Enhancing Secondary Mathematics Instruction: Connecting New Learning to Prior Knowledge

1. N E P F Nevada Educator Performance Framework Southern Nevada Regional Professional Development Program www.rpdp.net Secondary Mathematics Module 1 Part 2

2. Standard 1 Module for Mathematics Part I – What and Why • Goal 1: What is Standard 1? • Goal 2: What are the indicators for Standard 1? Part II – Implications for Mathematics • Goal 3: What activities/instruction in the classroom would provide evidence of them? • Goal 4: What specific plans can be designed to implement them?

3. Let’s review Explicit connections to prior knowledge?

4. Are we creating links to student’s prior knowledge? Let’s review

5. Let’s review Are we using humor to connect to prior knowledge?

6. NEPF: 5 High Leverage Instructional Standards and Indicators

7. Standard 1: New Learning is Connected to Prior Learning and Experience

8. Handout

9. Review of the Indicators On your chart, record key words (in the column for Standard 1 Indicators) that will trigger your thoughts of what the indicator is about. (Activate) Initial Understanding (Make) Explicit Connections (Make clear) Purpose & Relevance (Provide opportunities to) Build on/Challenge

10. Samples of Concepts for Instruction • GEOMETRY • Properties and attributes of polygons ALGEBRA Systems of linear equations • ALGEBRA 2 • Graph and write equations of hyperbolas • MATH 6 • Volume of rectangular • prisms • PRE- • ALGEBRA • Pythagorean Theorem and • the coordinate plane • MATH 7 • Surface area of rectangular • prisms

11. Handout Revisited For your course and identified concept, brainstorm a list of the skills students should have mastered prior to the start of the unit. Record this on your handout.

12. Back to the handout…. On your chart record prior knowledge/skills required

13. Time for Activity Algebra Systems of Linear Equations

14. Let’s identify strategies/activities/instruction that produce evidenceof connecting new learning to prior knowledge!

15. Resources for Launching Your Lesson We have all used quick, simple links to prior knowledge. Daily warm-up questions displayed as students enter the classroom might be one example…. THIS IS A REFERENCE TO HELP YOU THINK OF MORE VARIEDAND EFFECTIVE WAYS TO ACCESS PRIOR KNOWLEDGE!

16. www.rpdp.net Math -> Middle School -> NEPF Secondary Math Resources

17. Resource Reference List (abbrev)

18. Peruse the resource lists and examples • Choose a strategy new to you. • Share that strategy with a colleague sitting near you. • Commit to use that strategy next week in your classroom.

19. Back to the handout…. On your chart record strategies, activities or instruction that could demonstrate the indicator for this concept in your classroom. (Activate) Initial Understanding (Make) Explicit Connections (Make clear) Purpose & Relevance (Provide opportunities to) Build on/Challenge

20. NEPF: Evidence Indicators

21. What Teachers Need to Demonstrate • Indicator 1 • Teacher activates all students’ initial understandings of new concepts and skills

22. What Teachers Need to Demonstrate Indicator 2 Teacher makes connections explicit between previous learning and new concepts and skills for all students

23. What Teachers Need to Demonstrate Indicator 3 Teacher makes clear the purpose and relevance of new learning for all students

24. What Teachers Need to Demonstrate Indicator 4 Teacher provides all students opportunities to build on or challenge initial understandings

25. Student Work (evidence for Standard 1)

26. Direct observation or in lesson plans (evidence for Standard 1) In a lesson you could show explicit connections to previous learning as shown in the following video clip. (If this was not observed, it would be evident in your lesson plans.) Multiplying Polynomials (Using Previously Learned Math Concepts) Bill Hanlon

28. Explicit connections…. • http://www.screencast.com/t/uqe6Tgcv5kF Connecting Arithmetic Sequences to Skip Counting, Charts, Ordered Pairs and Functions • http://www.screencast.com/t/yFj290W9v900 Connecting Adding Fractions and Decimals • http://www.screencast.com/t/mWpECJA5Z5 Connecting Polynomial Addition to Place Value & Expanded Notation

29. Explicit Connections Resource: Linking Algebra with Basic Math Skills

30. Entrance Card (evidence for Standard 1) You could model a warm-up as seen in the My Favorite No with Leah Alcala. “I put a warm-up problem on the board, hand out index cards to all the kids, have them write their answer. I collect it, and then I sort it, and I say "Yes, no, yes, no", and I look for my favorite wrong answer, or my favorite "no." And, we analyze that.” Student response chosen on video

31. Resources • RPDP website • List of strategies: “Resources for Launching Your Lesson”

32. For additional NEPF resources rpdp.net Select NEPF

33. In this module… • We have introduced and supplied a resource with strategies/techniques/activities to use in the classroom that would provide evidence of connecting new learning to prior learning. • We have provided a template to help you make specific plans for future units/chapters/concepts to identify prior knowledge, implement the indicators, and choose strategies to address them.

34. IN CLOSING…. Write a few sentences addressing what the following quote means to you: “If I had to reduce all of educational psychology to just one principle, I would say this: the most important single factor influencing learning is what the learner already knows.” Ausubel, D., Novak, J. & Hanesian, H. 1978, Educational Psychology: A Cognitive View, Holt, Rinehart and Winston, New York, p. 163.