UCDMP Saturday Series 2013-14

The Vision of the Common Core:Changing Beliefs,

Transforming Practice

Kindergarten – 6th GradeSaturday, September 21, 2013

Introductions and OverviewProblem Solving: Jim and Jesse’s MoneyReview of SMP’sAssessment of and for LearningLunchPlanning a Common Core Unit and LessonStandards Analysis and Resource

EvaluationSharing and Reflections

Agenda

Wireless AccessGo to Moobilenet

Sign in information Email address: ucdmp@wireless.com Password: wireless

IntroductionsThe StaffPam Hutchison, Director, UCDMPAndrea Williams, UCDMP Teacher Leader

and 4th grade teacher, FSUSDDiana Zaragoza, UCDMP Teacher Leader

and District Math Coach, DJUSDRenee Yeasted, UCDMP Teacher Leader

and Content Area Specialist, VUSD

Overview of SaturdaysNovember 2, 2013Assessment of and for learningFormative assessmentsAssessing students’ ability to

Explain their reasoning, Construct viable arguments and Critique the reasoning of others.

The use of gamesPlanning for the CCSS-M

Overview of SaturdaysJanuary 25, 2014The use of mathematical tasks

As an instructional tool, As an assessment tool for

Problem solving Explanations

Connecting to prior knowledgeDeveloping a deep understandingPlanning for the CCSS-M

Overview of SaturdaysMarch 15, 2014Developing and using rubrics to assess

understanding, communication, and problem solving General rubrics, Task specific rubricsCCSS rubrics

K-2 “Construct viable arguments and critique the reasoning of others”

3-5 Using technology to learn mathPlanning for the CCSS-M

Overview of SaturdaysMay 3, 2014Summative AssessmentsPerformance tasksModel with MathematicsK-2 Using technology to learn math3-5 “Construct viable arguments and

critique the reasoning of others”Planning for the CCSS-M

UnitsAvailable for purchaseAttend 3 sessions

2 quarter units

Attend all 5 sessions 3 quarter units

Online CourseConstructive Classroom Conversations:

Mastering the Language of the Common Core State Standards

Standford OnlineOctober 21 – Dec 9

Andrea and Diana’s Money

Andrea and Diana each had the same

amount of money. Andrea spent $58

to fill the car up with gas for a road-

trip. Diana spent $37 buying snacks

for the trip. Afterward, Andrea had 1/4

as much money as Diana had. How

much money did each have at first?

The CCSS in Mathematics have two sections:Standards for Mathematical CONTENT

and Standards for Mathematical PRACTICE

The Standards for Mathematical Content are what students should understand, know, and be able to apply.

The Standards for Mathematical Practice are what students should do. Mathematical “Habits of Mind”

CCSS Mathematical PracticesO

VER

AR

CH

ING

HA

BIT

S O

F M

IND

1.M

ake

sens

e of

pro

blem

s an

d pe

rsev

ere

in

solvi

ng th

em6.

Atte

nd to

pre

cisio

nREASONING AND EXPLAINING2. Reason abstractly and quantitatively3. Construct viable arguments and critique the

reasoning of others

MODELING AND USING TOOLS4. Model with mathematics5. Use appropriate tools strategically

SEEING STRUCTURE AND GENERALIZING7. Look for and make use of structure8. Look for and express regularity in repeated

reasoning

Proficiency MatrixStandards for Mathematical Practice InitialIntermediateAdvanced

PS, QW, GE, etc. Student engagement strategies

Self-EvaluationWhere are you on this matrix?

What SMP’s are you already overtly fostering in students?

Are you getting them to the initial, intermediate, or advanced stage?

What SMP’s do you really not address at this point?

Make a PlanPick 1 to 2 SMP’s that you want to focus on in the next month or so.What are you going to do to support

students in developing those standards?Where are you (as the teacher) starting

from?What can you do to help “move” students

to the next stage on the matrix?

ShareShare your plan at your table.

What are your strategies and ideas?What are your concerns?

AssessmentsWhat are various ways in which we

assess:

what students know?

what students understand?

Assessment and Learning

“Assessment should be an integral

part of teaching. It is the mechanism

whereby teachers can learn how

students think about mathematics as

well as what students are able to

accomplish.”

Assessment and Learning

“Assessment should allow all

students to show what they know,

understand and can do.”

(Cockcroft Report 1982)

Assessment and Learning

“Assessment for learning is one of

the most powerful ways of improving

learning and raising standards“

(Black and Wiliam 1998)

AssessmentWhat are characteristics of “good”

assessment?

