – and how these data might help you in your mathematics Questions included in this report: How much should I direct As a mathematics Can I help my student learning in my teacher, how important students learn mathematics classes? is the relationship I have how to learn with my students? mathematics? 1 3 5 Teaching Cognitive Classroom strategies activation climate Memorisation Control 2 4 Are some mathematics What do we know about teaching methods more memorisation and effective than others? learning mathematics? A TEACHER’S GUIDE TO MATHEMATICS TEACHING AND LEARNING . 5 classes right now. The questions encompass teaching strategies, student learning strategies, curriculum coverage and various student characteristics, and how they are related to student achievement in mathematics and to each other. Each question is answered by the data and related analysis, and concludes with a section entitled “What can teachers do?” that provides concrete, evidence-based suggestions to help you develop your mathematics teaching practice. WHAT DO WE MEAN BY TEACHING AND LEARNING STRATEGIES? In simple terms, teaching strategies refer to “everything teachers do or should do in order to help their learners learn”.1 Also called teaching practices in this book, they can include everything from planning and organising lessons, classes, resources and assessments, to the individual actions and activities that teachers engage in during their classroom teaching. Learning strategies are the behaviours and thoughts students use as they attempt to complete various tasks associated with the process of learning a new concept or acquiring, storing, retrieving and using information.2 Should I encourage Should my teaching emphasise What can teachers learn students to use mathematical concepts or how from PISA? their creativity in those concepts are applied in 10 mathematics? the real world? 6 8 Elaboration Socio-economic Pure & applied Students’ Lessons strategies status maths attitudes drawn 7 9 Do students’ backgrounds Should I be concerned about influence how they learn my students’ attitudes towards mathematics? mathematics? 6 . TEN QUESTIONS FOR MATHEMATICS TEACHERS You’ll also find some data in this report from the Teaching and Learning International Survey, or TALIS, an OECD-led survey in which 34 countries and economies – and over 104,000 lower secondary teachers – took part in 2013. (Lower secondary teachers teach students of approximately the same age as the students who participate in PISA.) TALIS asked teachers about themselves, their teaching practices and the learning environment. These data provide information about how certain teaching strategies or behaviours might influence you as a teacher. In other words, could certain actions that you take actually improve your own feelings of self-confidence or your satisfaction with your work? THE BOTTOM LINE Teaching is considered by many to be one of the most challenging, rewarding and important professions in the world today. As such, teachers are under constant pressure to improve learning and learning outcomes for their students. This report tries to give you timely and relevant data and analyses that can help you reflect on how you teach mathematics and on how your students learn. We hope that you find it useful in your own development as a mathematics teacher. ABOUT THE DATA The findings and recommendations in this report are based on the academic research literature on mathematics education, on data from the PISA 2012 assessment and from the questionnaires distributed to participating students and school principals, and on teacher data from TALIS 2013. Keep in mind that the teaching and learning strategies discussed in this report were not actually observed; students were asked about the teaching practices they observed from their current teachers only, and teachers were asked to report on the strategies they use. PISA and TALIS are cross- sectional studies – data are collected at one specific point in time – and they do not – and cannot – describe cause and effect. For these reasons, the findings should be interpreted with caution. The OECD average is the arithmetic mean of 34 OECD countries: Australia, Austria, Belgium, Canada, Chile, the Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Israel, Italy, Japan, Korea, Luxembourg, Mexico, the Netherlands, New Zealand, Norway, Poland, Portugal, the Slovak Republic, Slovenia, Spain, Sweden, Switzerland, Turkey, the United Kingdom and the United States. Latvia acceded to the OECD on 1 July 2016. It is not included in the OECD average. A TEACHER’S GUIDE TO MATHEMATICS TEACHING AND LEARNING . 7 ACKNOWLEDGEMENTS This publication was written by Kristen Weatherby, based on research and analysis by Alfonso Echazarra, Mario Piacentini, Daniel Salinas, Chiara Monticone, Pablo Fraser and Noémie Le Donné. Giannina Rech provided analytical and editorial input for the report. Judit Pál, Hélène Guillou, Jeffrey Mo and Vanessa Denis provided statistical support. The publication was edited by Marilyn Achiron, and production was overseen by Rose Bolognini. Andreas Schleicher, Montserrat Gomendio, Yuri Belfali, Miyako Ikeda and Cassandra Davis provided invaluable guidance and assistance. 1. Hatch, E., and C. Brown (2000), Vocabulary, Semantics and Language Education, Cambridge University Press, Cambridge. 2. Dansereau, D. (1985), “Learning Strategy Research”, in J. Segal, S. Chipman and R. Glaser (eds.), Thinking and Learning Skills, Lawrence Erlbaum Associates, Mahwah, New Jersey. This publication has Look for the StatLinks at the bottom of the tables or graphs in this book. To download the matching Excel® spreadsheet, just type the link into your Internet browser, starting with the http://dx.doi.org prex, or click on the link from the e-book edition. T e a How much should c h I direct student i n g learning in my s t mathematics r a t classes? e g i e s HOW MUCH SHOULD I DIRECT STUDENT LEARNING IN MY MATHEMATICS CLASSES? . 9 The traditional view of a classroom that has existed for generations T E A in schools around the world consists of students sitting at desks, C H IN passively listening as the teacher stands in the front of the class G S T and lectures or demonstrates something on a board or screen. The R A T teacher has planned the lesson, knows the content she needs to E G IE cover and delivers it to the students, who are expected to absorb S that content and apply it to their homework or a test. This kind of “teacher-directed” instruction might also include things like lectures, lesson summaries or question-and-answer periods that are driven by the teacher. This form of teaching isn’t limited to mathematics, necessarily, and it’s a teaching strategy that everyone has experienced as a student at one time or another. For decades now, educationalists have encouraged giving students more control over their own learning; thus student-oriented teaching strategies are increasingly finding their way into classrooms of all subjects. As the name indicates, student- oriented teaching strategies place the student at the centre of the activity, giving learners a more active role in the lesson than in traditional, teacher-directed strategies. These student-oriented teaching strategies can include activities such as assigning student projects that might take a week or longer to complete or working in small groups through which learners must work together to solve a problem or accomplish a task. Which type of teaching strategy is being used to teach mathematics in schools around the world? And which one should teachers be using? Data indicate a prevalence of teacher-directed methods, but deciding how to teach mathematics isn’t as simple as choosing between one strategy and another. Teachers need to consider both the content and students to be taught when choosing the best teaching strategy for their mathematics lessons.