Math Realignment & Refinement Project
Curriculum Design Model
Adam Clayton
Brenda Martin
@Adam_Clayt0n
@BrendaCMartin
Township High School District #214
AC
AC
How We May Be Feeling?
A Replicable, Scalable Process
Research
Theory
•
•
•
•
Assessment for Learning
Standards Based Grading
College Readiness Standards
Common Core State Standards
Operationalize
the Research
• Frameworks / Structures
• Templates
Implementation
Examples
• Workshops
• Training
1
AC
Assessment and Curricular Framework
Theoretical Principles
Application of Principles into daily work
RB
Curricular Design Framework

What do we want each student to learn?

How will we know when each student has learned it?

RB
How will we respond when a student experiences
difficulty in learning?”
Curricular Design Framework

Identify an Assessment Cycle

Select a CURRICULAR framework/model

LEVEL skills in a defined scope and sequence

APPLY the model throughout an 4 year sequence

Build an INSTRUCTIONAL framework/model
2
RB
Assessment Framework
• 8th
ACT’s
• 9th
Educational
Planning and
Assessment
System
EXPLORE
PLAN
EPAS
ACT
IACT
• 11th
RB
• 10th
College & Career Readiness Standards
(CCRS) - Mathematics
“old” CRS








RB
Basic Operations & Applications (BOA)
Probability, Concepts, & Properties
(PSD)
Numbers, Concepts & Properties
(NCP)
Expressions, Equations & Inequalities
(XEI)
Graphical Representations (GRE)
Properties of Plan Figures (PPF)
Measurement (MEA)
Functions (FUN)
“updated” CRS

Number & Quantity (N)

Algebra (A)

Functions (F)

Geometry (G)

Statistics & Probability (S)
CCRS Improvements 2014
3
RB
CCRS Improvements 2014
BB
Curricular Framework
College-Career Readiness Standards AND Levels
ACT Score Range
13-15
16-19
20-23
24-27
28-32
33-36
200 Level
300 Level
400 Level
500 Level
600 Level
700 Level
BB
Select a Curricular Framework
Freshman
Prep
College Preparatory
Honors
Algebra 462/63
Algebra 470/71
Acc Honors Algebra 2
Review:
13-15
Focus:
16-19
Secondary 20-23
Review:
16-19
Focus:
20-23
Secondary 24-27
Geometry 464/65
Sophomore
Review:
16-19
Focus:
20-23
Secondary 24-27
Intermediate Algebra 466/67
Junior
Review:
20-23
Focus:
24-27
Secondary 28-32
Math Analysis
Senior
Review:
24-27
Focus:
28-32
Secondary 33-36
Geometry 472/73
Review:
20-23
Focus:
24-27
Secondary 28-32
Algebra 474/75
Review:
24-27
Focus:
28-32
Secondary 33-36
Pre-Calculus
or
AP-Stats
Review:
20-23
Focus:
24-27
Secondary 28-32
Acc Honors Geometry
or Honors Geometry
Review:
24-27
Focus:
28-32
Secondary 33-36
Acc Honors Pre-Cal
or Honors Pre-Cal
Focus: Pre-Calculus
AP Calculus BC
AP Calculus AB
Focus: AP Calculus
4
BB
Scope and Sequence
Pre-Prep
Algebra 460/61 or Math 1-4
Review:
1-12 (100 Level)
1-12 (100 level)
Freshman Focus:
Secondary 13-15 (200 level)
Approximately 10-20% review, 40-50% focus, and 30-50% secondary,
depending upon the levels and students prior mastery of skills.
CRS – Mathematics
Example at the 100 Level
AC
Basic Operations & Applications
(BOA)
101. Practice and apply estimation and computation using whole numbers
and decimals.
102. Choose the appropriate method of computation to solve multistep
problems (ex., calculator, mental, or pencil and paper)
1-12
(100)
103. Practice selecting appropriate units of measure (ex., inches or feet,
hours or minutes, centimeters or meters) and converting between units
104. Model and connect physical, verbal, and symbolic representations of
money
AC
Defining the Curriculum
LEVEL skills in a defined scope and sequence.
Review
(level 1)
The review skill can be one that is in a lower CRS band that would flow
naturally into the focus skill or it may be in the same band if the flow is natural
and one may assume that it has already been taught.
Focus
(level 2)
The focus skill (in isolation) is the problem that completely isolates the CRS
skill. In other words, it is the very basic, straightforward problem that uses the
CRS skill.
Secondary
(level 3)
The secondary skill (in context) problem takes the basic CRS skill and applies
it together with other skills in the same CRS band or a lower one (or in specific
courses – in the context of a specified topic). The problems at this level may
be multiple steps, may require multiple concepts (again, at the same CRS
band or lower), but the focus CRS skill is at the main purpose. The level 3
problems may be a word problem, or may require drawing a picture or
diagram before solving – in other words, something in addition to the basic
CRS skill must be used to solve it.
5
AC
Defining the Scope
Review (Level 1)




