curriculum mapping and cc mathematical standards/practices (dr. nicki newton)

Summer 2011 Presented by: Dr. Nicki Newton

Mapping is a bridge into the 21st Century. It leads the way !

Mapping is a bridge into the 21st Century.

It leads the way!It assures that our children will have a

successful passage into their future.

All that is shared in this slideshow is based on the work of Dr. Heidi Hayes Jacobs…

Mapping the Big Picture 1997, ASCD

Getting Results with Curriculum Mapping 2004, ASCD

Active Literacy Across the Curriculum 2006, Eye On Education

and …

A Guide To Curriculum Mapping: Planning, Implementing, and Sustaining the Process

Janet Hale

December, 2007 Corwin Press

Origin: 1625–35; < L: action of running, course of action, race, chariot,

equiv. to curr(ere) to run + -i- + -culum -2]

The verb map is first attested 1586; to put (something) on the

map "bring it to wide attention" is from 1913.

A verbal agreementisn’t worth the paper it’s written

on.—Samuel Goldwyn

Curriculum Mapping is all about the full written disclosure of both operational and planned learning. A learning organization collectively commits to no longer making decisions based on verbal statements. Instead, all decisions

and discussions are based on map documentation that is inter-related within

a mapping system.

Hale, J. (2007). Curriculum mapping101. Thousand Oaks, CA: Corwin Press.

Four Types of

Curriculum Maps

• Diary Map

• Projected Map • Consensus Map

• Essential Map

Hale, J. (2007). Curriculum mapping101. Thousand Oaks, CA: Corwin Press.

The “Essence” of Curriculum Mapping

Diary Map (Recorded Monthly)

• A personalized* map recorded by an individual person that contains data reflecting what REALLY took place during a month of learning and instruction

• Commonly due by the “7th” of the next month

*There is no such thing as “team” diary

mapping.

I am a data-

collection portal…

Hale, J. (2007). Curriculum mapping101. Thousand Oaks, CA: Corwin

The Nuts N’

Bolts of Mapping Language

Projected Map• A map that has been created by an individual

person for a discipline or course before the actual yearly testing out of its “planned itinerary”

These two types of maps are, in actually, the same map. Differentiation is based on the current month of the year. (Hale)

Consensus Map (An Entire School Year Of Months)

• A map designed by two or more educators wherein all designers have come to agreement on the course learning based on standards and serves as the planned-learning map wherein all who teach the course use the Consensus Map as a foundation* for his or her course learning and instruction

*Flexibility in additional learning, length of learning, assessments, resources, and how learning is executed is up to the discretion of each teacher teaching the course and is reflected in his or her Projected Map/Diary Map.

SCHOOL-SITE “LEVEL” MAPS (Hale)

The Nuts N’

Bolts of Mapping

Language

Essential Map (An Entire School Year Of Learning Usually Recorded By Grading Periods)

• A map created via a team of educators (Task Force) that is representative of District learning expectations.* The Essential Map serves as the base-instruction map wherein all who teach the course use the map to plan learning and create collaborative, Consensus Maps and/or personal Projected Maps

*There needs to two or more “like” schools or courses offered to warrant creation and use Essential Maps.

DISTRICT “LEVEL” MAPS (Hale)

“When we travel, road maps become more distinctive the closer we get to

the ‘main destination’.”

Quote By: Dr. Heidi Hayes Jacobs

Keynote Presentation, 2005 National Curriculum

Mapping Institute.

Weekly/Daily Lesson Plans

Diary Map Janet

Biggins Grade 1

Math

ConsensusMap

Grade 1 Math

Janet BigginsNicki McGraneSusan McGuire

Lincoln Elementary School

Bergenfield School

District

Grade 1 Essential

Maps

Base DETAIL

Most (Monthly) DETAIL

More DETAIL

Much More Specific Day By Day DETAIL

Hale, J. (2007). Curriculum mapping101

Sustained, systemic change

takes 3 to 5

years to full

implement!Curriculum Mapping is

an ongoing

process, not a

program!

