1. Linda Levi, TDG Seminar, 2-20061 Knowledge of Children's Mathematics: A Foundation for Classroom Discourse Perspectives from Cognitively Guided Instruction. Linda Levi

2. Linda Levi, TDG Seminar, 2-20062 Summary of Major Cognitively Guided Instruction (CGI) Research Thomas Carpenter, Megan Franke, Elizabeth Fennema, Penelope Peterson, Linda Levi, Victoria Jacobs, Susan Empson and others. 1970s Research on Children’s Thinking 1984-88: CGI Experimental Study 1989-95: CGI Longitudinal Study 1996-05: CGI/Algebra Development and Research

3. Linda Levi, TDG Seminar, 2-20063 1970s: Research on Children’s Mathematical Thinking Thomas Carpenter and James Moser research the development of children’s strategies for addition and subtraction problems

4. Linda Levi, TDG Seminar, 2-20064 1984 - 1988: CGI Experimental Study First grade teachers –20 participated in CGI professional development (summer workshop) –20 participated in general problem solving workshop Treatment and Control group were compared –Teachers’ knowledge –Teachers beliefs –Students’ achievement (problem solving and facts) –Classroom practice (amount of problem solving, type of teacher talk, type of student talk…)

5. Linda Levi, TDG Seminar, 2-20065 1989-1995:CGI Longitudinal Study Kindergarten through third grade teachers and students in four schools All teachers attended CGI professional development The following were assessed over three years: –Teachers’ knowledge and beliefs –Students’ achievement and beliefs –Classroom practice A study of these teachers’ classroom practice, knowledge and beliefs was done five years after the workshop ended.

6. Linda Levi, TDG Seminar, 2-20066 1996-2005: CGI/Algebra Research 1996 – 2000 CGI Algebra Professional Development Program was developed by researchers in conjunction with expert CGI teachers. 2000 -05 Experimental Research –90 Kindergarten – Sixth grade teachers attended CGI/Algebra professional development –These teachers were compared with 90 teachers who did not attend Student Achievement Teacher Knowledge

7. Linda Levi, TDG Seminar, 2-20067 Cognitively Guided Instruction Summary of Major Research Results CGI Students’ achievement on problem solving tasks is higher than non-CGI students’. CGI Students’ performance on computation and facts is not significantly different from that of non-CGI students. CGI Teachers have greater knowledge of their own students’ thinking than non-CGI teachers. CGI Teachers have greater knowledge of children’s mathematics than non-CGI teachers. CGI Classrooms involve a great deal of problem solving and student discussion. Most Teachers sustain their practice 5 years after PD ends. Some Teachers generated additional growth 5 years after PS ended.

8. Linda Levi, TDG Seminar, 2-20068 Outcomes of Classroom Discourse Discourse Students learn from students Students’ reflect on their own ideas Teachers learn about their students’ thinking Teachers learn about Children’s mathematics

9. Linda Levi, TDG Seminar, 2-20069 “I always knew it was important to listen to kids, but I didn’t know what to listen for.” CGI teacher, 1989

10. Linda Levi, TDG Seminar, 2-200610 Foundation for Discourse: Teacher’s Knowledge of Children’s Mathematics Teacher’s Knowledge of his/her individual students’ thinking.

11. Linda Levi, TDG Seminar, 2-200611 Rachel’s Problems Rodney is having some kids over for jelly donuts. 7 donuts can fit on one plate. How many plates will Rodney need for 28 donuts? Karina had 20 cupcakes. She put them into 4 boxes so that there were the same number of cupcakes in each box. How many cupcakes did Karina put in each box?

12. Linda Levi, TDG Seminar, 2-200612 Multiplication, Measurement Division and Partitive Division Problems Multiplication Susan has 8 boxes with 5 marbles in each bucket. How many marbles does Susan have? Measurement Division Susan has 40 marbles. She wants to put them into boxes with 5 marbles in each box. How many boxes would she need to hold all of her marbles? Partitive Division Susan has 40 marbles. She has 5 boxes to hold these marbles. How many marbles can she put in each box if she wants to put the same number of marbles in each box?

13. Linda Levi, TDG Seminar, 2-200613 Problems to classify: 1.I have 21 cents to buy candies with. If each gum drop costs 3 cents, how many gum drops can I buy? 2.Janelle has 21 beads. She wants to make 3 braids in her hair and put the same number of beads in each braid. How many beads can go in each braid? 3.Kevin earned 89 bonus points when playing his computer game. If it takes 7 bonus points to get an extra life, how many extra lives will he get?

14. Linda Levi, TDG Seminar, 2-200614 Multiplication Problems 1.There are 2 bags of soccer balls with 10 balls in each bag. There are also 4 extra balls. How many balls are there altogether? 2.Mia has 7 bags of beads. There are 10 beads in each bag. She also has 6 extra beads. How many beads does she have? 3.Ms. Keith has 6 packages of cookies. There are 10 cookies in each package. She also has 4 other cookies. How many cookies does she have?

15. Linda Levi, TDG Seminar, 2-200615 Measurement Division Problems 1.Matt has 36 pennies. He puts 10 pennies into each box. How many boxes can he fill with 10 pennies? 2.David has a rock collection. He has 54 rocks in his collection. He puts them into boxes with 10 rocks in each box. How many boxes does he use? 3.The second graders had 54 balloons for the school carnival. They put balloons into bunches of ten. How many bunches could they make?

16. Linda Levi, TDG Seminar, 2-200616 Strategies for Solving Multiplication and Measurement Division Problems with Tens Counting by Ones Counting by Tens Direct Place Value

17. Linda Levi, TDG Seminar, 2-200617 Sam eats 1/10 of a pound of fudge a day. How many days would it take him to eat 2 pounds of fudge?

18. Linda Levi, TDG Seminar, 2-200618 An animal at the zoo eats.1 of a pound of food each day. If the zookeeper has 65.4 pounds of food for this animal, how many days can she feed the animal before the food runs out?

19. Linda Levi, TDG Seminar, 2-200619 How many tens are in 387? How many tenths are in 387?

20. Linda Levi, TDG Seminar, 2-200620 In the early 1900’s, a farmer could pile up stones to construct.1 of a mile of fence a day. If a farmer worked for 35 days building a fence, how long would the fence be?

21. Linda Levi, TDG Seminar, 2-200621 Sam builds.35 mile of fence every day. How long would his fence be after 32 days?