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The relationship between teaching strategies, student learning strategies, and student achievement in mathematics based on pisa data. It examines the impact of active learning practices, cognitive-activation strategies, and classroom climate on student performance. The document also discusses the importance of addressing student anxiety and fostering positive attitudes towards mathematics.
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Pure & applied maths
Lessons drawn
Teaching strategies
Cognitiveactivation
Classroom climate
Memorisation
Control
Elaboration strategies
Socio-economicstatus
Students’ attitudes
Ten Questions for
Mathematics Teachers
... and how PISA can help answer them
A TEACHER’S GUIDE TO MATHEMATICS TEACHING AND LEARNING.^ 3
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.
A teacher’s guide to mathematics
teaching and learning
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
4. TEN QUESTIONS FOR MATHEMATICS TEACHERS
How much should I direct student learning in my mathematics classes?
Are some mathematics teaching methods more effective than others?
What do we know about memorisation and learning mathematics?
As a mathematics teacher, how important is the relationship I have with my students?
Can I help my students learn how to learn mathematics?
Teaching strategies
1
(^2 )
3 5
Cognitive activation Classroom climate Memorisation^ Control
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.
6. TEN QUESTIONS FOR MATHEMATICS TEACHERS
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
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
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.
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.
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.
HOW MUCH SHOULD I DIRECT STUDENT LEARNING IN MY MATHEMATICS CLASSES?.^ 9
In PISA, students were asked about the frequency with which their teachers use student-oriented or teacher-directed strategies in their lessons. Findings indicate that today, teacher-directed practices are used widely. For instance, across OECD countries, eight out of ten students reported that their teachers tell them what they have to learn in every lesson, and seven out of ten students have teachers who ask questions in every lesson to check that students understand what they’re learning.
On the other hand, the student-oriented practice that teachers most commonly use is assigning students different work based on their ability, commonly called differentiated instruction. However, according to students, this practice is used only occasionally, as fewer than one in three students in OECD countries reported that their teachers use this practice frequently in their lessons. Figure 1.1 shows the reported frequency of both teacher-directed and student-oriented instructional strategies for mathematics.
10. TEN QUESTIONS FOR MATHEMATICS TEACHERS
The PISA survey also indicates that students may be exposed to different teaching strategies based on their socio-economic status or gender. For example, girls reported being less frequently exposed to student-oriented instruction in mathematics class than boys did. Conversely, disadvantaged students, who are from the bottom quarter of the socio-economic distribution in their countries, reported more frequent exposure to these strategies than advantaged students did. Teachers might have reasons for teaching specific classes in the ways they do; and other factors, such as student motivation or disruptive behaviour, might be at play too. Ideally, however, all students should have the opportunity to be exposed to some student-oriented strategies, regardless of their gender or social status. Also, when considering an entire country, the more frequently teacher- directed instruction is used compared with student-oriented instruction, the more frequently students learn using memorisation strategies (Figure 1.2).
Figure 1.2 How teachers teach and students learn Results based on students’ reports
Source: OECD, PISA 2012 Database. Statlink: http://dx.doi.org/10.1787/
12. TEN QUESTIONS FOR MATHEMATICS TEACHERS
Australia Austria Canada Belgium Chile
Czech Republic Denmark Estonia
Finland
France
GermanyGreece Hungary
Iceland
Ireland
Israel
Italy
Japan
Korea
Luxembourg
Mexico
Netherlands
New Zealand Norway
Poland
Portugal
Slovak Republic
Slovenia
Spain
Sweden TurkeySwitzerland
United Kingdom
United States OECD average
Albania
Argentina
Brazil
Bulgaria
Colombia
Costa Rica
Croatia
Hong Kong-China
Indonesia
Jordan
Kazakhstan
Latvia
Lithuania
Macao-China Malaysia
Montenegro Qatar Peru
Romania
Russian Federation
Serbia
Shanghai-China
Singapore
Chinese Taipei
Thailand
Tunisia
Uruguay
Viet Nam
R² = 0.
More student-oriented instruction
More teacher-directed Teaching instruction
More
memorisation
Learning
Moreelaboration
United ArabEmirates
Students in Ireland reported the most frequent use of teacher-directed instruction compared to student-oriented instruction
The TALIS study asked mathematics teachers in eight countries about their regular teaching practices. The study included four active-learning teaching practices that overlap in large part with student-oriented practices: placing students in small groups, encouraging students to evaluate their own progress, assigning students long projects, and using ICT for class work. These practices have been shown by many research studies to have positive effects on student learning and motivation. TALIS data show that teachers who are confident in their own abilities are more likely to engage in active-teaching practices. This is a somewhat logical finding, as active practices could be thought of as more “risky” than direct-teaching methods. It can be challenging to use ICT in your teaching or have students work in groups if you are not confident that you have the skills needed in pedagogy, content or classroom management.
