Common Core MathematicsMyths & Shifts

Michelle Dupree, SDMA Instructional Math Coach

Kid President

Defining My Role

I am NOT…

an administrator an evaluator the keeper of all

knowledge

I am…

a resource a colleague a co-planner a co-teacher a collaborator a sounding board an advocate

explain the “gist of” the history of the Common

Core. decipher standards from curriculum. communicate my understanding of the three MAJOR

shifts of the Common Core. explain the relationship between: the Common Core

State Standards, classroom instruction, the Focus Documents, Webb’s Cognitive Rigor Matrix, and the Smarter Balanced Assessment.

access key resources for guiding my instruction.

Goals - I can…

Myth #1The Common Core Initiative began

with the Federal Government.

The Common Core State Standards Initiative

(CCSSI) was a state-led effort coordinated by the:

National Governors Association (NGA) Council of Chief State School Officers (CCSSO)

Governors and state commissioners of education from 48 states, 2 territories and the District of Columbia committed to developing common core state standards for K-12 English-language arts (ELA) and mathematics.

Facts:

The Common Core State Standards equate to a

national curriculum for our schools.

Myth #2

The Common Core is NOT a curriculum.

It is a clear set of shared goals and expectations for what knowledge and skills will help our students succeed.

Local teachers, principals, superintendents, etc. will decide how the standards are to be met.

Teachers will continue to devise lesson plans and tailor instruction to the needs of the students in their classrooms.

Facts:

The standards are not based on research or evidence.

Myth #3

In mathematics, the standards draw on

conclusions from the Trends in International Mathematics and Science Study (TIMSS) as well as other studies of high-performing countries.

These studies called for mathematics in the United States to become substantially more coherent and focused in order to improve student achievement.

Facts:

The Common Core State Standards call for teachers to remain in lock-step with co-workers at the same grade level in their building, or

across the district.

Myth #4

We do not have to teach our students in the same

exact way, but we should all be striving for the same results.

The CCSS do not require fidelity to a specific resource or for teachers to deliver the same lesson in exactly the same way, or on the same day.

We do need a commitment to: professional collaboration a common scope and sequence common assessments

Facts:

Promises

These Standards are not intended to be new names for old ways of doing business. They are a call to take the next step. It is time for states to work together to build on lessons learned from two decades of standards based reforms. It is time to recognize that these standards are not just promises to our children, but promises we intend to keep.

-CCSS (2010 pg. 5)

Close Reading – CCSS “Promise Statement”

Think of each standard as a promise we make to our students.

What does this mean to you? Your students? School? Our District? Families? Co-workers? Etc.

Write one idea on a sticky note & be prepared to share.

Promises Activity

Shift #1 - Focus

FOCUS strongly where the standards focus. Gone are the days of implementing mathematics with the

“mile wide and inch deep” philosophy.

The Common Core calls for greater focus on fewer topics. Math teachers should significantly narrow & deepen the way time

and energy are spent in the classroom. Focus deeply only on what is emphasized in the standards, so

that students gain strong foundations. The goal is that students will be ale to apply the math they know

to new situations inside and outside of the classroom.

Fidelity to a resource no longer out-weighs fidelity to the standards, and/or the needs of our students.

Shift #1 - Focus

CCSSM does not spiral, it is a foundational model.

The standards are constructed so that each year, teachers support students in deepening their understanding so that students gain strong foundations.

Future teachers will support students in building upon that knowledge the following year.

Teachers that skip standards that they “feel” are not important create gaps, which need to be filled in future years, as the foundation was not established.

This model lends itself to the importance of teachers knowing what comes before them, and what comes after them.

Teachers should not have to “undo” previous learning in order to teach the work of their grade level.

