Juli K. Dixon, Ph.D. University of Central Florida [email protected] Empowering Learners through...

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

University of Central University of Central FloridaFlorida

[email protected]@ucf.edu

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

Grades K-2Grades K-2

A student was asked to A student was asked to solve 48 + 25 and the solve 48 + 25 and the student did this…student did this…

40 + 20 = 60


40 + 20 = 60 8 + 2 = 10


40 + 20 = 60 8 + 2 = 10

60 + 10 = 70


40 + 20 = 60 8 + 2 = 10

60 + 10 = 7070 + 3 = 73

Perspective…Perspective…

We know we want students to explain and justify mathematics in these ways, but how do we get them here?


We know we want students to explain and justify mathematics in these ways, but how do we get them here?

How is this related to the Common Core State Standards (CCSS)?

Background of the Background of the CCSSMCCSSM

• Published by the National Governor’s Association and the Council of Chief State School Officers in June 2010

• Result of collaboration among 48 states

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

• Consists of Content Standards and Standards for Mathematical Practice


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).


“… 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).

So what do these standards look like anyway?

Content Standards Content Standards Wordle for Grades K-2Wordle for Grades K-2

Content StandardsContent Standards

• Define expectations for students at each grade level

• Use concepts from earlier grades

• Emphasize need to justify mathematical moves

• Indicate understanding and skill are equally important

• Include expectations that students demonstrate understanding of procedures


• Critical Areas – describe areas of focus

• Domains – group related clusters

• Clusters – group related standards

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


Measurement and Data K.MDDescribe and compare measurable attributes.

1.Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object.

2.Directly compare two objects with a measurable attribute in common, to see which object has “more of”/“less of” the attribute, and describe the difference. For example, directly compare the heights of two children and describe one child as taller/shorter.

Classify objects and count the number of objects in each category.

3.Classify objects into given categories; count the numbers of objects in each category and sort the categories by count.


Measurement and Data K.MDDescribe and compare measurable attributes.

1.Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object.

2.Directly compare two objects with a measurable attribute in common, to see which object has “more of”/“less of” the attribute, and describe the difference. For example, directly compare the heights of two children and describe one child as taller/shorter.

Classify objects and count the number of objects in each category.

3.Classify objects into given categories; count the numbers of objects in each category and sort the categories by count.

Domain

Cluster

Standard

Standard

Standard

Cluster


“One hallmark of mathematical understanding is the ability to justify, in a way appropriate to the student’s mathematical maturity, why a particular mathematical statement is true or where a mathematical rule comes from” (CCSS, 2010, p. 4).

“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)


The Standards for Mathematical Practice are based on:

Making Sense of the Making Sense of the Mathematical Mathematical PracticesPractices

• The National Council of Teachers of Mathematics’ (NCTM) Principles and Standards for School Mathematics (NCTM, 2000), and

• The National Research Council’s (NRC) Adding It Up (NRC, 2001).

NCTM Process Standards:


• Problem Solving

• Reasoning and Proof

• Communication

• Representation

• Connections

NRC Strands of Mathematical Proficiency:


• Adaptive Reasoning

• Strategic Competence

• Conceptual Understanding

• Procedural Fluency

• Productive Disposition

Standards of Standards of 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


The following represents a recommendation from the Center for the Study of Mathematics Curriculum (CSMC, 2010)


Lead with Mathematical Practices1Implement CCSS beginning with mathematical practices,2Revise current materials and assessments to connect to practices, and3Develop an observational scheme for principals that supports developing mathematical practices.

(CSMC, 2010)


Counting and Cardinality K.CCCompare Numbers.

6. Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, eg., by using matching and counting strategies.

Domain

Cluster

Standard

Solve this…Solve this…


What do you think Kindergarten children will do?


What do you think Kindergarten children will do?

Consider how the student is allowed to struggle through a problem in this kindergarten video.


Are you observing this sort of productive struggle in classrooms?

Is it 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 grade K students the grade K students engaged?engaged?




reasoning

The 8 Standards for Mathematical Practice:1 Make sense of problems and persevere in

solving them2 Reason abstractly and quantitatively3 Construct viable arguments and critique the


reasoning



In an effort to simplify students’ learning pathways and minimize barriers (stigler, et. al., 1999), teachers often provide students with efficient procedures too early.

When we do this – we minimize students’ opportunities to engage in these practices.