And remember

…

The General Architecture of a Curriculum Map

• A. Essential questions

• B. Content/Alternative Texts

• C. Standards

• D. Precise and Measurable Skills

• E. Targeted Assessments

• F. Resources

Sample Curriculum Map TemplateEssential Question

Conceptual Statements/

Content

Standards Skills Assessment

Visual Alignment

Essential Questions…

•They touch our hearts and souls. •They are central to our lives. •They help to define what it means to be human. •They probe the deep and often confounding issues confronting us •They pass the test of SO WHAT?

Essential Questions • Have no simple right answer; they are meant to be

argued discussed (discovered , uncovered)

• Lead to more questions

• CAN’T GOOGLE THE ANSWER

Essential Questions . . .Essential questions are at the heart of a search for Truth. Many of us believe that schools should devote more time to essential questions and less time to Trivial Pursuit.

Essential Questions . . .From Trivial Pursuit to Essential Questions and Standards-Based Learning

by Jamie McKenzie

Essential Questions . . .There are so many more important and more intriguing questions we could explore about gargoyles. When we limit students to trivial pursuit, we make a mockery of authentic research and deprive them of a chance to explore the tough issues, choices, dilemmas and questions that really matter.

• Why did people place gargoyles on cathedrals? • What good are gargoyles? • How are gargoyles (gargouilles) and chimeras (chimeres) different and

which are better? • Why do some people place gargoyles in their gardens?

(http://www.fno.org/feb01/pl.html)

Heidi Hayes Jacobs says…

Essential Questions are the Velcro of the unit. Everything in the unit should stick to them.

Essential Questions – Doorways to Understanding

Given particular subject matter or a particular concept, it is easy to ask trivial questions…it is also easy to ask impossibly difficult questions. The trick is to find the medium questions that can be answered and that take you somewhere.

Jerome Bruner, The Process of Education, 1960, p. 40

Essential Questions In addition, essential questions should

be few in number — “two to five per unit.”

Traditional School Question Go find out about Robert or Elizabeth Browning (or any other poet, general, prime minister, hero, character, celebrity, scoundrel or seer. What did he or she do?

Upgraded Version What were the five most distinguishing

characteristics of Browning and how did they

contribute to her success or failure? What made

her great or not so great? What are the two or

three most important things you learned about her

that might serve you well?

Examples of Essential Questions• Where can I see geometric shapes?• How are geometric shapes represented in

architecture?• Where do I see flips, slides and turns in real

life? Is this an important mathematical concept for me to learn? Why?

More Examples

• Who am I in 2011?• Where do I stand as a 7th grader?

– Personality– With Family– Community– In Each Subject Area

More Examples...

• Why did the American Revolution occur? • How can we look at the Revolution from

alternate points of view? • Why is Paul Revere more famous than Sybil

Ludington? • Why did you do it George?

More Examples…• Why would people leave their homeland and start

a new life in a foreign country?

• What contributions did immigrants from various lands and creeds make to our nationhood?

• What factors contributed to making life better or easier for some people and why?

NJ Math EQ’s• How can change be best represented mathematically? • How can measurements be used to solve problems? • How can spatial relationships be described by careful use of

geometric language? • How can the collection, organization, interpretation, and display

of data be used to answer questions?

NJ Visual and Performing Arts EQ’s

• Why should I care about the arts?

• How does creating and performing in the arts differ from viewing the arts?

• Does art have boundaries?

(Petner, Skinner et al.)

Mapping Content

•Essential Understandings

•Content Descriptors


• “education with inert ideas is not only

useless: it is above all things, harmful… Let the main ideas which are introduced be few and important, and let them be thrown into every combination possible.” Whitehead 1929

Conceptual StatementsWe are obliged to make deliberate choices and set

explicit priorities. As Bruner (1960) put it years ago:

For any subject taught in primary school, we might ask [is it] worth an adult’s knowing, and whether having known it as a child makes a person a better adult. A negative or ambiguous answer means the material is cluttering up the curriculum. (p. 52)

The Concepts

• The big ideas may be thought of as the linchpins of the unit.

