1. MATH INTERVENTION MATERIAL REVIEW: Number Worlds Grades Pre-K – 8 and Algebra Readiness SRA
In December Laura Clarke shared that Campbell Ridge is using Number Worlds as their intervention program. Today we will review that program.
Peggy Cunningham

2. Number Worlds Math prevention/intervention program
Grades Pre-K – 8, Algebra Readiness
Activity based
Incorporates technology
Supported by the Kentucky Center for Mathematics

3. Research-and Standards-based Curriculum
The program incorporates the findings of several different types of research:
• Field Tests
• Effectiveness Studies
• Educational Research
• Research on How Children Learn
Program authors Sharon Griffith, Doug Clements, and Julie Sarama have been leaders in the research that has identified how children learn mathematics.
It is a research and standards-based curriculum. The program authors have been leaders in the research that has identified how children learn mathematics.

4. Research-and Standards-based Curriculum
Number Worlds is built to deliver on the five key proficiencies identified by the mathematics research community as crucial for gauging children’s understanding of math. These proficiencies are as follows: • Understanding: Comprehending mathematical concepts, operations, and relations, and knowing what mathematical symbols, diagrams, and procedures mean • Computing: Carrying out mathematical procedures, such as adding, subtracting, multiplying, and dividing numbers flexibly, accurately, efficiently, and appropriately • Applying: Being able to formulate problems mathematically and devise strategies for solving them using concepts and procedures appropriately • Reasoning and Problem Solving: Using logic to explain and justify a solution to a problem or to extend from something known to something not yet known • Engaging: Seeing mathematics as sensible, useful, and feasible
The program is built on five proficiencies that gauge children’s understanding of mathematics. (List)

5. Research-and Standards-based Curriculum
Building Blocks™ software, incorporated into the Number Worlds program, is the result of National Science Foundation-funded research. Building Blocks includes research-based computer tools with activities and a management system that guides children through research-based learning trajectories.

6. Levels A-C (Prevention) Grades Pre-K, K, and 1
30 weeks Daily instruction
Levels D-J and Algebra Readiness (Intervention)
Grades 2 – 8, Six 4-week intensive units per grade on specific skill areas 48-page booklets per unit
Number World consists of eleven different levels. Prevention program for grades Pre-K-1 which can be used in the regular classroom.
Intervention program for Grades 2-8 for Tier 2 (place students in specific unit) and Tier 3 (take all units) students. Placement in the program can be determined via the placement test found in the Assessment booklet or online.

7. CONTENT
The content focus is one or two grade levels below the Grade level for each book. For example, level D is for 2nd grade, but the content focus is for grades K-1. This chart shows the different content covered in each level.

8. Lesson Overview – Prevention Level C
Lessons are all structured the same way throughout the program: 1. Warm Up, 2. Engage, 3. Reflect, and 4. Assess.
1. Warm Up exercises provide cumulative review and computation practice for students and gives the teacher an opportunity to assess students’ skills quickly.
2. Engage is the heart of the lesson instruction. Introduce and develop concepts with engaging activity cards. Also included are suggestions for differentiating instruction.
Here is an example of a lesson from Prevention level C. Each lesson is designed to take minutes each day. Every lesson throughout the program is structured using four steps. Lessons begin with a warm up activity. Warm Up exercises provide cumulative review and computation practice for students and gives the teacher an opportunity to assess students’ skills quickly. These activities give students the opportunity to sharpen their counting and mental math skills daily. The second step is the engage section. Engage is where concepts are introduced and developed. In the prevention levels this is through the use of activity cards. Also included are suggestions for how to introduce lesson concepts, ideas for guided discussion, skill building, game demonstration, and strategy building activities to develop student understanding. There are suggestions to differentiate instruction as well.

9. Lesson Overview – Prevention Level C
3.Reflect is a vital part of the lesson that offers ways to help students summarize their understanding.
4. Assess helps you use informal assessment to summarize and analyze evidence of student understanding.
The next part of the lesson is Reflect. Reflect offers ways to help students summarize their understanding. When children talk about their thinking, using their own words, they engage in mathematical generalizing and communicating. Allowing children to discuss what they did during an activity helps build mathematical reasoning and a solid mathematical foundation.
The final part of the lesson is assess. Assess helps the teacher use informal and formal assessments to summarize and analyze evidence of student understanding. The goals of assessment include promoting student growth by identifying where they need additional instruction and support, as well as recognizing student achievement and progress.

10. Lesson Overview – Intervention Level E
Lesson Structure
Warm Up
Engage
Reflect
Assess
This is a lesson from Level E. The lesson structure of Levels D-J is the same as the prevention levels. In these levels, all instruction and discussion questions are provided in the teacher guide, as well as minis of the student pages. The lesson opens with warm-up to get students thinking mathematically. It continues with the engage section where instruction occurs and student pages are assigned. The lesson continues with reflect to get student feedback and finishes with assessment.

11. Technology Resources
Number Worlds integrates technology throughout the lessons.
Building Blocks software provides computer math activities that address specific developmental levels of the math learning goals. The research based activities provide motivating development and support of concepts.
Number Worlds integrates eMath Tools in appropriate lessons throughout the program. This component provides multimedia formats for demonstrating and exploring concepts and solving problems. It consists of games and virtual manipulatives.
The eMathtools include: data organization and display tools, such as a spreadsheet tool
Measurement and conversion tools like stopwatches and metric/customary conversion tool
Geometric exploration tools such as shape tools and geometry sketch tool
to help students develop richer mathematical skills and conceptual understanding. This software helps engage students to enrich, apply, and extend learning.
Building Blocks software provides computer math activities that address specific developmental levels of the math learning goals. The activities are research based and provide motivating development and support of concepts.
Number Worlds integrates eMath Tools in appropriate lessons throughout the program. eMath Tools are virtual manipulatives that demonstrate and explore concepts and solve problems. The eMathtools include: data organization and display tools, such as a spreadsheet tool; Measurement and conversion tools like stopwatches and metric/customary conversion tool;
Geometric exploration tools such as shape tools and geometry sketch tool; and calculation and counting tools such like calculators, base ten blocks, coins & money, etc.

12. Weekly Overview – Prevention Level C
Background provides a refresher of the math principles relevant to the chapter.
How Children Learn offers insight into how children learn and gives research based teaching strategies.
Skills Focus outlines the skills that will be covered throughout the week.
Teaching for Understanding provides the big ideas of the chapter.
Math at Home extends learning to provide extra practice students need and encourage support at home.
Math Vocabulary and English Learners outline vocabulary for the chapter and defines vocabulary in English and Spanish to improve students’ understanding of concepts.
Let’s look at what else is included in the teacher resources for Levels A-C.
Each chapter begins with a weekly overview that includes: Background This section provides a refresher of the math principles relevant to the chapter.
How Children Learn section offers insight into how children learn and gives research based teaching strategies.
The Skills Focus outlines the skills that will be covered throughout the week.
Teaching for Understanding provides the big ideas of the chapter.
Math at Home extends learning to provide extra practice students need and encourage support at home.
In the bulletin board at the bottom of the page, Math Vocabulary and English Learners outline vocabulary for the chapter and defines vocabulary in English and Spanish to improve students’ understanding of concepts.

13. Weekly Planner – Prevention Level C
Weekly Planner includes objectives that explain how the key concepts are developed lesson by lesson and which resources can be used with each lesson for quick and easy teacher preparation.
The Weekly Planner includes objectives that explain how the key concepts are developed lesson by lesson and which resources can be used with each lesson for quick and easy teacher preparation. (Go over each heading.) Note the far right column labeled technology. This column references the building blocks activity that corresponds with the lesson. Building Blocks software provides additional exposure to and practice with foundational math concepts. The software combines visual displays, animated graphics, and voice to provide a fun and interactive way for students to practice. The software was created by Doug Clements and Julie Sarama after years of research. The research based software was created with a grant from the National Science Foundation.

