Writing CurriculumUnderstanding the Philosophy and Process of

Eric Bright8th Grade MathCharleston Middle Schoolericbright2002@yahoo.com

for the Common Core Mathematics Standards

Types of Curriculum

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.

Types of Curriculum

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.

Types of Curriculum

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?

Types of Curriculum

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.

Types of Curriculum

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?

Teacher-Written Curriculum

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.

How Do We Write Curriculum?

Line up the types of curriculum.

The Written CurriculumThe Enacted

CurriculumThe Assessed Curriculum T

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The Achieved Curriculum

The Agenda for Writing Curriculum

1. Common Core Publisher’s Criteria• Focus, Coherence, Rigor

Conceptual Understanding, Procedural Fluency, Application

2. Scope and Sequence• PARCC Blueprints• PARCC Frameworks

3. Unit Maps4. Lessons5. Model Curriculum

1. Publisher’s Criteria

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

Teach the standards and the standards only.

1. Publisher’s Criteria

Self-Assessment Is your curriculum focused?

Do you know where you need to focus your personal professional development?

1. Publisher’s Criteria

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.

1. Publisher’s Criteria

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)

1. Publisher’s Criteria

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?

1. Publisher’s Criteria

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.

1. Publisher’s Criteria

Coherence - Common 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.

1. Publisher’s Criteria

Self-Assessment Is your curriculum coherent?

Do you know where you need to focus your personal professional development?

1. Publisher’s Criteria

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.

1. Publisher’s Criteria

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)

1. Publisher’s Criteria

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?

1. Publisher’s Criteria

Assessment Implications: Coherence Nothing assessed for mastery out of

grade-level content. Interleaving builds coherence.

1. Publisher’s Criteria

Rigor - Common 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.

1. Publisher’s Criteria

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.

1. Publisher’s Criteria

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

1. Publisher’s Criteria

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.

1. Publisher’s Criteria

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

1. Publisher’s Criteria

Self-Assessment Is your curriculum rigorous?

Do you know where you need to focus your personal professional development?

1. Publisher’s Criteria

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?

1. Publisher’s Criteria

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”.

1. Publisher’s Criteria

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?

1. Publisher’s Criteria

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.

1. Publisher’s Criteria

Resources for Focus: Common Core Standards for Mathematic

s Appendix A PARCC Model Content Frameworks PARCC Blueprints PARCC Prototype Items▪ Dana Center – CCSS Toolbox▪ Illustrative Mathematics▪ MARS Tasks

ISBE Model Math Curriculum

1. Publisher’s Criteria

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?

1. Publisher’s Criteria

Additional Resources for Coherence: Progressions Documents Bill McCallum’s Blog

Additional Resources for Rigor: Common Core Standards Publisher’s Crit

eria CPA Documents by Jennie Winters, Lake

County ROE

2. Scope and Sequence

PARCC Model Content Frameworks 70/20/10

PARCC Blueprints MYA vs. EOY

2. Scope and Sequence

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?

2. Scope and Sequence

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?

2. Scope and Sequence

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?

3. Unit Maps

Focus Content standards, essential questions,

vocab, practice standards Coherence

Prior, current, and coming next Remediation and enrichment

Rigor Learning targets

3. Unit Maps

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?

3. Unit Maps

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

3. Unit Maps

Let’s create a unit map!

What are the benefits of this layout? What impedes its use? How would you change this

document?

4. Lessons

Multi-Day Experience Lesson Formats

Whole group, small group, individual Modeled, guided, collaborative,

assessment Modalities

Concrete, picture/graph, table, symbolic, language, real-life

4. Lessons

Let’s look at a sample lesson format!

What are the benefits of this layout? What impedes its use? How would you modify it?

5. Other Model Curriculum

ISBE Model Curriculum Engage New York Georgia Dana Center

Develop a Plan

What do you need to do next?

What did you learn this evening?

What do you still have questions about?

Writing CurriculumUnderstanding the Philosophy and Process of

Eric Brightericbright2002@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!