designing an understanding- based curriculum around common … · 2017-02-06 · designing an...

Designing an Understanding-based Curriculum around Common Core Standards

presented by

Jay McTigheAuthor and Educational Consultant

e-mail: [email protected]: jaymctighe.com

© 2012 Jay McTighe and Grant Wiggins 2

Understanding-based Curriculum

STANDARDS

Definition Standards specify established learning goals. A content standard provides a written description of what students should know and be able to do in a particular discipline or subject area. A performance standard specifies how well students need to perform in order to meet the standard.

Some standards are broad and overarching (e.g., Write arguments to support claims in an analysis of substantive topics or texts, using valid reasoning and relevant and sufficient evidence), while others are grade/level-specific (e.g., Grade 4 – Ask and answer questions to demonstrate understanding of a text, referring explicitly to the text as the basis for the answers.)

Standards specify goals related to content (e.g., Grade 6 – Write and evaluate numerical expressions involving whole-number exponents) as well as process (e.g., Make sense of problems and persevere in solving them). RecommendationsStandards are not curriculum; they provide the framework upon which curricula are developed. Educators must translate Standards into a teachable curriculum to insure a guaranteed set of desired results. Since Standards documents often contain a mix of knowledge, skills, conceptual understandings, transfer abilities and habits of mind, it is necessary to “unpack” them to clarify the desired results and develop appropriate assessments and instruction.

The Common Core Standards have been developed with long-term outcomes in mind (e.g., College and Career Anchor Standards in English Language Arts), and their components are intended to work together (e.g., Content and Practice Standards in mathematics). It is important for educators to understand the intent and structure of the Standards in order to work with them most effectively. Accordingly, I recommend that schools set the expectation and schedule the time for staff to read and discuss the Standards, beginning with the “front matter,” not the grade-level Standards. Consider using the following essential question to guide staff reading and discussion: What are the new emphases in these Standards and what do they mean for our practice?



Areas of Emphasis in the

Common Core State Standards

The Common Core State Standards in Mathematics“…the mathematics curriculum in the United States must become substantially more focused and coherent in order to improve mathematics achievement .... To deliver on the promise of common standards, the standards must address the problem of a curriculum that is a mile wide and an inch deep. That is, what and how students are taught should reflect not only the topics that fall within a certain academic discipline, but also the key ideas that determine how knowledge is organized and generated within that discipline. This implies that ‘to be co-herent,’ a set of content standards must evolve from particulars… to deeper structures inher-ent in the discipline.” -- Common Core State Standards for Mathematics

The Common Core State Standards in English/Language Arts“Students can, without significant scaffolding, comprehend and evaluate complex texts across a range of types and disciplines, and they can construct effective arguments and convey intricate or multifaceted information. Likewise, students are able independently to discern a speaker’s key points, request clarification, and ask relevant questions. They build on others’ ideas, articulate their own ideas, and confirm they have been understood. Without prompting, they demonstrate command of standard English and acquire and use a wide-rang-ing vocabulary. More broadly, they become self-directed learners, effectively seeking out and using resources to assist them, including teachers, peers, and print and digital reference materials.” -- Common Core State Standards for English Language Arts

The (Draft) Common Core State Standards in Science“The framework focuses on a limited number of core ideas in science and engineering both within and across the disciplines. The committee made this choice in order to avoid shal-low coverage of a large number of topics and to allow more time for teachers and students to explore each idea in greater depth. Reduction of the sheer sum of details to be mastered is intended to give time for students to engage in scientific investigations and argumentation and to achieve depth of understanding of the core ideas presented. Delimiting what is to be learned about each core idea within each grade band also helps clarify what is most impor-tant to spend time on, and avoid the proliferation of detail to be learned with no conceptual grounding. -- Common Core Science Standards (draft)



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ReadingThe standards establish a “staircase” of increasing complexity in what students must be able to read so that all students are ready for the demands of college- and career-level reading no later than the end of high school. The standards also require the progressive development of reading comprehen-sion so that students advancing through the grades are able to gain more from whatever they read.Through reading a diverse array of classic and contemporary literature as well as challenging infor-mational texts in a range of subjects, students are expected to build knowledge, gain insights, explore possibilities, and broaden their perspective. Because the standards are building blocks for success-ful classrooms, but recognize that teachers, school districts and states need to decide on appropriate curriculum, they intentionally do not offer a reading list. Instead, they offer numerous sample texts to help teachers prepare for the school year and allow parents and students to know what to expect at the beginning of the year.

WritingThe ability to write logical arguments based on substantive claims, sound reasoning, and relevant evidence is a cornerstone of the writing standards, with opinion writing – a basic form of argument – extending down into the earliest grades.Research – both short, focused projects (such as those commonly required in the workplace) and longer term in depth research – is emphasized throughout the standards but most prominently in the writing strand since a written analysis and presentation of findings is so often critical.

Speaking and ListeningThe standards require that students gain, evaluate, and present increasingly complex information, ideas, and evidence through listening and speaking as well as through media. An important focus of the speaking and listening standards is academic discussion in one-on-one, small-group, and whole-class settings. Formal presentations are one important way such talk occurs, but so is the more infor-mal discussion that takes place as students collaborate to answer questions, build understanding, and solve problems.

LanguageThe standards expect that students will grow their vocabularies through a mix of conversations, direct instruction, and reading. The standards will help students determine word meanings, appreciate the nuances of words, and steadily expand their repertoire of words and phrases.The standards recognize that students must be able to use formal English in their writing and speaking but that they must also be able to make informed, skillful choices among the many ways to express themselves through language.Vocabulary and conventions are treated in their own strand not because skills in these areas should be handled in isolation but because their use extends across reading, writing, speaking, and listening.

Media and TechnologyJust as media and technology are integrated in school and life in the twenty-first century, skills related to media use (both critical analysis and production of media) are integrated throughout the standards.

Key Points in the English Language Arts Standards



English Language Arts Standards College and Career Readiness

Anchor Standards for Reading

Key Ideas and Details1. Read closely to determine what the text says explicitly and to make logical inferences from it; cite specific textual evidence when writing or speaking to support conclusions drawn from the text.2. Determine central ideas or themes of a text and analyze their development; summarize the key supporting details and ideas.3. Analyze how and why individuals, events, and ideas develop and interact over the course of a text.

Craft and Structure4. Interpret words and phrases as they are used in a text, including determining technical, connotative, and figurative meanings, and analyze how specific word choices shape meaning or tone.5. Analyze the structure of texts, including how specific sentences, paragraphs, and larger portions of the text (e.g., a section, chapter, scene, or stanza) relate to each other and the whole.6. Assess how point of view or purpose shapes the content and style of a text.

Integration of Knowledge and Ideas7. Integrate and evaluate content presented in diverse media and formats, including visually and quantitatively, as well as in words.8. Delineate and evaluate the argument and specific claims in a text, including the validity of the reasoning as well as the relevance and sufficiency of the evidence.9. Analyze how two or more texts address similar themes or topics in order to build knowledge or to compare the approaches the authors take.

Range of Reading and Level of Text Complexity10. Read and comprehend complex literary and informational texts independently and proficiently.



English Language Arts Standards College and Career Readiness

Anchor Standards for Writing

Text Types and Purposes1. Write arguments to support claims in an analysis of substantive topics or texts, using valid reasoning and relevant and sufficient evidence.2. Write informative/explanatory texts to examine and convey complex ideas and information clearly and accurately through the effective selection, organization, and analysis of content.3. Write narratives to develop real or imagined experiences or events using effective technique, well-chosen details, and well-structured event sequences.

Production and Distribution of Writing4. Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience.5. Develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach.6. Use technology, including the Internet, to produce and publish writing and to interact and collaborate with others.

Research to Build and Present Knowledge7. Conduct short as well as more sustained research projects based on focused questions, demonstrating understanding of the subject under investigation.8. Gather relevant information from multiple print and digital sources, assess the credibility and accuracy of each source, and integrate the information while avoiding plagiarism.9. Draw evidence from literary or informational texts to support analysis, reflection, and research.

Range of Writing10. Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of tasks, purposes, and audiences.



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Common Core Standards for Mathematics

Introduction – Articulates the philosophical and conceptual foundation for the Standards. Describes their organization and how they should be applied.

Standards for Mathematical Practice – These overarching standards apply across the content standards in each grade • Standards for mathematical proficiency: reasoning, problem solving, modeling, decision making, and engagement • Mathematical “habits of mind”

Grade-Level Standards – Define what students should know and be able to do at each grade level

K-8 grade-by-grade standards are organized by domain - Domains: overarching ideas that connect topics across the grades - Clusters: illustrate progression of increasing complexity from grade to grade

9-12 high school standards are organized around five conceptual categories - Number and Quantity, Algebra, Functions, Geometry, and Statistics and Probability - Content categories: overarching ideas that describe strands of content - Domains/Clusters: groups of standards that describe coherent aspects of the content category • Standards indicated as (+) are beyond the college and career readiness level but are necessary for advanced mathematics courses (calculus, discrete mathematics, and advanced statistics.)



• The mathematics curriculum in the United States must become substantially more focused and coherent in order to improve mathematics achievement .... To deliver on the promise of common standards, the standards must address the problem of a curric-ulum that is ‘a mile wide and an inch deep.’ That is, what and how students are taught should reflect not only the topics that fall within a certain academic discipline, but also the key ideas that determine how knowledge is organized and generated within that discipline. This implies that ‘to be coherent,’ a set of content standards must evolve from particulars… to deeper structures inherent in the discipline.

• The standards stress not only procedural skill but also conceptual understanding, to make sure students are learning and absorbing the critical information they need to succeed at higher levels - rather than the current practices by which many students learn enough to get by on the next test, but forget it shortly thereafter, only to review again the following year.

• The K-5 standards provide students with a solid foundation in whole numbers, addi-tion, subtraction, multiplication, division, fractions and decimals—which help young students build the foundation to successfully apply more demanding math concepts and procedures, and move into applications.

• Having built a strong foundation K-5, students can do hands on learning in geome-try, algebra and probability and statistics. Students who have completed 7th grade and mastered the content and skills through the 7th grade will be well-prepared for algebra in grade 8.

• The high school standards call on students to practice applying mathematical ways of thinking to real world issues and challenges; they prepare students to think and reason mathematically. The high school standards set a rigorous definition of college and career readiness, by helping students develop a depth of understanding and ability to apply mathematics to novel situations, as college students and employees regularly do.

• The high school standards emphasize mathematical modeling, the use of mathemat-ics and statistics to analyze empirical situations, understand them better, and improve decisions.

Key Points in the Mathematics Standards



Mathematics Standards Standards for Mathematical Practice

The Standards for Mathematical Practice describe ways in which developing student practitioners of the discipline of mathematics increasingly ought to engage with the subject matter as they grow in mathematical maturity and expertise throughout the elementary, middle and high school years.

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 Standards for Mathematical Content are a balanced combination of procedure and understanding. Expectations that begin with the word “understand” are often especially good opportunities to connect the practices to the content. Students who lack understanding of a topic may rely on procedures too heavily. Without a flexible base from which to work, they may be less likely to consider analogous problems, represent problems coherently, justify conclusions, apply the mathematics to practi-cal situations, use technology mindfully to work with the mathematics, explain the mathematics accurately to other students, step back for an overview, or deviate from a known procedure to find a shortcut. In short, a lack of understanding effectively prevents a student from engaging in the mathematical practices. In this respect, those content standards which set an expectation of understanding are potential “points of intersection” between the Standards for Mathematical Content and the Standards for Mathematical Practice. These points of intersection are intended to be weighted toward central and generative concepts in the school mathematics curriculum...