According to the Shell Centre, high quality assessment has:Curriculum balanceCurriculum valueFitness for purpose

Formative Assessments

Assessment for learning

Occurs continuously in classroom both within and between lessons

Used to adjust teaching strategiesProvides students with useful and

meaningful feedback

Formative Assessments

Focus: To determine what learning comes next

Examples: Feedback Open questioning Exit tickets Observations Discussions Ungraded classwork/homeworks

Summative Assessments

Assessment of learning

Occur within, between, and among instructional units

Used to identify strengths and gaps in curriculum and instruction Curriculum may be refined Teachers may modify instruction

Summative Assessments

Focus: To determine:how student groups are progressinghow well program is working

Examples Graded class work or homework Quizzes End of unit tests Midterms District benchmarks

Large Scale Assessments

Assessment of learning

Frequently high stakesExamine trends over timeUsed to develop long-term evaluation of

curriculum and programsUsed to monitor school site, district and

state progress

Large Scale Assessments

Focus: To determine how schools, districts and states are progressing over time

Examples: End of course exams CST NAEP SAT/ACT Exams AP Exams

AssessmentThink of how and when you assess your

students.

Which ones are assessments for learning?

Which ones are assessments of learning?

Assessment“What a difference a word makes”

Read the articleRecord1 thing with which you agree1 thing with which you might argue1 thing to which you aspire1 Aha!

SharingGo around the group and share one of the following:the thing with which you agreethe thing with which you might arguethe thing to which you aspireyour Aha!

Pick one thing from your group to share with the whole group

Large Scale Assessment

WYTIWYG!

Large Scale Assessment

What you test is what you get!

Goals of Assessment

“We must ensure that tests measure

what is of value, not just what is easy

to test. If we want students to

investigate, explore, and discover,

assessment must not measure just

mimicry mathematics.”

Everybody Counts

PARCC States

PARCC States

CCSS-M SMARTER Claims

Claim #1: Concepts and Procedures “Students can explain and apply mathematical concepts and interpret and carry out mathematical procedures with precision and fluency.”

CCSS-M SMARTER Claims

Claim #2: Problem Solving “Students can solve a range of complex well-posed problems in pure and applied mathematics, making productive use of knowledge and problem solving strategies.”

CCSS-M SMARTER Claims

Claim #3: Communicating Reasoning

“Students can clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others.”

CCSS-M SMARTER Claims

Claim #4: Modeling and Data Analysis

“Students can analyze complex, real-world scenarios and can construct and use mathematical models to interpret and solve problems.”

Score Reporting-Individual

“Total Mathematics” score The composite mathematics score

will need to have scaling properties that allow for the valid determination of student growth over time. This score will be a weighted composite from the four claims

Claim #1: 40%Claims #2-4: about 20% each.

Smarter Balanced Assessment Consortium

Problem TypesSR – selected-response itemCR – constructed-response itemER – extended-response itemTE – technology-enhanced itemPT – performance task

CCSS-M SMARTER Claims

Claim #1: Concepts and Procedures “Students can explain and apply mathematical concepts and interpret and carry out mathematical procedures with precision and fluency.”

Claim 1Selected ResponseTypical Multiple ChoiceSelected Response

Constructed ResponseExtended ResponseTechnology Enhanced

Assessment Items Group 1

Claim 1 – Selected ResponseTypical Multiple Choice

Answer the problems.

Assessment Items Group 1

Claim 1 – Selected ResponseTypical Multiple Choice

How are these problems similar and/or different from the typical CST questions?

Assessment Items Group 2

Claim 1 – Selected ResponseSelected Response

Answer the problems.

Assessment Items Group 2

Claim 1 – Selected Response

How are these problems different from the typical CST questions?

What do students have to know and/or understand to do these problems that they don’t have know/understand to do a typical multiple choice question.

5th Grade Multiplication Models

Smarter Balanced Assessment Consortium

Problem TypesSR – selected-response itemCR – constructed-response itemER – extended-response itemTE – technology-enhanced itemPT – performance task

3rd Grade – CR

4th Grade – CR

5th Grade – CR

6th Grade – CR

Rubric Scoring

3rd Grade – ER

5th Grade – ER

4th Grade – TE

6th Grade – TE

6th Grade – TE, cont.

Claim 1“Students can explain and apply mathematical concepts and interpret and carry out mathematical procedures with precision and fluency.”

So what are the classroom implications if we are assessing students in these ways?

Multiple Representations

Look at the standards for your grade level.

Which standards clearly imply that students need to be familiar with a variety of models, representations, and/or strategies?

Unit Planning

Unit PlanningUnit Planning TemplateUnit Planning Questions

2nd Grade

Unit Planning Questions

Topic: What is the big idea that you will be

addressing in this unit?

Unit Planning Questions

Content Standards: Which common core standards (or parts of

standards) will be addressed in this unit?

Use place value understanding and properties of operations to add and subtract.5. Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

6. Add up to four two-digit numbers using strategies based on place value and properties of operations.

7. Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.

7.1 Use estimation strategies to make reasonable estimates in problem solving. CA

8. Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900. 9. Explain why addition and subtraction strategies work, using place value and the properties of operations.3

3 Explanations may be supported by drawings or objects.

Unit Planning Questions

Practice Standards: What standards for mathematical practice

(1-2) do I want to focus on and promote during this unit?