Is the review skill one that is in a lower CRS band?
Is the review skill in the same band if other skills are
used to introduce the skill?
If other skills are used as an introduction with the
Review level, can we assume that those skills have
already been taught?
Has vocabulary demands been considered in the
question development?
AC
Defining the Scope
Focus (Level 2)

Does the problem isolate the CRS skill?

AC
There is no ambiguity to the question. The question
directly assesses the skill in isolation?
Defining the Scope
Secondary (Level 3)



Is the basic CRS skill placed in a context?
Does this problem apply the basic CRS skill?
Does this problem apply the basic CRS skill with other skills
from a lower CRS.




Have the other CRS skills been previously taught?
If the problem requires multiple steps, have those steps been
experienced in the packets during the week?
Has there been a progression of work leading to a problem requiring
multiple steps?
You may require the student to draw a picture or diagram
before solving.
6
Connecting the Curricular
Framework to Instructional Process
AC

Concrete/Pictorial (Review – Level 1)



Semi-Concrete (Focus – Level 2)



graphical representation of the skills
use appropriate drawing techniques or appropriate picture
representations of concrete objects
symbolic representations such as numbers or letters in combination with
the language of the skill
graphical representation + mathematical representation together
Abstract (Secondary – Level 3)

Language representation of the target skill (secondary)
File 01
Building a Sequence of Skills
AC
Build an INSTRUCTIONAL framework/model
WK # of Topic
Days Content
Review
Skill
Focus
Skill
Secondary
Skill
Assigned
(2)
Pre-Alg.
Review
BOA 101
BOA 201
RMHS
Pre-Alg.
Review
BOA 102
BOA 201
PHS
5
8/268/30
(3)
9/029/06
3
(R) Pre-Algebra Review: Complete
basic math operations (Addition,
Subtraction, Multiplication, and
Division)
(F) BOA 101: Practice and apply
estimation and computation using
whole numbers and decimals.
(S) BOA 201: Perform one-operation
computation with whole numbers and
decimals
(R) Pre-Algebra Review: Model and
Connect Physical, Verbal, and
Symbolic Representation of money.
(R) Pre-Algebra Review: Practice
and Apply estimation and
computation using whole numbers
and decimals.
(F) BOA 102: Choose the appropriate
method of computation to solve singlestep problems (eg. Calculator, Mental,
or Pencil and Paper).
(S) BOA 202: Solve problems in one
step using whole numbers.
BM
Standards Based Grading
Theoretical Principles
Application of Principles into daily work
7
BM
Standards Based Grading
Principle 2
Principle 1

Grades and Reports Should
Be Based on Clearly
Specified Learning Goals
and Performance
Standards
BM

Grading Should Be
Based on Established
Criteria, Not on
Arbitrary Norms
Standards Based Grading
Principle 3

BM
Focus on Achievement
and Report Other
Factors Separately
Principle 4

Grading is Based on
Trends (Mode) Rather
than Averages (Mean)
Applying Standards Based Grading
Grading Practices


