Leading Math Success Mathematical Literacy Grades 7-12 (PDF)

2 0 0 4 math math Leading Leading Success Success Mathematical Literacy Grades 7–12 The Report of the Expert Panel on Student Success in Ontario Ontario Education excellence for all ISBN 0-7794-6386-2 (Print)� ISBN 0-7794-6387-0 (Internet)   math math Leading Leading Success Success Mathematical Literacy Grades 7–12 The Report of the Expert Panel on Student Success in Ontario   3 From the Chairs of the Expert Panels on Student Success in Ontario: Mathematical Literacy, Grades 7–12 May 2004 Fellow Educator: This handbook is one of the two documents prepared by our panels for use in English- and French-language schools across the province of Ontario. These documents represent the Final Reports of the Expert Panels on Student Success in Ontario: Mathematical Literacy, Grades 7–12. They describe a vision and make recommendations to help create a brighter future for Ontario adolescents who are currently at risk of leaving high school without the mathematics skills and understanding they need to reach their full potential in the twenty-first century. Our Expert Panels have worked with the Ministry of Education to develop these reports. We acknowledge with deep appreciation the Ministry’s support during our deliberations and in the preparation and publishing of these reports. These reports emphasize instructional and assessment strategies that will benefit all students. For struggling students, the use of these strategies is more than desirable: it is necessary. We must apply the latest thinking and research to the way mathematics is taught and learned. Providing improved educational opportunities, however, is only part of the picture. Attitudes also have to change. A re-culturing of Ontario schools and, indeed, of Ontario society itself is necessary to affirm the value of mathematical literacy for all and to make this vision a reality. The Expert Panels believe we must say to all struggling students: We will not give up on you. Our combined effort in moving the Leading Math Success reports forward represents another key phase in making success a reality for all students. We wish you well as you continue this important work. Yours in education, Marilyn Gouthro, Chair Janine Griffore, Chair Expert Panel (English) Expert Panel (French)   CONTENTS About the Expert Panel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Why Mathematical Literacy Matters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 The Purpose of This Report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Foundations for Action . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Priorities for Action . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2. The Ontario Context . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 A Focus on Students at Risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 Initiatives to Improve Mathematics Teaching and Learning . . . . . . . . . . . . . . . . 18 Provincial Education Policy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 International, National, and Provincial Results . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3. What Mathematical Literacy Is . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 4. What Research Tells Us . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Needs of Adolescent Learners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 Making Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 Conceptual Foundation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 Instructional Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Professional Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 Information and Communication Technologies . . . . . . . . . . . . . . . . . . . . . . . . . . 35 Leadership and Planning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 Students at Risk in Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 5. Closing the Gap: Instructional and Assessment Strategies . . . . . . . 41 Establishing a Positive Classroom Climate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 Planning and Delivering Effective Classroom Instruction and Assessment . . . . . . . 45 Delivering Targeted Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 In Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 6. Professional Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 Professional Learning Communities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 A Deeper Understanding of Mathematical Content and Teaching Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 Une publication équivalente est disponible en français sous le titre suivant : La numératie en tête, de la 7e à la 12e année : Rapport du Groupe d’experts pour la réussite des élèves. This publication is available on the Ministry of Education’s website, at http://www.edu.gov.on.ca.  Integrating New Technologies into the Classroom . . . . . . . . . . . . . . . . . . . . . . . 57 Embedding Manipulatives into Instructional Practice . . . . . . . . . . . . . . . . . . . . . 58 Research on Adolescent Learners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 The Needs of Principals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 7. Using Information to Guide Improvement in Learning . . . . . . . . . 60 The Improvement Planning Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 Making the Most of Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 8. Leadership: Roles and Responsibilities . . . . . . . . . . . . . . . . . . . . . . . . . 71 Role of the Ministry of Education . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 Role of School Boards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 Role of Schools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 Role of Universities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 9. Family and Community Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 Role of the Family . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 Role of the Community . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 Role of the School Council . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 Role of the Special Education Advisory Committee . . . . . . . . . . . . . . . . . . . . . . 82 Role of Student Volunteers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 10. Encouraging Innovation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 A More Flexible School Day . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 Staffing Flexibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 Overcoming Cultural Barriers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 Equitable Resource Allocation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 Innovation in Professional Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 Gap-Closing Programs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 New Partnerships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 Curriculum Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 11. List of Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 Closing the Gap: Instructional and Assessment Strategies . . . . . . . . . . . . . . . . . 