1. Development of the Algebra II Units

2. The Teaching Principle Effective teaching requires understanding what ALL students know and need to learn and challenging and supporting them to learn it well. (NCTM, 2000) Slide developed by Gail Burrill, MSU 2009

3. TIMSS Video Study - Tasks Stigler & Hiebert, 2004 Slide developed by Gail Burrill, MSU 2009

4. TIMSS Video Study - Implementation Stigler & Hiebert, 2004 Slide developed by Gail Burrill, MSU 2009

5. Students learn if they are actively involved in choosing and evaluating strategies, considering assumptions, and receiving feedback. they are actively involved in choosing and evaluating strategies, considering assumptions, and receiving feedback. they encounter contrasting cases- notice new features and identify important ones. they encounter contrasting cases- notice new features and identify important ones. National Research Council, 1999 Slide developed by Gail Burrill, MSU 2009

6. Which shape will hold the same amount of spaghetti and be the most economical? Area of base Surface area Volume Ratio of surface area to volume Cylinder Rectangular prism Shape 3 MDE, 2003 Slide developed by Gail Burrill, MSU 2009

7. Technology is often used Technology is often used For Performance: - To carry out difficult computations or manipulation - To make the graph or find the equation of a line - After the content has been taught - Review, consolidate concepts NOT as a Tool for Learning Slide developed by Gail Burrill, MSU 2009

8. Technology can Technology can explicitly engage teachers in exploration, inquiry, and conjecture with their students around specific mathematical concepts. create new opportunities for students to reason and make sense out of the mathematics world Slide developed by Gail Burrill, MSU 2009

9. Ways technology materials have gone astray Ways technology materials have gone astray Emphasis on mastering the technology - mathematics is of secondary importance Demonstration of concept - students are spectators Revisiting a topic in a simple way - students ’ role is verification Replicating activities from the point of view of current instructional materials, underutilizing the technology ’ s potential Fragmented ideas - obtaining a formula as an objective (adapted from Belfort & Guimaraes, 2004) Slide developed by Gail Burrill, MSU 2009

10. A Possible Solution Use technology to provide different learning experiences that allow students to interact with the mathematics in new ways. Structure lessons that take account of well documented trouble spots. Ask questions that reveal student thinking - questions that promote reasoning and sense making. Slide developed by Gail Burrill, MSU 2009

11. In the context of: The tasks in which students engage Developing conceptual understanding as well as supporting fluency What teachers do with a task What questions teachers ask and how What questions teachers answer and how What research tells us about learning Slide developed by Gail Burrill, MSU 2009

12. Reasoning/Sense Making Questions Compare and contrast: How are they alike? How different? Predict forward: “What would happen if.. ?” Predict backward: “How can I make.. happen?” “Is it possible to... ?” Analyze a connection/relationship : “When will... be (larger,equal to, exactly twice, …) compared to...?” “When will.. be as big as possible?” Generalize/make conjectures : “When does... work?” “Under what conditions does … behave this way?” “Describe how to find...?” “Is this always true?” Justify/prove mathematically : “Why does... work?” Consider assumptions inherent in the problem and what would happen if they were changed Interpret information, make/ justify conclusions : “The data support… ; “This… will make ….happen because…” Burrill & Dick, 2008 Slide developed by Gail Burrill, MSU 2009

13. “…when teachers learn to see and hear students’ work during a lesson and to use that information to shape their instruction, instruction becomes clearer, more focused, and more effective.” (NRC, 2001, p.350 ) Managing Discussions Slide developed by Gail Burrill, MSU 2009

14. How Students Learn Mathematics in the Classroom Principle #1: Teachers Must Engage Students’ Preconceptions Principle #2: Understanding Requires Factual Knowledge and Conceptual Frameworks Principle #3: A Metacognitive Approach Enables Student Self-Monitoring NCR 2004

15. Implications for teaching: Recognize that many students are learning for the moment not for understanding and retention. Take advantage of technology that can allow students into math in new ways. Focus on the questions, plan for them, and use them to create classrooms where the focus is on developing understanding of the math Slide developed by Gail Burrill, MSU 2009

16. References Belfort, E. & Guimaraes, C. (2004). Teachers' practices and dynamic geometry. In Hoines, M. & Fuglestad, A. (Eds.), Proceedings of the 28 th Conference of the International Group for the Psychology of Mathematics Education. (2, pp. 503-510). Burrill, G. & Dick, T. (2008). What state assessments tell us about student achievement in algebra. Paper presented at NCTM 2008 Research Presession Florida Department of Education (2006). FCAT Mathematics Released Items, Grade 9. Maine Department of Education. Maine Educational Assessment (MEA) Released Items 2004, 2005. Mathematics Augmentation Sample Items. Michigan Department of Education. (2003). MMLA Lesson Study Project. Burrill, G., Ferry, D., & Verhey R. (Eds). Lansing, MI Michigan Department of Education. (2007). Released items mathematics grades 7, 8 fall. www.michigan.gov/mde/0,1607,7-140- 22709_31168_31355-95470--,00.html www.michigan.gov/mde/0,1607,7-140- 22709_31168_31355-95470--,00.htmlwww.michigan.gov/mde/0,1607,7-140- 22709_31168_31355-95470--,00.html National Assessment for Educational Progress (2005). Released Item. National Center for Educational Statistics. (2005). Slide developed by Gail Burrill, MSU 2009

17. National Council of Teachers of Mathematics. (2000). Principles and Standards for School Mathematics. Reston VA: The Council National Research Council (2001). Adding It Up. Kilpatrick, J., Swafford, J., & Findell, B. (Eds.) Washington DC: National Academy Press. Also available on the web at www.nap.edu. www.nap.edu New Hampshire Department of Education. (2006). End of Grade 10 Common Items Released Items Ohio Department of Education. (2006). Released end of course tests algebra & geometry, Ohio Graduation Test. Spring. Columbus OH. Ohio Department of Education. (2006). Ohio graduation tests item analysis. March. Columbus OH. Schwartz, & Branford, J. (2000) A time for telling. Cognition and Instruction. Stigler, J. & Hiebert, J. (2004). Improving Mathematics Teaching, Improving Achievement in Math and Science, 61(5), p. 12 – 17 Slide developed by Gail Burrill, MSU 2009

18. Texas Education Agency (2004). TAKS Texas assessment of knowledge and skills. Spring. Exit level mathematics, pp. 37-74. Austin TX. Texas Education Agency (2004). TAKS. Texas assessment of knowledge and skills item analysis summary report, all students. Spring. Austin TX. Slide developed by Gail Burrill, MSU 2009