1. CHAPTER 1 Teaching Mathematics in the 21st Century
Elementary and Middle School Mathematics Teaching Developmentally
Ninth Edition
Van de Walle, Karp and Bay-Williams
Developed by E. Todd Brown /Professor Emeritus University of Louisville

2. Changing World: Factors to Consider
International and national assessments provide strong evidence that mathematics teaching must change:
for our students to be competitive in the global market
for our students to be able to understand the complex issues they must confront as responsible citizens.

3. Movement Toward Shared Standards
1980s response to “back to basics” 1989 NCTM published Curriculum and Evaluation Standards for School Mathematics 1991 NCTM published Professional Standards for Teaching Mathematics 2000 NCTM published Principles and Standards for School Mathematics 2010 Common Core State Standards initiative

4. PSSM guidance and direction for teachers and leaders
Six principles fundamental to high-quality mathematics education
Equity
Curriculum
Teaching
Learning
Assessment
Technology

5. The Equity Principle
Excellence in mathematics education requires equity—high expectations and strong support for all students. (NCTM 2000, p. 12) Pause and reflect: Where would this be evident in the teaching and learning in your classroom?

6. The Curriculum Principle
A curriculum is more than a collection of activities: It must be coherent, focused on important mathematics, and well articulated across the grades. (NCTM 2000, p. 14) Pause and reflect: Who makes the curricula decisions in your classroom?

7. The Teaching Principle
Effective mathematics teaching requires understanding what students know and need to learn and then challenging and supporting them to learn it well. (NCTM 2000, p. 16) Pause and reflect: What teacher actions will best facilitate students doing mathematics?

8. The Learning Principle
Students must learn mathematics with understanding, actively building new knowledge from experience and prior knowledge. (NCTM 2000, p. 20) Pause and reflect: Do you believe that learning mathematics is essential?

9. The Assessment Principle
Assessment should support the learning
of important mathematics and furnish
useful information to both teachers and
students. (NCTM 2000, p. 22)
Pause and reflect:
What are examples of effective assessment
techniques that will guide your understanding of
student knowledge?

10. The Technology Principle
Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students’ learning. (NCTM 2000, p. 24) Pause and reflect: How does technology enhance the learning of mathematics?

11. The Five Content Standards
Numbers and Operations
Algebra
Geometry
Measurement
Data Analysis and Probability
Pause and reflect:
Are all five content standards equally addressed at ALL grade bands?

12. The Five Process Standards
Process standards direct the methods of doing all mathematics (Table 1.1)
Problem Solving
Reasoning and Proof
Communication
Connection
Representation

13. Common Core State Standards
Common Core State Standards for Mathematics (CSSM-M)
Standards for Mathematical Practice (Table 1.2)
Longstanding important processes and proficiencies
Teachers must develop these practices in all students

14. Guiding Principles from NCTM Principles to Action
Pause and reflect on these statements
Use meaningful instructional tasks
Provide instructional opportunities for students to demonstrate their competence in different ways
Avoid thinking of a curriculum as a checklist or disconnected set of daily lessons
Consider the use of multiple assessments to capture a variety of student abilities

15. An Invitation to Learn and Grow
Knowledge of Mathematics-profound, flexible and adaptive knowledge
Persistence-stave off frustration and demonstrate persistence
Positive attitude-changing attitudes toward mathematics is easy
Readiness for change-unlearn and relearn mathematical concepts
Life-Long learning-highly effective teachers never “finish” learning