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Framework for K-12 Science Education

The Framework outlines the three dimensions that are needed to provide students a high quality science education. The integration of these three dimensions provides students with a context for the content of science, how science knowledge is acquired and understood, and how the sciences are connected through concepts that have universal meaning across the disciplines. The following excerpt is quoted from the Framework.

Dimension 1: PracticesDimension 1 describes (a) the major practices that scientists employ as they investigate and build models and theories about the world and (b) a key set of engineering practices that engineers use as they design and build systems. We use the term “practices” instead of a term such as “skills” to emphasize that engaging in scientific investigation requires not only skill but also knowledge that is specific to each practice.

Similarly, because the term “inquiry,” extensively referred to in previous standards documents, has been interpreted over time in many different ways throughout the science education community, part of our intent in articulating the practices in Dimension 1 is to better specify what is meant by inquiry in science and the range of cognitive, social, and physical practices that it requires. As in all inquiry-based approaches to science teaching, our expectation is that students will themselves engage in the practices and not merely learn about them secondhand. Students cannot comprehend scientific practices, nor fully appreciate the nature of scientific knowledge itself, without directly experiencing those practices for themselves.

Dimension 2: Crosscutting ConceptsThe crosscutting concepts have application across all domains of science. As such, they provide one way of linking across the domains in Dimension 3. These crosscutting concepts are not unique to this report. They echo many of the unifying concepts and processes in the National Science Education Standards, the common themes in the Benchmarks for Science Literacy, and the unifying concepts in the Science College Board Standards for College Success. The framework’s structure also reflects discussions related to the NSTA Science Anchors project, which emphasized the need to consider not only disciplinary content but also the ideas and practices that cut across the science disciplines.

Dimension 3: Disciplinary Core IdeasThe continuing expansion of scientific knowledge makes it impossible to teach all the ideas related to a given discipline in exhaustive detail during the K-12 years. But given the cornucopia of informa-tion available today virtually at a touch—people live, after all, in an information age—an important role of science education is not to teach “all the facts” but rather to prepare students with sufficient core knowledge so that they can later acquire additional information on their own. —An education focused on a limited set of ideas and practices in science and engineering should enable students to evaluate and select reliable sources of scientific information, and allow them to continue their devel-opment well beyond their K-12 school years as science learners, users of scientific knowledge, and perhaps also as producers of such knowledge.



Practices for K-12 Science Classrooms1. Asking questions (for science) and defining problems (for engineering)2. Developing and using models3. Planning and carrying out investigations4. Analyzing and interpreting data5. Using mathematics, information and computer technology, & computational thinking6. Constructing explanations (for science) and designing solutions (for engineering)7. Engaging in argument from evidence8. Obtaining, evaluating, and communicating information

Crosscutting Scientific and Engineering Concepts

1. Patterns – Observed patterns of forms and events guide organization and classifica-tion, and they prompt questions about relationships and the factors that influence them.2. Cause and Effect – Mechanism and explanation. Events have causes, sometimes simple, sometimes multifaceted. A major activity of science is investigating and explaining causal relationships and the mechanisms by which they are mediated. Such mechanisms can then be tested across given contexts and used to predict and explain events in new contexts.3. Scale, Proportion, and Quantity – In considering phenomena, it is critical to rec-ognize what is relevant at different measures of size, time, and energy and to recognize how changes in scale, proportion, or quantity affect a system’s structure or perfor-mance.4. Systems and System Models – Defining the system under study – specifying its boundaries and making explicit a model of that system – provides tools for understand-ing and testing ideas that are applicable throughout science and engineering.5. Energy and Matter – Flows, cycles, and conservation. Tracking fluxes of energy and matter into, out of, and within systems helps one understand the systems’ possibilities and limitations.6. Structure and Function – The way in which an object or living thing is shaped and its substructure determine many of its properties and functions. 7. Stability and Change – For natural and built systems alike, conditions of stability and determinants of rates of change or evolution of the system are critical elements of study.

Key Conceptual Understandings and Processes in the Science Standards



Next Generation Arts Standards



Stage 2 – Assessment Evidence

Stage 1 – Desired Results

Stage 3 – Learning Plan

What “real-world” tasks will reveal students’ under-standing and proficiency? What transfer performan-ces should students be able to do well if they have met this standard?

What should students come to understand if they really learn this content well?

What should students eventually be able to do on their own if they can meet the Standard?

What important ques-tions are raised by this content?What essential ques-tions will guide inquiry into it?

What instruction is needed to equip students to meet this standard?What learning experiences will help learners acquire the knowledge and skills, make meaning of the impor-tant ideas and equip them to transfer their learning?

What evidence of learning is called for by the standard (and its indicators)?What assessments are needed?

Curriculum Planning with Standards using UbD

What big ideas and transfer goals are embedded in this Standard?

What factual knowledge must students acquire to meet the Standard?

What specific skills are stated or implied in the Standard? What proficiencies must students attain to meet the Standard?

What Standard(s) will the unit focus on? Given your reasons for teaching the unit, which Standard(s) are most relevant?



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sofcurriculumagainstdesignstan

dards

enha

ncecurricularqua

lityan

deffectiven

ess.

8.UbD

refl

ectsa“continuo

usim

provem

ent”app

roach.The

resultsofcurriculumdesigns–stude

ntperform

ance-in

form

sne

eded

adjustm

ents.

Stag

e 1:

Des

ired

Res

ults

Stag

e 2:

Evi

denc

e

Stag

e 3:

Lea

rnin

g Pl

an

• W

hat

long

-ter

m t

rans

fer

goal

s ar

e so

ught

?

• W

hat

mea

ning

s sh

ould

stu

dent

s m

ake

in o

rder

to

arri

ve

at i

mpo

rtan

t un

ders

tand

ings

?

• W

hat

esse

ntia

l qu

esti

ons

wil

l st

uden

ts e

xplo

re?

• W

hat

know

ledg

e &

ski

ll w

ill

stud

ents

acq

uire

?

• W

hat

esta

blis

hed

goal

s/St

anda

rds

are

targ

eted

?

• W

hat

perf

orm

ance

s an

d pr

oduc

ts w

ill

reve

al e

vide

nce

of

m

eani

ng-m

akin

g an

d tr

ansf

er?

• By

wha

t cr

iter

ia w

ill

perf

orm

ance

be

asse

ssed

, in

lig

ht o

f

St

age

1 de

sire

d re

sult

s?

• W

hat

addi

tion

al e

vide

nce

wil

l be

col

lect

ed f

or a

ll S

tage

1

D

esir

ed R

esul

ts?

• W

hat

acti

viti

es,

expe

rien

ces,

and

les

sons

wil

l le

ad t

o

ac

hiev

emen

t of

the

des

ired

res

ults

and

suc

cess

at

the

asse

ssm

ents

?

• H

ow w

ill

the

lear

ning

pla

n he

lp s

tude

nts

of A

cqui

siti

on,

Mea

ning

Mak

ing,

and

Tra

nsfe

r?

• H

ow w

ill

the

unit

be

sequ

ence

d an

d di

ffer

enti

ated

to

op

tim

ize

achi

evem

ent

for

all

lear

ners

?

• A

re a

ll t

hree

sta

ges

prop

erly

ali

gned

?

Gui

ding

Pri

ncip

les

of U

nder

stan

ding

by

Des

ign

Key

Que

stio

ns o

f B

ackw

ard

Des

ign

UbD

in a

Nut

shel

l



Frequently Asked Questions

1. Why did you change the UbD Template?Just as computer software programs are regularly updated to incorporate new ideas and adjustments based on user feedback, the new Template reflects the most current thinking on UbD, based on our own observations and the constant feedback we get from users throughout the world. In particular, we have seen the need to highlight transfer goals and the coding of Stages 2 and 3 because too often well-intentioned designers were not focusing on long-term transfer in their units, and the unit assess-ments often did not closely align with the stated goals of Stage 1.

2. Do you have to follow the UbD Template order (top to bottom) when you design?No. Backward design does not demand a rigid sequence. The process of thinking through a design is inherently non-linear, with various entry points, leading eventu-ally to a logically-organized product. Regardless of approach, designers should rou-tinely check the emerging design against the UbD Design Standards to ensure that the process yields a desired high-quality unit design.

3. Should you use the 3-stage UbD Template for planning lessons as well as units?We do not recommend isolated lesson planning separate from unit planning. We have chosen the unit as a focus for design because the key elements of UbD – understandings, essential questions, and transfer performances – are too complex and multi-faceted to be satisfactorily addressed within a single lesson. For instance, essential questions should be revisited over time, not answered by the end of a single class period.

Nonetheless, the larger unit goals provide the context in which individual lessons are planned. Teachers often report that careful attention to Stages 1 and 2 sharpens their lesson planning, resulting in more purposeful teaching and improved learning.

Wiggins, G. and McTighe, J. (2011) The Understanding by Design Guide to Creating High Quality Units. Association for Supervision and Curriculum Development (ASCD).

<http://www.ascd.org/publications/books/109107.aspx>

The Understanding by Design Template 2.0

Acq

uisi

tion

of

Kno

wle

dge

& S

kill

Est

ablis

hed

Goa

ls

Mea

ning

Tra

nsfe

r

Stud

ents

wil

l kno

w...

Stag

e 1

– D

esir

ed R

esul

ts

UN

DE

RST

AN

DIN

GS

Stud

ents

wil

l und

erst

and

that

...

Stud

ents

wil

l be

able

to in

depe

nden

tly

use

thei

r le

arni

ng to

...

ESS

EN

TIA

L Q

UE

STIO

NS

Stud

ents

wil

l kee

p co

nsid

erin

g...

UbD

Tem

plat

e 2.

0

Stud

ents

wil

l be

skil

led

at...

© 2011 Grant Wiggins & Jay McTighe 19

T1

driv

e co

urte

ousl

y an

d de

fens

ivel

y w

ithou

t acc

iden

ts o

r ne

edle

ss r

isk.

T2

antic

ipat

e an

d ad

apt t

heir

kno

wle

dge

of s

afe

and

defe

nsiv

e dr

ivin

g to

va

riou

s tr

affic

, roa

d an

d w

eath

er c

ondi

tions

.

K1

the

driv

ing

law

s of

thei

r st

ate,

pro

vinc

e or

cou

ntry

K2

rule

s of

the

road

for

lega

l, co

urte

ous

and

defe

nsiv

e dr

ivin

gK

3 ba

sic

car

feat

ures

and

fun

ctio

nsK

4 w

hat t

o do

in c

ase

of a

n ac

cide

nt

Q1

Wha

t mus

t I a

ntic

ipat

e an

d do

to

min

imiz

e ri

sk a

nd a

ccid

ents

whe

n I

driv

e?

Q2

Wha

t mak

es a

cou

rteo

us a

nd d

efen

sive

dr

iver

?

