All students can learn mathematics with understanding. It is through the teacher’s actions, a positive classroom environment, and by allowing students to develop their own strategies and learn from others that every student can have success and develop confi dence in their abilities. We want students to see the connections among mathematical topics and the real world, value mathematics that is all around them, and feel empowered to use it.
The text covers concepts and procedures specifi c to mathematical topics encountered in grades K—8, using real experiences and assessment techniques to address the foundations of how children learn. The previous edition’s focus on teaching through problem solving now takes a broader focus on mathematical inquiry through rich tasks and classroom discourse.
Hallmark Learning Features
- Big Ideas. Much of the research and literature espousing a student-centered approach suggests that teachers plan their instruction around big ideas rather than isolated skills or concepts. At the beginning of each chapter in Part II, you will find a list of the big mathematical ideas associated with the chapter. Teachers fi nd these lists helpful to quickly envision the mathematics they are to teach.
- Mathematics Curriculum Connections. These fi gures at the beginning of each content chapter highlight the key ideas in the topic and the approximately grade level they appear in curriculum across Canada.
- Adaptations for Students with Difficulties and English Learners. Chapter 6 provides some background and strategies for how to support diverse learners, but many adaptations are specifi c to an activity or task. Therefore, Part II chapters off er diff erentiation strategies within activities (look for the icon) that can meet the needs of students with diffi culties and English learners.
- Literature Connections. Here you will fi nd examples of great children’s literature for launching into the mathematics concepts in the chapter just read. For each title suggested, there is a brief description of how the mathematics concepts in the chapter can be connected to the story. These literature-based mathematics activities will help you engage students in interesting contexts for doing mathematics. Children’s literature is also identifi ed with an asterisk in the list of references for each chapter at the end of the text.
- Formative Assessment Notes. Assessment is an integral process within instruction. Similarly, it makes sense to think about what to be listening for (assessing) as you read about diff erent areas of content development. Throughout the content chapters, there are formative assessment notes with brief descriptions of ways to assess the topic in that section. Reading these assessment notes as you read the text can help you understand how best to assist students who struggle.
- Technology Notes. Infusing technological tools is important in learning mathematics. We have infused technology notes throughout Part II. A technology icon is used to identify places within the text or activity where a technology idea or resource is discussed. Descriptions include open-source (free) soft-ware, applets, and other Web-based resources, as well as ideas for calculator use.
- Video examples. Embedded throughout all chapters, these examples allow you to see key concepts in action through authentic classroom video, as well as clips of children solving math problems. Additional videos feature experts introducing and briefl y explaining strategies for teaching important topics.
New to the Sixth Canadian Edition
- Learner Outcomes. Each chapter now begins with a set of learner outcomes. The outcomes are intended to provide a summary of the organization and content of each chapter, as well as the knowledge, skills, and expectations readers should attend to in the course of completing the chapter readings, activities and refl ections. Note that learner outcomes are not a matter of recalling information, but involve a wide range of actions such as exploring, describing, investigating, connecting, critiquing, explaining, analyzing, demonstrating, justifying, summarizing, and so on.
- Canadian Curriculum Update. Provincial governments tend to revise or update their mathematics curriculum every fi ve to ten years. Since the last edition of this textbook, only the Ontario mathematics curriculum has been revised. In the summer of 2020, Ontario Ministry of Education revealed a new mathematics curriculum for grades 1 to 8. Similar to British Columbia, the Ontario curriculum now includes fi nancial literacy as a topic. It also includes new expectations in mathematical modelling and coding. These changes are addressed in multiple ways throughout the sixth Canadian edition. Revisions were made to the overview of curriculum across Canada in Chapter 1 and to the Mathematics Curriculum Connections snapshots at the beginning of each content chapter. Chapter specifi c changes described in more detail below include attention to mathematical modelling, coding, and fi nancial literacy.
- Common Concerns and How to Help. Every chapter in Part II off ers a table that summarizes common diffi culties students encounter in learning that topic. The table includes the common concerns for that topic, provides an ex-ample of what that might look like in either a sample of student work or a statement, and then off ers some brief ideas of what you might do to help. Knowing common student diffi culties is a critical part of planning and can greatly infl uence how a lesson is structured and what problems you select. Research from many sources has been merged into these practical references.
- Infusion of Technology. You may notice that Chapter 7 Tools for Learning Mathematics from the previous edition is gone. Readers and reviewers have commented that this chapter is no longer needed, in part be-cause discussing tools and technology is more helpful in context and when applied to specifi c tasks and problems.