Practice NOT graded
No grade of zero


Level 1 – Level 3


Formative Assessments

Mastery is the focus
Weekly


5-10 days of instruction
Summative Assessments

Unit Exams

Benchmark
Review/Focus/Secondary
Reassessment Policy


Zero correct = 50%
Leveling System

Grade Book Practices


3-4 weeks
8-10 weeks
8
CCRS Weekly Formative Assessment
Template
BM
Principle 1:
Grades and
Reports Should Be
Based on Clearly
Specified Learning
Goals and
Performance
Standards
Principle 4:
Grading is
Based on
Trends (Mode)
Rather than
Averages
(Mean)
Principle 2:
Grading Should
Be Based on
Established
Criteria, Not on
Arbitrary Norms
File 02
BM
Benchmark Aligned to Formative Assessments
Principle 2:
Grading
Should Be
Based on
Established
Criteria, Not
on Arbitrary
Norms
BM
1-12 vs. 13-15 Benchmark
1-12 CRS


100 Level
12 Questions Semi-Concrete
(Focus)




symbolic representations such as
numbers or letters in combination with
the language of the skill
graphical representation +
mathematical representation together
12 Questions Abstract
(Secondary)

13-15 CRS

Language representation of the
target skill (secondary)
200 Level
10 Questions Semi-Concrete
(Focus)



symbolic representations such as
numbers or letters in combination with
the language of the skill
graphical representation +
mathematical representation together
10 Questions Abstract
(Secondary)

Language representation of the
target skill (secondary)
9
AC
Assessment for Learning
Theoretical Principles
Application of Principles into daily work
AC
7 Strategies - Assessment for Learning
Where Am I Going?

Strategy 1: Provide
students with a
clear and
understandable
vision of the
learning target.
Where Am I Now?



Strategy 3: Offer
regular descriptive
feedback.
Strategy 4: Teach
students to selfassess and set goals.
Strategy 2: Use
examples and
models of strong
and weak work.
AC
How Can I Close the Gap?



Strategy 5: Design
lessons to focus on one
learning target or
aspect of quality at a
time.
Strategy 6: Teach
students focused
revision.
Strategy 7: Engage
students in selfreflection, & let them
keep track of and
share their learning.
AFL Template Activity
Identify which of the 7 Strategies of Assessment for
Learning are applied in the templates.
Formative
Assessment
 Rubric-Assessment
 CRS Skill Practice
 College/Career
Readiness (CCR)

Focus Check
Remediation
 Reassessment
 Rubric-Reassessment
 Instructional Notes


10
BB
Theoretical Application - Templates
Strategy 5: Design
lessons to focus on
one learning target
or aspect of quality
at a time.
File 03
RB
Theoretical Application - Templates
Strategy 1: Provide
students with a clear
and understandable
vision of the learning
target.
Strategy 5: Design
lessons to focus on one
learning target or aspect
of quality at a time.
Strategy 4: Teach students to
self-assess and set goals.
Strategy 7: Engage students in
self-reflection, and let them
keep track of and share their
learning
File 04
AC
Theoretical Application - Templates
Strategy 3: Offer regular
descriptive feedback.
Strategy 4: Teach students
to self-assess and set goals.
Strategy 6: Teach students
focused revision.
File 05
11
BM
Core Curriculum + an Intervention
Scholastic Math180
BM
Intervention (Math180) + Core
Math 180 – Skill Spine





Expression with Variables
Geometric Measurements
Statistics and Data Analysis
Functions
Proportional Relationships
Core Curriculum








AC
Basic Operations & Applications
Probability, Concepts, &
Properties
Numbers, Concepts & Properties
Expressions, Equations &
Inequalities
Graphical Representations
Properties of Plan Figures
Measurement
Functions
Standards of Mathematical Practice

Make sense of problems and persevere in solving them (MP1)
Common

Reason abstractly and quantitatively (MP2)
Core

Construct viable arguments and critique reasoning (MP3)
State

Model with mathematics (MP4)
Standards

Use appropriate tools strategically (MP5)

Attend to precision (MP6)

Look for and make use of structure (MP7)

Look for and express regularity in repeated reasoning (MP8)
12
AC
Intervention (Math180) + Core
College & Career Readiness
Standards (CCSR)
M180
Standards of Mathematical Practice





AC
Reason Abstractly &
Quantitatively
Express Regularity in
Repeated Reasoning
Look Make Use of Structure
Attend to precision
Construct Viable Arguments

Secondary Skills (L3)

Leveled Skills (L1, L2, L3)