89 Professional Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 Using Information to Guide Improvement in Learning . . . . . . . . . . . . . . . . . . . . 90 Leadership: Roles and Responsibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 Family and Community Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 Encouraging Innovation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 12. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 Appendix: Suggested Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 LEADING MATH SUCCESS: MATHEMATICAL LITERACY, GRADES 7–12 6  About the Expert Panel This report has been prepared by the English-language Expert Panel on Student Success in Ontario. The Ministry of Education established this Expert Panel to provide direction to Ontario school boards on mathematical literacy for at-risk students in Grades 7 to 12. Members participating in the preparation of this report on mathematical literacy include the following education and community leaders from across the province: 7 CHAIR Marilyn Gouthro Director of Education, Secretary to the Board Lakehead District School Board MEMBERS Anne Atkinson Superintendent of Education Wellington Catholic District School Board Odette Bartnicki Principal Halton District School Board Ruth Baumann Secretary-Treasurer Ontario Teachers’ Federation Mary Ellen Diamond Program Chair of Mathematics Niagara Catholic District School Board Sandy DiLena Education Officer Education Quality and Accountability Office Judy Dussiaume Curriculum Coordinator Rainbow District School Board Wayne Fletcher Vice-Principal Lakehead District School Board Suzana Greenaway Vice-Principal Toronto District School Board Julie Anne Heidman Parent Representative Ontario Parent Council Victoria Hemming Chief Assessment Officer Education Quality and Accountability Office Ruth Mattingley Superintendent of Education Lambton Kent District School Board Irene McEvoy Instructional Coordinator, Mathematical Literacy Peel District School Board Eric Muller Professor Department of Mathematics, Brock University Mary Puopolo Principal York Catholic District School Board Kit Rankin Director Curriculum and Assessment Policy Branch, Ministry of Education Pat Rogers Dean Faculty of Education, University of Windsor Tom Steinke Educational Consultant Ottawa-Carleton Catholic District School Board Kerry Stewart Student Success Leader Limestone District School Board Karen Timson Curriculum Consultant, Secondary Mathematics York Region District School Board Annette Webber Principals’ Groups Representative Minister’s Advisory Council on Special Education (MACSE) Lynn Ziraldo Chair Minister’s Advisory Council on Special Education (MACSE)  Expert Panel Support Lolita Singh Manager Curriculum and Assessment Policy Branch, Ministry of Education Myrna Ingalls Education Officer Curriculum and Assessment Policy Branch, Ministry of Education Daniel Jarvis Researcher Faculty of Education, University of Western Ontario Ruth Swan Researcher Curriculum and Assessment Policy Branch, Ministry of Education James Dorey Writer LEADING MATH SUCCESS: MATHEMATICAL LITERACY, GRADES 7–12 8  9 Mathematics is a fundamental human endeavour that empowers individuals to describe, analyse, and understand the world we live in. The Expert Panel on Student Success in Ontario: Mathematical Literacy, Grades 7–12, was formed to help create a brighter future for Ontario adolescents who are currently at risk of leaving high school without the mathematics skills and understanding they need to reach their full potential in the twenty-first century. The statistics are troubling. To cite just one indicator, in the 2002–2003 province-wide assessment of the Grade 9 applied program in mathematics, 28 per cent of students scored well below the provincial standard (Education Quality and Accountability Office [EQAO], 2003b). Unless immediate, sustained, and effective action is taken, a sizable portion of the student population will leave school unprepared for the challenges they will face as adults. Too often, society has accepted the stereotype that mathematics is for the few, not the many. The reality is that mathematics is deeply embedded in the modern workplace and in everyday life. It is time to dispel the myth that mathematics is for some and to demand mathematics success for all. We must truly embrace the fact that every adult and therefore every child can do mathematics. If we convey the conviction that mathematical literacy is for everyone, our confidence in students will build their self-confidence. Self-confidence is a key ingredient in learning and success in mathematics. INTRODUCTION 1 9 “All teachers can make a differ- ence for at-risk students with an emphasis on the moral purpose of educating our students.” (Program Pathways for Students at Risk Work Group, 2003, p. 25)  WHY MATHEMATICAL LITERACY MATTERS Mathematical literacy involves more than executing procedures. It implies a knowledge base and the competence and confidence to apply this knowledge in the practical world. A mathematically literate person can estimate; interpret data; solve day-to-day problems; reason in numerical, graphical, and geometric situations; and communicate using mathematics. As knowledge expands and the economy evolves, more people are working with technologies or working in settings where mathematics is a cornerstone. Problem solving, the processing of information, and communication are becoming routine job requirements. Outside the workplace, mathematics arises in everyday situation after situation. Mathematical literacy is necessary both at work and in daily life. It is one of the keys to coping with a changing society. Mathematical literacy is as important as proficiency in reading and writing. Mathematics is so entwined with today’s way of life that we cannot fully comprehend the information that surrounds us without a basic understanding of mathematical ideas. Confidence and competence in mathematics lead to productive participation in today’s complex information society and open the door to opportunity. THE PURPOSE OF THIS REPORT This report aims to provoke discussion and debate and to change how we view students at risk of underachieving in mathematics – and how we as a society support their learning. Not all of the factors that influence educational success fall within the school system. For example, research shows that the foundation for learning is laid well before Kindergarten, let alone high school. The care and