• The linchpin is the device that keeps the wheel in place on an axle.

.

The Concepts

• Thus, a linchpin is one that is essential for understanding.

• Without grasping the idea and using it to “hold together” related content knowledge, we are left with bits and pieces of inert facts that cannot take us anywhere.

The Concepts

• Thus, a linchpin is one that is essential for understanding.

Big Ideas/Essential Understandings

• Without grasping the idea and using it to “hold together” related content knowledge, we are left with bits and pieces of inert facts that cannot take us anywhere.

Essential Understandings

I want students to understand - – The Constitution – The three branches of government

This is not a learning goal - this just states what the content is.

Essential UnderstandingsI want students to leave my course having understood that: -the Constitution was a solution based oncompromise to real and pressing problems anddisagreements in governance; not an idea out ofthin air


Essential UnderstandingsI want students to leave my course having understood that:

-the Constitution was a brilliant balance andlimit of powers but was grounded in a long andsometimes bitter history, with many fights that areand always will be with us.

Examples1. Olsen’s example2. NYC Unit of Study


Writing Clear Content Descriptors

• Anyone should be able to read your map!

Descriptive Or Not Descriptive? That is the

Question!Content listings serve as a Table of “Content.” It is important that the map writer or writers include descriptors that clear and precise.

Activity 1

Look at the sample content listings in the first column. Indicate if each one is a quality recording or needs revision in the second column. If it needs revision, write your suggested revision(s) in the last column.

(J. Hale, Curriculum Mapping 101)

• Let’s Practice!

1. Look at your content

2. Think about the 2-4 Big Ideas in your unit.

3. State those as conceptual statements.

4. Bullet supporting ideas, topics, vocabulary under that idea

Check-in …

• Discuss three important ideas about your essential understandings and content descriptors.

• Discuss any questions or concerns you have about your essential understandings and content descriptors.

Evaluating Content Descriptors

• Examine your mapped essential understandings/content against the rubric.

• What did you discover?

Integrating the New Common Core Standards

• Let’s take a look at the NYDOE Focus sections.

1.What do you notice about the math focus?

2.How will you begin to integrate this into your maps?

(NY Dept. of Ed Focus)

Selected Common Core Standards in Literacy

Grade Band Literacy Focus

Pre-K-2 Written response to informational texts through group activities and with prompting and support (Reading Informational Text Standards 1 and 10; Writing Standard 2)

3-8 Written analysis of informational texts (Reading Informational Text Standards 1 and 10) OR Written opinion or argument based on an analysis of informational texts (Reading Informational Text Standards 1 and 10; Writing Standard 1)

9-12 Written opinion or argument based on an analysis of informational texts (Reading Informational Text Standards 1 and 10; Writing Standard 1)

Selected Common Core Standards in Mathematics

Grade Band Standards of Practice Domain of Focus

Pre-K-K

Models with Mathematics and/or

Construct Viable Arguments and Critique

the Reasoning of Others

AND

Operations and Algebraic Thinking

1-2 Number and Operations in Base Ten

3 Operations and Algebraic Thinking

4-5 Numbers and Operations - Fractions

6-7 Ratios and Proportional Relationships

8 Expressions and Equations

Algebra Reasoning with Equation and Inequalities

Geometry Congruence

Teach us to

Skills Activity

A skill is what students must be able to do.

An activity provides practice concerning a particular skill or skill set.

Skills versus Activities

T- Chart Activity:

Categorize the statements under skill or activity on the T-Chart.

