ac how we may be feeling?...pre-alg. boa 101 boa 201 rmhs (3) 9/02-9/06 3 (r) pre-algebra review:...

1

Math Realignment & Refinement Project

Curriculum Design Model

Township High School District #214

Adam Clayton

Brenda Martin

@Adam_Clayt0n

@BrendaCMartin

How We May Be Feeling? AC

A Replicable, Scalable Process

• Assessment for Learning

• Standards Based Grading

• College Readiness Standards

• Common Core State Standards

Research

Theory

• Frameworks / Structures

• Templates

Operationalize the Research

• Workshops

• Training

Implementation Examples

AC

2

Theoretical Principles

Application of Principles into daily work

Assessment and Curricular Framework

AC

Curricular Design Framework

What do we want each student to learn?

How will we know when each student has learned it?

How will we respond when a student experiences

difficulty in learning?”

RB

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

RB

3

Assessment Framework

ACT’s

Educational

Planning and

Assessment

System

EPAS

• 10th • 11th

• 9th • 8th

EXPLORE PLAN

IACT ACT

RB

College & Career Readiness Standards

(CCRS) - Mathematics

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)

Number & Quantity (N)

Algebra (A)

Functions (F)

Geometry (G)

Statistics & Probability (S)

“old” CRS “updated” CRS

RB

CCRS Improvements 2014 RB

4

CCRS Improvements 2014 RB

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

Prep

College Preparatory

Honors

Freshman

Algebra 462/63

Review: 13-15

Focus: 16-19

Secondary 20-23

Algebra 470/71

Review: 16-19

Focus: 20-23

Secondary 24-27

Acc Honors Algebra 2

Review: 20-23

Focus: 24-27

Secondary 28-32

Sophomore

Geometry 464/65

Review: 16-19

Focus: 20-23

Secondary 24-27

Geometry 472/73

Review: 20-23

Focus: 24-27

Secondary 28-32

Acc Honors Geometry

or Honors Geometry

Review: 24-27

Focus: 28-32

Secondary 33-36

Junior

Intermediate Algebra 466/67

Review: 20-23

Focus: 24-27

Secondary 28-32

Algebra 474/75

Review: 24-27

Focus: 28-32

Secondary 33-36

Acc Honors Pre-Cal

or Honors Pre-Cal

Focus: Pre-Calculus

Senior

Math Analysis

Review: 24-27

Focus: 28-32

Secondary 33-36

Pre-Calculus

or

AP-Stats

AP Calculus BC

AP Calculus AB

Focus: AP Calculus

BB

5

Scope and Sequence

Pre-Prep

Freshman

Algebra 460/61 or Math 1-4

Review: 1-12 (100 Level)

Focus: 1-12 (100 level)

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.

BB

CRS – Mathematics

Example at the 100 Level

Basic Operations & Applications

(BOA)

1-12

(100)

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)

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.

AC

6

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?

There is no ambiguity to the question. The question

directly assesses the skill in isolation?

AC

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.

AC

7

Connecting the Curricular

Framework to Instructional Process

Concrete/Pictorial (Review – Level 1) graphical representation of the skills

use appropriate drawing techniques or appropriate picture representations of concrete objects

Semi-Concrete (Focus – Level 2) 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)

AC

File 01

Building a Sequence of Skills Build an INSTRUCTIONAL framework/model

WK # of

Days

Topic

Content

Review

Skill

Focus

Skill

Secondary

Skill

Assigned

(2)

8/26- 8/30

5 (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

Pre-Alg. Review

BOA 101 BOA 201 RMHS

(3)

9/02- 9/06

3 (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 single-

step problems (eg. Calculator, Mental,

or Pencil and Paper).

(S) BOA 202: Solve problems in one

step using whole numbers.

Pre-Alg. Review

BOA 102 BOA 201 PHS

AC



Standards Based Grading

BM

8


Grades and Reports Should

Be Based on Clearly

Specified Learning Goals

and Performance

Standards

Grading Should Be

Based on Established

Criteria, Not on

Arbitrary Norms

Principle 1

Principle 2

BM


Focus on Achievement

and Report Other

Factors Separately

Grading is Based on

Trends (Mode) Rather

than Averages (Mean)

Principle 3 Principle 4

BM

Applying Standards Based Grading

Practice NOT graded

No grade of zero

Zero correct = 50%

Leveling System

Level 1 – Level 3

Review/Focus/Secondary

Reassessment Policy

Mastery is the focus

Formative Assessments Weekly

5-10 days of instruction

Summative Assessments

Unit Exams 3-4 weeks

Benchmark 8-10 weeks

Grading Practices

Grade Book Practices

BM

9

CCRS Weekly Formative Assessment

Template

Principle 1:

Grades and

Reports Should Be

Based on Clearly

Specified Learning

Goals and

Performance

Standards

Principle 2:

Grading Should

Be Based on

Established

Criteria, Not on

Arbitrary Norms

Principle 4:

Grading is

Based on

Trends (Mode)

Rather than

Averages

(Mean)

BM

File 02

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

100 Level

12 Questions Semi-Concrete (Focus) symbolic representations such as

numbers or letters in combination with the language of the skill


12 Questions Abstract (Secondary) 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


10 Questions Abstract (Secondary) Language representation of the

target skill (secondary)

1-12 CRS 13-15 CRS

BM

10



Assessment for Learning

AC

7 Strategies - Assessment for Learning

Strategy 1: Provide

students with a

clear and

understandable

vision of the

learning target.

