1. Understanding the Philosophy and Process of Eric Bright 8 th Grade Math Charleston Middle School ericbright2002@yahoo.com for the Common Core Mathematics Standards

2. 1. The Intended Curriculum Common Core Mathematics Content and Practice Standards. This our guidepost or plumb line by which we measure every other aspect of our curriculum in order to bring about proper alignment.

3. 2. The Written Curriculum What is created and/or gathered which we plan to use in the classroom in order to bring about the intended curriculum. This is the giant binder that gets puts together but usually sits on a shelf gathering dust. If it is only a trap for dust bunnies, don’t bother making the binder.

4. 3. The Enacted Curriculum What is actually done in the classroom. Did the binder get used? Were those carefully planned activities and learning opportunities used?

5. 4. The Assessed Curriculum A measure of what is expected of students by the end of instruction. Do we have content mastery? Notice that our assessed curriculum generally lines up most closely with the enacted curriculum without careful planning.

6. 5. The Achieved Curriculum Based on our assessments, what did we actually accomplish? At the end of the day, have we done the job we are hired to do?

7. Why do we need curriculum written by and for teachers? 1. Publisher’s don’t have it right. 2. Too much choice is paralyzing. 3. Teaching is an art, and we are the artists. 4. We need ownership of our curriculum. Caution: Change will not happen overnight.

8. Line up the types of curriculum. The Written Curriculum The Enacted Curriculum The Assessed Curriculum The Intended Curriculum The Achieved Curriculum

9. 1. Common Core Publisher’s Criteria Focus, Coherence, Rigor  Conceptual Understanding, Procedural Fluency, Application 2. Scope and Sequence PARCC Blueprints PARCC Frameworks 3. Unit Maps 4. Lessons 5. Model Curriculum

10.  Focus  Significantly narrowing the scope of content in each grade so that students achieve at higher levels and experience more deeply that which remains. “Teaching less, learning more.” – Common Core Publisher’s Criteria K-8 Common Core Publisher’s Criteria K-8  Teach the standards and the standards only.

11.  Self-Assessment  Is your curriculum focused?  Do you know where you need to focus your personal professional development?

12.  Instructional Implications: Focus  What does it look like to teach a focused curriculum?  What am I already doing to achieve focus?  What changes need to occur in my classroom to gain more focus?  Note: Much of the focus shift can be taken care of by careful curriculum cultivation.

13.  Instructional Implications: Focus  We have to let go of “pet” projects.  Choose your rabbit trails wisely during class.  Enrichment is at grade-level, not above. (K-8 p.13)  Remediation is through grade-level standards, not below. (K-8 p.13)

14.  Assessment Implications: Focus  What does it look like to assess in a focused manner?  What am I already doing to achieve focused assessment?  What changes need to occur in my classroom assessments to gain more focus?

15.  Assessment Implications: Focus  No above grade-level standards are assessed. (K-8 p.10)  Partial credit may be necessary to get a better picture of grade-level standard mastery.  Extra credit should probably not exist.

16.  Coherence - Common Core Publisher’s Criteria K-8Common Core Publisher’s Criteria K-8  Coherence is about making math make sense. Mathematics is not a list of disconnected tricks or mnemonics.  Vertical: It is critical to think across grades and examine the progressions in the standards to see how major content develops over time. ▪ Ex. Solving Proportions  Horizontal: Connections at a single grade level can be used to improve focus, by closely linking secondary topics to the major work of the grade. For example, in grade 3, bar graphs are not “just another topic to cover.” Rather, the standard about bar graphs asks students to use information presented in bar graphs to solve word problems using the four operations of arithmetic.

17.  Self-Assessment  Is your curriculum coherent?  Do you know where you need to focus your personal professional development?

18.  Instructional Implications: Coherence  What does it look like to teach a coherent curriculum?  What am I already doing to achieve coherence?  What changes need to occur in my classroom to gain more coherence?  Note: Much of the coherence shift can be taken care of by careful curriculum cultivation.

19.  Instructional Implications: Coherence  Problems (not exercises) make connections wherever possible within grade-level rather than teaching in isolation. (K-8 p.13, 6b)  Relate grade-level concepts explicitly to prior knowledge. (K-8 p.13, 5c)  No microstandards. (K-8 p.5)

20.  Assessment Implications: Coherence  What does it look like to assess in a coherent manner?  What am I already doing to achieve coherent assessment?  What changes need to occur in my classroom assessments to gain more coherence?

21.  Assessment Implications: Coherence  Nothing assessed for mastery out of grade-level content.  Interleaving builds coherence.

22.  Rigor - Common Core Publisher’s Criteria K-8Common Core Publisher’s Criteria K-8  To help students meet the expectations of the Standards, educators will need to pursue, with equal intensity, three aspects of rigor in the major work of each grade: ▪ (1) conceptual understanding, ▪ (2) procedural skill and fluency, and ▪ (3) applications.

23.  Rigor: Conceptual Understanding  Materials amply feature high-quality conceptual problems and questions. This includes ▪ brief conceptual problems with low computational difficulty (e.g., ‘Find a number greater than 1/5 and less than 1/4’); ▪ brief conceptual questions (e.g., ‘If the divisor does not change and the dividend increases, what happens to the quotient?’); ▪ and problems that involve identifying correspondences across different mathematical representations of quantitative relationships.

