CHAPTER 1Teaching 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
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.
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
PSSM guidance and direction for teachers and leaders Six principles fundamental to high-quality mathematics education • Equity • Curriculum • Teaching • Learning • Assessment • Technology
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?
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?
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?
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?
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?
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?
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?
The Five Process Standards Process standards direct the methods of doing all mathematics (Table 1.1) • Problem Solving • Reasoning and Proof • Communication • Connection • Representation
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
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
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