START! Known to New College/Career Anchors and Math Performance

START!Known to New

College/Career Anchors and Math Performance

Agenda

1. What are College/Career Anchors?2. What are Math Performance

Standards?3. Why are they Important?4. Leading Change = Making Priorities5. Broadest Impact6. Plan for Success

Reading

InferenceEvidenceAnalyzeSummarizeInterpretIntegrateEvaluateDelineate

Math Mathematically proficient students can…Explain meaningConjectureReason abstractlyCritique Reasoning

A Shift in Perspective

The CCSS for Mathematics compel a change in the culture of traditional mathematics classroom.

• In the typical mathematics classroom students are “too busy covering content” to be engaged with mathematics.

The CCSS attempt to tell teachers when to slow down and emphasize student understanding of significant mathematical ideas.

http://www.ted.com/talks/dan_meyer_math_curriculum_makeover.html

What Needs to Change?

Cognitive Targets – CCSS Requires Focus on Rigorous Elements

NAEP 2009 PISA 2009

Locating / Recalling

Integrating / Interpreting

Critiquing / Evaluating

Accessing and retrieving

Integrating and interpreting

Reflecting and evaluating

What is Changing?

1. Textbook?2. Core Curriculum?3. State Tests?4. RtI / ELL5. Math EOCs?

CHANGE TODAY

Common Core State Standards

The First and Most Fundamental Change is Depth and Rigor

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The Foundation

Questions for Implementation

1. What can I affect? 2. What is most important?3. What will be most difficult, and

therefore take the most time to change?

But what does “higher standards” mean?

• More topics? – No. The U.S. curriculum is already cluttered with too

many topics

• Teaching topics in earlier grades?– No. Analyses of the standards of high-performing

countries suggest otherwise.– In Singapore, division of fractions is a 6th grade

expectation; in the U.S. it is typically a 4th or 5th grade expectation.

– In Japan, probability is introduced in the 7th grade; in the U.S., it can be found anywhere throughout grades 3-6, depending on the state.


Current U.S. curricula (“mile wide, inch deep”) coupled with high-stakes testing pressures teachers to

– “cover” at “pace”

– turn the page regardless of student needs

However, the study of mathematics should not be reduced to merely “a list of topics to cover”

Singapore preaches, “Teach less, learn more”

Agenda

1. What are College/Career Anchors?2. What are Math Performance

Standards?3. Why are they Important?4. Leading Change = Making Priorities5. Broadest Impact6. Plan for Success

Broad Impact The College / Career Readiness Anchors & Math Performance Standards have the Broadest Impact Across All School Personnel

Define Learning Targets

They Define Learning Targets Which Identify Student Skills and Skill Types

• Specific and Measureable– Order a group fractions and label them on a

number line• Contain a performance verb that describes what

students will do to demonstrate achievement– Order, Label

• State the specific context in which the student will apply that performance– e.g. written, oral, short answer, presentation

Criteria for Learning Target Statements

Learning Progression

Draw a basic number line from 0 to 10

Locate simple whole

numbers on a number line

Place halves in fraction form on a number

line

Locate tenths in decimal form

on a number line

Indicate the approximate location of

thirds, fourths, and fifths on a number line

Identify and locate the

approximate location of decimals in

hundredths on a number line

Compare fractions,

decimals and mixed numbers by identifying their relative position on a number line

Standard: Identify the relative position of simple positive fractions, positive mixed numbers, and positive decimals and be able to evaluate the values based on their position on a number line.

Classifying Targets

ProductsThe ability to create tangible products, such as term papers, science fair projects, and art sculptures that meet certain standards of quality and present concrete evidence of academic proficiency.

ReasoningThe ability to use knowledge and understanding to figure things out and solve problems.

PerformanceThe development of proficiency in doing something where it is the process that is important such as playing a musical instrument, reading aloud, speaking in a second language or using psychomotor skills.

KnowledgeMastery of substantive subject content where mastery includes both knowing and understanding it.