Figure 1.3 How teachers’ self-efficacy is related to the use of active-learning instruction
Notes : All differences are statistically significant, except in Portugal and Singapore. Teachers with higher/lower self-efficacy are those with values above/below the country median. The index of active-learning instruction measures the extent to which teachers use “information and communication technologies in the classroom”, let “students evaluate their own progress”, work with “students in small groups to come up with a joint solution to a problem” or encourage students to work on long projects. The index of self-efficacy measures the extent to which teachers believe in their own ability to control disruptive behaviour, provide instruction and foster student engagement. Countries are ranked in descending order of the frequency with which teachers with higher self-efficacy use active-learning instruction. Source : OECD, TALIS 2013 Database. Statlink: http://dx.doi.org/10.1787/
HOW MUCH SHOULD I DIRECT STUDENT LEARNING IN MY MATHEMATICS CLASSES?.^ 13
Mexico Australia Latvia Romania Portugal Singapore Spain Finland
Teachers with lower self-efficacy Teachers with higher self-efficacy
Less
More
Active learning instruction
HOW MUCH SHOULD I DIRECT STUDENT LEARNING IN MY MATHEMATICS CLASSES?.^ 15
Therefore, just as one teaching method is not sufficient for teaching a class of students with varying levels of ability, a single teaching strategy will not work for all mathematics problems, either. Past research into the teaching of mathematics supports this claim too, suggesting that teaching complex mathematics skills might require different instructional strategies than those used to teach basic mathematics skills.^1 More recent research furthers this argument, saying that more modern teaching methods, such as student-oriented teaching strategies, encourage different cognitive skills in students.^2
Some countries, such as Singapore, are taking this research to heart and are designing mathematics curricula that require teachers to use a variety of teaching strategies (Box 1.1). Yet rather than doing away with more traditional, teacher-directed teaching methods altogether, these methods should be used in tandem. In other words, teachers need a diverse set of tools to teach the breadth of their mathematics curriculum and to help students advance from the most rudimentary to the most complex mathematics problems.
16. TEN QUESTIONS FOR MATHEMATICS TEACHERS
The objective of the mathematics curriculum in Singapore is to develop students’ ability to apply mathematics to solve problems by developing their mathematical skills, helping them acquire key mathematics concepts, fostering positive attitudes towards mathematics and encouraging them to think about the way they learn. To accomplish this objective, teachers use a variety of teaching strategies in their approach to mathematics. Teachers typically provide a real-world context that demonstrates the importance of mathematical concepts to students (thereby answering the all-too-common question: “Why do I have to learn this?”). Teachers then explain the concepts, demonstrate problem-solving approaches, and facilitate activities in class. They use various assessment practices to provide students with individualised feedback on their learning.
Students are also exposed to a wide range of problems to solve during their study of mathematics. In this way, students learn to apply mathematics to solve problems, appreciate the value of mathematics, and develop important skills that will support their future learning and their ability to deal with new problems.
Box 1.1 T EACHING AND LEARNING STRATEGIES FOR MATHEMATICS IN SINGAPORE
Singapore Mathematics Curriculum Framework
Processes
Attitudes
Metacognition
Concepts
MATHEMATICAL PROBLEM SOLVING Skills
Beliefs Interest Appreciation Confidence Perseverance
Numerical Algebraic Geometric Statistical Probabilistic Analytical
Monitoring of one’s own thinking Self-regulation of learning
Numerical calculation Algebraic manipulation Spatial visualisation Data analysis Measurement Use of mathematical tools Estimation
Reasoning, communication and connections Applications and modelling Thinking skills and heuristics
Source: Ministry of Education, Singapore
Cognitive activation
Are some
mathematics
teaching methods
more effective than
others?
As the previous chapter discusses, using a variety of teaching strategies is particularly important when teaching mathematics to students with different abilities, motivation and interests. But student data indicate that, on average across PISA-participating countries, the use of cognitive-activation strategies has the greatest positive association with students’ mean mathematics scores.^1 These types of teaching strategies give students a chance to think deeply about problems, discuss methods and mistakes with others, and reflect on their own learning. Teachers should understand the importance of this kind of teaching and should have a strong grasp of how to use these strategies in order to give learners the best chance of success in mathematics.
WHAT IS COGNITIVE ACTIVATION IN MATHEMATICS TEACHING? Cognitive activation is, in essence, about teaching pupils strategies, such as summarising, questioning and predicting, which they can call upon when solving mathematics problems. Such strategies encourage pupils to think more deeply in order to find solutions and to focus on the method they use to reach the answer rather than simply focusing on the answer itself. Some of these strategies will require pupils to link new information to information they have already learned, apply their skills to a new context, solve challenging mathematics problems that require extended thought and that could have either multiple solutions or an answer that is not immediately obvious. Making connections between mathematical facts, procedures and ideas will result in enhanced learning and a deeper understanding of the concepts. 2
ARE SOME MATHEMATICS TEACHING METHODS MORE EFFECTIVE THAT OTHERS?.^ 19