Skills Activity

Relate visually wooden art works to

religious beliefs in 2 geographic

regions: Africa, Asia

Look at artwork to see if the pieces

incorporate religious icons

Evaluate orally and in writing

technological developments that have

influenced how humans work with

genetically engineered crops

Interview, in person, by phone,

or via e-mail 3 biochemists using

personal pre-generated questions

Analyze in writing similarities and

differences in political contributions of

3 presidents: Washington, Lincoln,

Roosevelt

Research using the Internet the

president’s political arenas: state,

national, international in teams of 3

Self-evaluate in writing personal

physical activities that promote

lifelong involvement, well-being

Keep a daily personal fitness journal

for 1 month

Skill Versus Activity Answer Key


Skill Versus Activity Answer Key conDraw transformational figures using

rigid body movement while keeping

point fixed in 2-D plane

Practice rotations

using polygons

Describe visually and in writing

historical examples of recession in

United States history

Make a chart board display of ebb and

flow of USA economic factors for

20th century and onset of 21st century


Check-in …

• Discuss three important ideas about your mapped skills.

• Discuss any questions or concerns you have about your mapped skills.


Evaluating Our Mapped Skills

• Examine your skills against the rubric.


• Are all your skills precise and measurable?

D3b,D3d

AssessmentTalk at your table about the types of assessments that you do in your school?

Do you interviews across the curriculum?

Do you do performance assessments at all grade levels?

How balanced is your overall assessment?

Assessment Quiz

Poll Everywhere

Quick Poll

1.Do you use interactive boards at your school?

2.Do you use the web for informal assessments?

Evidence for and of learning…Assessment is a scrapbook of evidence, not a

snapshot.

Does your map reflect balanced assessment?

McTighe & Wiggins

Why Assess?

• Assessments are not just to provide a ‘grade’

• Purpose of assessment : • Determine students ‘ get it ’ …….. Gather evidence with demonstrations that

learning outcomes were achieved

• Help teachers determine extent of student understanding

• Guide next steps of instruction

• Provide appropriate scaffolding / differentiated instruction for students throughout the learning experience

• Provide feedback to stakeholders (students / parents)

Just because the student

“knows it” … Evidence of understandings is a greater

challenge than evidence that the student knows a correct or valid answer.

2 validity questions for a practical ‘test of the test’

1. Could the test be passed but without deep understanding?

Wiggins Summer Institute, 2008

2 validity questions for a practical ‘test of the test’

2. Could the specific test performance be poor but the student still reveal understanding in various ways before, during, and after?

The goal is to answer NO to both

Wiggins Summer Institute, 2008

We often confuse the drills with the game

‘Drills’ – test items– Short-term objective– Out of context– Discrete, isolated element– Set up and prompted for

initial simplified learning– Doesn’t transfer to new

situations on its own

The ‘game’ – real task– The point of the drills– In context, with all its

messiness and interest value– Requires a repertoire, used

wisely– Not prompted: you judge

what to do, when

(Wiggins, 2008)

Continuum of Assessments• Checks of understanding (such as oral questions, observations,

dialogues)• Traditional quizzes, tests, and open-ended prompts• Performance tasks and projects• Vary in terms of scope (from simple to complex)• Time frame (from short to long term)• Setting (from decontextualized to authentic contexts)• Structure (from highly directive to unstructured)• Snap shots versus pictures • COLLECTION OF EVIDENCE OVERTIME RATHER THAN AN

EVENT

The research could not be clearer, though: Increasing formative

assessment is the key to improvement on tests of all kinds, including traditional

ones.

"Formative assessment is an essential component," …"We know of no other

way of raising standards for which such

a strong prima facie case can be made.”Richard J. Light, Walter H. Gale Professor of Education at Harvard University, buttressed these findings in his book Making the Most out of College: Students Speak

Their Minds:

"The big point -- it comes up over and over again as

crucial… is the importance of quick and detailed feedback. Students overwhelmingly report that the single most important ingredient for making a course effective is getting rapid response on assignments and quizzes. ... An overwhelming majority are convinced that their best learning takes place when they have a chance to submit an early version of their work, get detailed feedback and criticism, and then hand in a final revised version. ...

"The big point -- it comes up over and over again as

crucial… Students improve and are engaged when they receive feedback (and opportunities to use it) on realistic tasks requiring transfer at the heart of learning goals and real-world demands."

How was understanding shown? Verbally? Written?

Body language?

Where did they get stuck?

