1. Parkston, January 19, 2007 Use each of the digits 1,2,4,and 8 once to make a number sentence that equals zero. You may use any operation (add, subtract, multiply, or divide) as many times as you wish. You may use parentheses in your solution.

2. Parkston, January 19, 2007 SD Math Science Partnership Project Jan Martin - SD DOE Math Curriculum Specialist

3. Parkston, January 19, 2007 South Dakota Counts is a three year elementary math initiative focused on implementing research- based instructional practices to improve student learning in mathematics. It is not a curriculum or a quick fix.

4. Parkston, January 19, 2007 GOALS:  To build broad-based expertise and leadership for improving student achievement in elementary mathematics.  Develop a statewide educational community with a cadre of skilled professionals to serve as resources and trainers in the ongoing effort to improve elementary mathematics instruction.

5. Parkston, January 19, 2007 Suppose everyone in this room shakes hands with all the other people in this room. How many handshakes will that be?

6. Parkston, January 19, 2007 What was good enough for us in learning mathematics is not good enough for our children. Despite the reality that learning math was a bust for so many of us, we have pressed on with ineffective teaching approaches that clearly don’t work. The way we have traditionally been taught mathematics has created a recurring cycle of math phobia, generation to generation, that has been difficult to break. (M. Burns, 1998)

7. Parkston, January 19, 2007 Why elementary math? 1. Data sources indicate gaps at the elementary levels NAEP data DSTEP data gaps between all students and Native American students, low socioeconomic status 2. Elementary teachers need to broaden their knowledge base about math content, math pedagogy, and student mathematical thinking.

8. Parkston, January 19, 2007 Selling a Horse A man bought a horse for $50 and sold it again for $60. He then bought back the horse for $70 and sold it again for $80. What was the financial outcome of the transactions?

9. Parkston, January 19, 2007 Nationally, the negative attitudes and beliefs that people hold about mathematics have seriously limited them, both in their daily lives and in their long-term options. (M. Burns, 1998) It is culturally ok to say that you are not good in math while most of us would not admit to not being a good reader.

10. Parkston, January 19, 2007 Best Practices in Teaching Mathematics Making Sense – elements of classrooms Adding It Up – five strands of mathematical proficiency Relearning to Teach Arithmetic NCTM Process Standards Cognitively Guided Instruction

11. Parkston, January 19, 2007 Making Sense Nature of Classroom Tasks Role of Teacher Social Culture of Classroom Mathematical Tools Equity and Accessibility

12. Parkston, January 19, 2007 What is a good problem? A good problem or task is any task or activity for which the students have no prescribed or memorized rules or methods, nor is there a perception by the student that there is a specific “correct” solution method.

13. Parkston, January 19, 2007 How can you make this typical “naked number” problem a good problem? 26  

14. Parkston, January 19, 2007 Adding It Up Five strands of mathematical proficiency Adaptive Reasoning Strategic Competence Conceptual Understanding Productive Disposition Procedural Fluency

15. Parkston, January 19, 2007 Adaptive Reasoning Example If a student solved this problem correctly. How many bows could you make from 12 yards of ribbon if each bow used 1/3 yard of ribbon? Answer: 36 bows An example of adaptive reasoning would be understanding that you would make fewer bows if you used 2/3 yard per bow.

16. Parkston, January 19, 2007 Strategic Competency Non-Example At ARCO, gas sells for $1.13 per gallon. This is 5 cents less per gallon than gas at Chevron. How much does 5 gallons of gas cost at Chevron? $1.13 $1.08 -.05 X 5 $1.08 $5.40

17. Parkston, January 19, 2007 Conceptual Understanding Non-Example 9.83 X 7.65 = 7519.95 A student with conceptual understanding of place value using decimals would know the answer is under 80.

18. Parkston, January 19, 2007 Productive Reasonsing Students are saying “Don’t tell me the answer. I want to get it by myself.” Rather than, “I don’t get it!”

19. Parkston, January 19, 2007 Procedural Fluency Non-Example 62 - 48 26

20. Parkston, January 19, 2007 National Council of Teachers of Mathematics Content and Process Standards State standards aligned to NCTM Content Standards Instruction should incorporate the process standards: Representation Communication Connections Reasoning and Proof Problem Solving

21. Parkston, January 19, 2007 Relearning to the Arithmetic Key concepts: –Building students' procedural fluency in computation based on children's conceptual understanding. –Use of number talks as part of daily instruction. –Use of mental math to develop fluency and flexibility.

