Van de Walle, Karp, Bay-Williams, Brass, Livy
2nd Australian Edition
An Australian-adapted text that guides teachers to help all Foundation to Year 9 learners make sense of mathematics.
Primary and Middle Years Mathematics is designed to support Foundation to Year 9 teachers in implementing research-informed approaches for teaching mathematics. This comprehensive resource aims to enhance teachers' knowledge of effective teaching approaches, encompassing assessment for learning, understanding students' learning processes in mathematics, and addressing common misconceptions. Each chapter refers to the Australian Mathematics Curriculum and presents classroom-ready, hands-on problem-solving tasks specifically designed to challenge students' thinking and foster positive attitudes towards mathematics.
"This second edition has undergone numerous valuable changes and updates, making it an excellent resource not only for pre-service teachers and classroom educators but also for mathematics leaders and teacher educators."
- Sharyn Livy, Co-Author
SECTION 1: TEACHING MATHEMATICS: FOUNDATIONS AND PERSPECTIVES
SECTION 2: DEVELOPMENT OF MATHEMATICAL CONCEPTS AND PROCEDURES
Appendix A: Australian Curriculum 9.0: Mathematics
Appendix B: Mapping the content to the Australian Curriculum
Appendix C: Mapping the content to the AITSL Standards
Appendix D: NCTM mathematics teaching practices: From Principles to Actions
Appendix E: Guide to the supplementary resources
Learning aids supplemental to the text:
Provides detailed concepts, discussion topics and activities to enrich lessons.
A wide variety of question types for homework and quizzing, arranged by section.
Digital Image PowerPoint slides
All diagrams and tables from the textbook are available for lecturer use.
BlackLine Masters & Worksheets guide
Lists the Teacher Resources, Activities, Expanded Lessons and BLMs that appear throughout the textbook.
You will notice many section headings throughout each chapter, a large number of figures and various special features. All are designed to make the text more useful as a long-term resource. Here are a few things to look for.
(images are included from the 1st edition for illustrative purposes)
A list of key mathematical ideas at the beginning of each chapter helps readers envision how to form their lesson plans around major themes rather than isolated skills or concepts.
There are numerous activities in every chapter in Section 2. Every activity is a problem-based task, is aligned with the Australian Curriculum and is designed to engage students in doing mathematics.
Adaptations for students with additional learning needs and EAL/D students
Detailed background and strategies on meeting student needs are provided in Chapter 6, and adaptations and instructions are included within specific activities offered in Section 2 chapters.
Blackline Masters, activity pages and teacher resource pages
More than 130 ready-to-use pages are provided to support the problems and activities in the book. These are highlighted in the text and can be downloaded.
Formative assessment notes
Throughout the content chapters, formative assessment notes help educators evaluate students' understanding of content areas and offer the best methods to assist struggling students.
The end of each chapter includes written and discussion questions to help readers reflect, and a variety of useful resources including children's literature suggestions and an annotated list of recommended readings.
The late Dr John A. Van de Walle was a professor emeritus at Virginia Commonwealth University. He was a leader in mathematics education who regularly gave professional development workshops for K–8 teachers in the United States and Canada focused on mathematics instruction that engaged students in mathematical reasoning and problem solving. He visited and taught in many classrooms and worked with teachers to implement student-centred mathematics lessons. He co-authored the Scott Foresman-Addison Wesley Mathematics K–6 series and contributed to the original Pearson School mathematics program enVisionMATH. Additionally, John was very active in the National Council of Teachers of Mathematics (NCTM), writing book chapters and journal articles, serving on the board of directors, chairing the educational materials committee and speaking at national and regional meetings.
Dr. Karen S. Karp is a professor at Johns Hopkins University (Maryland). Previously, she was a professor of mathematics education at the University of Louisville for more than twenty years. Prior to entering the field of teacher education, she was an elementary school teacher in New York. She is the coauthor of Strengths-Based Teaching and Learning in Mathematics: 5 Teaching Turnarounds for Grades K-6; the three book series, The Math Pact: Achieving Instructional Cohesion within and across Grades; and the What Works Clearinghouse Practice Guide on Assisting Students Struggling with Mathematics: Intervention in the Elementary Grades. She is a former member of the board of directors for the National Council of Teachers of Mathematics (NCTM) and a former president of the Association of Mathematics Teacher Educators. In 2020, she received the NCTM Lifetime Achievement Award and in 2021 became a member of the United States National Committee on Mathematics Instruction. She continues to work in classrooms to support teachers in ways to instruct students with special needs in math.
Dr. Jennifer Bay-Williams is a professor at the University of Louisville. She is a leader in mathematics education, regularly working to support mathematics instruction. Beyond her work on this book and the related Teaching Student Centered Mathematics book series, Jennifer has written other books that focus on effective mathematics teaching. Most recently she has written a book series called Figuring out Fluency in Mathematics K-12 and Math Fact Fluency: 60+ Games and Assessment Tools to Help Learning and Retention. For teacher leaders, she has authored Everything You Need for Mathematics Coaching, and in the area of financial literacy, she authored a three-book series titled On the Money (a financial literacy book series). Over the years, Jennifer has taught elementary, middle, and high school in the United States and in Peru. She continues work with teachers around the world and in her local school districts to support their work. Jennifer has been actively involved in NCTM, NCSM, AMTE, and TODOS: Mathematics for All. Currently, she is serving as an associate editor for Mathematics Teacher: Learning and Teaching in preK-12.
Lead Australian authors
Amy Brass is currently a doctoral candidate in mathematics education at Pennsylvania State University. She was previously a mathematics education lecturer at the University of Melbourne Graduate School of Education and also taught mathematics content and mathematics pedagogy classes at Arizona State University and the University of Cincinnati.