College and Career Packet
Math Reasoning Inventory
Standards in Action



Attend to precision (MP6)
Look for and make use of
structure (MP7)
Look for and express
regularity in repeated
reasoning (MP8)
Is there a general rule for this pattern?
7s
AC
Standards in Action


Reason abstractly and
quantitatively (MP2)
Construct viable
arguments and critique
reasoning (MP3)
13
AC
Assessing the same SKILLS
Scholastic Math Inventory
290Q – 315Q
AC
Assessing the same SKILLS
Scholastic Math Inventory
290Q – 315Q
AC
CCRS – Benchmark
NCP 100 (1-12 Range – Focus)
CCRS – Benchmark
GRE 101 (1-12 Range – Focus)
Assessing the same SKILLS
Scholastic Math Inventory
520Q – 680Q
CCRS – Benchmark
BOA 13-15
14
AC
The Influence of PARRC
Math Reasoning/Critical Thinking Rubric
1. Type II and Type III Tasks (PARRC)
2. Standards of Mathematical Practice
3. Use of the College and Career Readiness Packet
AC
PARRC - Three Types of Tasks
Type II
Type II tasks call for written arguments, justifications,
critique of reasoning, or precision in mathematical
statements.
AC
PARRC - Three Types of Tasks
Type III

Type III tasks call for modeling/application in a
real-world context or scenario and can also involve
other mathematical practice standards.
15
RB
Theoretical Application – Templates
(CCR Packet)
Use appropriate
tools strategically
(MP5)
Make sense of problems and
persevere in solving them
(MP1)
Model with
mathematics (MP4)
Attend to precision
(MP6)
Construct viable arguments and
critique reasoning (MP3)
File 06
RB
Theoretical Application – Templates
(CCR – Error Analysis)
Strategy 2: Use examples
and models of strong and
weak work.
Attend to precision (MP6)
BB
Theoretical Application – Templates
(CCR – Multiple Representations)
Make sense of problems and
persevere in solving them
(MP1)
Model with mathematics (MP4)
Attend to precision (MP6)
Look for and make use of
structure (MP7)
16
BM
Math Reasoning Rubric Template
Type II Questions: arguments,
justifications, reasoning, or
precision in mathematical
statements.
BM
Math Reasoning Rubric Template
AfL Strategy 7: Engage students in selfreflection, and let them keep track of and
share their learning
AfL Strategy 3: Offer
regular descriptive
feedback.
Reason
abstractly and
quantitatively
(MP2)
Construct
viable
arguments
and critique
reasoning
(MP3)
BM
Standards in Action
Identify

The value can/can’t be
____ because____.
Analyze




I can find ___ by ___
because ___.
The relationship between
___ and ____ is ______?


This problem is asking
me to ____.
The quantities in this
problem are ______.
They are related
because _______.
I already know that
______.
17
BM
Putting This Into Practice
Instructional Timeline
The Use of Technology
Proven Results
BM
Instructional Material Timeline Use
Option 1
(1 Week)




BM
Day 1
 CRS Skill Practice
Day 2
 CRS Skill Practice
Day 3
 Focus Check
 CCR Packet
Day 4
 Formative Assessment
Instructional Material Timeline Use
Option 2
(2 Weeks)




Day 1
 CRS Skills Practice
Day 2
 CRS Skill Practice
Day 3
 Focus Check
 CRS Skill Practice
Day 4
 CCR Packet




Day 1
 CRS Skill Practice
Day 2
 Focus Check
 CRS Skill Practice
Day 3
 CCR Packet
Day 4
 Formative Assessment
18
AC
AC
AC
Using Technology to Innovate
Using Technology to Innovate
Using Technology to Innovate
Teacher accesses students work through
the iPad and provides immediate
feedback to the student.
Students submit al their work through the
iPad in a 1:1 setting.
AfL Strategy 3: Offer
regular descriptive feedback.
19
Using Technology to Innovate
Brenda Martin
brenda.martin@d214.org
@BrendaCMartin
Rolling Meadow HS
Adam Clayton
adam.clayton@d214.org
@Adam_Clayt0n
Elk Grove HS
Questions, Discussions, Dialogue
20