Nat

iona

l Dri

ver

Dev

elop

men

t St

anda

rds

G1

Dem

onst

rate

a w

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know

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ills

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in c

orre

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form

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n an

d m

ake

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risk

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for

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and

posi

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adju

stm

ents

G3

Inte

ract

with

oth

er u

s-er

s w

ithin

the

Hig

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rans

port

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n Sy

stem

by

adju

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spa

ce, a

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com

mun

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void

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nflic

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educ

e ri

sk

G4

Dem

onst

rate

bal

ance

d ve

hicl

e m

ovem

ent t

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gh

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king

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ac-

cele

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se a

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timel

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anne

r th

roug

hout

a

vari

ety

of a

dver

se c

ondi

-tio

ns

Sour

ce:

Am

eric

an D

rive

r &

Tr

affic

Saf

ety

Ass

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tion

S1 p

roce

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saf

e dr

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der

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ried

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fic, r

oad

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eath

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co

nditi

ons

S2 s

igna

lling

/com

mun

icat

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inte

ntio

nsS3

qui

ck r

espo

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to s

urpr

ises

S4 p

aral

lel p

arki

ng

U1

A m

otor

veh

icle

can

bec

ome

a le

thal

wea

pon,

an

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man

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onst

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ttent

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U

2 D

efen

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dri

ving

ass

umes

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oth

er

dr

iver

s ar

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e an

d th

at th

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ight

m

ake

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en o

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-adv

ised

mov

es.

U3

Eff

ectiv

e dr

iver

s co

nsta

ntly

ada

pt to

the

vari

-ou

s tr

affic

, roa

d, &

wea

ther

con

ditio

ns.

Eva

luat

ive

Cri

teri

aA

sses

smen

t E

vide

nce

OT

HE

R E

VID

EN

CE

PE

RF

OR

MA

NC

E T

ASK

(S)

Stag

e 2

– E

vide

nce

UbD

Tem

plat

e 2.

0

Cod

ing


1. T

ask:

dri

ve f

rom

hom

e to

sch

ool a

nd b

ack,

with

par

enta

l and

teac

her

supe

rvis

ion.

The

goa

l is

to d

emon

stra

te s

killf

ul, r

espo

nsiv

e, a

nd d

efen

sive

dr

ivin

g un

der

real

-wor

ld c

ondi

tions

.

2. T

ask:

Sam

e ta

sk a

s #1

but

with

rai

ny c

ondi

tions

.

3. T

ask:

Sam

e ta

sk a

s #1

but

with

rus

h ho

ur tr

affic

.

4. B

ookl

et: W

rite

a b

ookl

et f

or o

ther

you

ng d

rive

rs o

n th

e bi

g id

eas

of

safe

and

eff

ectiv

e dr

ivin

g

5. S

elf-

asse

ss y

our

driv

ing

and

park

ing

in T

asks

1 -

3 in

term

s of

co

urte

ous

& d

efen

sive

. Dis

cuss

adj

ustm

ents

mad

e.

6. O

bser

vatio

n of

stu

dent

dri

ver

in a

dri

ving

sim

ulto

r or

car

off

roa

d.

7. W

ritte

n te

st r

equi

red

for

getti

ng a

lice

nse.

8. R

oad

test

req

uire

d fo

r ge

tting

a li

cens

e.

• kn

ows

the

law

• dr

ives

wel

l en

ough

to

mee

t dri

ving

te

st c

rite

ria

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cura

te•

perc

eptiv

e

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illfu

l

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urte

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defe

nsiv

e

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ticip

ates

wel

l

• re

spon

sive

• sk

illed

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sfer

goals

Mea

ning

Goa

ls

Skill&

Tran

sfer

Goa

ls

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ledg

e&Skill

Goa

ls;

simple

tran

sfer

Mea

ning

Goa

ls

Stag

e 3

– L

earn

ing

Pla

n

UbD

Tem

plat

e 2.

0

Cod

ing

LE

AR

NIN

G E

VE

NT

S

Pro

gres

s M

onit

orin

g

Pre

-ass

essm

ent


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ckC

ircl

esA

ntic

ipat

ion

& P

lann

ing

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adSa

fety

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cks

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stri

an C

ross

ings

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of

Spee

dC

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ols

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umen

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ighw

ays

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er T

raffi

cSt

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g up

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ing

and

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ping

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nsIn

ters

ectio

nsSa

fe P

ositi

onin

gR

ever

sing

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knes

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irro

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rkin

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eath

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tions

Sign

als

Em

erge

ncy

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ping

Rul

es &

Law

sSe

curi

ty

Exp

erie

nce

and

equi

ppin

g vi

a di

rect

inst

ruct

ion

and

vido

e si

mul

taor

s is

pro

vide

d in

term

s of

how

to

hand

le: W

et R

oads

, Dry

Roa

ds, D

arkn

ess

Day

light

, Hig

hway

, City

, Cou

ntry

.

Sepa

rate

ski

ll de

velo

pmen

t and

rea

l-w

orld

pra

ctic

e in

–

All

inst

ruct

ion

is c

arri

ed o

ut a

nd f

orm

ativ

ely

asse

ssed

und

er a

5-l

evel

sys

tem

of

incr

ease

d au

tono

my:

• th

e sk

ill is

intr

oduc

ed•

it ca

n be

car

ried

out

und

er f

ull i

nstr

uctio

n•

it ca

n be

car

ried

out

cor

rect

ly w

hen

prom

pted

• it

seld

om n

eeds

to b

e pr

ompt

ed•

you

can

carr

y it

out c

onsi

sten

tly w

ithou

t any

pro

mpt

ing

Exp

ert d

rivi

ng is

mod

eled

via

vid

eo a

nd th

e dr

ivin

g in

stru

ctor

; the

dri

ving

exa

m is

intr

oduc

ed a

nd s

tudi

ed.

Refl

ectio

n an

d ge

nera

lizat

ions

pro

mot

ed v

ia d

iscu

ssio

n of

the

esse

ntia

l que

stio

ns a

fter

eac

h vi

rtua

l an

d re

al r

oad

expe

rien

ce. W

ritte

n se

lf-a

sses

smen

t req

uire

d af

ter

each

dri

ving

exp

erie

nce.

Not

e: t

his

is a

mer

ely

sugg

esti

ve o

verv

iew

of

a un

it p

lan.

A

typi

cal u

nit

sum

mar

izes

all

lear

ning

eve

nts

in m

ore

deta

il.

Pre-

asse

ssm

ent o

f dr

ivin

g kn

owle

dge,

ski

ll, u

nder

stan

ding

s, a

nd a

ttitu

des

usin

g su

rvey

s an

d si

mul

ator

s.

Form

ativ

e as

sess

men

t an

d in

form

al f

eedb

ack

by in

stru

ctor

as

stud

ent

trie

s to

app

ly s

kills

le

arne

d w

hile

dri

ving

of

f-ro

ad

• L

ook

for

such

com

-m

on m

isco

ncep

tions

an

d sk

ill d

efici

ts a

s -

* fa

ilure

to c

heck

m

irro

rs a

nd p

erip

h-er

al v

isio

n*

not a

ccur

atel

y re

spon

ding

dur

ing

chan

ges

in r

oad

cond

ition

s*

not p

erce

ivin

g sp

eed

of o

ncom

ing

cars

dur

ing

mer

ges

and

turn

s

T A M A,T

Code

Key

:T=tran

sfer,M=Mea

ning-m

aking,A=Acq

uisition

A,T

Acq

uisi

tion

of

Kno

wle

dge

& S

kill

Est

ablis

hed

Goa

ls

Mea

ning

Tra

nsfe

r

Stud

ents

wil

l kno

w...

Stag

e 1

– D

esir

ed R

esul

ts

UN

DE

RST

AN

DIN

GS

Stud

ents

wil

l und

erst

and

that

...

Stud

ents

wil

l be

able

to in

depe

nden

tly

use

thei

r le

arni

ng to

...

ESS

EN

TIA

L Q

UE

STIO

NS

Stud

ents

wil

l kee

p co

nsid

erin

g...

UbD

Tem

plat

e 2.

0

Stud

ents

wil

l be

skil

led

at...


Wha

t spe

cific

ally

do

you

wan

t st

uden

ts to

und

erst

and?

Wha

t inf

eren

ces

shou

ld th

ey m

ake?

Wha

t tho

ught

-pro

voki

ng q

uest

ions

w

ill fo

ster

inqu

iry,

mea

ning

mak

ing,

an

d tr

ansf

er?

Wha

t kin

ds o

f lon

g-te

rm, i

ndep

ende

nt a

ccom

plis

hmen

ts a

re d

esir

ed?

Wha

t Con

tent

Sta

ndar

ds,

Prog

ram

and

/or M

issi

on

rela

ted

goal

(s) w

ill th

is

unit

add

ress

?

Wha

t fac

ts a

nd b

asic

con

cept

s sh

ould

stu

dent

s kn

ow a

nd b

e ab

le

to re

call?

Wha

t dis

cret

e sk

ills

and

proc

esse

s sh

ould

stu

dent

s be

abl

e to

use

?

Eva

luat

ive

Cri

teri

aA

sses

smen

t E

vide

nce

OT

HE

R E

VID

EN

CE

PE

RF

OR

MA

NC

E T

ASK

(S)

Stag

e 2

– E

vide

nce

UbD

Tem

plat

e 2.

0

Cod

ing


How

will

stu

dent

s de

mon

stra

te th

eir u

nder

stan

ding

(mea

ning

-m

akin

g an

d tr

ansf

er) t

hrou

gh c

ompl

ex p

erfo

rman

ce?

Wha

t cri

teri

a w

ill b

e us

ed in

ea

ch

as

sess

men

t to

eva

luat

e at

tain

men

t of

the

Des

ired

Re

sult

s?

Rega

rdle

ss

of th

e form

at

of th

e as

sess

-m

ent,

wha

t qu

alit

ies

are

mos

t im

port

ant?

Wha

t oth

er e

vide

nce

will

you

col

lect

to d

eter

min

e w

heth

er S

tage

1 g

oals

wer

e ac

hiev

ed?

Cons

ider

the

six

fac

ets

whe

n de

velo

ping

ass

essm

ents

of

unde

rsta

ndin

g.O

ptio

nal:

Use

the

G.R

.A.S

.P.S

. el

emen

ts t

o fr

ame

an a

uthe

ntic

con

text

fo

r th

e ta

sk(s

).

Are

all

of th

e D

esir

ed

Resu

lts

bein

g ap

-pr

opri

-at

ely

as-

sess

ed?

Stag

e 3

– L

earn

ing

Pla

n

UbD

Tem

plat

e 2.

0

Cod

ing

LE

AR

NIN

G E

VE

NT

S

Pro

gres

s M

onit

orin

g

Pre

-ass

essm

ent


Whi

le d

etai

led

less

on p

lans

are

not

exp

ecte

d he

re,

you

shou

ld i

nclu

de

suffi

cien

t in

form

atio

n so

tha

t an

othe

r te

ache

r w

ho i

s fa

mil

iar

wit

h th

e un

it’s

con

tent

cou

ld u

nder

stan

d an

d fo

llow

the

bas

ic le

arni

ng p

lan.

Tha

t m

eans

not

jus

t st

atin

g W

HAT

lear

ners

wil

l do

but

WH

Y t

he e

vent

is

prop

osed

-

its

purp

ose

Opt

iona

l: U

se t

he c

olum

n on

the

left

to

code

you

r le

arni

ng a

ctiv

itie

s; e

.g.,

th

eir

alig

nmen

t w

ith

Stag

e 1

elem

ents

, T-

M-A

, or

W.H

.E.R

.E.T

.O.

