MATH INTERVENTION MATERIAL REVIEW: Number Worlds Grades Pre-K – 8 and Algebra Readiness SRA

1. MATH INTERVENTION MATERIAL REVIEW:Number WorldsGrades Pre-K – 8 andAlgebra ReadinessSRA 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.

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

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 weeksDaily instruction • Levels D-J and Algebra Readiness (Intervention) • Grades 2 – 8, Six 4-week intensive units per grade on specific skill areas48-page booklets per unit

7. CONTENT

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.

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.

10. Lesson Overview – Intervention Level E • Lesson Structure • Warm Up • Engage • Reflect • Assess

11. Technology Resources

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.

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.

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.

15. Placement Placement Tests are provided to identify where students should begin the Number Worlds curriculum. 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 InformalAssessment • 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

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.

20. Number Worlds Intervention Package • Teacher Edition • Activity Cards: Level A-C • Activity Sheets • Student Workbook: Levels D-J • Assessment • Manipulatives • Technology

21. COST Unit Teacher Kits A-C $613.59 (materials for 5 students) D-J $655.20 (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?

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

24. Creating or Selecting Intervention Programs NCTM http://www.nctm.org/intervention.aspx Questions to Consider When Creating or Selecting an Intervention 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?

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?

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?

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?

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?