Empowering Learners through the Common Core State Standards Juli K. Dixon, Ph.D. University of Central Florida [email protected]

Empowering Empowering Learners through Learners through the Common Core the Common Core State StandardsState Standards

Juli K. Dixon, Ph.D.Juli K. Dixon, Ph.D.

University of Central University of Central FloridaFlorida

[email protected]@ucf.edu

Solve this…Solve this…

3 ÷ 1/7


3 ÷ 1/7

Tell someone near you how you Tell someone near you how you solved it.solved it.

Perspective…Perspective…

A student said this…A student said this…

When asked to justify the solution to 3 ÷ 1/7




“Just change the division sign to multiplication and flip the fraction after the sign. 3 ÷ 1/7 becomes 3 x 7/1. So I find 3/1 x 7/1 which is 21/1 or 21.”




“Just change the division sign to multiplication and flip the fraction after the sign. 3 ÷ 1/7 becomes 3 x 7/1. So I find 3/1 x 7/1 which is 21/1 or 21.”

Is this an acceptable Is this an acceptable justification?justification?


Another student said Another student said this…this…


“I know there are 7 groups of 1/7 in one whole. Since there are three wholes, I have 3 x 7 or 21 groups of 1/7 in 3 wholes so 3 ÷ 1/7 = 21.”


Another student said Another student said this…this…


“I know there are 7 groups of 1/7 in one whole. Since there are three wholes, I have 3 x 7 or 21 groups of 1/7 in 3 wholes so 3 ÷ 1/7 = 21.”

How is this justification different and How is this justification different and what does it have to do with State what does it have to do with State Standards?Standards?

Background of the Background of the CCSSMCCSSM(Common Core State (Common Core State Standards)Standards)• Published by the National Governor’s Association and the Council of Chief State School Officers in June 2010

• Result of collaboration from 48 states

• Provides a focused curriculum with an emphasis on teaching for depth

Background of the Background of the CCSSMCCSSM

Minnesota adopted the CCSS in ELA/literacy only

45 States + DC have adopted the Common Core State Standards


“… standards must address the problem of a curriculum that is ‘a mile wide and an inch deep.’ These Standards are a substantial answer to that challenge” (CCSS, 2010, p. 3).

CCSSM Content CCSSM Content Standards WordleStandards Wordle

Content StandardsContent Standards

• Critical Areas – much like our big ideas

• Domains – group related clusters

• Clusters – group related standards

• Standards – define what students should know and be able to do


The CCSSM consist of Content Standards and Standards for Mathematical Practice.

“The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students” (CCSS, 2010, p. 6).

NCTM Process Standards:

Making Sense of the Making Sense of the Mathematical Mathematical PracticesPractices

• Problem Solving

• Reasoning and Proof

• Communication

• Representation

• Connections

NRC Strands of Mathematical Proficiency:


• Adaptive Reasoning

• Strategic Competence

• Conceptual Understanding

• Procedural Fluency

• Productive Disposition

Standards for Standards for Mathematical Practice Mathematical Practice WordleWordle

The 8 Standards for Mathematical Practice:


1 Make sense of problems and persevere in solving them

2 Reason abstractly and quantitatively3 Construct viable arguments and critique the

reasoning of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated

reasoning

Number & Operations in Base Ten4.NBTUse place value understanding and properties of operations to perform multi-digit arithmetic

5. Multiply multi-digit numbers using strategies based on place value and the properties of operations. Illustrate and explain the calculations by using equations, rectangular arrays, and/or area models.

Domain

Cluster

Standard

Impact on Depth… Impact on Depth… (CCSS)(CCSS)



What did you do?What did you do?


What do you think fourth grade students would do?

How might they solve 4 x 7 x 25?


Are you observing this sort of mathematics talk in classrooms?

Is this sort of math talk important?


What does this have to do with the Common Core State Standards for Mathematics (CCSSM)?


With which practices were With which practices were the fourth grade students the fourth grade students engaged?engaged?




reasoning


With which practices were With which practices were the fourth grade students the fourth grade students engaged?engaged?




reasoning

What does it mean to use strategies to multiply?