Are

all

thre

e ty

pes

of g

oals

(acq

uisi

tion

, mea

ning

, and

tran

sfer

) ad

dres

sed

in th

e le

arni

ng p

lan?

Doe

s th

e le

arni

ng p

lan

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TRANSFER GOALS

Definition Transfer Goals highlight the effective uses of understanding, knowledge, and skill that we seek in the long run; i.e., what we want students to be able to do when they con-front new challenges – both in and outside of school. There are a small number of over-arching, long-term transfer goals in each subject area. For example, a long-term aim in mathematics is for students to be able to solve “real world” problems on their own. A long-term transfer goal in history is for students to apply the lessons of history when considering contemporary issues.

In every case, the ability to transfer learning manifests itself in not just one setting but varied real-world situations. Transfer is about independent performance in context. You can only be said to have fully understood if you can apply your learning without someone telling you what to do and when to do it. In the real world, no teacher is there to direct and remind you about which lesson to plug in here or there. Transfer is about intelligently and effectively drawing from your repertoire, independently, to handle new contexts on your own. In the real world, no teacher is there to direct and remind you about which lesson to plug in here or there: transfer is about intelligently and effectively drawing from your repertoire, independently, to handle particular contexts on your own. The goal of transfer thus requires that an instructional plan (in Stage 3) help the student to become increasingly autonomous, and the assessments (in Stage 2) need to determine the degree of student autonomy.

Transfer goals have several distinguishing characteristics: • They require application (not simply recognition or recall). • The application occurs in new situations (not ones previously taught or encoun tered; i.e., the task cannot be accomplished as a result of rote learning). • The transfer requires a thoughtful assessment of which prior learning applies here – i.e. some strategic thinking is required (not simply “plugging in” skill and facts). • The learners must apply their learning autonomously (on their own, without coaching or teacher support). • Transfer calls for the use of habits of mind (i.e., good judgment, self regulation, persistence) along with academic understanding, knowledge and skill.



Students will be able to independently use their learning to:

History • Apply lessons of the past to current and future events and issues, and to other historical eras • Critically appraise political, social, and historical claims/decisions in light of available evidence and reasoning

Health and Physical Education • Make healthful choices and decisions regarding diet, exercise, stress management, alcohol/drug use• Play a chosen game skillfully and with good sportsmanship Mathematics• Investigate and find patterns in phenomena/data, and model them mathematically • Apply sound mathematical reasoning to clarify and solve novel mathematical problems

Performing & Fine Arts • Find meaning and interest in varied works and performances of art • Create/perform works in one or more media to express ideas and/or to evoke mood and emotion

Reading• Read and respond to text in various genres (literature, non-fiction, technical) for various purposes (entertainment, to be informed, to perform a task)• Comprehend text by inferring and tracing the main idea, interpreting (“between the lines”), criti-cally appraising, and making personal connections

Research• Locate pertinent information from varied sources (print, on-line; primary, secondary)• Critically evaluate sources and information (e.g., for accuracy, completeness, timeliness, lack of bias, properly referenced)

Science • Evaluate scientific claims and analyze current issues involving science or technology • Conduct a sound investigation to answer an empirical question

World Language• Communicate effectively in the target language in common “real world” situations• Demonstrate sensitivity in behavior and speech to culture and context

Writing• Write in various genres for various audiences in order to explain (expository), entertain (narrative/poem), argue (persuasive), guide (technical), and challenge (satirical)• Carefully draft, write, edit, and polish one’s own and others’ writing to make it publishable

Long Term Transfer Goalsexamples



Transfer Goals examples from schools and districts

Science Transfer GoalsStudents will be able to independently use their learning to:

• Apply knowledge of science and engineering to engage in public discussions on relevant issues in a changing world.• Conduct investigations, individually and collaboratively, to answer questions.• Evaluate scientific claims for validity.• Think systemically.

Source: North Slope Borough School District, Barrow, Alaska (July 2012)

Visual Arts Transfer GoalsStudents will be able to independently use their learning to:

• Create engaging and purposeful artistic expressions in forms that vary in terms of media and style. • Communicate ideas, experiences, and stories through art. • Respond to the artistic expression of others through global understanding, critical stance, personal connection, and interpretation. • Respond to technical and conceptual challenges of his/her own. • Develop an independent artistic vision.

Source: Sheridan School, Washington, DC (June 2011)

World Languages Transfer Goals Students will be able to independently use their learning to:

• Communicate effectively in the target language(s) in realistic situations while displaying a sensitivity to culture and context. • Emulate native speakers.• Willingly taking risks with language, both within and outside of the classroom.

Source: The Dalton School, New York, NY (March 2012)

Special Education Students will be able to independently use their learning to:

• Function in the community while respecting social/cultural norms.• Advocate for their personal needs – academic, behavioral, emotional, and physical. • Communicate effectively based on purpose, task, and audience using appropriate vocabulary.• Explore and pursue viable options based on aspirations, interests, and experience.

Source: Prosper ISD, TX (April 2013)



UNDERSTANDINGS

Definition Identify the important, transferrable ideas and processes that students should come to understand. Understandings differ in scope and breadth. Overarching understand-ings point beyond the specifics of a unit to the larger, transferrable ideas that spiral throughout the curriculum. Topical understandings target the particular insights we want students to attain within a unit of study. Topical understandings are less likely to transfer to other topics. Effective understandings… • Reflect important, transferrable ideas • Are stated as full-sentence generalizations — Students will understand that…

Desired understandings are identified in Stage 1 for the purpose of: 1. focusing curriculum around enduring, transferable learning to avoid educator and student fixation on narrow objectives; 2. encouraging active meaning making by students; and 3. are necessary for transfer of learning to new situations.

Examples

Overarching Understandings

EconomicsPrice is a function of supply and demand.ScienceGravity is not a physical thing but a term describing the constant rate of acceleration of all falling objects.Physical EducationA muscle that contracts through its full range of motion will generate more forceMathematicsMathematics allows us to see patterns that might have remained unseen.

Topical UnderstandingsUnit on Money (elementary)The cost of a Beanie Baby depends on demand and availability at any given time.Unit on Gravitational ForceVertical height, not the angle and distance of descent, determines the eventual speed of a falling object.Unit on GolfA full stroke with follow-through will increase your distance on a drive.Unit on StatisticsStatistical analysis and graphic displays often reveal patterns in seemingly random data or populations, enabling predictions.



State specifically what it is about the topic that students are expected to grasp. Many curricularframeworks, content standards documents, and teacher objectives make the mistake of framing “understandings” as a topic (e.g., Students will understand the water cycle.) or skill (e.g., Students will understand how to multiply.). We recommend that you summarize the particular understanding(s) you are after, being as specific as possible about the insights that should result from exploring the topic (e.g., Data analysis and graphic displays often reveal helpful patterns and enable prediction.). A practical way to accomplish this is to frame the understanding(s) in response to the stem: “the students will understand that...” (e.g., The Civil War was fought initially over states rights issues and regional economic politics, not just the morality of slavery.). This approach helps to clarify the desired generalizations that we want students to come to understand, while avoiding the problems of stating the understanding in terms of a topic or skill. Another way to think about it: If your unit topic is a “story,” then what is (are) the moral(s) of your story? By stating the understanding as a “moral of the story,” designers move beyond topics to clarify the complete understanding they seek. For example, in a unit on animal adaptation, one of the “morals” can be stated as, Living organisms have developed adaptive mechanisms to enable them to survive harsh or changing environments.

Tips on Framing Understandings

Frame the desired understanding as a full-sentence generalization in response to the phrase, “Students will understand that...”

Beware of stating an understanding as a truism or vague generality.

Avoid the phrase, “Students will understand how to....”

Avoid truisms – statements that are true by definition (e.g., Triangles have 3 sides) or state the obvious (e.g., Musicians work with sounds to create music). Likewise, vague generalities (e.g., America is a complex country or Writing involves many different elements) are too global to provide useful and transferrable insights into important ideas. A practical tip: Check to see that your stated understandings do not end in an adjective (e.g., Fractions are important).

Such a statement is ambiguous. One meaning is that the student will develop certain skills. This kind of objective is best placed in the Skills section on the design template. Another meaning of “understand how” implies that there are insights essential to wise use of the skill – e.g., knowing whysomething works or is useful. Those desired insights should be made explicit and framed as understandings in that section of the template. A practical way to accomplish this is to specify “why?” “how?” and “so what?” as a means of identifying desired understandings in skill areas.



ESSENTIAL QUESTIONS

Definition Open-ended questions designed to promote sustained inquiry and meaning making. Essential questions differ in scope and breadth. We distinguish between overarching and topical questions. Overarching essential questions point beyond the particulars of a unit to the larger, transferable ideas and enduring understandings. They recur fruitfully across the grades, spiraling throughout the curriculum to provide conceptual through lines. Effective overarching essential questions: • are broad and general in nature; and • lead to overarching understandings

Topical essential questions are more specific. They guide the exploration of ideas and processes within particular topics within a unit of study.

Essential questions are identified in Stage 1 for the purpose of: 1. Provoking deep thought, lively discussion, sustained inquiry, and additional questions leading to new and/or deeper insight(s) 2. Asking students to consider alternatives, weigh evidence, support their ideas and rethink key ideas 3. Support connections within and across content and context

Examples

Overarching Essential Questions

• In what ways does art reflect culture as well as shape it? • How do artists choose tools, techniques, and materials to express their ideas?

• What makes a great story?• How do effective writers hook and hold their readers?

Topical Essential Questions

unit on masks• What do masks and their use reveal about the culture? What tools, techniques, and materials are used in creating masks from different cultures?unit on mysteries• What is unique about the mystery genre?• How do great mystery writers hook and hold their readers?



Big Ideas, Understandings and Essential Questions

The following visual represents the interrelationship among big ideas, understandings and essential questions.

big idea

Topic or Content Standard

Understanding – a full-sentence generalization, specifying what we want students to come to understand about the big idea(s).(e.g., Students will understand that...Living organisms (populations) adapt in order to survive harsh or changing environments.)

Essential Question – a provocative, open-ended question, designed to guide inquiry into the big idea(s). By actively exploring the essential question(s), students make meaning and deepen their understanding. (e.g., How do living organisms survive in harsh or changing environments?)

essential question

Big Idea – an abstract and transferable concept, theme, or process at the heart of a subject or topic.

(e.g., adaptation, survival)

(e.g., The student will understand biological adaptation.)

QU

understanding



Tips for Using Essential Questions

1. Organize programs, courses, units of study, and lessons around the questions. Make the “content” answers to questions.

2. Select or design assessment tasks (up front) that are explicitly linked to the questions. The task(s) and performance standards should clarify what acceptable pursuit of, and answers to, the ques-tions actually look like.

3. Use a reasonable number of questions per unit (2-5). Make less be more. Prioritize ‘content’ for students to make the work clearly focus on a few key questions.

4. Frame the questions in “kid language” as needed to make them more accessible. Edit the ques-tions to make them as engaging and provocative as possible for the age-group.

5. Ensure that every child understands the questions and sees their value. Conduct a survey or in-formal check, as necessary, to ensure this.

