Development of the Big Picture of Mathematics

1. Development of the Big Picture of Mathematics Allison Zmuda, Facilitator allison@allisonzmuda.com

2. My Promise to YOU for Our Two Days • Explain key principles of backward design and how it connects at a K-12 level and unit level • Work shoulder to shoulder to articulate broader aims of schooling for your curricular program • Help make sense of the standards for an audience of teachers and students

3. Three Stages of Backward Design Stage 1: DESIRED RESULTS Stage 2: EVIDENCE Stage 3: LEARNING PLAN

4. What Understanding by Design IS • A way of thinking purposefully about our curricular planning by keeping the “end in mind” • An emphasis on transfer, meaning, and acquisition in all three stages. • An instructional emphasis on educators are coaches of understanding.

5. Understand the Big Picture before Zooming in on the Details

6. What does a curriculum designer using this framework think about? “As things are now, education is so cluttered and tangled up with a thousand senseless notions and stupidities, that the task of reformation is almost a superhuman one. It is entirely a task of taking away and reducing – not one of adding to or explaining. It is the task of the sculptor, who cuts the superfluous marble off, rather than that of the wax-workman who lays on the stuff thicker and thicker.” – Walt Whitman

7. Curriculum is NOT a Script “The job of teaching is not to ‘execute’ the paper curriculum irrespective of results, any more than it is the coach’s job to execute the playbook irrespective of the score. The teacher’s job is to flesh out the lessons in the curriculum and adjust instruction, whenever needed, to ensure optimal learning and performance. Given that purpose, teachers need a curriculum that provides troubleshooting advice and builds in opportunities to alter courses, as warranted.” — Jay McTighe and Grant Wiggins

8. Acquire Make Meaning Authentic Learning Transfer

9. Transfer

10. Make Meaning

11. Acquire

12. What Understanding by Design IS NOT • A rigid program or recipe. • A set of lesson plans. • A different way of “packaging” what you are already doing. • An exercise you are engaging in for “new teachers” • A way to show that you are following the new standards. • An unbalanced focus on getting students ready for the “test”

13. K-12 Curricular Framework Transfer Goals Understandings Essential Questions

14. Three stages of Backward Design Stage 1: DESIRED RESULTS Stage 2: EVIDENCE Stage 3: LEARNING PLAN

15. Weatherford ISD Glossary • To promote clarity of each component (definition and value) • To give every educator a “measuring stick” of what quality looks like • To provide space for an illustrative example that resonates with staff

16. Essential Questions to focus on when viewing the Glossary • What does it mean? • How do I know a good one when I see it ? • What is a powerful example for me?

17. Acquire Make Meaning Learning Goals Transfer

18. K-12 Curriculum Framework

19. Transfer Transfer Goals Design Standards • Long-term in nature • Emphasis is on independent and contextualized performance • Help to establish purpose and relevance by answering common student questions such as: “Why should I learn this? “What can I do with this?”

20. Content isa tool...

21. Toward what end?

22. Sample Math Transfer Goals • Demonstrate automaticity in basic computation so that they can focus on the interesting aspects of the problem • Based on an understanding of any problem, initiate a plan, execute it, and evaluate the reasonableness of the solution • Examine and apply a variety of methods to accurately and efficiently solve problems • Use appropriate tools/strategies to deepen understanding of mathematical concepts • Articulate how mathematical concepts relate to one another in the context of a problem or abstract relationships • Communicate effectively based on purpose, task, and audience using appropriate vocabulary

23. Create a set of K-12 transfer goals • Honor the design standards (see glossary) • Inspired by the illustrative examples (see previous slide and sets I gave you) • Aligned to Mathematics TEKS – focus on content as well as …

24. Make Meaning Understandings Design Standards • Are inferences students should realize or derive as a result of the work of the unit • Are framed as full sentences in response to the prompt, “The students will understand THAT…” • Help learners make sense of otherwise discrete facts and skills; they “connect the dots” • Cannot be simply transmitted; they must be “earned” by the learner

25. Sample Understandings • The value of a number is quantified by the placement of its digits. • Certain mathematical manipulations preserve the relationship in an expression or equation, even though they change the representation. • The properties of a shape do not change when it is reflected, rotated, or translated. • There are many appropriate units that can be used to measure an object(s), but the precision is dependent on the situation.

26. Make Meaning Essential Questions Design Standards • Encourage active meaning-making by the learner about important ideas and issues • Are open ended; have no simple right answer • Are meant to be investigated, argued, looked at from different points of view • Raise other important questions • Naturally arise in every day life and/or “doing” the subject • Are meant to recur; can be fruitfully asked over time

27. Sample Essential Questions • What rule do I know OR what pattern can I recognize to help me make a prediction/solve this problem? • What patterns do I see in this data set? (Gr. 6-12) Could this be random behavior? • How do I use measurements about the shape to calculate additional information about it? • What value(s) can I use/substitute to make this relationship true?

28. Take a Look at Some Examples to find Out What They Have in Common Understandings Essential Questions Your thoughts… • Your thoughts…

29. How K-12 Impacts Grade and Unit-Level Design