How could you have assisted them?

Why Use Informal Assessments?

According to Marzano’s book: Classroom Assessment and Grading that Work

“…To the surprise of some educators, major reviews of the research on the effects of classroom assessment indicate that it might be one of the most

powerful weapons in a teacher’s arsenal.”

(Chapter 1).

Let’s Listen to a discussion about Formative Assessment:

Dylan Williams (Video)

http://ktschutt.vodspot.tv/video/4154648-formative-assessment-dylan-wiliam-learning-and-teaching


Types of Informal Assessments

Whole Group AssessmentsThumbs up/ down

E.P.R.– Every Pupil Response

Think – Pair – Share

Whip Around

Individual Informal Assessments Interview

Warm- up

Exit card

Observe/ listen in

Things to think about! A simple device for ongoing assessment of understanding is the “one-minute essay.” At the end of each class, students are asked to answer two questions:

• What is the big point you learned in class today?• What is the main unanswered question you leave

class with today? - Harvard study showed this to be very effective (Light, 2001) – It gives immediate feedback on understanding and mis/understandings

Some other terms needed to understand other evidence are…

AcademicPrompts

open-ended questions that require critical thinking for response

Assessment measurement of understanding

ConstructedResponse

open-ended, short answer responses, often application specific

FormativeAssessment

feedback on progress towards the development of knowledge, understanding, skills, and attitudes

rather than assessment for marks or grades

Some other terms needed to understand other evidence are…

Informal Checks

uncritical assessment of progress on a given task or understanding

Observations teacher or student visual and/or oral assessment

PerformanceTasks

complex, authentic tasks and issues that differ from academic prompts designed to aid transference

of knowledge and understanding

Rubric visual assessment tool

Self-Assessment

reflection and observation by student of own work and progress

Summative-Assessment

assessment designed to be used to determine grades or marks

3 things to remember…

1. Remember that teachers collect evidence for and of learning.

2. Assessments should show what students know and can do.

There 635 students and only 16 students can fit on each bus.

How many buses will be needed to go to the county fair?

3. Assessment is a scrapbook of evidence, not

a snapshot.

Does your map reflect balanced assessment?

McTighe & Wiggins

Assessment Versus Evaluation Exercise

An assessment is a product or performance.An evaluation is the criteria used and judgment made

for the product or performance.

Match the assessment name with its appropriate evaluation.

Janet A. Hale www.CurriculumMapping101.com [email protected]


20 Item Quiz Thomas JeffersonEssay

African Mask 25 MC Test

Basketball Basic Plays Checklist

Penny Hardness Lab Self Evaluation: Audio Recording/Rubric

ORF Diagnostic Guidelines

Musical Scales Performance Task

No Evaluation Data Needed

Peer Review/ Geometric Checklist

No Evaluation Data Needed

Biography Writing Rubric

Oral Reading Fluency Test

5 Member Teams Performance Task

Teacher Ob/ Procedure Checklist/ Findings Report

Assessment Versus Evaluation Exercise Chart


Assessment Versus Evaluation ExerciseAnswer Key

Assessment Name Evaluation

20 Item Quiz No Evaluation Data Needed

25 MC Test No Evaluation Data Needed

Thomas Jefferson Essay Biography Writing Rubric

Penny Hardness Lab Teacher Ob/ Procedure Checklist/ Findings Report

Oral Reading Fluency Test ORF Diagnostic Guidelines

African Mask Peer Review/ Geometric Checklist

5 Member Team Performance Task Basketball Basics Plays Checklist

Musical Scenes Performance Task Self Evaluation: Audio Recording/Rubric


Assessment Versus Evaluation ExerciseAnswer Key Continued

When including evaluations in a map andnot yet using a mapping system’s attachment or inclusion features

write the assessment name followed by a brief evaluation summary in parenthesis.

