1. An Introduction to Mathematics Curriculum Topic Study EMPOWERR Summer Institute July 27, 2011

2. 3 Goals for the CTS Intro Session (Learn about) To develop awareness of Curriculum Topic Study (CTS) as a tool you can use for connecting standards and research on learning to classroom practice. (Practice) To provide guided practice in using CTS. (Apply) To consider ways you might apply CTS to your work.

3. Bridging the Gap Photo from stoxchng National Standards Research on Learning Classroom Practice State Standards

4. What is CTS? A process that incorporates a systematic study of standards and research A set of tools and collective resources for improving curriculum, instruction, assessment, and teacher content knowledge An intellectually rigorous and engaging professional development experience

5. What CTS Is Not CTS IS NOT: A remedy for weak content knowledge A collection of teaching activities A description of “how to’s” A quick fix The end-all for professional development

6. Having State and National Standards Is Not Enough… What has been missing is a systematic, scholarly, deliberate process to help educators intellectually engage with standards and research on student learning so they can make effective use of them. ( Keeley, 2005) CTS provides that “missing link”

7. A First Glance at the CTS Book Pair up with someone at your table. Open the CTS book at random. With your partner or table group, do a quick scan of the page you opened to. What do you see that provides you with a “preview” of CTS? Mark the page with a sticky note. Repeat 2-3 times to get an initial sense of what is contained in the CTS book. Share something you found that particularly interests you and tell why.

8. Components of a CTS Study Guide CTS Sections and Outcomes Selected Readings from CTS Resources Web Site- Supplementary Material http://www.curriculumtopicstudy.org/

9. The CTS Guide Each guide has 6 CTS sections (Left Column) o Purposes of the sections  I : Identify Adult Content Knowledge  II : Consider Instructional Implications  III : Identify Concepts and Specific Ideas  IV : Examine Research on Student Learning  V : Examine Coherency and Articulation  VI : Clarify State Standards and District Curriculum Each section links to CTS sources and pre- vetted Readings (Right Column) Supplementary materials for each topic can be found at www.curriculumtopicstudy.orgwww.curriculumtopicstudy.org

10. CTS: The Swiss Army Knife of Curriculum, Instruction, and Assessment Improve adult science literacy (I) Improve knowledge of content teachers teach (I) Examine curricular and instructional considerations (II) Identify difficulties and misconceptions (IV) Identify “Big Ideas”, Concepts, Specific Ideas, and Skills (III) Consider developmental implications (II, IV) Examine scope and sequence (III) See connections and articulation within and across topics (V) Clarify state standards and district curriculum (VI)

11. CTS Collective Resources- Experts at Your Fingertips 24/7     Indicates the resource is online  Indicates parts of the resource are online

12. Getting to Know the Resources Science Pages 24-26 Science for All Americans Science Matters Benchmarks for Science Literacy The National Science Standards Making Sense of Secondary Science Atlas of Science Literacy Mathematics Pages 27-30 Science for All Americans Beyond Numeracy Benchmarks for Science Literacy Principles and Standards for School Mathematics Research Companion Atlas of Science Literacy Parallel Resources in Science CTS

13. Getting to Know the CTS Resources Introduction to CTS Using K-12 Snapshots

14. The CTS Scaffold Scaffold: The structure and supports that a teacher or more knowledgeable helper provides to allow a learner to perform a task he or she cannot yet perform independently. (Vygotsky, 1978; Dixon-Krauss, 1996; Wertsch,1991.)

15. Quick Summary of the CTS Scaffold STEP 1: Scan and select the CTS category.  STEP 2: Scan the list of topics within the category that include the content you are examining.  STEP 3:Select the CTS guide you will use.  STEP 4: Determine which section(s) of the CTS guide will help you find the information you need.  STEP 5: Select the resource(s) you will use, the grade span(s), and the readings.  STEP 6: Examine the reading for information relevant to your topic and task.  STEP 7: Record your findings. If you do not find what you need, go back to Step 2 and repeat with another topic.

16. Quick Scaffold Practice Steps 1-3 “What kinds of experiences should I provide my middle school students when they are learning about percent?” Category? Numbers and Operations CTS Topic Guide? Percent Page Number of CTS Guide? Page 129

17. Quick Scaffold Practice- Step 4 “What kinds of experiences should I provide my middle school students when they are learning about percent?” Section? Section II Outcome? Consider Instructional Implications

18. Quick Scaffold Practice- Step 5 “What kinds of experiences should I provide my middle school students when they are learning about percent?” Which resource, grade level, and page numbers do I read? Benchmarks (6-8)- Numbers, grade span essay, p 123 and/or PSSM (6-8)-Number and Operations, p 215 Understanding Numbers, pp 215-217 What part of the page do I focus on? Just the essay, not the bullets!

19. More Quick Scaffold Practice Steps 1-3 “What specific ideas about statistics should I focus on at the 3-5 grade level?” Category? Data Analysis CTS Topic Guide? Statistical Reasoning or Summarizing Data Page Number of CTS Guide? Page 186 or 187

20. More Quick Scaffold Practice- Step 4 “What specific ideas about statistics should I focus on at the 3-5 grade level?” Section? Section III (Could also include Section V and VI) Outcome? Identify Concepts and Specific Ideas

21. More Quick Scaffold Practice- Step 5 “What specific ideas about statistics should I focus on at the 3-5 grade level?” Which resource, grade level, and page numbers do I read? Benchmarks (3-5) 9D Uncertainty pages 227-230; 9E Reasoning pages 232-234; 12E Critical Response Skills pages 298-300 PSSM (3-5) Data Analysis and Probability page 176 or 400 What part of the page do I focus on? Just the bulleted learning goals, not the essay.