6. Derive and design specific concrete exploratory activities and inquiries for each question.

7. Sequence the questions so they “naturally” lead from one to another.

8. Post the essential questions in classroom(s), and encourage students to organize notebooks around them to make clear their importance for study and note-taking.

9. Help students to personalize the questions. Have them share examples, personal stories, and hunches. Encourage them to bring in clippings and artifacts to help make the questions come alive.

10. Allot sufficient time for “unpacking” the questions — examining sub-questions and probing implications — mindful of student age, experience, and other instructional obligations. Use question/concept maps to show relatedness of questions.

11. Share your questions with other faculty to make planning and teaching for cross-subject matter coherence more likely. Ideas to promote overarching questions school-wide — ask teachers to post their questions in the faculty room and/or in department meeting/planning areas. Type and circulate questions in the faculty bulletin. Present and discuss at faculty and P.T.S.A. meetings.

Other tips: _______________________________________________________________________

________________________________________________________________________________

© Wiggins & McTighe 2012 page 33

Unpacking Standards Worksheets

Stated/implied performances in VERBS:Stated/implied “big ideas” in NOUNS:

Unpacking Standards - “Inside Out” Method

STANDARD

Understandings

Essential Questions

Transfer Goal(s)

Performance Task(s)

ADJECTIVES and ADVERBS:

Criteria

• Write for the same purpose to different audiences, and explain the influence of the target audience on thestyle, word choice, etc.• Write on the same content in two different genres and explain each genre’s influence on organization, style, word choice.

• A writer’s purpose (e.g., to inform, entertain, persuade, etc.) and audienceshapes the style, development and organization of the writing.• Different writing genres and purposes have unique organizational patterns.

• clear • coherent• appropriate to task, purpose, audience

•development•organization•style•task•audience•purpose(“formfollowsfunction”)

• What is my goal? For whom am I writing? • How does purpose and audience affect a writer’s style and organization? • How do effective writers hook and hold their readers in different genres (e.g., mystery, essay, poem, historical fiction)?

• clear • coherent• appropriate

Produceclearandcoherentwritinginwhichthedevelopment,organization,andstyleareappropriatetotask,purpose,andaudience.

Produce(writing)

Produceclearandcoherentwritinginwhichthedevelopment,organiza-tion,andstyleareappropriatetotask,purpose,andaudience.

Source:CommonCore–CollegeandCareerReadinessAnchorStandards–Writing





STANDARD

Understandings

Essential Questions

Transfer Goal(s)

Performance Task(s)


Criteria

Source:CommonCore–CollegeandCareerReadinessStandards–Writing

•arguments•claims•topicsortexts•evidence•reasoning

•write•support(claims)•analyze(topics/texts)•reasoning

•valid•relevant•sufficient

•relevantevidence•sufficientevidence•validreasoning

Basedonyourreadingofinformationaltextsonalocalornationalissue,preparea(report,lettertoeditor,essay)foraspecificaudiencetoconvincethemofyourposition.Yourargumentshouldfollowalogicalsequencewithsupportingevidenceforyourposition(claim).

• What makes an argument convincing? • What is the best evidence I can use to support my argument? • How do I best organize and present my argument?

•Theeffectivenessofanargumentisdependentuponthequalityofthesupportingevidenceused(validity,appropriateness)andhowitiscon-veyed.

produceclearandcoherentwritingtopersuadeatargetaudience

Writeargumentstosupportclaimsinananalysisofsubstantivetopicsortexts,usingvalidreasoningandrelevantandsufficientevidence.





STANDARD

Understandings

Essential Questions

Transfer Goal(s)

Performance Task(s)


Criteria

Determinecentralideasorthemesofatextandanalyzetheirdevelopment;summarizethekeysupportingdetailsandideas.Source:CommonCore–CollegeandCareerReadinessAnchorStandards–Reading

•ideas •development•themes•details•text

•determine•analyze•summarize

•Authorsdonotalwaysstatethecentralideaorthemeovertly;readershavetoinferit“betweenthelines.”•Effectivereadersusespecificstrate-giestohelptheminfertheimpliedmainideasofatext.

•HowcanItodeterminethecentralideaorthemeofwhatIread?•HowcanIread“betweenthelines”todeterminetheauthor’smeaning?•Whatstrategiesdoeffectiveread-ersusetomakemeaningfromatext?

•Preparea“studyguide”forstudentsbysummarizingthecentralideasorkeythemesofatext.•Usethe“AddinguptheFacts”orga-nizertoshowhowsupportingdetailsleadtoaninferenceaboutmainideas.

•appropriateinference•effectivesummary•supportedbykeydetails

Determinecentralideasorthemesofatextandanalyzetheirdevelop-ment.Summarizethekeysupportingdetails

•central•key•supporting





STANDARD

Understandings

Essential Questions

Transfer Goal(s)

Performance Task(s)


Criteria

•mathematicalmodel(s)•“reallife”problems•disciplinesandlife

• How can I best model this phenomena in this situation?• Do these results make sense?• What are the limits of this mathematical model in this context?• What do effective problem solvers do?

•Mathematicalmodelssimplifyand connectphenomenatoassistinunder-

standingandproblemsolving. •Mathematicalmodelsmustbeviewed

criticallysothattheydonotmislead. •Effectiveproblemsolversalwayscheck

forthereasonablenessofsolutions.

•Createamathematicalmodelforaselected“real-world”situation(e.g.,seasonaltemperatures).•Criticallyreviewandimproveamathematicalmodelforitsappropri-atenesstoagivensituation.

•model •apply•solve

Applythemathematicstheyknowtodevelopmathematicalmodelsforsolvingrealworldproblems

•appropriatemodeling•accurate•reasonablenessofsolution

Model with Mathematics Mathematicallyproficientstudentscanapplythemathematicstheyknowtosolveproblemsarisingineverydaylife,society,andtheworkplace....routinelyinterprettheirmathemati-calresultsinthecontextofthesituationandreflectonwhethertheresultsmakesense,possiblyimprovingthemodelifithasnotserveditspurpose.

Source:CommonCoreStateStandards–Mathematics

•interpret •reflecton•improve





STANDARD

Understandings

Essential Questions

Transfer Goal(s)

Performance Task(s)


Criteria



Directions: Usethefollowingscaletorateyour“levelofuse”ofeachofthefollowingassessmenttools(attheclassroom,schoolordistrictlevel).Whatdothesurveyresultssuggest?Whatpatternsdoyounotice?Areyoucollectingappropriateevidenceforallthedesiredresults,oronlythosethatareeasiesttotestandgrade?Isanimportantlearninggoal“fallingthroughthecracks”becauseitisnotbeingassessed?

4=FrequentUse

3=UseSometimes

2=OccasionalUse

1=DoNotUse

______1.selected-responseformat(e.g.,multiple-choice,true-false)quizzesandtests

______2.written/oralresponsestoacademicprompts(short-answerformat)

______3.performanceassessmenttasks,yielding:

____extendedwrittenproducts(e.g.,essays,labreports)

____visualproducts(e.g.,PowerPointshow,mural)

____oralperformances(e.g.,oralreport,foreignlanguagedialogues)

____demonstrations(e.g.,skillperformanceinphysicaleducation)

______4.long-term,“authentic”projects(e.g.,seniorexhibition)

______5.portfolios-collectionsofstudentworkovertime

______6.reflectivejournalsorlearninglogs

______7.informal,on-goingobservationsofstudents

______8.formalobservationsofstudentsusingobservableindicatorsorcriterionlist

______9.studentself-assessments

______10.peerreviewsandpeerresponsegroups

______11.other:_____________________________________________________

SourcesofAssessmentEvidence:SelfAssessment



Understanding:

Part 1 – How would you define “understanding”? What does it mean to “really understand” or “get it”?

Indicators of UnderstandingIndicators of Knowledge without Understanding

Part 2 - What are concrete indicators of really understanding something (as apposed to merely knowing important facts about it)? What can the person with understanding do that the person with only knowledge—even lots of knowledge—cannot do?

What is understanding?



Performance Tasks:

Student Self-Assessment and Reflection:

Other Evidence:(e.g., tests, quizzes, prompts, work samples, observations, etc.)

You Are What You Eat – Students create an illustrated brochure to teach younger children about the importance of good nutrition for healthful living.

Camp Menu – Students develop a 3-day menu for meals and snacks for an upcoming Outdoor Education camp experience. They write a letter to the camp director to explain why their menu should be selected (by showing that it meets the USDA Food Pyramid recommendations, yet tasty enough for the students).

Quiz - the food groups and the USDA recommendations

Quiz - Skill Check – reading food labels for nutrition info.

Prompt - Describe two health problems that could arise as a result of poor nutrition and explain how these could be avoided.

1. self assess the brochure, You are What You Eat 2. self assess the camp menu3. self assess the extent to which you “eat healthy” at the

end of unit (compared to the beginning)

A Collection of Assessment Evidence example - unit on Nutrition - grades 5-6



Performance tasks can be used as rich learning activities or as assessments. They ask students to apply knowledge and skills to a new situation, and typically yield tangible products and performances that serve as evidence of learning. Performance tasks (as distinct from long-term projects) can usually be completed within a relatively short time frame, generally between one and four class periods. Here are general characteristics of performance tasks; they: • demand thoughtful application of knowledge and skills, not just recall; • yield tangible products and performances that serve as evidence of learning; • establish authentic contexts for performance; • can integrate two or more subjects as well as 21st century skills (e.g., critical thinking, technology use, teamwork); • do not have a “single, best” answer or one, “right way” to accomplish the task; • evaluate performance with established criteria and rubrics; and • may be used as rich learning activities and/or assessments. Performance tasks may be content-specific (e.g., mathematics, science, social studies) or integrated (i.e., involving two or more subjects). One natural interdisciplinary connection is to include a reading, research and/or communication (writing, graphics, presentation) component to tasks in content areas. Such tasks encourage students to see meaningful learning as integrated, rather than something which occurs in isolated segments. Two examples of performance tasks are provided below.

Fairy Tales [grades 3-4]

You have just finished reading three fairy tales that all have the same general pattern – characters overcoming a confrontation with an animal when the animal’s intent is to harm the character(s). Your task is to write a story that includes all the characteristics of a fairy tale and also uses this same general pattern. You will then read your story to your kindergarten reading buddy and teach him/her about the characteristics and general pattern of a fairy tale. Source: Assessing Outcomes: Performance Assessment Using Dimensions of Learning

City Park [high school physics]

Your design team has been asked by the City Park Department to construct a model for a new playground near the elementary school. The playground will have swing sets and see-saws. For the safety of the children who will be using the playground equipment, you must design your swings so that they don’t swing too fast or “loop-the-loop “ over the top of the swing set. Design and conduct an experiment to determine how the variables - length, mass, height of release - affect the rate of back-and-forth movement of a swing. Be prepared to present your find-ings, recommendations, and a demonstration to the City Park officials. Source: A Tool Kit for Professional Developers: Alternative Assessment

Performance Tasks



The facets of understanding provide indicators of understanding and thus can be used to select or develop assessments.

If someone really understands something, they can...

Explanation

Inte

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Pers

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Self-Knowledge

The Facets of Understanding

Empathy

• Explain it in their own words.•Represent it in a different form.