When do students begin to develop these strategies?

Impact on Depth…Impact on Depth…


Operations & Algebraic Thinking3.OAUnderstand properties of multiplication and the relationship between multiplication and division.

5. Apply properties as strategies to multiply and divide…

Multiply and divide within 100.

7. Fluently multiply within 100, using strategies such as the relationship between multiplication and division or properties of operations...


Operations & Algebraic Thinking3.OAUnderstand properties of multiplication and the relationship between multiplication and division.

5. Apply properties as strategies to multiply and divide…

Multiply and divide within 100.

7. Fluently multiply within 100, using strategies such as the relationship between multiplication and division or properties of operations...

Consider 6 x 7Consider 6 x 7



What strategies can we use?What strategies can we use?



What strategies can we use?What strategies can we use?

How might this sort of thinking influence How might this sort of thinking influence the order in which facts are introduced in the order in which facts are introduced in grade 3?grade 3?



With which practice were the With which practice were the third grade students third grade students engaged?engaged?




reasoning


With which practice were the With which practice were the third grade students third grade students engaged?engaged?




reasoning

How do we support How do we support this empowerment?this empowerment?““… … a lack of understanding [of a lack of understanding [of mathematical content] effectively mathematical content] effectively prevents a student from engaging in the prevents a student from engaging in the mathematical practicesmathematical practices”” (CCSS, 2010, p. 8).(CCSS, 2010, p. 8).

When and how do we develop this When and how do we develop this understanding?understanding?

Where do we start?Where do we start?

…….in Kindergarten..in Kindergarten.

Making Sense of Making Sense of Numbers to 20Numbers to 20

How do we help students to How do we help students to truly make sense of truly make sense of number patterns?number patterns?

Making Sense of Making Sense of Numbers to 20Numbers to 20

How do we help students to How do we help students to truly make sense of number truly make sense of number patterns?patterns?

Consider number pairs for 8.Consider number pairs for 8.

K.OA.3:K.OA.3: Decompose numbers less than or equal Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).= 2 + 3 and 5 = 4 + 1).

Describing the Describing the StandardsStandards


Watch the following video of a Kindergarten class as they explore Number Pairs for 8.


Watch the following video of a Kindergarten class as they explore Number Pairs for 8.

Look for how patterns are addressed.


Which practice was of focus Which practice was of focus here?here?




reasoning


Which practice was of focus Which practice was of focus here?here?

Engaging Students in Engaging Students in Reasoning and Sense Reasoning and Sense MakingMaking We need to question students when We need to question students when

they are wrong they are wrong and and when they are right.when they are right. We need to create an environment We need to create an environment

where students are expected to share where students are expected to share their thinking.their thinking.

We need to look for opportunities for We need to look for opportunities for students to reason about and make students to reason about and make sense of mathematics.sense of mathematics.


What is your biggest take away What is your biggest take away regarding the practices and your regarding the practices and your role?role?




reasoning

How do we support How do we support this empowerment?this empowerment? Teachers need content knowledge for Teachers need content knowledge for

teaching mathematics to know the tasks teaching mathematics to know the tasks to provide, the questions to ask, and to provide, the questions to ask, and how to assess for understanding.how to assess for understanding.

Math Talk needs to be supported in the Math Talk needs to be supported in the classroom.classroom.

Social norms need to be established in Social norms need to be established in classroom classroom andand professional professional development settings to address development settings to address misconceptions in respectful ways.misconceptions in respectful ways.

How do we support How do we support this empowerment?this empowerment? What we know best might be the What we know best might be the

most difficult to change.most difficult to change. We need to be aware of the We need to be aware of the

changes so that we can prepare changes so that we can prepare ourselves to meet the needs of our ourselves to meet the needs of our students.students.

Empowering Empowering Learners through Learners through the Common Core the Common Core State StandardsState Standards

Juli K. Dixon, Ph.D.Juli K. Dixon, Ph.D.

University of Central University of Central FloridaFlorida

[email protected]@ucf.edu

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Empowering Learners through the Common Core State Standards Juli K. Dixon, Ph.D. University of Central Florida [email protected]