FocusCritical Understandings

CCSSM

CCSSM Grade 1 Introduction

In Grade 1, instructional time should focus on four critical areas: (1) developing understanding of addition, subtraction, and strategies for addition and subtraction within 20; (2) developing understanding of whole number relationships and place value, including grouping in tens and ones; (3) developing understanding of linear measurement and measuring lengths as iterating length units; and (4) reasoning about attributes of, and composing and decomposing geometric shapes.

FocusStandards For Mathematical

Practice

FocusStandards For Mathematical

Practice

Pra

ctices

Mathematical Practices (2-3)

Traditional U.S. Approach

Common Core

Think across grades, and link to major topics within

grades.

Carefully connect the learning within and across grades so that students can build new understanding onto foundations built in previous years.

Begin to count on solid conceptual understanding of core content and build upon it. Each standard is not a new event, but an extension of previous learning.

Shift #2 - Coherence

“The coherence and sequential nature of mathematics dictate the foundational skills that are necessary for the learning of algebra. The most important foundational skill not presently developed appears to be proficiency with fractions (including decimals, percents, and negative fractions). The teaching of fractions must be acknowledged as critically important and improved before an increase in student achievement in algebra can be expected.”

Final Report of the National Mathematics Advisory Panel (2008, p. 18)

Coherence ExampleProgression Across Grades

Study the progression from grade 1 – 5. Make notes of your thinking in the section

labeled: We notice…

Use corestandards.org - decide which Kindergarten standard(s) would be foundational for this progression and write it/them above the 1st grade standards.

Gallery Walk Be ready to share & justify your thinking.

Coherence Activity(Progressions)

1.G.3 Partition circles and rectangles into two and four equal

shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.

2.G.3 Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.

CoherenceAcross Grades – Fractions

(Geometry Domain)

3.NF.A.3.D Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

4.NF.2 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >,=, or <, and justify the conclusions, e.g., by using a visual fraction model.

5.NF.A2 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.

The standards make explicit connections at a single grade.

Coherence ExampleGrade 3

Draft K–6 Progression on Geometry Draft K–5 Progression on Measurement and Da

ta (measurement part) Draft K–5 progression on Measurement and Da

ta (data part) Draft K–5 Progression on Number and Operatio

ns in Base Ten Draft K–5 Progression on Counting and Cardin

ality and Operations and Algebraic Thinking Draft 3–5 progression on Number and Operati

ons—Fractions

Progression Documents

Pursue conceptual understanding, procedural skills

and fluency, and application with equal intensity.

The CCSSM require a balance of: solid conceptual understanding. procedural skill and fluency. application of skills in problem solving.

This requires equal intensity in time, activities, and resources in pursuit of all three.

Shift #3 - Rigor

Teach more than “how to get the right answer”

and instead support students’ ability to access concepts from a number of perspectives.

Students are able to see math as more than a set of mnemonics or discrete procedures.

Conceptual understanding supports the other aspects of rigor (fluency and application).

Solid Conceptual Understanding

Traditional/CCSSM

Molly has a quarter, 2 nickels, and a dime. How much money does she have?

Find two equivalent fractions for ½.

Molly has 6 coins in her piggy bank. She has more than .85¢, but less than $1.10. What coins could she have? Explain your answer.

Build a fraction model. Fold a piece of paper in half. Color one half yellow. Write ½. Fold the paper in half again. Write 1/2=2/4. Continue until you get to 8/16. Look for and explain patterns that name the yellow area of the paper.

Procedural Skill & Fluency

The standards require speed and accuracy in calculation.

Teachers structure class time and/or homework time for students to practice core functions such as single-digit multiplication so that they are more able to understand and manipulate more complex concepts.

Required Fluencies in K-6

Students can use appropriate concepts and procedures for

application even when not prompted to do so.

Provide opportunities at all grade levels for students to apply math concepts in “real world” situations, recognizing this means different things in K-5, 6-8, and HS.

Teachers should present tasks that: include multiple entry points.

are open-ended/have multiple solutions.

Application

Kindergarten

At the zoo I saw 8 animal legs. Who might they belong to? Show your thinking.

I had 6 buttons. Some were green. Some were purple. How many were green? How many were purple? Record as many different solutions as you can.

First Grade Lia’s dad baked 8 pies. Some were apple and some were

cherry. How many were apple? How many were cherry? Show as many different solutions as you can.

A teacher turned over 3 dot cards and counted 20 dots. The first card had 8 dots. How many dots did the other two cards have? Show as many different solutions as you can.

Examples (K-1)http://www.k-5mathteachingresources.com

Second Grade

The difference between two numbers is 7. What might the two numbers be? Show as many different solutions as you can.

Peter wants to find the sum of 6+7 in his head. Explain how he could use a doubles fact to do this. Show some other problems where you could use this strategy.

Third Grade A teacher has 24 students in her class. She wants to place the

students into groups with an equal number in each group. How many different ways can the teacher group the students?

There are 16 apples to be put into bowls. Each bowl must have the same number of apples. How many different ways can the apples be put into bowls?

Examples (2-3)

Fourth Grade

__ x 3 = ___ What factor can you use in this equation to make a product that is even and between 20 and 50? Show all possible solutions . Explain your strategy.

I added two prime numbers together and got a sum that is less than 15. What might the two numbers be? Show all possible solutions.

Fifth Grade I wrote an equation using parentheses and all four operations

with an answer of 25. What might the equation have been? Show 5 possible solutions for each statement: a) the sum of

2 decimals is less than 1b) the sum of 2 decimals is equal to 1c) the sum of 2 decimals is greater than 1

Examples (4-5)

Write two character names, two settings, two

numbers.

Place them in the appropriate container.

Ex: Character – Superman Setting –up an elephant’s nose

Two Numbers – 17, 8

There was a tragic accident at the zoo. Some visitors got sniffed up into an elephant’s nose! The Zookeeper called for Superman’s help. If Superman can rescue 4 people each time he flies into the elephant’s nose, how many trips will he have to make in order to save all 17 people? Model your thinking.

Student Involvement Math Task Writing

The Coming CCSS Assessments Will Focus Strongly on the Major Work of

Each Grade

A quality assessment should strive to reinforce focus and coherence at each grade level by testing for proficiency with central and pivotal mathematics rather than covering too many ideas superficially – a key point of the Common Core Standards.

A Common Core Classroom…

does NOT look like this -

A Common Core Classroom…

looks like this -

Michelle’s Top 10 CCSSM Lesson Look-

Fors:1. Interactive Student Discourse

2. Interactive Student Discourse

3. Interactive Student Discourse

4. Interactive Student Discourse

5. Interactive Student Discourse

6. Interactive Student Discourse

7. Need I continue???

Questions That Lead to Rich Discourse:

1. What do you think?

2. Why do you think that?

3. How do you know this?

4. Can you tell me/us more?

5. What questions do you still have?

I used to think…

Now I think…

Individual Reflection

explain the “gist of” the history of the Common

Core. decipher standards from curriculum. communicate my understanding of the three MAJOR

shifts of the Common Core. explain the relationship between: the Common Core

State Standards, classroom instruction, the Focus Documents, Webb’s Cognitive Rigor Matrix, and the Smarter Balanced Assessment.

access key resources for guiding my instruction.

Revisit - I can…

www.achievethecore.org (green Focus pgs) www.corestandards.org (anything CC) http://www.curtiscenter.math.ucla.edu/ http://commoncoretools.me/category/progressions/

(progression docs & more) http://www.nciea.org/publications/cognitiverigorpaper_KH11.pdf

(Webb) www.k-5mathteachingresources.com

(sneak peek-journals) http://www.schoolimprovement.com/common-core-what-it-is-and-isn

t/ (great article on CC shifts)

AWSA New Math Standards – Steven Leinwand https://www.engageny.org/ (resource supplemental/main) Jordan School District, Utah (Practice Posters)

Sources/Resources