14. Weekly Overview & Planner – Intervention Level E
Weekly Planners map out an entire week of lessons, complete with pacing options, goals, and resources necessary to get the most out of every lesson.
The resource material for levels D-J also include a weekly overview and planner. This includes math background, how children learn, skills focus and teaching for understanding. In the teaching for understanding box, note the suggestions to help the teacher evaluate the students and monitor their progress. In the bulletin board, you notice the letter to home. These letters are in backline form in the back of the Teacher Guide for each week.
After the background and overview is the planning guide for the week. It outlines the lesson, goals, materials needed, and technology that can be used that week for quick and easy planning. This page also highlights the math vocabulary that will be used along with English Learner Support.

15. Placement
Placement Tests are provided to identify where students should begin the Number Worlds curriculum.
Now let’s look at assessment. Each level of Number Worlds contains a placement test to determine whether students understand the content in each level of the program. Every placement test assesses knowledge of two adjacent levels of Number Worlds so you can observe and compare information about which level’s content is appropriate for each student. The tests include complete instructions and scoring guides. The best practice is to assess a student’s knowledge of the entire level of content and to place him or her in the first unit in which he or she begins to show difficulty. These placement tests can be found in each level Assessment package, the TE sampler, and online at sranumberworlds.com.
Level C Placement Test
Level E Addition Placement Test
Level C Placement Test Instructions

16. PLACEMENT TESTS LEVELS A - C
Levels A-C have individual Placement test
Test is read by teacher using teacher instructions and reproducible test masters
Teacher records student responses
Students scoring greater than 75% (14/18) continue to the next level
If students score less than 75%, they begin in that level
Use Number Knowledge test to get a more thorough understanding of a student’s knowledge of numbers (knowledge of numbers typically acquired by children around 4, 6, 8 and 10 years of age)

17. PLACEMENT TESTS: LEVELS D-J
Placement test for each Concept Unit
Levels D-J are given as a group test
Each level’s test assesses the level below (first page) and the stated level (second page)
If students score less than 75% on the first page teacher administers the placement test for the previous level
Students scoring greater than 75% on the first page continue the test
If students do not demonstrate understanding of more than 75% of the items on the second page of the test, but have demonstrated understanding of the items on the first page, they should begin instruction in the level being tested
If students demonstrate understanding of more than 75% of the items on the second page of the test, administer the unit placement test for the next level
The best practice is to assess a student’s knowledge of the entire level of content and to place him or her in the first unit in which he or she begins to show difficulty

18. ASSESSMENTS Weekly Tests Assesses lesson content knowledge
Identifies where students are having difficulty for quick intervention
Cumulative Reviews (A-C)
Six week cumulative oral assessment
Checks student progress
Unit Tests (D-J)
Tests knowledge of topic at the end of unit
Multiple choice unit tests may be used in place of regular unit test, or as an additional assessment after any necessary remediation
Informal Assessment
Part of every daily lesson
Analytic rubrics available for informal assessment
Documentation
Student Assessment Record in back of book
Pre and Post
Placement can work as a pre-assessment
Placement can be re-given for post test
Can also give the end of the unit assessment as a post-test
Other assessments include:

19. Lesson 5 Review – Intervention Level E
Review & Assess
Lesson 5 of every chapter is the formal review and assessment.
Includes suggestions for differentiating instruction based on student results.
Here is an example of the weekly tests. Lesson 5 of the week in all levels is always the review and formal assessment. Activities and extended response are provided to review the weeks learning. In part 4 of the final lesson of the week, the formal assessment takes place and the teacher is guided in how to differentiate instruction for those students who may not have mastered the concepts of the week.

20. Number Worlds Intervention Package
Teacher Edition
Activity Cards: Level A-C
Activity Sheets
Student Workbook: Levels D-J
Assessment
Manipulatives
Technology
The Number Worlds program includes the following resources: These are packaged as The Intervention Package that contains everything a teacher needs to teach a level of the program. It includes all student, teacher, and manipulative materials needed to teach that level of the program. Let’s look at what’s included:
In the The Teacher Guide the teacher will find invaluable background information, complete lesson plans, and explanations of when and how to use the additional resources within the program.
Activity cards are a part of the prevention program (levels A-C). These cards are designed for teachers to lead each activity. They include directions and suggested questions to ask during an activity.
Activity Sheets are black line masters found in the back of the Teacher Guide at levels A-C that can be copied for use with the daily activity.
Student Workbooks at levels C-H provide activities to help students develop what they’ve been learning in the lesson and practice basic skills.
Assessment is an integral part of the program. The placement test helps the teacher place students in the right level for their needs. There are weekly tests to see how the student is progressing in that weeks lesson along with unit tests to evaluate if the student is understanding the unit concepts. The placement test is found in the assessment booklet as well as in the TE sampler and online.
Manipulatives and games play a significant role in this program as well. They are included in the intervention package. SRA Math topic modules are available for purchase if additional material are desired.
Technology The building blocks software for additional student practice is an integral part of the program. Also available are the E-math tools for the student and an e-Assess for the teacher.

