MATH INTERVENTION
MATERIAL REVIEW:
Number Worlds
Grades Pre-K – 8 and
Algebra Readiness
SRA
Peggy Cunningham
Number Worlds
•Math prevention/intervention program
•Grades Pre-K – 8, Algebra Readiness
•Activity based
•Incorporates technology
•Supported by the Kentucky Center for
Mathematics
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.
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
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.
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
CONTENT
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.
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.
Lesson Overview – Intervention Level E
Lesson Structure
•
Warm Up
•
Engage
•
Reflect
•
Assess
Technology Resources
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.
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.
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.
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
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)
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
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
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.
Number Worlds
Intervention Package
• Teacher Edition
• Activity Cards: Level A-C
• Activity Sheets
• Student Workbook: Levels D-J
• Assessment
• Manipulatives
• Technology
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
How Are My Students Progressing?
CONTACT INFORMATION
Sharon Burt
1-800-201-7103
www.sranumberworlds.com
Creating or Selecting
Intervention Programs
NCTM
http://www.nctm.org/intervention.aspx
Questions to Consider When
Creating or Selecting an
Intervention Program
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?
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?
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?
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?
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?