24.  Rigor: Procedural Skill and Fluency  Manipulatives and concrete representations such as diagrams that enhance conceptual understanding are connected to the written and symbolic methods to which they refer (see, e.g., 1.NBT).  As well, purely procedural problems and exercises are present. These include cases in which opportunistic strategies are valuable—e.g., the sum 698 + 240 or the system x + y = 1, 2x + 2y = 3—as well as an ample number of generic cases so that students can learn and practice efficient algorithms (e.g., the sum 8767 + 2286).  Methods and algorithms are general and based on principles of mathematics, not mnemonics or tricks. ▪ Ex: FOIL

25.  Rigor: Applications  Materials in grades K–8 include an ample number of single-step and multi-step contextual problems that develop the mathematics of the grade, afford opportunities for practice, and engage students in problem solving.  Materials for grades 6–8 also include problems in which students must make their own assumptions or simplifications in order to model a situation mathematically.  Applications take the form of problems to be worked on individually as well as classroom activities centered on application scenarios.  Problems and activities are grade-level appropriate, with a sensible tradeoff between the sophistication of the problem and the difficulty or newness of the content knowledge the student is expected to bring to bear.

26.  Additional Rigor from Publisher’s Criteria  (1) The three aspects of rigor are not always separate in materials. (Conceptual understanding and fluency go hand in hand; fluency can be practiced in the context of applications; and brief applications can build conceptual understanding.)  (2) Nor are the three aspects of rigor always together in materials. (Fluency requires dedicated practice to that end. Rich applications cannot always be shoehorned into the mathematical topic of the day. And conceptual understanding will not always come along for free unless explicitly taught.)  Rigor: Applications from ISBE  Application can come in two forms: ▪ Mathematics applied to the real-world ▪ Mathematics applied to mathematics

27.  Self-Assessment  Is your curriculum rigorous?  Do you know where you need to focus your personal professional development?

28.  Instructional Implications: Rigor  What does it look like to teach a rigorous curriculum?  What am I already doing to achieve rigor?  What changes need to occur in my classroom to gain more rigor?

29.  Instructional Implications: Rigor  Balance CPA in classroom instruction and homework.  Utilize both problems and exercises.  Students must make their own assumptions or simplifications in order to model a situation mathematically. (K-8 p.12)  Explicitly teach and use math vocab. (K-8, p.16)  Take advantage of cognitive disfluency or “desirable difficulties”.

30.  Assessment Implications: Rigor  What does it look like to assess in a rigorous manner?  What am I already doing to achieve rigorous assessment?  What changes need to occur in my classroom assessments to gain more rigor?

31.  Assessment Implications: Rigor  Formal observational formative assessments may be needed.  Summative assessments need a balance of CPA questions. (Asking students to find the error for example.)  Assessing conceptual knowledge may take discussion and/or writing.

32.  Resources for Focus:  Common Core Standards for Mathematics Appendix A Common Core Standards for Mathematics Appendix A  PARCC Model Content Frameworks PARCC Model Content Frameworks  PARCC Blueprints PARCC Blueprints  PARCC Prototype Items PARCC Prototype Items ▪ Dana Center – CCSS Toolbox Dana Center – CCSS Toolbox ▪ Illustrative Mathematics Illustrative Mathematics ▪ MARS Tasks MARS Tasks  ISBE Model Math Curriculum ISBE Model Math Curriculum

33.  Focus: Traditional or Integrated?  What has your district decided and why?  What does ISBE think?  What are the implications of the pathway you choose? ▪ Traditional is not the same thing. ▪ How will colleges accept integrated coursework? ▪ What about Illinois law and high school course codes for the state?  What questions do you have?

34.  Additional Resources for Coherence:  Progressions Documents Progressions Documents  Bill McCallum’s Blog Bill McCallum’s Blog  Additional Resources for Rigor:  Common Core Standards Publisher’s Criteria Common Core Standards Publisher’s Criteria  CPA Documents by Jennie Winters, Lake County ROE

35.  PARCC Model Content Frameworks PARCC Model Content Frameworks  70/20/10  PARCC Blueprints PARCC Blueprints  MYA vs. EOY

36.  How big should a unit be?  Will each unit have a summative assessment?  Should units stretch across grading periods (quarters or semesters)?  Try making two versions of the scope and sequence: one assuming no time constraints and the other keeping quarters in mind. Are they very different?

37.  What order should the units go in so they build on one another?  What order should the units go in so they are complete in time for the MYA and EOY?  How should time frames be listed? By weeks? By quarters?

38.  Let’s look at a sample scope and sequence!  What are the benefits of this layout?  What impedes its use?  How would you modify it?

39.  Focus  Content standards, essential questions, vocab, practice standards  Coherence  Prior, current, and coming next  Remediation and enrichment  Rigor  Learning targets

40.  Assessments  Formative ▪ Prior knowledge ▪ Pre-test for growth ▪ In-progress checks ▪ Observation checklists ▪ Self-assessments  Summative ▪ Post-test for growth ▪ Common assessments ▪ 40-day plan?

41.  Instructional Resources  Order of lessons ▪ Lessons are multi-day experiences  Resources to help with the lessons ▪ Power Points / Smart Notebooks ▪ Learning tasks ▪ Effective instructional strategies ▪ Independent practice

42.  Let’s create a unit map!  What are the benefits of this layout?  What impedes its use?  How would you change this document?

43.  Multi-Day Experience  Lesson Formats  Whole group, small group, individual  Modeled, guided, collaborative, assessment  Modalities  Concrete, picture/graph, table, symbolic, language, real-life

44.  Let’s look at a sample lesson format!  What are the benefits of this layout?  What impedes its use?  How would you modify it?

45.  ISBE Model Curriculum ISBE Model Curriculum  Engage New York Engage New York  Georgia Georgia  Dana Center Dana Center

46.  What do you need to do next?  What did you learn this evening?  What do you still have questions about?

47. Understanding the Philosophy and Process of Eric Bright ericbright2002@yahoo.com for the Common Core Mathematics Standards If you would like a copy of this presentation or would like to have me work with your district or staff, please email me!