21. COST Unit Teacher Kits A-C $613.59 (materials for 5 students)
D-J $ (materials for 5 students)
Additional student workbooks $29.10/5
Algebra Readiness – per student
Building Blocks Online: $10.50/student, minimum 20
Training is available and price depends on how much is purchased

22. How Are My Students Progressing?
For the teacher, an eAssess CD-ROM is provided for every level. This tool allows teachers to create tests as well as record daily formal and informal assessment results for each student. Student and class reports can be printed to determine where additional instruction is needed.
Teachers can monitor progress of each student, and compare class and individual progress.

23. Sharon Burt 1-800-201-7103 www.sranumberworlds.com
CONTACT INFORMATION
Sharon Burt

24. Creating or Selecting Intervention Programs NCTM
Questions to Consider When Creating or Selecting an Intervention Program
We’ve looked at the program. Now let’s use the NCTM suggestion to evaluate this program.

25. Diagnostic Assessment
1.1. Does the intervention program include diagnostic assessments that identify students’ specific strengths and weaknesses with respect to both conceptual understanding and procedures?
1.2. Do the assessments investigate students’ knowledge of fundamental mathematics concepts that are grade appropriate?
1.3. Does the content that is assessed align with the school’s prescribed curriculum?
1.4. Do the assessments communicate students’ strengths and weaknesses in ways that teachers and parents can understand?
A placement test is given to students to determine placement in the program. The units are aligned with Kentucky’s Core Content and alignments are also available for several textbook series. A weekly letter for parents is available in the teacher materials.

26. Instructional Activities
2.1. Does the intervention program include a series of instructional activities that are carefully linked with the diagnostic assessments?
2.2. Do the program’s instructional activities support and enhance, but not supplant or duplicate, regular classroom instruction?
2.3. Are tools for ongoing, formative assessment embedded in the instructional activities?
2.4. Is the mathematics in the instructional activities correct?
2.5. Do the instructional activities advance the school’s curriculum and promote reasoning and conceptual understanding?
2.6. Do the instructional activities contain challenging tasks that are appropriate for students’ interests and backgrounds?
Methods of delivering lessons are researched based. Weekly formative assessment is included. The program includes teacher directed lessons and lessons using technology.

27. Post-assessment
3.1. Does the intervention program contain post-assessments that indicate whether the instructional activities have been effective?
3.2. Are follow-up assessments administered in a timely fashion?
3.3. Do the assessments communicate students’ growth or need for further instruction in ways that teachers and parents can understand?
The placement test may be used as a post assessments after each unit. The weekly assessments page in the teacher material also includes ways to help student who are still having difficulty with the content.

28. Organizational structure of the intervention
4.1. Is the structure of the intervention program feasible given the organizational structure of the school?
4.2. Does the school have the necessary resources to implement the intervention program as designed?
4.3. Does the intervention program include adequate and ongoing professional development to ensure effective implementation?
4.1 and 4.2 must be school assessed Number Worlds does require computers for the Building Blocks and e-tools part of the program Professional development is available.

29. Research supporting the intervention
5.1. Have rigorous and appropriate methods been used to evaluate the intervention program and determined it to be successful?
5.2. Does theoretical and empirical evidence support the efficacy of the intervention program in a setting that is similar to your school?
The program is based on research foundations and designs and uses widely-accepted principles of effective intervention instruction for struggling students. Development of the software was funded by the National Science Foundation. The Kentucky Center for Mathematics supports the program. What Works Clearing House: No Studies Meeting Eligibility Screens as of July 2007