Prior to entering the field of teacher education, Amy was a lower secondary maths teacher. Amy’s research interests include people’s understanding of large numbers and their magnitude, the relationships across mathematics, mathematics education and citizenship and mathematical modelling.
Dr Sharyn Livy is a Senior Lecturer of mathematics education in the School of Curriculum, Teaching and Inclusive Education, Faculty of Education, Monash University. Sharyn enjoys supporting both primary school teachers and pre-service teachers to enhance their skills and knowledge of best practices in mathematics education for primary school children. Her motivation is to enhance the quality of mathematics education for young students and equip teachers with the necessary skills and knowledge to achieve this goal. Her work involves conducting research, developing, and delivering professional development programs for teachers, and collaborating with schools and education partners to promote student-centred instructional approaches and collaborative mathematical learning experiences.
Dr Brendan Bentley is a lecturer in education. He is a multi-award winning teacher and the Associate Head of Learning and Teaching and the Director Professional Experience in the School of Education at the University of Adelaide. He has designed and written both undergraduate and postgraduate educational courses in mathematics education at national and international levels and is a consultant in professional formation and development for teachers and school leaders. His PhD research focused on the teaching of ratio and proportional reasoning and the subsequent implications of cognitive load on a learner’s working memory. Brendan has published in the subject domains of STEM, science and mathematics education, and educational leadership and is currently researching the impact of instructional gesturing during the teaching of mathematics and science content. Prior to him working in teacher education he was a school principal, curriculum leader and classroom teacher having taught mathematics at both a primary and secondary level.
Wendy Goff is an Associate Professor School Partnerships and Mathematics Education and Deputy Chair of the Department of Education at Swinburne University of Technology, Victoria. Wendy’s previous experience spans over a variety of higher education, primary and early childhood settings. She has worked full time in the university setting since 2009, teaching mathematics education in undergraduate and postgraduate programs. Her research focuses on adult relationships and how they facilitate the mathematical learning of children. Wendy has published in the areas of mathematics education, family–school partnership and the transition to school. She is an active member of the Mathematics Education Research Group of Australasia and has presented her work in mathematics education to national and international audiences.
Kate Manuel teaches in Education Futures at the University of South Australia. Prior to this role, Kate was the Manager of National Projects with the Australian Association of Mathematics Teachers. She has had long career as a teacher of secondary mathematics; also as a moderator and Chief Assessor of senior mathematics.
Dr David Martin is a Senior Lecturer of mathematics, technologies, and STEM education in the Department of Teacher Education (Primary), Edith Cowan University. Prior, David lectured in mathematics and technologies education at the University of Southern Queensland, University of the Sunshine Coast, and in the USA, Florida Atlantic University and Indian River State College. During this tenure, David has been awarded multiple teaching awards. His teaching and research interests align with developing pre-service teachers’ mathematics and educational technologies pedagogical content knowledge. Prior to university teaching, David held positions in the state school system: deputy principal, dean of student discipline, head of department: mathematics, middle school mathematics and literacy teacher and primary school teacher.
Andrea Ng is an Early Childhood and Primary qualified teacher. Andrea is currently completing her PhD in Monash University. Her research interest is in STEAM Education and Mathematics education from early years and primary education. She has published and presented her research output in both Australia and International conferences and journals. Andrea is currently an educator in both Monash University and Swinburne University of Technology teaching the Bachelor of Education, Bachelor of Teaching and Master of Education with various specialisations. She is also the Unit Coordinator for the first- and second-year Mathematics unit in Swinburne University of Technology.
Dr Cath Pearn is a Senior Lecturer in Mathematics Education at The University of Melbourne and teaches in all levels of Master of Teaching programs – early childhood, primary and secondary. Cath provides professional development for early childhood, primary and secondary teachers and is particularly interested in the identification and support of students needing additional assistance in mathematics. Cath developed Mathematics Intervention, a program for Year 1 students mathematically ‘at risk’, which she continues to support. Her PhD investigated the links between fractional competence and algebraic thinking. Cath is also a Senior Research Fellow at the Australian Council for Educational Research (ACER).
Dr Karina Wilkie has taught school mathematics across the full range of year levels, Foundation to Year 12, spanning 20 years in Australia and England. She completed her PhD at the University of Melbourne in 2011 and currently lectures undergraduate and postgraduate pre-service teachers and supervises doctoral students at Monash University. She consults for individual schools, Independent Schools Victoria and Melbourne Archdiocese Catholic Schools, particularly on teaching primary and secondary mathematics through investigative and challenging problem-solving. Karina’s research interests include developing student algebraic reasoning through visualisation and multiple-representational activity, student engagement, argumentation in mathematics, and teacher professional learning processes.
Jonathan Wray is the technology contributor to the US edition of this text. He is Coordinator for Secondary Mathematics in the Howard County Public School System. He has served as the president of the Association of Maryland Mathematics Teacher Educators (AMMTE), the Maryland Council of Teachers of Mathematics (MCTM), and the manager of the Elementary Mathematics Specialists and Teacher Leaders (ems&tl) Project. Jon also served as an elected member of the National Council of Teachers of Mathematics (NCTM) Board of Directors (2012–2015). He has been recognized for his expertise in infusing technology in mathematics teaching and was named an outstanding technology leader in education by the Maryland Society for Educational Technology (MSET). Jon is the recipient of the 2020 Ross Taylor/Glen Gilbert National Mathematics Leadership Award given by the National Council of Supervisors of Mathematics.
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