Strategy 2: Use

examples and

models of strong

and weak work.

Where Am I Going?

Where Am I Now?

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 self-

reflection, & let them

keep track of and

share their learning.

How Can I Close the Gap?

Strategy 3: Offer

regular descriptive

feedback.

Strategy 4: Teach

students to self-

assess and set goals.

AC

AFL Template Activity

Formative

Assessment

Rubric-Assessment

CRS Skill Practice

College/Career

Readiness (CCR)

Focus Check

Remediation

Reassessment

Rubric-Reassessment

Instructional Notes

Identify which of the 7 Strategies of Assessment for

Learning are applied in the templates.

AC

11

Theoretical Application - Templates

Strategy 5: Design

lessons to focus on

one learning target

or aspect of quality

at a time.

BB

File 03


Strategy 1: Provide

students with a clear

and understandable

vision of the learning

target.

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

Strategy 5: Design

lessons to focus on one

learning target or aspect

of quality at a time.

RB

File 04


Strategy 3: Offer regular

descriptive feedback.

Strategy 4: Teach students

to self-assess and set goals.

Strategy 6: Teach students

focused revision.

AC

File 05

12

Scholastic Math180

Core Curriculum + an Intervention

BM

Intervention (Math180) + Core

Expression with Variables

Geometric Measurements

Statistics and Data Analysis

Functions

Proportional Relationships

Basic Operations & Applications

Probability, Concepts, & Properties

Numbers, Concepts & Properties

Expressions, Equations & Inequalities

Graphical Representations

Properties of Plan Figures

Measurement

Functions

Math 180 – Skill Spine Core Curriculum

BM

Standards of Mathematical Practice

Common

Core

State

Standards

Make sense of problems and persevere in solving them (MP1)

Reason abstractly and quantitatively (MP2)

Construct viable arguments and critique reasoning (MP3)

Model with mathematics (MP4)

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)

AC

13

Intervention (Math180) + Core

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

M180

Standards of Mathematical Practice

College & Career Readiness Standards (CCSR)

AC

Standards in Action


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)

AC

14

Assessing the same SKILLS

Scholastic Math Inventory

290Q – 315Q

CCRS – Benchmark

NCP 100 (1-12 Range – Focus)

AC



290Q – 315Q

CCRS – Benchmark

GRE 101 (1-12 Range – Focus)

AC



520Q – 680Q

CCRS – Benchmark

BOA 13-15

AC

15

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

The Influence of PARRC

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.

AC

16

Theoretical Application – Templates

(CCR Packet)

Construct viable arguments and

critique reasoning (MP3)

Model with

mathematics (MP4)

Make sense of problems and

persevere in solving them

(MP1)

Attend to precision

(MP6)

Use appropriate

tools strategically

(MP5)

RB

File 06


(CCR – Error Analysis)

Strategy 2: Use examples

and models of strong and

weak work.


RB


(CCR – Multiple Representations)

Look for and make use of

structure (MP7)

Model with mathematics (MP4)

Make sense of problems and

persevere in solving them

(MP1)


BB

17

Math Reasoning Rubric Template

Type II Questions: arguments,

justifications, reasoning, or

precision in mathematical

statements.

BM

Math Reasoning Rubric Template

AfL Strategy 3: Offer

regular descriptive

feedback.

AfL Strategy 7: Engage students in self-

reflection, and let them keep track of and

share their learning

Reason

abstractly and

quantitatively

(MP2)

Construct

viable

arguments

and critique

reasoning

(MP3)

BM

Standards in Action

The value can/can’t be

____ because____.

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 ______.

Analyze

BM

Identify

18

Instructional Timeline

The Use of Technology

Proven Results

Putting This Into Practice

BM

Instructional Material Timeline Use

Option 1

(1 Week)

Day 1

CRS Skill Practice

Day 2

CRS Skill Practice

Day 3

Focus Check

CCR Packet

Day 4

Formative Assessment

BM

Instructional Material Timeline Use

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

Option 2

(2 Weeks)

BM

19

Using Technology to Innovate AC



AfL Strategy 3: Offer

regular descriptive feedback.

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.

20

Using Technology to Innovate

Questions, Discussions, Dialogue

Brenda Martin

[email protected]

@BrendaCMartin

Rolling Meadow HS

Adam Clayton

[email protected]

@Adam_Clayt0n

Elk Grove HS

mailto:[email protected]



ac how we may be feeling?...pre-alg. boa 101 boa 201 rmhs (3) 9/02-9/06 3 (r) pre-algebra review:...

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