The Professional Standards for Teaching Mathematics 1. Knowledge of Mathematics and General Pedagogy 2. Knowledge of Student Mathematical Learning 3. Worthwhile Mathematical Tasks 4. Learning Environment 5. Discourse 6. Reflection on Student Learning 7. Reflection on Teaching Practice Copyright © 2010 by Pearson Education, Inc. All rights reserved.

As you become a teacher of mathematics you will need: Knowledge of mathematics Persistence Positive attitude Readiness for change Reflective disposition Copyright © 2010 by Pearson Education, Inc. All rights reserved.

Traditional Views of School Mathematics Teacher represents the source of all that is known Review material from previous day Move on to explanation of new material Practice exercises Lesson’s focus is primarily on getting the answers. Students rely on teacher to determine whether or not their answers are correct

The Verbs of Mathematics Traditional –Work –Getting the Answer –Plussing –Doing Times –Listen –Copy –Memorize –Drill Reform –Explore –Investigate –Solve –Verify –Discover –Describe –Predict –Explain

What Does It Mean to DO MATHEMATICS? Engaging in the science of pattern and order Mastering mathematical concepts by doing NOT drilling Drill should NEVER come before understanding and will NEVER result in understanding

Schifter and Fosnot on the Role of Teachers "No matter how lucidly and patiently teachers explain to their students, they cannot understand for their students." From D. Schifter and C. T. Fosnot, Reconstructing Mathematics Education:Stories of Teachers Meeting the Challenge of Reform (New York: Teachers College Press, 1993), p. 9. What does this quote mean to you related to teaching mathematics?

An Environment of Doing Mathematics The teacher’s role is to create a spirit of inquiry, trust, and expectation where students feel comfortable taking risks Students are invited to do mathematics The focus is on students actively figuring things out, testing ideas, and making conjectures, developing reasons and offering explanation Students work in pairs, groups, or individually

What the Researchers said about Our Mathematics Standards “A Mile Wide, An Inch Deep” –For Florida’s Grades 1-7, the average number of mathematics grade level expectations (GLEs) = 83.3 –Singapore, the highest performing nation as measured by Trends in International Math and Science Study (TIMSS), has 15 GLEs per grade level

Top Achieving TIMSS Countries’ Mathematics Curriculum © Center for Research in Math and Science Education, Michigan State University

Mathematics Topics Intended at Each Grade by 1989 NCTM Standards © Center for Research in Math and Science Education, Michigan State University

Mathematics Proficiency The five process standards (NCTM, 2000): Problem Solving Reasoning and Proof Communication Connections Representations The five “strands” of mathematics proficiency (NRC, 2001): Conceptual Understanding – comprehension of mathematical concepts, operations, and relations Procedural Fluency – skill in carrying out procedures flexibly, accurately, efficiently, and appropriately Strategic Competence – ability to formulate, represent, and solve mathematical problems Adaptive Reasoning – capacity for logical thought, reflection, explanation, and justification Productive Disposition – habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy

Dispositions Skills Knowledge Pre-Professional Professional Academic ORIENTATION Humanistic ORIENTATION Practical ORIENTATION Teaching / Scientific ORIENTATION Critical / Social ORIENTATION Accomplished UCF, College of Education Conceptual Framework Revised: R E L E C O I T F N Professional Educator