stimulation of infants from birth to age three are critical in establishing a basis for learning over the life cycle (Willms, 2003). While this Expert Panel is conscious of the wider social context in which the factors that influence learning are established, its mandate is to speak primarily to educators. The people who work every day in education are closest to students and in the best position to identify students at risk and intervene to ensure their prospects for success. Among educators, the role of teachers1 of mathematics is pivotal. Teachers must be helped to develop the necessary mathematical understanding and must be given the tools they need to foster mathematical literacy. Teachers in many other disciplines can also create opportunities to help students appreciate the part that mathematics plays in their lives. And whether a teacher is teaching mathematics content or not, LEADING MATH SUCCESS: MATHEMATICAL LITERACY, GRADES 7–12 10 1. When referring to teachers of mathematics, this report includes specialist mathematics teachers, teachers who teach mathematics as well as other subjects, and special education/resource teachers.  he or she must be a supporter of mathematical literacy by conveying the belief that all students can and should do mathematics. Students’ success depends on school, board, and provincial government leadership. Beyond that, parents and the wider community, from business firms to volunteer groups, also have a part to play. Everyone shares the responsibility for guaranteeing that all students receive support on their journey towards mathematical literacy. Ultimately, success depends on the students themselves and their response to the learning experience offered them. This report is intended to inform and change educational practice, propose effective strategies and resources, and help shift attitudes both in our schools and in society. The challenge is to systematically identify students at risk and intervene decisively to close learning gaps. It is imperative that we apply the latest thinking and research to the way mathematics is taught and learned. We may use the best strategies to benefit all students, but we must use them to support struggling students. And even though we may use the best instructional and assessment practices with those students, some of them will remain at risk and will need targeted instruction and support. Everyone is capable of becoming mathematically literate. The path towards this social goal begins at home and in the classroom, supported by the family and the community. All students can learn mathematics – with enough support, resources, and time – and we must ensure that they do. We must re-culture Ontario schools and indeed Ontario society itself if we are to affirm the value of mathematical literacy for all and make this vision a reality. The Expert Panel believes that we must say to all at-risk students: We will not give up on you. FOUNDATIONS FOR ACTION Guiding Principles In preparing this report, the Expert Panel has been guided by the following principles: 1. Mathematical literacy is fundamental. It enables students to make life choices and participate productively in society. 2. All students can learn and be confident in mathematics, given appropriate support and time. 3. All students have the right to quality supports in learning mathematics to enable them to reach their potential. 4. It is the responsibility of the Ministry of Education, school boards, parents, and society to provide the necessary supports. 5. Effective classroom instruction can have a strong, positive impact on student attitudes and learning in mathematics. I N T R O D U C T I O N 11  6. Effective mathematics instruction must address the needs of the adolescent learner. 7. Connections to mathematical literacy should be made where they occur naturally across the curriculum. 8. All teachers of mathematics must be competent in teaching this subject and confident in their ability to do so. They must be given appropriate collaborative professional learning and resources to achieve this competence and confidence. 9. Teachers of mathematics must have a strong content knowledge, good instruc- tional skills, and sound pedagogy to teach mathematics effectively. 10. All teachers can and should support the development of mathematical literacy. 11. Collaborative professional learning communities are essential to increasing student success. 12. Effective district and school leadership is crucial to improving student learning. Constructing the Groundwork To base its advice and recommendations on a solid footing, the Expert Panel: • assessed the current Ontario context; • explored the meaning of mathematical literacy; and • reviewed current research on adolescent learners and on mathematics teaching and learning. An overview of this groundwork is presented in chapters 2–4 of this report. PRIORITIES FOR ACTION Having studied the Ontario context, the meaning of mathematical literacy, and current research on mathematics pedagogy, the Expert Panel has established the following priorities and calls on educators to work on them. Educators should: • adopt the best mathematics instructional and assessment strategies for all students, emphasizing approaches that especially benefit students at risk and delivering additional targeted support as needed; • build and sustain professional learning communities committed to meeting the needs of all students; • gather and use information more effectively to identify students at risk in mathematics, make plans to provide the support those students need, track progress, and adjust strategies as required; • show leadership and take action at all levels of the education system – classroom, school, district, and province – to promote mathematical literacy for all; LEADING MATH SUCCESS: MATHEMATICAL LITERACY, GRADES 7–12 12  • forge links with families and the larger community to support students at risk in mathematics; • encourage innovation designed to overcome the barriers to success that at-risk student face. Chapters 5–10 of the report explain why the panel has adopted these priorities and show how they can be implemented. In each priority area, the report offers detailed, practical advice to educators on achieving the goal of mathematical literacy for all. For each priority, the Expert Panel also makes recommendations to guide classroom practice, the use of resources, and the expenditure of funds to meet the needs of students at risk in mathematics. I N T R O D U C T I O N 13 “All students can learn mathematics, and they deserve the opportunity to do so…. However, recognizing the diversity among … children, educators do not expect all students to learn the material in the same manner, using the same resources, and in the same time frame.” (Sutton & Krueger, 2002, p.1)