22. Parkston, January 19, 2007 Solve this Problem 701 - 499

23. Parkston, January 19, 2007 Cognitively Guided Instruction CGI is not a set of procedures to implement but rather a philosophy or a way of thinking about teaching that starts with the students’ thinking. In the past I thought children didn’t understand subtraction with regrouping, when what they didn’t understand was how to use the process that I was insisting that they use, rather than really understanding the concept of subtraction that might encompass regrouping. Kerri Burkey, second-grade teacher

24. Parkston, January 19, 2007 (CGI continued) Based on more than 20 years of research, greater understanding of how children come to understand basic number concepts. From this research, a framework of problem types and strategies have emerged which enables teachers to strategically guide learning in a mathematics classroom.

25. Parkston, January 19, 2007 Problem Types Join * Separate * Part-Part-Whole Compare Multiplication Measurement Division Partitive Division Strategies Students will naturally use Direct modeling * Counting strategies Using derived number facts and known number facts

26. Parkston, January 19, 2007 Change is easier together than alone. Never doubt that a small group of thoughtful, committed citizens can change the world; indeed, it is the only thing that ever does. Margaret Mead

27. Parkston, January 19, 2007 Trains of Five Using two colors of unifix cubes, determine how many unique trains of five cubes you can make. Determine a way to represent your results visually and numerically.

28. Parkston, January 19, 2007 What do you think? Some people say that to add four consecutive numbers, you add the first and the last numbers and multiply by 2. What can you find out about the statement? Agree or disagree? Why?

29. Parkston, January 19, 2007 Change – go slow to go fast. What is one thing you can do differently in your classroom to make mathematics more problematic for your students?

30. Parkston, January 19, 2007 Eric the Sheep Eric the sheep is lining up to be shorn before the hot summer ahead. There are 50 sheep in front of him. Eric can’t be bothered waiting in the queue properly, so he decided to sneak towards the front. Every time 1 sheep is taken to be shorn, Eric sneaks past 2 sheep. How many sheep will be shorn before Eric?

31. Parkston, January 19, 2007 CGI Problem –The class baked 84 cookies. We want to put them into boxes at the school bake sale. If we put 12 cookies into each box, how many boxes can we fill?

32. Parkston, January 19, 2007 Partners SD Department of Education CAMSE (Center for the Advancement of Mathematics and Science Education) - BHSU TIE Grant Awardees – ESA 1 – 7, Sioux Falls Sub-Grantees – participating school districts External Evaluator – Inverness Research Associates

33. Parkston, January 19, 2007 Professional Development Components  Summer Institute (1 week each summer)  On-going coaching – math specialists and teacher leaders  Regional workshops during school year  Lenses on Learning workshops for principals  On-going collaborative planning to ensure implementation of research-based math instruction at the school and classroom levels

34. Parkston, January 19, 2007 Project Objectives:  Increase student academic achievement as measured by the state mathematics standards.  Train and place one Mathematics Specialist in 8 different sites in SD. Status: ESA 1 – 7 and Sioux Falls  Provide training for one Mathematics Teacher Leader for potentially each elementary building in South Dakota. Status: 149 teacher leaders 06-07 with plans for 50 more to be added in 07-08  Support work in each participating district to train additional K-5 teachers.  Provide training for building principals to support the work of the Teacher Leaders.

35. Parkston, January 19, 2007 Elementary Principals role: Participate in professional development designed to help administrator, as instructional leaders in their schools, to understand and support effective mathematics instruction. Support participating staff in the implementation of grant activities. Collaborate with math specialist and teacher leader to develop implementation plans for their school.

36. Parkston, January 19, 2007 Math Specialist role: Collaborate with SDDOE, CAMSE, and TIE to coordinate and deliver professional development components Collect data, data analysis, and reporting of data to SDDOE and Inverness Attend professional development centered on mathematics content, mathematics pedagogy, student mathematical thinking, and educational leadership. Support the work of the teacher leaders.

37. Parkston, January 19, 2007 Math Teacher Leader role: Attend professional development centered on mathematics content, mathematics pedagogy, student mathematical thinking, and educational leadership Utilize professional development content in mathematics instruction to impact student achievement Upon completion of one year of training, provide training for other K-5 teachers in building Create a model classroom as one component of the training for other teachers in building

38. Parkston, January 19, 2007 Year 1 Courses Math Specialists Leadership Institute Cognitively Guided Instruction Best Practices Summer Institute - Foundations Teacher Leaders Summer Institute – Foundations Cognitively Guided Instruction Principals Lenses on Learning