CHAPTER 1 Teaching Mathematics in the 21 st Century
CHANGE IN THE MATHEMATICS CLASSROOM 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 Make sure that you read this material and understand how it impacts your future career
PRINCIPLES AND STANDARDS FOR SCHOOL MATHEMATICS Six principles fundamental to high-quality mathematics education Equity Curriculum Teaching Learning Assessment Technology
EQUITY PRINCIPLE Excellence in mathematics education requires equity—high expectations and strong support for all students. (NCTM 2000, p. 12). All students must have the opportunity and adequate support to learn mathematics “regardless of personal characteristics, backgrounds, or physical challenges” (p. 12).
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). Students must be helped to see that mathematics is an integrated whole, not a collection of isolated bits and pieces.
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). What students learn about mathematics depends almost entirely on the experiences that teachers provide every day in the classroom. Teachers must… understand the math they teach, understand how students learn math, and select meaningful instructional tasks.
LEARNING PRINCIPLE Students must learn mathematics with understanding, actively building new knowledge from experience and prior knowledge. (NCTM 2000, p. 20). Two fundamental ideas are… learning math with understanding is essential, and your students can learn math with understanding. Don’t ever let your students say they are “bad at math” or have “never been good at math.” Oh yeah. Don’t you say it either. Let your guard down.
ASSESSMENT PRINCIPLE Assessment should support the learning of important mathematics and furnish useful information to both teachers and students. (NCTM 2000, p. 22). By continuously gathering data about students’ understanding of concepts and growth in reasoning, teachers can better make the daily decisions that support student learning. For assessment to be effective, teachers must use a variety of assessment techniques, understand their math goals deeply, and have a research-supported notion of students’ thinking or common misunderstandings of the math that is being developed.
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). Technology enhances the learning of mathematics by allowing for increased exploration, enhanced representation, and communication of ideas.
FIVE CONTENT STANDARDS Numbers and Operations Algebra Geometry Measurement Data Analysis and Probability Note: These are not all equally represented across all grade bands!
FIVE PROCESS STANDARDS Problem Solving Reasoning and Proof Communication Connection Representation Note: These process standards direct the methods of “doing” mathematics. You will be required to incorporate all of them into your lesson plans.
COMMON CORE STATE STANDARDS DOMAINS B Y GRADE LEVEL
STANDARDS FOR MATHEMATICAL PRACTICE FROM THE CC STATE STANDARDS.
HOMEWORK Carefully read chapter 1 in the book. The first exam will cover material from this chapter, so do not skip or skim. Pay close attention to the principles and standards contained therein. We will have a short quiz on Monday pertaining to material from Chapters 1 and 2. To prepare, you should make sure you have read those chapters, make sure you have read your notes/slides, and make sure you have reflected on class activities.