Reason abstractly and Reason abstractly and quantitativelyquantitatively

2


Reasoning abstractly and quantitatively Reasoning abstractly and quantitatively often involves making sense of often involves making sense of mathematics in real-world contexts.mathematics in real-world contexts.

Word problems can provide examples of Word problems can provide examples of mathematics in real-world contexts.mathematics in real-world contexts.

This is especially useful when the This is especially useful when the contexts are meaningful to the students.contexts are meaningful to the students.

2


Consider the following problems:Consider the following problems:

Jessica has 8 key chains. Calvin has 9 key Jessica has 8 key chains. Calvin has 9 key chains. How many key chains do they have chains. How many key chains do they have all together?all together?

Jessica has 8 key chains. Alex has 15 key Jessica has 8 key chains. Alex has 15 key chains. How many more key chains does Alex chains. How many more key chains does Alex have than Jessica?have than Jessica?

2



Jessica has 8 key chains. Calvin has 9 key Jessica has 8 key chains. Calvin has 9 key chains. How many key chains do they have chains. How many key chains do they have all together?all together?


Key words seem helpfulKey words seem helpful

2



Jessica has 8 key chains. Calvin has 9 key Jessica has 8 key chains. Calvin has 9 key chains. How many key chains do they have all chains. How many key chains do they have all together?together?


Key words seem helpful, or are they….Key words seem helpful, or are they….

2


Now consider this problem:Now consider this problem:

Jessica has 8 key chains. How many Jessica has 8 key chains. How many more key chains does she need to have more key chains does she need to have 13 key chains all together?13 key chains all together?

2




How would a child who has been How would a child who has been conditioned to use key words solve it?conditioned to use key words solve it?

2




How would a child who has been How would a child who has been conditioned to use key words solve it?conditioned to use key words solve it?

How might a child reason abstractly and How might a child reason abstractly and quantitatively to solve these problems?quantitatively to solve these problems?

2


Consider this problem:Consider this problem:

Jessica has 8 key chains. Calvin has 9 Jessica has 8 key chains. Calvin has 9 key chains. How many key chains do key chains. How many key chains do they have all together?they have all together?

I know that 8 + 8 = 16, so…I know that 8 + 8 = 16, so…

2


Consider this problem:Consider this problem:

Jessica has 8 key chains. Alex has 15 Jessica has 8 key chains. Alex has 15 key chains. How many more key chains key chains. How many more key chains does Alex have than Jessica?does Alex have than Jessica?

I know that 8 + 8 = 16, so…I know that 8 + 8 = 16, so…

2




8 + __ = 138 + __ = 13

(How might making a ten help?)(How might making a ten help?)

2


What happens when this child gets to What happens when this child gets to 22ndnd grade? grade?

2

Consider this Kindergarten class.Consider this Kindergarten class.

With which Standard(s) for Mathematical With which Standard(s) for Mathematical Practice are they engaged?Practice are they engaged?

Empowering Young Empowering Young LearnersLearners

Consider this Kindergarten class.Consider this Kindergarten class.

What did you notice?What did you notice?







reasoning

Use appropriate tools Use appropriate tools strategicallystrategically

This practice supports hands-on learningThis practice supports hands-on learning Tools must include technologyTools must include technology

Tools also include non-technological Tools also include non-technological tools such as manipulatives, number tools such as manipulatives, number lines, and paper and pencillines, and paper and pencil

Mathematically proficient students know Mathematically proficient students know which tool to use for a given task.which tool to use for a given task.

5






reasoning

Construct viable Construct viable arguments and critique arguments and critique the reasoning of othersthe reasoning of others

3

What does this look like in a What does this look like in a grade K-2 class?grade K-2 class?

How can we be intentional about How can we be intentional about providing opportunities for providing opportunities for students to engage in this students to engage in this practice?practice?

Consider this:Consider this:



Was the language you used in talking through the solution “precise”?







reasoning


I heard a student say this…


Attend to precisionAttend to precision


6

Does our math talk sound more like this?

http://video.google.com/videoplay?docid=7106559846794044495






reasoning

How do we support the How do we support the transition to the Common transition to the Common Core?Core? 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.

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

University of Central University of Central FloridaFlorida

[email protected]@ucf.edu

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

Grades K-2Grades K-2

Juli K. Dixon, Ph.D. University of Central Florida [email protected] Empowering Learners through...

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