Grades Pre-K-2 (Volume I)
A practical, comprehensive, student-centered approach to effective mathematical instruction for grades Pre-K-2.
New to This Edition
Key content changes include:
- The use of color in the figures, tables, and text helps to enhance and clarify the concepts presented.
- NCTM Teaching Practices Appendix. The Principles to Actions (NCTM, 2014) eight teaching practices are provided in Appendix C. These describe the actions that teachers do to support student thinking and provide guidance on how to enact student-centered mathematics.
- Activities corresponding to the CCSS have been added. Numerous problem-based tasks, designed to engage students in doing mathematics, are presented in the activities and now connect to the appropriate CCSSs. Most include adaptation and accommodation suggestions for English Learners and students with special needs. Appendix D includes a table listing all of the activities at a glance.
- Tables of Common Errors and Misconceptions help readers avoid or move beyond common problems in learning mathematics. Each chapter in Part 2 includes a new table addressing chapter-related mathematical topics. The tables often include examples of student work or responses that reflect the common errors.
Major changes to chapters in Part 1 include:
- Chapter 1: A new table that relates NCTM’s process standards (2000) and CCSS-M’s mathematical practices (CCSSO, 2010), clarification about the difference between modeling mathematics and modeling with mathematics, and an additional emphasis on the characteristics of productive classrooms that promote student understanding.
- Chapter 2: A new section on the eight mathematics teaching practices from Principles to Actions (NCTM, 2014); a new section on “Evaluating and Adapting Tasks”; a new section on growth versus fixed mindsets and their relationship to productive struggle and learning from mistakes; a new section on aspects of questioning that helps teachers think, in particular, about the level of questions asked and the pattern of questions used; and more detail pertaining to the three-phases (before, during, and after) to better highlight that these phases occur during (not after) the lesson.
- Chapter 3: A more detailed discussion about assessment for learning (AFL) on how to collect evidence from students on their progress, interpret that evidence, make informed decisions about the next instructional steps, and provide actionable feedback to students; and an expanded section on using writing to learn mathematics.
- Chapter 4: This chapter was revised to better highlight differentiated tasks for whole-classroom instruction. New team-building activities for working in groups are also included.
- Chapter 5: Twenty-two new references reflect research in the field, including increased attention to Culturally Responsive Mathematics Instruction (CRMI), developed around four key aspects and an expanded section on nurturing students’ mathematical identities.
- Chapter 6: Features several new tools, including: a printable set of cards, each with a Strategy for Making Math Accessible for learners who struggle, which can be used when planning core instruction modifications or interventions for students with special needs; and a Mathematics Integration Plan Template to support planning for gifted students or students with a high interest in exploring mathematical topics in relation to other subject areas or perspectives.
- Chapter 7: This chapter was significantly revised to focus on advocacy across stakeholders, including creased attention to communicating about CCSS Mathematics. The homework section was expanded, including new activities and games for families.
Major changes in the chapters in Part 2 include:
- Chapter 8: Includes a new learning progression for counting that identifies increasingly sophisticated levels of reasoning and includes:
- Several new activities focusing on developing early counting skills, and
- A new section on thinking about zero.
- Chapter 9: Features an increased focus on helping children write equations from word problems, using both computational and semantic forms. Also included are:
- An improved section on helping children analyze contextual problems by detailing strategies that can help children prepare to solve problems, and
- A new section about helping children solve multistep problems, including the use of hidden questions to help children progress from one-step to multistep problems.
- Chapter 10: Includes an increased focus on assessing basic facts, presents the risks of using timed tests, and offers a collection of alternative assessment ideas.
- Chapter 12: Includes an expanded discussion of the written records of computing multiplication and division problems including lattice multiplication, open arrays, and partial quotients.
- Chapter 16: The geometry chapter is now reorganized around the four geometry strands (shapes and properties, location, transformations, visualization) to provide more cohesiveness. Examples of appropriate activities help clarify each level as it’s introduced.
- Chapter 17: The new addition of driving questions (Hourigan and Leavy) is introduced as a way to motivate involvement in the processes of doing statistics. There is an increased emphasis on helping children consider the shape of the data as they engage in the analysis and interpretation phases of doing statistics.