•Teach it to someone else.•Make and support an

inference.

• Make meaning from a text or data set.• See and describe patterns.• Make new connections.

• Use their learning effectivelyin a new situation.• Transfer.

• Get “inside” another person’s feelings and world view.• Recognize merit in the odd, unorthodox, or unfamiliar.

• Realize their strengths and weaknesses.

• Recognize the limits of their own understanding.

• Reflect on their learning and actions.

• Recognize different points of view. • See the “big picture.”• Take a critical stance.

Facets of Understanding

Application



Use the six facets of understanding to generate possible ways in which students might reveal understanding.

Explanation

ApplicationIn

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Pers

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Brainstorming Assessment Ideas Using the Facets

Em

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• Explain how a battery causes a light bulb to glow.

• Interpret a schematic diagram and predict the outcome.

• Design an electrical circuit to accomplish a specific task.• Troubleshoot a faulty electrical circuit.

• Describe an electron’s experience as it passes through a simple current.

• Reflect on your deepening understandingof electricity (e.g., I used to think that..... but now

I understand that....).

• Why does the United States use AC instead of DC current? (historical perspective)

electriccircuits



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Colle

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patte

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stem

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ning

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syst

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inan

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ates

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e sy

stem

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cri

tical

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rmat

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pute

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chno

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puta

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stru

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8. O

btai

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mun

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Designan

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gene

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lana

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ppen

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the

future.

Considerthisqu

estion

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How

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bor

syst

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mer

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pact

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row

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erns

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Am

eric

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In1998,UNESCO

decreed

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efocusofthisyear’s

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Teaching and Learning for Understanding

Transferlearning to new

situations

Make Meaning of “big ideas”(key principles and processes)

Acquire important knowledge and skills

What does it mean to teach and learn for understanding? We have found it useful to consider this question by examining three distinct, yet interrelated, learning goals: 1) acquisition of new information and skill, 2) making meaning of that content (i.e., coming to understand), and 3) transfer of one’s knowledge (i.e., apply-ing one’s learning to new situations). These three categories link directly to elements identified in Understanding by Design. In Stage 1 teachers specify the knowledge and skill that they intend students to acquire. They also decide upon the “big ideas” they want students to come to understand and develop essential questions to help students make meaning of those ideas. In Stage 2, teachers develop performance tasks requiring transfer as evidence that students understand and can apply their knowledge in authentic contexts.



What is Fair?Who won this year’s 7th grade race around the campus?Every year at Birdsong Middle School, there is an all-class race. Below are the results for the 7th grade (which is made up of four different classes). But there is a problem: no one agrees on who won! One person thinks Class C should win the trophy because they had the 1st runner overall in the race. Another person thinks Class D should win because they had 3 runners come in under 10th place. A third person says: just find the average. But a 4th person said: wait a minute – Class C had more students in their class than Class D. Averages won’t be fair! A 5th person says: use the scoring system in Cross Country – just add up the place of finish of the top 5 finishers in each class and the lowest total wins. A 6th person says – unfair! Some classes did well in the first few runners but poorly in the middle! Why should they win? Now, everyone is confused and arguing.

What is the fairest way to determine the winner? Which class should win the trophy? Your group, well-known in the school as a group of expert mathematicians (and respected for your sense of fairness) is being consulted as to who should win the trophy. What will you recommend and why?

Class rank Class A Class B Class C Class D 1 4 6 1 2 2 9 7 3 5 3 11 10 14 8 4 12 13 18 15 5 20 16 19 17 6 21 22 23 31 7 25 24 28 33 8 26 27 30 36 9 29 34 32 37 10 35 39 41 38 11 43 40 44 46 12 45 42 47 51 13 49 48 50 55 14 54 52 56 57 15 61 53 60 58 16 65 62 63 59 17 69 66 64 67 18 70 72 68 19 71 73 20 74

Notes on the chart:• The numbers in the chart, from 1 to 74 represent the place of finish of that runner. So, the overall race winner was from Class C, the number two runner overall was in Class D, etc.• Class rank refers to the rank of finish place in that class, not the overall race. So, the first runner in class A was 4th overall in the race, the 2nd best runner in class A came in 9th overall, etc.• The blanks reflect the fact that each of the 4 classes has a different number of students.



A = acquiring basic knowledge and skills M = making meaning T = transfer

Mathematics Unit on Measures of Central Tendency

Essential Question: What is fair - and how can mathematics help us answer the question?

1. Introduce and discuss the essential question, first part - What is “fair”? What is “unfair’? M

2. Introduce the 7th grade race problem. Which of the 7th-grade classes won the race? What is a fair way to decide? Small-group inquiry, followed by class discussion of answers. M

3. Teacher informs students about the mathematical connections derived from the problem analysis, and lays out the unit and its culminating transfer task. A

4. In small-group jigsaw, students share their answers to the INQUIRY sheet, then return to their team to generalize from all the small-group work. Discuss other examples related to the concept of “fairness” such as the following. M - What is a fair way to rank many teams when they do not all play each other? - What is a fair way to split up limited food among hungry people of very different sizes? - When is it ‘fair’ to use majority vote and when is it not fair? What might be fairer? - Is it fair to have apportioned Representatives based on a state’s population, yet have two Senators from each state irrespective of their size? What might be fairer? - What are fair and unfair ways of representing how much money the “average” worker earns, for purposes of making government policy?

5. Teacher connects the discussion to the next section in the textbook - measures of central tendency (mean, median, mode, range, standard deviation). A

6. Students practice calculating each type of measure. A

7. Teacher gives quiz on mean, median, mode from textbook. A

8. Teacher leads a review and discussion of the quiz results. A M

9. Group task worked on in class: What is the fairest possible grading system for schools to use? M T10. Individuals and small teams present their grading policy recommendations and reasons. M T 11. Culminating transfer task: Each student determines which measure (mean, median or mode) should be used to calculate their grade for the marking period and writes a note to the teacher show-ing their calculations and explaining their choice. T

12. Students write a reflection on the essential question and their learnings as a result of the unit. M

Coding a Learning Plan Using A - M - T



UNITED STATES SOCCER FEDERATION

USSOCCER.COM62

Our challenge is to develop players that are:• Technically Gifted• Tactically Sound• Composed• Creative• Risk Takers• “Own the Game” and are focused on solving the problems that the game presents, instead of

primarily thinking about coach imposed solutions to the game

EVOLVING COACHES –> EVOLVING PLAYERSIn order to affect change on the players a shift in coaching methodology may need to take place.The development of creative, intuitive players is greatly impacted by coaching style anddemands.

When conducting training sessions, there needs to be a greater reliance on game orientedtraining that is player centered and enables players to explore and arrive at solutions while theyplay. This is in contrast to the “coach centered” training that has been the mainstay of coachingmethodology over the years.

GAME CENTERED TRAINING DEFINED“Game centered training” implies that the primary training environment is the game as opposedto training players in “drill” type environments. This is not to say that there is not a time for amore “direct” approach to coaching. At times, players need more guidance and direction as theyare developing. However, if the goal is to develop creative players who have the abilities tosolve problems, and interpret game situations by themselves, a “guided discovery” approachneeds to be employed.

This approach taps in to certain essentials that are always present within the team. Players wantto play and enjoy playing the game first and foremost. Since the “game” is used in training, thisallows for players to be comfortable with the pace, duration, and physical and mental demandsthat the game provides. The reason why the players play is because they enjoy the game. Theyhave a passion for the game. This is where they find and express their joy and creativity.

Games vs. Drills: a comparison

GAME• This is what the players actually face during competition. It is 100% realistic.• Therefore, the players are more competent at transferring what they have learned in training to

the game itself.• Game Experience = 100% of Training Time



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Teaching and Assessing for Understanding – Observable Classroom Indicators

To what extent are...

1. Instruction and assessment focused on “big ideas” and essential questions based on established standards/outcomes?

2. Essential questions posted and revisited throughout a unit?

3. Pre-assessments used to check students’ prior knowledge and potential misconceptions regarding new topics of study?

4. Opening ”hooks” used to engage students in exploring the big ideas and essential questions?

5. Students’ understanding of the “big ideas” and core processes assessed through authentic tasks involving one or more of the six facets?

6. Evaluations of student products/performances based upon known criteria/rubrics, performance standards, and models (exemplars)?

7. Appropriate instructional strategies used to help learners’ acquire knowledge and skills, make meaning of the big ideas, and transfer their learning?

8. Students given regular opportunities to rethink, revise and reflect on their work based on feedback from on-going (formative) assessments?

9. The students expected to self-asses/ reflect on their work/learn-ing and set goals for improvement?

10. Other: _____________________________________

4 3 2 1

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Policies,Structures,Governance

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Curriculum Design: Macro and Micro Views

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CornerstoneTasks

OverarchingEssential Questions

recurringtasks



The pressures of high-stakes accountability testing have led many schools and districts to encourage their teachers to engage in “test prep” instruction, especially in the tested grades and subject areas. Additionally, there has been an increase in the use of “interim” or benchmark assessments that mimic the state tests. While these practices may have their place, they typically focus on decontextualized content knowledge and skills at the expense of more relevant and engaging learning. As a counter-balance to “test prep” teaching and “practice” testing, Grant Wiggins and I have argued for the inclusion of more robust and authentic tasks as part of a local curriculum and assessment system. We refer to these as “cornerstone” tasks. The Cornerstones are curriculum-embedded tasks that are intended to engage students in applying their knowledge and skills in an authentic context. Like a cornerstone anchors a building, these tasks are meant to anchor the curriculum around the most important performances that we want learners to be able to do (on their own) with acquired content knowledge and skills. They honor the intent of the Standards, within and across subject areas, instead of emphasizing only the tested (a.k.a. “eligible”) content. Moreover, they support effective instructional practices that engage learners in “meaning making” and transfer. More specifically, Cornerstone tasks: • are curriculum embedded (as opposed to externally imposed); • recur across the grades, becoming increasingly sophisticated over time; • establish authentic contexts for performance; • call for understanding and transfer via genuine performance; • may be used as rich learning activities or assessments; • integrate 21st century skills (e.g., critical thinking, technology use, teamwork) with subject area content; • evaluate performance with established rubrics; • engage students in meaningful learning while encouraging the best teaching; • provide content for student portfolios so that they graduate with a resume of demonstrated accomplishments rather than simply a transcript of courses taken.

Cornerstone Tasks



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Mathematical Modeling

Grade2/3 Everysevenweeksstudentsworkingroupsoffourtomeasuretheheightofeachotherusingtapemeasuresaffixedtotheclassroomwalls.Bymid-May,theclasshasob-tainedsixheightmeasures.Then,studentscreateasimplegraph(heightininchesplottedagainstthemonthsoftheschoolyear)andplotthedata.Usingrulers,theyconnectthedotstosee“riseoverrun”(avisualrepresentationoftheirgrowthovertime).Thechartpapersarepostedthroughouttheroom,andthestudentscirculateinagallerywalktoviewthechangesinheightsofthevariousgroups.Studentsthenanalyzethedatatoanswerguidingquestions:“Inwhatmonthsdidwegrowthemostthisyear?”“Isthereadifferencebetweenhowboysandgirlshavegrowninsecondgrade?”“Howdoesourclassgrowthcomparetothatintheothersecondgrades?”“Whatcanwepredictfornextyear’ssecondgradersabouthowtheywillgrowbasedonourdata?”Studentsarethenworkintheirgroupstodevelopapresentationforthecurrent1st/2ndgraderstopredicthowmuchtheywillgrownextschoolyear.

MiddleSchool AformerNBAlegend,HoopsMcGinty,haspledgedmoneytothelocalsciencemuseumforanexhibitonoursolarsystem.Hepledgesthemoneyunderonecondition:thataregulationNBAbasketballbeusedtorepresentsomeaspectofthescaledisplayandthatotherNBA-relatedshapesandsizesbeused(e.g.,abasketballbeusedtorepresentaplanetormoon).Thebuildingfloorspaceis300by800feet. Yourjobistocreateamodelofthesolarsystemthatisbuilttoscaletofitwithinthisspace.Prepareadiagramwithaccuratemeasurementsdrawntoscale.ShowyourworksothatHoopswillapproveandfundyourdesign.

HighSchool Createamathematicalmodelinorderto: •recommendthemostcosteffectivecellphonecontractwhileconsidering differentvariables(e.g.,typeofcellphone,lengthofcontract,calling/data amounts). •comparehomemortgageoptionsforvariedpurchaseprices,downpayments, interestrateplans,andlengthofterm(includingvariablerates). •predictfutureOlympiceventwinningtimes(e.g.,men’sandwomen’s marathon). •

Cornerstone Assessments – Examples of Recurring Tasks



The Literacy Design Collaborative Task Templates

Funded through the Bill and Melinda Gates Foundation, the Literacy Design Collaborative (LDC) has developed a set of Modules designed to support the integration of the Common Core Standards (6-12) in English/ Language Arts with core content in Science, Social Studies and Technical areas. Each Module consists of a task and associated instructional procedures intended to provide a rigor-ous, authentic classroom experience for students at the secondary level.

The Tasks require students to read, analyze, and comprehend written materials and then write cogent arguments, explanations, or narratives in the subjects they are studying. A key feature of the LDC’s work is a set of generic Task Templates -- fill-in-the-blank “shells” that allow teachers to design their own tasks.

Here are several samples:

Argumentation Task TemplateAfter researching ________ (informational texts) on ________ (content topic or issue), write a/an ________ (essay or substitute) that argues your position on ________ (topic, issue, essential ques-tion). Support your position with evidence from research. Be sure to acknowledge competing views. Give examples from from past or current events issues to illustrate and clarify your position.

Social Studies Example: After researching academic articles on censorship, write a/an blog or editorial that argues your position on the use of filters the use of Internet filters by schools. Support your position with evidence from research. Be sure to acknowledge competing views.

ELA Example: What makes something something funny? After reading selections from Mark Twain and Dave Barry, write a review that compares their their humor and argues which type of humor works for a contemporary audience and why. Be sure to support your position with evidence from the texts.. Be sure to support your position with evidence from the texts.

Informational or Explanatory Task Template

[Insert question] After reading ________ (literature or informational texts), write a/an __________ (essay, report, article, or substitute) that defines and explains (term or concept). Support your discus-sion with evidence from the text(s). What ________ (conclusions or implications) can you draw?

Social Studies Example: What did the authors of the American Constitution mean by “rights”? After reading the Bill of Rights, write an essay that defines “rights” and explains “rights” as the authors use it in this foundational document. Support your discussion with evidence from the text. What implications implications can you draw?



Social Studies

UpperElementary/MiddleSchool Youhaveanideathatyoubelievewillmakeyourschoolbetter,andyouwanttoconvinceschoolleadersthattheyshouldactonyouridea.Identifyyouraudience(e.g.,principal,PTSABoard,students)and: •Describeyouridea. •Explainwhy&howitwillimprovetheschool. •Developaplanforactingonyouridea. Yourideaandplancanbecommunicatedtoyourtargetaudienceinaletter,e-mail,orpresentation.

HighSchool Afterinvestigatingacurrentpoliticalissue,prepareapositionpaper/presenta-tionforapublicpolicymaker(e.g.,Congressperson)orgroup(e.g.,schoolboard,legislativecommittee).Assumethatthepolicymakerorgroupisopposedtoyourposition.Yourpositionstatementshouldprovideananalysisoftheissue,consideroptions,presentyourposition,rebutopposingpositions,andattempttopersuadethepublicpolicymakerorgrouptovoteaccordingly. Yourpositioncanbecommunicatedinawrittenreport,viaawebblog,ordeliveredasapresentation.

Other:______________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________




Science

UpperElementary ThePooperScooperKittyLitterCompanyclaimsthattheirlitteris40%moreabsorbentthanotherbrands. YouareaConsumerAdvocatesresearcherwhohasbeenaskedtoevaluatetheirclaim.Developaplanforconductingtheinvestigation.Yourplanshouldbespecificenoughsothatthelabinvestigatorscouldfollowittoevaluatetheclaim.

MiddleSchool Designandconductaninvestigationtoanswerthequestion,Howdoesexerciseaffectthepulserate?Comparenormalpulseratetochangescausedbytwoselectedphysicalactivities(e.g.,jogging,push-ups,squats,swimming)fordesignatedintervals. Prepareareporttoexplaintheresultstootherstudentsinanewsarticle,e-mail,graphic,orotherappropriatemedia..

HighSchool Designaninvestigationtoanswerthequestion,Howmuchdoesitcosttotakeashower? Identifythevariablesthatmustbeconsideredandthendevelopaplanforconductingtheinvestigation.Yourplanshouldbespecificenoughsothatotherinvestigatorscouldfollowitandanswerthequestion.

_______________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________




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mbo

lic n

otat

ion

are

used

to

cons

olid

ate

mat

h th

inki

ng a

nd

to c

omm

unic

ate

idea

s.

Abs

trac

t or

sym

bolic

m

athe

mat

ical

rep

rese

nta-

tions

are

con

stru

cted

to

anal

yze

rela

tions

hips

, ex-

tend

thin

king

, and

cla

rify

or

inte

rpre

t phe

nom

enon

.

3 Pr

actit

ione

r

A c

orre

ct s

trat

egy

is c

hose

n ba

sed

on m

athe

mat

ical

situ

atio

n in

the

task

. Pla

nnin

g or

mon

itori

ng o

f st

rate

gy is

evi

dent

. Evi

denc

e of

so

lidif

ying

pri

or k

now

ledg

e an

d ap

plyi

ng it

to th

e pr

oble

m.

A c

orre

ct a

nsw

er is

ach

ieve

d.

Arg

umen

ts a

re c

onst

ruct

ed

with

ade

quat

e m

athe

mat

ical

ba

sis.

A s

yste

mat

ic a

ppro

ach

and/

or ju

stifi

catio

n of

cor

rect

re

ason

ing

is p

rese

nt. T

his

may

lead

to c

lari

ficat

ion

of

the

task

and

not

ing

patte

rns,

st

ruct

ures

and

reg

ular

ities

.

A s

ense

of

audi

ence

or

purp

ose

is c

omm

unic

ated

. and

/or

Com

mun

icat

ion

of a

n ap

-pr

oach

is e

vide

nt th

roug

h a

met

hodi

cal,

orga

nize

d, c

oher

-en

t seq

uenc

ed a

nd la

bele

d re

-sp

onse

. For

mal

mat

h la

ngua

ge

is u

sed

to s

hare

and

cla

rify

id

eas.

App

ropr

iate

and

acc

urat

e m

athe

mat

ical

rep

rese

nta-

tions

are

con

stru

cted

and

re

fined

to s

olve

pro

blem

s or

por

tray

sol

utio

ns.

2 A

ppre

ntic

e

A p

artia

lly c

orre

ct s

trat

egy

is

chos

en, o

r a

corr

ect s

trat

egy

for

only

sol

ving

par

t of

the

task

is

chos

en. E

vide

nce

of d

raw

ing

on s

ome

prev

ious

kno

wle

dge

is

pres

ent,

show

ing

som

e re

leva

nt

enga

gem

ent i

n th

e ta

sk.

Arg

umen

ts a

re m

ade

with

so

me

mat

hem

atic

al b

asis

.So

me

corr

ect r

easo

ning

or

just

ifica

tion

for

reas

onin

g is

pr

esen

t with

tria

l and

err

or, o

r un

syst

emat

ic tr

ying

of

seve

ral

case

s.

Som

e aw

aren

ess

of a

udie

nce

or p

urpo

se is

com

mun

icat

ed,

and

may

take

pla

ce in

the

form

of

par

aphr

asin

g of

the

task

. or

So

me

com

mun

icat

ion

of

an a

ppro

ach

is e

vide

nt th

roug

h ve

rbal

/wri

tten

acco

unts

and

ex

plan

atio

ns, u

se o

f di

agra

ms

or o

bjec

ts, w

ritin

g, a

nd u

sing

m

athe

mat

ical

sym

bols

.

An

atte

mpt

is m

ade

to

cons

truc

t mat

hem

atic

al

repr

esen

tatio

ns to

rec

ord

and

com

mun

icat

e pr

ob-

lem

sol

ving

, but

they

are

in

com

plet

e or

inap

pro-

pria

te.

1 N

ovic

e

No

stra

tegy

is c

hose

n, o

r a

stra

t-eg

y is

cho

sen

that

will

not

lead

to

a co

rrec

t sol

utio

n.

Arg

umen

ts a

re m

ade

with

no

mat

hem

atic

al b

asis

.N

o co

rrec

t rea

soni

ng n

or

just

ifica

tion

for

reas

onin

g is

pr

esen

t.

No

awar

enes

s of

aud

ienc

e or

pu

rpos

e is

com

mun

icat

ed.

or

Litt

le o

r no

com

mun

ica-

tion

of a

n ap

proa

ch is

evi

dent

or

Eve

ryda

y, f

amili

ar la

n-gu

age

is u

sed

to c

omm

unic

ate

idea

s.

No

atte

mpt

is m

ade

to

cons

truc

t mat

hem

atic

al

repr

esen

tatio

ns.