Examples:Thomas Jefferson Essay (Evaluation: Biography Writing Rubric)

FOR Solo and Duet Performance (Evaluation: Teacher Ob/Checklist)

5-Member Team Debate (Evaluation: Peer Review/Rubric Matrix)

3 Semi-regular Tessellation Configurations (Evaluation: Teacher Ob/Checklist)

FOR Dead Lift Performance Tasks (Evaluation: Teacher-Student Reflection/PersonalGoal Setting)

Depth of Knowledge LevelsJust glance at your maps…

Are the Depth of Knowledge levels reflected in your map?

How might you begin to think about integrating the various levels into your map?

Check-in …• Discuss three important ideas about mapping

assessments.

• Discuss any questions or concerns you have about mapping assessments.

Evaluating Our Mapped Assessments

• Examine your targeted assessments against the rubric.


Upgrading our curriculum maps to represent 21st technologies?

ictlic.eq.edu.au

D3c

Generation Z/Net Gen/ Digital Natives

Generation Z

Category 20th Century 21st Century

Number of Jobs 1-2 10-15

Job Skill Mastery of the Field Flexibility and Adaptability

Teaching Model Subject Matter Mastery Integration of 21st Century Skills into subject matter mastery

Assessment Model Consumption of Knowledge Consumption/Production of Knowledge; Synthesis

Teen’s Today•100% Use the Internet to seek information on colleges, careers and jobs•74% of teens use IM as a major communication vehicle vs. 44% of online adults•54% of students (grades 2-12) know more IM screen names than home phone numbers•The Internet is a primary communication tool• 81% email friends and relatives• 70% use instant messaging to keep in touch•56% prefer the Internet to the telephone

Adapted from http://www.amphi.com/departments/technology/files/76FA6DD3C6084D61B334C93C04A780B4.pdf

21st Century Teachers Mark Prensky: digital natives

and us… We’re all digital immigrants….

Lessons learned from Introducing the book!

Introducing the Book

Today’s Youth

I will have 10 to 14 careers

Education for today and tomorrow – tom woodward

“And most of the jobs don’t exist today.”

A Vision of K-12 Students Today –B. Nesbitt

“How will this Help?”


“or this?”


“How could this help me?”


“or this?”


How are we teaching?Web No Point O

I just don’t do it.

I’m not into technology. They can do that stuff outside of school. It’s not

part of the school world.

How are we teaching?Web 1.0Use it to:Offline

Find Info online

How are we teaching?Write reportsPowerpoint

Single CreatorLicensed or purchased

Isolated

How are we teaching?Web 2.0

Multitasking toolUse it to blog, wiki, email, im, talk,make and show movies,get immediate feedback from a

variety of sources

How are we teaching?Web 2.0

Multitasking toolUse it to post photos, videos, podcasts, and

other items. We meet each other on Facebook.We say,

“See ya on facebook.”

Web 2.0Web based, Collaborative,

Online, Free, Multiple Collaborators, Open source,

shared content

http://www.cabrillo.edu/~nstucker/images/zits.gif

Web 2.0Interconnectedness,

immediacy, interactivity, communications, and

community

http://www.cabrillo.edu/~nstucker/images/zits.gif

How do our maps reflect the 21st century, web 2.0 world?

What do you do differently to engage your students in this interactive, participatory environment in which they live?

21st Century Instructional Resources

Voice Thread Podcasting Glogster Animoto Virtual Tools and Manipulatives

Checking for Coherency

A. Did you assess the knowledge?

B. Did you assess the skills?

C. Did you answer the essential questions?

Checking for CoherencyD. Is internal alignment reflected in your

curriculum map?

E. Is the external alignment clear?

F. Does the map reflect developmentally appropriate activities for the designated grade level?

Wrap-up…Day 2

• Discuss one important ideas about curriculum mapping and 21st learners.

• Discuss 2 major take-aways from the past two days.• Discuss any questions or concerns you have about

curriculum mapping.

You can contact me at…

[email protected]

curriculum mapping and cc mathematical standards/practices (dr. nicki newton)

Education

map toplan learning

essential questions

curriculum mapping101

projected mapdiary map

mapping system

month of learning

century d3b

planned learning