BIG Ideas and Understandings as the Foundation for K-12 Mathematics

1. BIG Ideas and Understandings as the Foundation for K-12 Mathematics

2. �DI-Why Bother?� Discussion Sticks Activity Habits of Mind � Reflections Marzano�s Rubrics for EFFORT

3. Characteristics of Highly Effective Teachers (Ma 1999). Ask appropriate & timely questions. They are able to facilitate high-level classroom conversations focused on important content. They are able to assess students� thinking & understanding during instruction. The FOCUS of mathematics instruction is on CONCEPTUAL UNDERSTANDING. 4. Teaching practices are centered around a set of Big Mathematical Ideas (BIG IDEAS). TIMMS report--- We score under Lithuanea����no more excuses!!!!! Teaching to the test, rather than focusing on the math kids take away from our classes!!!!!TIMMS report--- We score under Lithuanea����no more excuses!!!!! Teaching to the test, rather than focusing on the math kids take away from our classes!!!!!

4. WHAT IS THE BIG IDEA? Teachers need to understand the big ideas of mathematics and be able to represent mathematics as a coherent and connected enterprise. (NCTM, 2000) DEFINITION: A �Big Idea� is a statement of an idea that is central to the learning of mathematics, one that links numerous mathematical understandings into a coherent whole. (NCSM, 2005) �We understand something if we see how it is related or connected to other things we know� and �The degree of understanding is determined by the number and strength of the connections� (Heibert & Carpenter) Show Singapore bar method to solve. On chart paper.Show Singapore bar method to solve. On chart paper.

5. Understanding: is motivating. promotes more understanding. promotes memory. influences beliefs. promotes the development of autonomous learners. enhances transfer reduces the amount that must be remembered. Teachers who understand the Big Ideas of mathematics translate that to their teaching practices by consistently connecting new ideas to Big Ideas and by reinforcing Big Ideas throughout teaching (Ma 1999). Also, effective teachers know how Big Ideas connect topics across grades; they know the concepts and skills developed at each grade and how those connect to previous and subsequent grades. And finally, Big Ideas are important in building and using curricula. The Curriculum Principle from the Principles and Standards for School Mathematics (NCTM, 2000)Teachers who understand the Big Ideas of mathematics translate that to their teaching practices by consistently connecting new ideas to Big Ideas and by reinforcing Big Ideas throughout teaching (Ma 1999). Also, effective teachers know how Big Ideas connect topics across grades; they know the concepts and skills developed at each grade and how those connect to previous and subsequent grades. And finally, Big Ideas are important in building and using curricula. The Curriculum Principle from the Principles and Standards for School Mathematics (NCTM, 2000)

6. When one understands Big Ideas, mathematics is no longer seen as a set of disconnected concepts, skills, and facts. Rather, mathematics becomes a coherent set of ideas. Singapore students use powers of 10 to solve, US uses long multiplication standards algorithmSingapore students use powers of 10 to solve, US uses long multiplication standards algorithm

7. Changing our Mind-Set from �Answer Getting� to Learning Mathematics Motto for Singapore and Japanese teachers is, �structured problem solving and how can I use this problem to teach mathematics my kids don�t already know.� Motto for United States teachers is, �learning terms and practicing procedures and how can I teach my kids to get the answer to this problem?� (Use math they already know. Easy, reliable and works only with the bottom half of the class).

8. Drill and Practice- There IS a Difference!! Practice means we are doing meaningful mathematics that we have recently learned in an attempt to achieve proficiency. Drill is activity designed to promote automaticity and speed in recall. (Timed tests or quizzes are considered drill and often cause more anxiety in students who do not work well under pressure). Practice Standards of CCS (Meaningful Practice)Practice Standards of CCS (Meaningful Practice)

9. A Philosophy or �Mind Set� of Problem Solving �Problems worthy of attack prove their worth by hitting back� Problem solving is usually more difficult for student than computation because it is such a different undertaking. It requires mathematical reasoning, rather than rote application of a memorized algorithm. It is also divergent and process-oriented rather than convergent and answer-oriented. Problem solving encourages multiple methods of solution rather than the single method usually encountered in computation. In addition, proficiency in computation doesn�t automatically make students problem solvers. Because of these differences, it often takes more time for students to build proficiency in problem solving than it does in computation. However, the time invested is well worth it. This is because students use computational skills in a meaningful context when they solve problems, so engaging in problem solving also gives students practice in computation. The reverse, however, is not true�students who only do computation don�t get to practice problem solving and build competence in this important life skill. Building proficiency in problem solving takes time, but then so do most worthwhile endeavors in life. Students can�t become problem solvers without continuous exposure to good problems. The following grook by Peit Hein, is an appropriate reminder as we embark on the problem solving journey this summer! (AIMS Ed. Foundation, 2004)

10. T.T.T. Put up in a place Where it�s easy to see The cryptic admonishment T.T.T. When you feel how depressingly slowly you climb, it�s well to remember Things Take Time -Piet Hein