Unit Planning Questions

What should students already know?What have students learned in previous

grades?How does what they should already know

connect to what they are going to learn?Where does this unit fall on the continuum

of “Concrete – Representational – Abstract”

Unit Planning Questions

What will students learn and how will I know what they have learned?What should students understand by the

end of the unit? What are some ideas for assessing student understanding?

Unit Planning Questions

What will students learn and how will I know what they have learned?What should students know and be able to

do by the end of the unit? What are some ideas for assessing procedural skills?

Unit Planning Questions

What will students learn and how will I know what they have learned?How should students be able to

demonstrate their ability to apply what they have learned by the end of the unit? What are some possible assessment ideas and/or tasks?

Unit Planning Questions

What will students learn and how will I know what they have learned?Key Vocabulary

Unit Planning Questions

What tools, models, and materials are necessary to fully address the standards for this unit?

Unit Planning Questions

Anticipated Number of DaysApproximately how many days do I

anticipate needing for this unit (including all assessments)?

How many days are needed for lessons related to: Conceptual understanding Procedures and skills Applications and problem solving

Unit Planning Questions

Sketch of Unit by Days (Overview)Brief description of big ideas for each day

Lesson Planning Questions

Topic: What is the topic of the lesson?

Lesson Day: Where is this lesson in the overall plan of the unit?

Lesson Planning Questions

OVERVIEW

Content Standard(s): What part of the standard(s) is being addressed today? This should be a brief statement or goal.

Practice Standard(s): What practice standard will I be focusing on today?

Lesson Planning Questions

Type of Lesson:Concept LessonProcedure or Skill LessonApplication or Problem Solving LessonReview Lesson Key Vocabulary: What vocabulary needs to be introduced or reviewed today? How and when will that take place?

Lesson Planning Questions

Materials Needed: What materials are needed for this lesson? Materials include (but are not limited to): textbook resources, supplemental student activity pages or worksheets, manipulatives, rulers, protractors, strategies, models, technology,…

Lesson Planning Questions

How and when will I support students in connecting to prior knowledge? What prior knowledge does this lesson build on and extend? It could be from the prior day or earlier in the year or the previous year.

How and when will I deal with homework?

Lesson Planning Questions

Opening prompt or problem: Leads in and connects to the topic of the day

Lesson Planning Questions

Lesson Part 1, 2, 3,…: Description of what happens in each part of the lesson. What am I doing? What are students doing? What specific problems or activities are

involved? What are some key questions that I want

to ask?What materials are needed for this part?

Lesson Planning Questions

Closure: What prompt can I use to help students review what they have learned? How will I know what they have learned?

CollaborationLesson planning is easier and more efficient when done with teams of teachersShare strategiesShare workload (if need to create, copy or

collect materials)Share struggles and successesReflect and revise

ResourcesIllustrative Mathematics Websitehttp://illustrativemathematics.org A work in progressDesigned to provide examples that help to

clarify what each CCSS means

ResourcesInside Mathematics Websitehttp://www.insidemathematics.org Resources on SMP’s, including: Classroom video examples illustrating the

math practice standards, including commentary

Videos of exemplary lessons integrating multiple math practices

ResourcesInside Mathematics WebsiteNew resources on SMC’s, including:- Common Core-aligned tasks, searchable

either by grade level or by Common Core content area, such as “Operations and Algebraic Thinking,” or “Geometry - Congruence.” 

ResourcesInside Mathematics WebsiteAdditional classroom videos of

Number Talks- Four new classroom videos of “

Number Talks” showing students engaged in mental math exercises and conversations about math, including one from a bilingual Spanish-English classroom.

ResourcesNCTM Illuminations Websitehttp://illuminations.nctm.org/ National Council of Teachers of

MathematicsContains activities, lessons and links

related to the CCSS

ResourcesCommon Core Flip Bookshttp://katm.org/wp/wp-content/uploads/ flipbooks Grade level books with additional

examples, strategies and ideas for teaching the CCSS-M

ResourcesSBAC WebsiteSample Itemshttp://www.smarterbalanced.org/smarter-b

alanced-assessments/

Scroll down to “Mathematics”Find “Mathematics 3-5” (ZIP) or

“Mathematics 6-8” (ZIP)Folder of currently released sample

assessment items for the 4 claims

ResourcesSBAC WebsitePractice Testshttps://sbacpt.tds.airast.org/student/

ResourcesCalifornia Department of EducationCommon Core State Standards – Mhttp://

www.cde.ca.gov/be/st/ss/documents/ccssmathstandardaug2013.pdf

Mathematics Framework (DRAFT)http

://www.cde.ca.gov/ci/ma/cf/draft2mathfwchapters.asp

Break-Out GroupsK-2:

3-5: