TerraNova™, Third Edition Mathematics · Teach strategies for solving problems 4. Integrate writing and interactive discussion as part of math instruction ... Ensure high levels

TerraNova™, Third Edition

Joan BuzickDRC/CTB Assessment

Consultant

Mathematics

Today’s Agenda

� What works? – What principals say

� A look back, and then into the future

� Research that has driven curriculum and instruction� Research based activities

� Staying connected with TerraNova data

� Questions / Comments

Strategies That Work:What Principals Say…

• Analyzing Test Data

• Parents support score-raising efforts

• Focusing on "BUBBLE" Students

• Constant Monitoring of Progress

• Regular staff meetings typically have agenda items related to test scores for Informing curriculum and instruction

• Looking at student work helps improve teaching

• Group Discussions in K-2, 3-5, 6-8, and 9-12 teams

http://www.educationworld.com/a_admin/admin/admin366.shtml

Making Progress…Taking a look back and

moving forward

Taking a look back…Math Research: TIME Matters

� Issue:

Many students have 3 or fewer hours of math instruction per week (Typical: 30-45 minutes daily)

� Finding:

Higher achieving schools provide 60-90 minutes per day for math instruction.

� Implication:

Schedule adequate time for Math instructionTrend: at least 60 minutes per day (K-8)

Taking a look back…Math Research:Rigorous and Aligned Math Curriculum� Issue:

Most K-8 students encounter a shallow math curriculum, often defined by the math textbooks.

� Finding:

Higher achieving schools align across math standards, teaching objectives, textbooks, supplementary materials and assessment.

� Implication:

Ensure that curriculum & instruction are…

1. adequately rigorous

2. aligned to State, NCTM, CCSSM Math standards

Taking a look back…Math Research:Learning Important Concepts in Math

� Issue:

Students perform computation adequately, but have limited understanding of fundamental concepts.

Pre-K-Grade 8 math instruction is heavy on routine arithmetic, memorization and repetition.

� Research Finding:

Math proficiency requires students to…

• Understand and apply important math concepts,

• Compute with ease,

• Formulate and solve problems, and

• Explain their reasoning.

Learning Important Concepts in Math

Instructional Implications…

1. Focus on conceptual understanding, not rote steps

2. Develop fluency with math facts and operations

3. Teach strategies for solving problems

4. Integrate writing and interactive discussion as part of math instruction

Research Finding

Math Research:Instructional Approaches in Math Curriculum

� Finding:

A balanced integrated program that emphasizes thinking strategies helps develop proficiency.

Effective interventions include flexible grouping, peer tutoring and math coaching.

� Implication:

Integrate principles of effective learning into math instruction.

� Ensure high levels of student engagement

� Build on prior knowledge, background experience

� Involve the social nature of learning

� Use visual organizers – graphic organizers, charts, tables…

� Provide constructive feedback – from teacher/peers, checklists, rubrics…

Five Principles for Effective Learning

Remember Piaget?(Contance Kamii, Ph.D.

Early Childhood Education Program Department of

Curriculum and Instruction at the University of Alabama at Birmingham.)

https://www.youtube.com/watch?v=D9ZGQ-xupZk

Double Column Addition taught in accordance to Piaget's theory

https://sites.google.com/site/constancekamii/videos

Constance KamiiHow Children Understand and Learn Math

Includes students engaged in an understanding of division in 2nd grade based on Piaget's theory

Use effective instructional practices

Integrate approaches for

active engagement

Direct instruction

Hands-on activities

Real life math

Problem solving

Ongoing review

What does a successful problem solver do?

Pape, S., Middle School Children’s Problem-Solving Behavior: A cognitive Analysis from a Reading Comprehension Perspective. Journal for Research in Mathematics Education, 2004, Vol. 35, No 3., 187-219

What research says.

What does a successful problem solver do?

• Grocery Store A sells 120 bottles of water a day.

• That is 2 times as many bottles as Grocery Store Bsells in a day.

• How many bottles of water does Grocery Store Bsell in 5 days?



• Grocery Store A sells 120 bottles of water a day.• That is 2 times as many bottles as Grocery Store B sells in a day.• How many bottles of water does Grocery Store B sell in 5 days?

Attempted Answer: Not proficient

• Reads Sentence 1 (S1) through Sentence 3 (S3).• States that he will reread.• Rereads S1-S3 and does not record information.• Rereads S1-S3.• Computes 120 X 2 audibly. “Okay. A hundred twenty

times two. Zero, four, two. Uh. Okay, 240 X 5. • Refers to problem briefly and calculates 240 x 5.• Does not state answer.

• Grocery Store A sells 120 bottles of water a day.• That is 2 times as many bottles as Grocery Store B sells in a day.• How many bottles of water does Grocery Store B sell in 5 days?

Limited Context

• Reads S1-S3• Automatically translates to computation stating “2

times.”• States intermediate answer with context, “bottles a

day.”• Computes 60 X 5 while referencing to problem and

stating “days.”• States answer with context,“in 5 days.”

Partial wording / limited justificationPape, S., Middle School Children’s Problem-Solving Behavior: A cognitive Analysis from a Reading Comprehension Perspective. Journal for Research in Mathematics Education, 2004, Vol. 35, No 3., 187-219

• Reads S1-S3• Rereads S1 and records following and as she reads sentence; “Store

A sells 120, 1 day.” • Rereads S2, records information, and begins to compute 120/2 stating,

“So you divide120 bottles that are sold at Store A by 2 because Store B…that is…that is 120 bottles is 2 times as many as Store B sells.”

• States steps of computation verbally. States, “Store A…Store B sells 60 bottles in one day. Multiply this by five because they want to know how many they sell in five days.”

• Writes – “Store B sells 60 bottles =1 day

X 5 days300 bottles = 5 days

• States answer with full context. “They sell 300 bottles in five days.”

Full answers with justification


Connection to test scores

Wrote down the #’s

Justification

Yes No

No No

Brief words

Yes No

Yes Yes

Pape, S., Middle School Children’s Problem-Solving Behavior: A cognitive Analysis from a Reading

Comprehension Perspective. Journal for Research in Mathematics Education, 2004, Vol. 35, No 3., 187-219

• Read or reread each sentence • Record information to support calculation• Provide justification for each step• Final answers are in complete sentences

What does a successful problem solver do? Research indicates…

Pape, S., Middle School Children’s Problem-Solving Behavior: A cognitive Analysis from a Reading Comprehension Perspective. Journalfor Research in Mathematics Education, 2004, Vol. 35, No 3., 187-219

Use Graphic Organizers

1. Restate the Question:__________________________________________

2. Find needed data:a._______________________________________________________ b._______________________________________________________ c._______________________________________________________ d._______________________________________________________

3. Plan what to do:1._________________________________________________________________________ 2._________________________________________________________________________ 3._________________________________________________________________________

4. Find the answer:Step 1 Step 2 Step 3 Step 4

5. Check: Why is answer reasonable?_________________________

6. Answer:__________

Graphic Organizers for Vocabulary

Word Webs

Measures ofCentral

Tendencies

Classroom Strategies:Use graphic organizers to teach math

Information from the Math Problem

Solution Step

• Amy spent the least on fish

• Darjon spent the most on fish

• Tim spent less than Darjonand more than Amy on fish;

• Lynn spent less on fish than Tim

1. Darjon = most

2. Tim = less than Darjon

3. Lynn = less than Tim

4. Amy = least

1. Fancy guppies = $2.99 a pair

2. Catfish = $2.89 each; A pair of catfish = 2x 2.892 catfish = $5.78

3. Most to Least spending on fish =Darjon = $5.78 (2 catfish)

Tim = 2 x $2.49 (2 sharks)

Lynn = 2 x $1.89 (2 swordtails)

Amy = $2.99 (2 guppies)

Classroom Strategies:Vocabulary matters

dataexperimental resultsformulate conclusions from graphsformulate predictionsfrom graphs

impossible outcomesline graphmeanpossible outcomesprobability

Probability and Statistics

Grade 5 Math vocabulary

Quadrilaterals

Attributes

4-sidesAll sides

equal4 right angles

2 pairs of

parallel sides

Opposite angles equal

Square X X X X X

Rectangle X X X X

Parallelogram X X X

Trapezoid X

Vocabulary used across subject areas… Art, Physical Education?

Classroom Strategies:

From first to eighth grade…Teachers are familiarizingyoung students to vocabulary and concepts

Eighth grade objectives…Teachers Guide

TerraNovaTM, Third Edition

Objectives and Subskills

Teacher’s Guide to TerraNova Third Edition

Classroom Connections

DOK Label

27

DOK Level DOK Label Math

1Recognizing and Recalling 20 + 10+=___ -(-5) x 4=____

2 Using Fundamental Concepts and Procedures

is the same as 5:45 or 9:25 or 2:25

3Concluding and explaining

If Jim has 10 mystery books, 45 history books, and 5 science books. What is the ratio of mystery and science books to history books?

4Evaluating, Extending, and Making Connections

Interpret data. Choose a recommendation the best recommendation from choices

A B C D

Learning StrategiesFrequent review

GeometryAlgebra

Measurement

Operation Concepts

Data Analysis

Problem Solving/Reasoning

Classroom Strategies:Integrate reading and writing

as part of Math� Write in Math Journals…

– to explain answers = Reasoning and Communication

– T-charts for solving problems (graphic organizer)

– Create math problems to fit real life situations

� Integrate POD (Problem of the Day)

1. Discuss with a partner or in a small group

2. Complete a graphic organizer to show solution

3. Discuss as a class or conduct teacher-group

conferences

The difference between Now and Not Yet

Assessment data informs

Dweck, C. (2006). Mindset: The New Psychology of Success, Random House

Learning Strategies…Are we there yet?

Staying connected

with TerraNova data

Reports ACSI Online…The Big Picture

The information from TerraNova 3rd Edition with Plus

ACSI Online: Group MasterySample Data

Is the student working above or below their mathematical ability?

TerraNova with InView

ACSI Online Objectives Summary by Group - Curriculum review

Math Computation

Math Objectives

Assessment Summary I

Assessment Summary

Math

Objectives Report Part IEducators working together to share ideas…

Instruction…What works and what doesn’t work

Strengths-Challenges

Grouping for instructional needs

Individual Profile Report

Strengths-Challenges-Critical Needs analysis

ACSI Online:Scale Scores: Grade 1,3,5,7,9

ACSI Online

Developed under Contract with ACSI by CTB/McGraw-Hill LLC (CTB)

Sample Performance Level Report

Loss / HossLow andHighs of Scale ScoresGrades 1-12

Student Performance Level(Optional Report)

Bringing It All Together in Math

Using TerraNova 3 Math Assessment Results

� Strengths-Challenges-Critical Needs analysisObjectives Report, Part I: faculty meeting review and discussion

� Flexible Grouping based on assessment dataObjectives Report, Part II

� Administrator Review of Grade-level Math resultsAssessment Summary; Objectives Summary

� Math Curriculum Update, using TerraNova, Third Edition

Teacher’s Guide

Integrating Key Mathematics Research Elements

� Adequate Time: 60-90 minutes daily

� A rigorous, well-aligned Math curriculum

� Focus on vocabulary and concept development within grade spans and looking to advanced grades when possible

� Effective learning techniques used in all lessons(active engagement, relevance, peer interaction, visual organizers,

constructive feedback)

� Varied instructional approaches to support student needs, e.g., partner work, flexible groups, modeling

Questions and Answers

Comments to Share

Developed under Contract with ACSI by CTB/Mcgraw-Hill LLC (CTB)

Developed under Contract with ACSI by CTB/Mcgraw-Hill LLC (CTB)

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TerraNova™, Third Edition Mathematics · Teach strategies for solving problems 4. Integrate writing and interactive discussion as part of math instruction ... Ensure high levels