22. More Quick Scaffold Practice Steps 1-3 “What should adults know about mathematical equations? Category? Algebra CTS Topic Guide? Expressions and Equations Page Number of CTS Guide? Page 136

23. More Quick Practice- Step 4 “What should adults know about mathematical equations? Section? Section I Outcome? Identify Adult Content Knowledge

24. More Quick Scaffold – Step 5 “What should adults know about mathematical equations? Which resource, grade level, and page numbers do I read? Science for All Americans- Ch 9 pp 132-34 and/or Beyond Numeracy- Algebra, Some Basic Principles, pp 7-9

25. And Even More Practice- Steps 1-3 “I’m curious to see how the concepts and skills related to proportional reasoning develop from elementary grades through high school.” Category? Integrated Topics CTS Topic Guide? Proportionality Page Number of CTS Guide? Page 198

26. And Even More Practice- Step 4 “I’m curious to see how the concepts and skills related to proportional reasoning develop from elementary grades through high school.” Section? Section V Outcome? Examine Coherency and Articulation

27. And Even More Practice- Step 5 “I’m curious to see how the concepts and skills related to proportional reasoning develop from elementary grades through high school.” What Atlas strand map will you use? Ratios and Proportionality Is there a conceptual strand or strands within a map you should focus on? Parts and Wholes, Description or Comparison, and Computation

28. Last One! “I wonder what difficulties or common misconceptions I should anticipate when students create and interpret graphs?” Category? Integrated Topics CTS Topic Guide? Graphic Representation Page Number of CTS Guide? Page 196

29. Step 4? “I wonder what difficulties or common misconceptions I should anticipate when students create and interpret graphs?” Section? Section IV Outcome? Examine Research on Student Learning

30. Read and Examine Related Parts Students of all ages often interpret graphs of situations as literal pictures rather than as symbolic representations of the situations. Many students interpret distance/time graphs as the paths of actual journeys. In addition, students confound the slope of a graph with the maximum or the minimum value and do not know that the slope of a graph is a measure of rate. When constructing graphs, middle-school and high-school students have difficulties with the notions of interval scale and coordinates even after traditional instruction in algebra. For example, some students think it is legitimate to construct different scales for the positive and the negative parts of the axes. Alternatively, students think that the scales on the X and Y axes must be identical, even if that obscures the relationship. When interpreting graphs, middle-school students do not understand the effect that a scale change would have on the appearance of the graph. Finally, students read graphs point-by-point and ignore their global features. This has been attributed to algebra lessons where students are given questions that they could easily answer from a table of ordered pairs. They are rarely asked questions about maximum and minimum values; intervals over which a function increases, decreases or levels off; or rates of change. (Benchmarks for Science Literacy page 351)

31. Related Parts Students of all ages often interpret graphs of situations as literal pictures rather than as symbolic representations of the situations. Many students interpret distance/time graphs as the paths of actual journeys. In addition, students confound the slope of a graph with the maximum or the minimum value and do not know that the slope of a graph is a measure of rate. When constructing graphs, middle-school and high-school students have difficulties with the notions of interval scale and coordinates even after traditional instruction in algebra. For example, some students think it is legitimate to construct different scales for the positive and the negative parts of the axes. Alternatively, students think that the scales on the X and Y axes must be identical, even if that obscures the relationship. When interpreting graphs, middle-school students do not understand the effect that a scale change would have on the appearance of the graph. Finally, students read graphs point-by-point and ignore their global features. This has been attributed to algebra lessons where students are given questions that they could easily answer from a table of ordered pairs. They are rarely asked questions about maximum and minimum values; intervals over which a function increases, decreases or levels off; or rates of change. (Benchmarks for Science Literacy page 351)

32. Let’s Get Started! CTS is like learning any new skill. It takes practice, perseverance, focus, time, and effort!

33. Eliciting Your Prior Knowledge Choose a snapshot that interests you. Record your response to the question, based only on your prior knowledge before using CTS. Save your response for later.

34. CTS Snapshot Practice Practice using the scaffold to answer the snapshot question. Do not take shortcuts this first time! Record notes from your reading that address the question (not the entire topic). Complete a reflection note. Post your reflection note on the reflection wall charts. Begin another snapshot if you have time.

35. Reflection Wall Examine your response to the snapshot question before doing CTS. How did you respond after doing a CTS?  Write a reflection on a Post-It note describing the value of using CTS to address your snapshot question. What new knowledge did you gain by doing the CTS?

36. Applying CTS to Our Work Turn to page 35 and examine the list of ways CTS can be applied to mathematics education. Turn to Chapter 4 on p 53 to scan examples of using CTS in content, curricular, instructional, and assessment contexts. Which of these applications do you think you might use CTS for (or do you have a new one)? Do a “Quick Write” on your thoughts about using CTS in our EMPOWERR work.

37. For Additional Information Visit the CTS web site at www.curriculumtopicstudy.org www.curriculumtopicstudy.org Contact: EMPOWERR Project Staff