1. C MATH 2 CLARAN EINFELDT claran@cmath2.com www.cmath2.com claran@cmath2.com CLARAN EINFELDT claran@cmath2.com www.cmath2.com claran@cmath2.com

2. Senses on Geometry Manipulative-based activities help students move from the Concrete to the Representational to the Abstract Manipulative-based activities help students move from the Concrete to the Representational to the Abstract

3. Statistics for the Ages The Study of Statistics... Engages the learner Comes in many forms Is used to make decisions Allows analysis of different situations and claims The Study of Statistics... Engages the learner Comes in many forms Is used to make decisions Allows analysis of different situations and claims

4. Calculators for Learning Mathematics The calculator... Engages students Enhances their learning Adds motivation Is allowed on the ISAT Levels the playing field at the middle level Enables the study of significant mathematics The calculator... Engages students Enhances their learning Adds motivation Is allowed on the ISAT Levels the playing field at the middle level Enables the study of significant mathematics

5. Teaching Algebra with Manipulatives Algebra manipulatives can open the door for students to be successful... Computation with Integers Evaluating Expressions Writing & Solving Equations Working with Polynomials Integrating with Geometry Concepts Algebra manipulatives can open the door for students to be successful... Computation with Integers Evaluating Expressions Writing & Solving Equations Working with Polynomials Integrating with Geometry Concepts

6. What is algebraic thinking or reasoning? Forming generalizations from experiences with number and computation Formalizing these ideas with the use of a meaningful symbol system Exploring the concepts of patterns and functions Forming generalizations from experiences with number and computation Formalizing these ideas with the use of a meaningful symbol system Exploring the concepts of patterns and functions Van De Walle, Elementary and Middle School Mathematics: Teaching Developmentally

7. Linking Mathematics and Literature in a Meaningful Way Literacy and mathematics require development of many of the same skills, including pattern recognition, classifying, organizing thoughts, and solving problems. Literature can provide a means for mathematics and literacy skills to develop simultaneously as students read, write, listen, and talk about math. Engagement with literature allows students to connect the abstract language of mathematics to their personal world in a natural way. Literacy and mathematics require development of many of the same skills, including pattern recognition, classifying, organizing thoughts, and solving problems. Literature can provide a means for mathematics and literacy skills to develop simultaneously as students read, write, listen, and talk about math. Engagement with literature allows students to connect the abstract language of mathematics to their personal world in a natural way.

8. Deal or No Deal? Using Games for Mathematics A game can provide the platform for students to be reflective about mathematical relationships. It is this reflective thought that promotes growth.

9. Words Matter in Mathematics conversation understanding Word Walls vocabulary Visual cues Similarities/differences symbols

10. Illuminations © Website Activities 92 online activities Organized by grade-band Lessons 521 lessons Organized by grade-band and content strand Activities 92 online activities Organized by grade-band Lessons 521 lessons Organized by grade-band and content strand Standards NCTM Principles and Standards Grade-band electronic examples Web Links 726 online resources Identified by an editorial panel Organized by content strand

11. Making Probability Real with Simulations Using simulations: motivates interest provides a level of concrete experiences leading to later levels of abstraction addresses misconceptions about probabilistic situations allows for the exploration of sophisticated probability concepts develops intuitive understanding of probability concepts (e.g., the central tendency of large samples of data) Using simulations: motivates interest provides a level of concrete experiences leading to later levels of abstraction addresses misconceptions about probabilistic situations allows for the exploration of sophisticated probability concepts develops intuitive understanding of probability concepts (e.g., the central tendency of large samples of data)

12. Five Instructional Practices that WORK 1. Make Prime Time Count 2. Create a language-rich classroom 3. Ensure Daily Residue 4. Connect with Context 5. Foster visualization 1. Make Prime Time Count 2. Create a language-rich classroom 3. Ensure Daily Residue 4. Connect with Context 5. Foster visualization

13. Key elements of good questioning practices Plan and collaborate Ensure rich tasks and a safe environment Use questions to access understanding rather than find answer Plan and collaborate Ensure rich tasks and a safe environment Use questions to access understanding rather than find answer