Sour

ce:

Exe

mpl

ars.

com

Com

mon

Rub

ric

for

Mat

hem

atic

al P

robl

em S

olvi

ng



Common Analytic Rubric for Persuasive Writing

2/3

/03

S

KIL

L

AR

EA

6

Resp

on

ses

at

this

lev

el:

5

Resp

on

ses

at

this

lev

el:

4

Resp

on

ses

at

this

lev

el:

3

Resp

on

ses

at

this

lev

el:

2

Resp

on

ses

at

this

lev

el:

1

Resp

on

ses

at

this

lev

el:

Mea

nin

g:

the e

xte

nt

to w

hic

h t

he w

riti

ng

exh

ibit

s so

un

d

un

der

stan

din

g,

anal

ysi

s, a

nd

exp

lan

atio

n,

of

the

wri

tin

g t

ask

an

d

tex

t(s)

• c

on

vey

an

accu

rate

an

d i

n-

dep

th u

nd

erst

and

ing

of

the

top

ic,

aud

ien

ce,

an

d p

urp

ose

for

the

wri

tin

g t

ask

• o

ffer

insi

gh

tfu

l an

d t

ho

rou

gh

anal

ysi

s an

d e

xp

lan

ati

on

in

sup

po

rt o

f th

e a

rgu

men

t o

r

po

siti

on

• c

on

vey

an

accu

rate

an

d

com

ple

te u

nd

erst

and

ing

of

the

top

ic,

aud

ien

ce,

an

d

pu

rpo

se f

or

the

wri

tin

g t

ask

• o

ffer

clea

r an

d e

xp

licit

anal

ysi

s an

d e

xp

lan

ati

on

in

sup

po

rt o

f th

e a

rgu

men

t o

r

po

siti

on

• c

on

vey

an

accu

rate

alth

ou

gh

so

mew

hat

basi

c

un

der

stan

din

g o

f th

e t

op

ic,

aud

ien

ce,

and

pu

rpo

se f

or

the

wri

tin

g t

ask

• o

ffer

part

ial

anal

ysi

s an

d

exp

lan

atio

n i

n s

up

po

rt o

f

the

arg

um

ent

or

po

siti

on

• c

on

vey

a p

artl

y a

ccu

rate

un

der

stan

din

g o

f th

e t

op

ic,

aud

ien

ce,

and

pu

rpo

se o

f

the

wri

tin

g t

ask

• o

ffer

lim

ited

an

aly

sis

or

sup

erfi

cial

ex

pla

nati

on

th

at

on

ly p

arti

all

y s

up

po

rt t

he

arg

um

ent

or

po

siti

on

• c

on

vey

a c

on

fuse

d o

r

larg

ely

in

accu

rate

un

der

stan

din

g o

f th

e t

op

ic,

aud

ien

ce,

and

pu

rpo

se f

or

the

wri

tin

g t

ask

• o

ffer

un

clear

an

aly

sis

or

un

war

ran

ted

ex

pla

nati

on

s

that

fai

l to

su

pp

ort

th

e

arg

um

ent

or

po

siti

on

• p

rov

ide n

o e

vid

ence

of

un

der

stan

din

g t

he

wri

tin

g t

ask

or

top

ic

• m

ake

inco

here

nt

exp

lan

atio

ns

that

do

no

t su

pp

ort

th

e

arg

um

ent

or

po

siti

on

Dev

elo

pm

ent:

th

e

exte

nt

to w

hic

h i

deas

are

elab

ora

ted

usi

ng

speci

fic

and

rel

evan

t

det

ail

s an

d/o

r

evid

ence

to

su

pp

ort

the

thesi

s

• s

up

po

rt t

he p

osi

tio

n c

learl

y

and

fu

lly

wit

h a

rgu

men

ts t

hat

effe

ctiv

ely

in

teg

rate

an

d

elab

ora

te o

n s

pec

ific

id

eas

and

tex

tual

ev

iden

ce

fro

m a

var

iety

of

sou

rces

• e

ffect

ivel

y a

nti

cip

ate

and

con

vin

cin

gly

refu

te o

pp

osi

ng

vie

w p

oin

ts

• s

up

po

rt t

he p

osi

tio

n

clea

rly

an

d c

on

sist

entl

y

wit

h a

rgu

men

ts t

hat

inco

rpo

rate

an

d e

xp

lain

idea

s an

d s

peci

fic

tex

tual

evid

ence

fro

m a

vari

ety

of

sou

rces

• a

nti

cip

ate

an

d s

om

ewh

at

con

vin

cin

gly

refu

te

op

po

sin

g v

iew

po

ints

• s

up

po

rt t

he p

osi

tio

n w

ith

arg

um

ents

th

at

use

id

eas

and

rel

evan

t te

xtu

al

evid

ence

fro

m a

vari

ety

of

sou

rces

• a

nti

cip

ate

an

d a

ttem

pt

to

refu

te o

pp

osi

ng

vie

wp

oin

ts a

t a

bas

ic l

evel

• s

up

po

rt t

he p

osi

tio

n

par

tiall

y,

usi

ng

so

me i

dea

s

and

tex

tual

evid

ence b

ut

wit

ho

ut

mu

ch e

lab

ora

tio

n

or

fro

m l

imit

ed s

ou

rces

• p

arti

ally

an

tici

pat

e an

d

wit

h a

lim

ited

or

con

fuse

d

atte

mp

t to

refu

te o

pp

osi

ng

vie

wp

oin

ts b

ut

• a

ttem

pt

to s

up

po

rt t

he

po

siti

on

, b

ut

tex

tual

ideas

and

ev

iden

ce

is v

agu

e,

rep

etit

ive,

or

un

just

ifie

d

• a

llu

de t

o o

pp

osi

ng

vie

wp

oin

ts b

ut

mak

e n

o

atte

mp

t to

refu

te t

hem

• c

om

ple

tely

lac

k

dev

elo

pm

ent

and

do

no

t in

clu

de

tex

tual

evid

ence

• m

ake

no

att

emp

t t o

anti

cip

ate

or

refu

te

op

po

sin

g v

iew

po

ints

Org

an

iza

tio

n:

the

exte

nt

to w

hic

h t

he

wri

tin

g e

stab

lish

es a

clea

r th

esi

s an

d

mai

nta

ins

dir

ecti

on

,

focu

s, a

nd

co

here

nce

• s

kil

lfu

lly

est

abli

sh a

nd

mai

nta

in c

on

sist

ent

focu

s o

n a

clea

r an

d c

om

pel

lin

g t

hes

is

• e

xh

ibit

lo

gic

al a

nd

co

her

ent

stru

ctu

re w

ith

cla

ims,

evid

ence

an

d i

nte

rpre

tati

on

s

that

co

nv

incin

gly

su

pp

ort

th

e

thes

is

• m

ake

skil

lfu

l u

se o

f

tran

siti

on

wo

rds

and

ph

rase

s

• e

ffect

ivel

y e

stab

lis h

an

d

mai

nta

in c

on

sist

ent

focu

s

on

a c

lear

thes

is

• e

xh

ibit

a l

og

ical

seq

uen

ce

of

cla

ims,

ev

iden

ce,

and

inte

rpre

tati

on

s to

su

pp

ort

the

thesi

s

• m

ake

effe

cti

ve u

se o

f

tran

siti

on

wo

rds

and

ph

rase

s

• e

stab

lish

an

d m

ain

tain

focu

s o

n a

cle

ar t

hesi

s

• e

xh

ibit

a l

og

ical

seq

uen

ce o

f cl

aim

s,

evid

ence

, an

d

inte

rpre

tati

on

s b

ut

ideas

wit

hin

par

agra

ph

s m

ay b

e

inco

nsi

sten

tly

org

aniz

ed

• m

ake

som

e a

ttem

pt

to

use

bas

ic t

ran

siti

on

wo

rds

and

ph

rase

s

• e

stab

lish

bu

t fa

il t

o

con

sist

entl

y m

ain

tain

fo

cus

on

a b

asi

c th

esi

s

• e

xh

ibit

a b

asic

str

uctu

re

bu

t la

ck t

he

coh

ere

nce

of

con

sist

ent

clai

ms,

ev

iden

ce,

and

in

terp

reta

tio

ns

• m

ake

an i

nco

nsi

sten

t

atte

mp

t to

use

so

me

bas

ic

tran

siti

on

wo

rds

or

ph

rase

s

• e

stab

lish

a c

on

fuse

d o

r

irre

lev

ant

thes

is a

nd

fail

to

mai

nta

in fo

cus

• e

xh

ibit

an

att

emp

t to

org

aniz

e id

eas

in

t o a

beg

inn

ing

, m

idd

le,

and

end

, b

ut

lack

co

her

ence

• m

ake

litt

le a

ttem

pt

to

use

tra

nsi

tio

n w

ord

s an

d

ph

rase

s

• f

ail

to i

nclu

de

a

thes

is o

r m

ain

tain

focu

s

• c

om

ple

te l

ack

of

org

aniz

atio

n a

nd

coh

eren

ce

• m

ake

no

att

emp

t t o

use

tra

nsi

tio

n w

ord

s o

r

ph

rase

s

La

ng

ua

ge:

th

e

exte

nt

to w

hic

h t

he

wri

tin

g r

eveal

s an

aware

nes

s o

f

aud

ien

ce a

nd

pu

rpo

se

thro

ug

h w

ord

ch

oic

e

and

sen

ten

ce

vari

ety

• a

re s

tyli

stic

ally

sop

his

ticat

ed,

usi

ng

lan

gu

age

that

is

pre

cis

e a

nd

en

gag

ing

,

wit

h a

no

tab

le s

ense

of

vo

ice

and

aw

aren

ess

of

aud

ien

ce

and

pu

rpo

se

• e

ffect

ivel

y i

nco

rpo

rate

a

ran

ge o

f v

arie

d s

ente

nce

pat

tern

s to

rev

eal

sy

nta

cti

c

flu

ency

• u

se l

ang

uag

e t

hat

is f

luen

t

and

ori

gin

al, w

ith

ev

iden

t

aware

nes

s o

f au

die

nce

an

d

pu

rpo

se

• i

nco

rpo

rate

vari

ed

sen

ten

ce

pat

tern

s th

at

rev

eal

an a

ware

nes

s o

f d

iffe

ren

t

syn

tact

ic s

tru

ctu

res

• u

se a

pp

rop

riat

e

lan

gu

age, w

ith

so

me

aware

nes

s o

f au

die

nce

an

d

pu

rpo

se

• m

ake

som

e a

ttem

pt

to

incl

ud

e d

iffe

ren

t se

nte

nce

pat

tern

s b

ut

wit

h a

wk

war

d

or

un

even

su

cces

s

• r

ely

on

bas

ic v

oca

bu

lary

,

wit

h l

ittl

e aw

are

ness

of

aud

ien

ce o

r p

urp

ose

• r

eveal

a l

imit

ed a

war

eness

of

ho

w t

o v

ary

sen

ten

ce

pat

tern

s an

d r

ely

on

a

lim

ited

ran

ge

syn

tact

ic

stru

ctu

res

• u

se l

ang

uag

e t

hat

is

imp

recis

e o

r u

nsu

itab

le f

or

the

aud

ien

ce o

r p

urp

ose

• r

eveal

a c

on

fuse

d

un

der

stan

din

g o

f h

ow

to

wri

te i

n c

om

ple

te

sen

ten

ces

and

lit

tle o

r n

o

abil

ity

to

vary

sen

ten

ce

pat

tern

s

• u

se l

ang

uag

e t

hat

i s

inco

her

ent

or

inap

pro

pri

ate

• i

nclu

de

a

pre

po

nd

eran

ce

of

sen

ten

ce

frag

men

ts

and

ru

n-o

ns

that

sig

nif

ican

tly

hin

der

com

pre

hen

sio

n

Co

nv

enti

on

s:

the

exte

nt

to w

hic

h t

he

wri

tin

g e

xh

ibit

s

con

ven

tio

nal

spel

lin

g, p

un

ctu

ati

on

,

par

agra

ph

ing

,

cap

ital

izat

ion

, an

d

gra

mm

ar

• d

emo

nst

rate

co

ntr

ol

of

the

con

ven

tio

ns

wit

h e

ssen

tiall

y

no

err

ors

, ev

en w

ith

sop

his

ticat

ed l

ang

uag

e

• d

emo

nst

rate

co

ntr

ol

of

the

con

ven

tio

ns,

ex

hib

itin

g

occ

asio

nal

err

ors

on

ly w

hen

usi

ng

so

ph

isti

cat

ed

lan

gu

age (

e.g

., p

un

ctu

atio

n

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