• Identify sight words• Identify similes and metaphors• List defining characteristics of various literary

genres• Count and group concrete manipulatives by

ones, tens, and hundreds to 1,000

Knowledge Target Examples

• Make a prediction based on evidence• Distinguish between fact and opinion• Evaluate information from a variety of

resources• Classify and compare triangles by sides and

angles

Reasoning Target Examples

• Read aloud with fluency and expression• Demonstrate the use of self-correction

strategies• Find and justify the laws of exponents with

numeric bases using inductive reasoning• Model, identify and describe square, prime

and composite numbers

Performance Target Examples

• Produce a grammatically correct sentence• Develop a proper paragraph form in a written

composition• Compose a written composition using the

five-step writing process• Create a design with more than one line of

symmetry

Product Target Examples

Begin by analyzing the level of thinking required by the standard

Assess the degree of depth or complexity of knowledge reflected in the content standards and assessments

Determine how deeply a student needs to understand the content for a given response/assessment

Types of Target = Level of Thinking

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How to Start?

Learning Goals

1. What is Cognitive Demand?2. What are the SKILLs

involved?3. How do I teach it / change

my teaching?4. What does it look it?

Assess?


•Too often, students view mathematics as a trivial exercise because they are rarely given the opportunity to grapple with and come to appreciate the intrinsic complexity of the mathematics.•Despite our instincts and best intentions, we need to stop “GPS-ing” our students to death.

Source: Shannon, A. (2010). Common Core: Two Perspectives on Tasks and Assessments. Presentation at the Urban Mathematics Leadership Network Retreat, June 2010.

“The Standards for Mathematical Practice

describe varieties of expertise that

mathematics educators at all levels should

seek to develop in their students. These

practices rest on important processes and

proficiencies with longstanding importance in

mathematics education.” (CCSS, 2010)

The Standards for Mathematical Practice


Source: Briars, D. & Mitchell, S. (2010). Getting Started with the Common Core State Standards. A National Council of Supervisors of Mathematics webinar. November 2010.



Strategic Competence

AdaptiveReasoning

ProductiveDisposition

ProceduralFluency

Conceptual Understanding

“Encouraging these practices in students of all ages should be as much a goal of the mathematics curriculum as the learning of specific content” (CCSS, 2010).

1.Make sense of problems and persevere in solving them.2.Reason abstractly and quantitatively.3.Construct viable arguments and critique the reasoning of others.4.Model with mathematics.5.Use appropriate tools strategically.6.Attend to precision.7.Look for and make use of structure.8.Look for and express regularity in repeated reasoning.


The description of each Mathematical Practice begins with the same first three words:

Mathematically proficient students …



The Mathematical Practices “describe the

thinking processes, habits of mind and

dispositions that students need to develop a

deep, flexible, and enduring understanding of

mathematics; in this sense they are also a

means to an end.”



MP #1: Make sense of problems and persevere in solving them.•Mathematically proficient students … •analyze givens, constraints, relationships •and goals … they monitor and evaluate •their progress and change course if •necessary … and continually ask •themselves, “Does this make sense?”



MP #3: Construct viable arguments and critique the reasoning of others

Consider the following subtraction algorithm: • How could I demonstrate the idea that the

algorithm always works?

400 – 139 399 – 138

43 – 17 46 – 20

Points of Intersection: Content and Practices

MP #7: Look for and make use of structure

Partitioning• 8 x 7• 33 + 58


MP #7: Look for and make use of structure

Example:

Understanding and interpreting the equation of a line expressed in “Point-Slope Form”

• y – y1 = m(x – x1)


Target : Embed

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First Things First

If I cannot teach in a manner which engages at the higher levels of cognitive demand, content standards do not

matter.

First Things First

The Change in Depth isPrimaryEssential

FoundationalImmediate

To Dos

1. Training = Awareness2. Direct Instruction 3. Daily Planning4. Curriculum Tagging5. Resource ID & Sharing

Lesson Modification

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Resources

standardstoolkit.k12.hi.us

[email protected]

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Documents

START! Known to New College/Career Anchors and Math Performance