14. Texas Instruments http://education.ti.com For FREE Activities: click “Classroom Exchange” For support programs: click “Funding, Research & Support” http://education.ti.com For FREE Activities: click “Classroom Exchange” For support programs: click “Funding, Research & Support”

15. Texas Instruments Doug Harnish Your IL and WI contact for product information, workshops, trainings, etc. dharnish@ti.com 630-877-0085 Doug Harnish Your IL and WI contact for product information, workshops, trainings, etc. dharnish@ti.com 630-877-0085

16. Barbara Jo Evans Educational Consultant Illinois**

17. Research tell us …  The strongest predictor of earnings nine years after graduation from high school is the number of mathematics classes the student has taken.  The odds that a student who enters college will complete a bachelor’s degree more than double if that student completed a mathematics course beyond Algebra II content.  Jobs that do not require a college degree, but will support a family and have the potential for advancement require mathematics content that is equivalent to Algebra II, as well as four years of English.

18. Research from… Improving Adolescent Mathematics, Findings from Research NWREL 2005

19. How Teachers Inspire …  Although my school days are as distant a memory to me as my first date, I can vividly recall a few magic moments in learning … … from USA Today, 6/19/07

20. Not Lost … Just Exploring Some people choose to live their lives on quiet avenues While others find a place in the parade Some like me … and Claran, and Sharon, and Tom, and Dean, and Linda, and Mary, and Nancy…are seekers We take less traveled roads Believing we can find a better way

21. Not lost … just Exploring And though we get discouraged, We won’t be turning back We have joy as our compass, and faith as our map … I am not lost … I am exploring Life is an adventure worth enjoying Though I may not know where I’m going I am not lost … I am exploring

22. Inspire and Explore! When your student say they are lost … Remember to tell them that they are NOT lost, but they ARE exploring! Inspire yourselves and your students … to explore the magic world of mathematics.

23. Barbara Jo Evans Educational Consultant Illinois

25. 1. Students come to the classroom with preconceptions about how the world works. 2. To develop competence... Students must (a) have a deep foundation of factual knowledge, (b) understand facts and ideas in the context of a conceptual framework, and (c) organize knowledge to facilitate retrieval and application. 3. A “metacognitive” approach to instruction can help students learn to take control. 1. Students come to the classroom with preconceptions about how the world works. 2. To develop competence... Students must (a) have a deep foundation of factual knowledge, (b) understand facts and ideas in the context of a conceptual framework, and (c) organize knowledge to facilitate retrieval and application. 3. A “metacognitive” approach to instruction can help students learn to take control. 3 Principles of How People Learn

26. A Fish Story “I have been about the world – hopping here and there,” said the frog, “and I have seen extraordinary things.” “Like what?” asked the fish. “Birds”, said the frog mysteriously. and he told the fish about the birds, “I have been about the world – hopping here and there,” said the frog, “and I have seen extraordinary things.” “Like what?” asked the fish. “Birds”, said the frog mysteriously. and he told the fish about the birds,

28. (birds) who had wings, and two legs, and many, many colors. As the frog talked, his friend saw the birds fly through his mind like large feathered fish.

30. The frog continues with descriptions of cows, which the fish imagines as black-and-white spotted fish with horns and udders...

32. And Humans, which the fish imagines as fish walking upright and dressed in clothing. And Humans, which the fish imagines as fish walking upright and dressed in clothing.

34. Leo Lionni’s Fish Is Fish © 1970. Copyright renewed 1998 by Leo Lionni. Random House Children’s Books a division of Random House, Inc.

35. 1 Build It concrete, manipulative 3 Symbol It abstract symbolic 4 Say It Write It communications 2 Draw It representational pictorial graphical

36. C.COLLABORATION M.MATHEMATICS A.ACTIVITIES T. TIME H.HAPPINESS 2. FLEXIBILITY C.COLLABORATION M.MATHEMATICS A.ACTIVITIES T. TIME H.HAPPINESS 2. FLEXIBILITY

37. WHETHER YOU THINK YOU CAN OR NOT YOU ARE PROBABLY RIGHT WHETHER YOU THINK YOU CAN OR NOT YOU ARE PROBABLY RIGHT

38. CLOSING AND DOOR PRIZES QUESTIONS FINAL EVALUATIONS