Strategies for Mathematics Intervention

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Strategies for Mathematics Intervention
Presented by Sara Johnson sjohnson_at_tcmpub.com
Emily R. Smith esmith_at_tcmpub.com
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Airline Problems

• If 460 flights are canceled on Tuesday, 1,094 on
  Wednesday, and 900 on Thursday, estimate how many
  you think will be canceled on Friday?
• One-third of 2,200 daily flights are on MD-80s.
  Write an expression that shows how many flights
  that is. Do not solve.
• How many total airplanes are there if 60 are
  fixed, 119 are being worked on, and 121 are not
  inspected yet?

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Airline Problems

• If a certain airlines stock dropped 1.15 and is
  now at 9.17, where did it start. Write an
  expression or equation and solve this problem.
  What percent drop is this?
• There have been 1,554 flights canceled in two
  days. Approximately 100 people are on each
  flight. Write an expression to figure out how
  many people are stuck in airports or having to
  return home around the country.

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Todays Goals

• Learn how to
• motivate students with high-interest and engaging
  activities
• differentiate mathematics instruction
• improve students problem-solving skills
• assess students effectively
• introduce great resources from Teacher Created
  Materials

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Opening Activity

• Build a Sentence
• Use these words and numbers to make a true
  sentence
• 10
• 50
• twice
• difference

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Opening Activity

• Build a Sentence
• Use these words and numbers to make a true
  sentence
• 10
• equals
• 1/2
• 40

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TCM Mathematics Intervention

• 78 of adults cannot explain how to compute the
  interest paid on a loan
• 71 cannot calculate miles per gallon on a trip
• 58 cannot calculate 10 tip on a bill

Foundations for Success The Final Report of the
National Mathematics Advisory Panel, U.S.
Department of Education 2008
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TCM Mathematics Intervention

• All students need to be more mathematically
  proficient than in the past, and many more
  students need to pursue careers in the fields of
  mathematics and science.
• Cathy Seeley 2005

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TCM Mathematics Intervention

• The National Mathematics Advisory Panel States
• To prepare students for Algebra, the curriculum
  must simultaneously develop conceptual
  understanding, computational fluency, and
  problem-solving skills.

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TCM Mathematics Intervention
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Exploring Math
An Intervention and Reinforcement Resource
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Exploring Math
14 Real-Life Problem-Solving Cards w/
transparencies
7 Problem-Solving Strategy Cards with
transparencies
Teacher Resource Guide
7 Stand-Alone Units
Teacher Resource CD
14 Skill Application Game Boards
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Targeted Mathematics Intervention
for Summer School, After School, and Other
Instructional Programs
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Targeted Mathematics Intervention
240-page Teacher Resource Guide with 30 lessons
30 problem-solving transparencies
8 double-sided game boards
Student Guided Practice Book
Punchouts of needed manipulatives and game
materials
CD with reproducibles, PowerPoint presentations,
problem-solving cards
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TCM Mathematics Intervention

• Increase student achievement
• Prepare students for state standardized tests
• Differentiate instruction
• mathematical vocabulary activities
• small-group guided practice
• open-ended activities

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TCM Mathematics Intervention

• Develops students mathematical understanding
  through . . .
• concrete examples
• multiple representations
• multiple algorithms

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TCM Mathematics Intervention

• Targeted instruction of key content standards
• Different from regular classroom curriculum
• Easy to implement
• Compact and portable

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Strategies to Engage Students

1. Developing vocabulary
2. Using manipulatives
3. Solving real-life problems
4. Playing games

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Developing Vocabulary
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Developing Vocabulary

• The language of mathematics is very precise
  compared with English used in common discourse,
  and this difference separates mathematics from
  most curricular areas.
• California Department of Education 2006

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Developing Vocabulary

• Frontload the lesson
• Revisit past vocabulary words
• Repeat games and activities
• Clearly set up expectations

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Developing Vocabulary
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Developing Vocabulary

• teach/taught
• conceptual understanding
• procedural proficiency
• multiple representations
• multiple algorithms
• problem solving
• manipulatives

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Differentiation
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Tiered Lessons
Differentiating Activities
above
Objective
on
below
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Differentiating Activities

• Tiering/Leveling Activities

• Start with whole class activity
• Below grade levelNarrow the scope of the
  activity and make it more concrete
• English language learnersAdd context to the
  activity and make it more concrete
• Above grade levelIncrease the complexity of the
  activity

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Differentiating Activities

• Differentiate through
• Content (what is taught)
• Process (how it is taught)
• Product (what they produce)

• Differentiate because of
• Readiness
• Learning styles
• Interests

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Differentiating Activities
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Developing Vocabulary
How would you differentiate this activity?
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Developing Vocabulary
Reflection and Application
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Developing Vocabulary

• Get into groups of 34 and develop your own
  differentiated vocabulary activity.
• Be ready to share this with others in five
  minutes.

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Assessing Students
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Assessment

• Assessments are learning opportunities for
  students and for teachers. Students can learn
  more mathematics, and teachers can learn more
  about their studentsand sometimes more
  mathematics, as wellfrom all types of
  assessments.
• Long 2000

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Assessment

• Summative assessments
• individual
• grade-level criterion-referenced tests
• authentic assessments
• Formative assessments
• group and individual
• authentic assessments

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Assessment
Four Steps to Quality Instruction

• Diagnose
• Placement tests quickly pinpoint students needs.
• Decide
• Placement test answer key shows where to place
  students in the program.
• Develop
• Choose a program with multiple components that
  allow you to easily develop a plan that works
  best for your students.
• Deliver
• Incorporate easy-to-follow lesson plans that
  allow you to deliver quality instruction.

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Assessment

• Diagnostic Pre-test
• Formative Assessment Opportunities
• Summative Assessment/Post-test

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Assessment
Reflection and Application
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Assessment

• Answer this question by yourself or with your
  elbow partner.
• How do you assess mathematical thinking?

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Using Manipulatives
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Using Manipulatives

• When students use concrete objects to represent
  mathematical ideas, they learn to organize their
  thinking and reflect on concrete representations.
• Dean and Florian 2001

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Using Manipulatives

• Concrete representations of concepts
• Hands-on models
• Gives students personal experiences with concepts

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Using Manipulatives
Lesson Plans

• Comprehensive list of Materials
• Engaging Warm-up Activity
• Interactive Vocabulary

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Using Manipulatives
Lesson Plans

• Step-by-step instructions for Whole-Class
  Skills Lesson

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Using Manipulatives
Lesson Plans

• Differentiated Guided Practice for small groups

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Using Manipulatives
Two-Dimensional Shapes
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Using Manipulatives
How would you differentiate this activity?
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Using Manipulatives
Reflection and Application
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Using Manipulatives

• Find someone else who teaches the same grade as
  you.
• Together, pick one manipulative.
• Create a flow chart that shows the steps you
  would take to teach a concept with this
  manipulative.

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Playing Games
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Playing Games

• Application of concepts
• Motivates students
• Different way to access the content
• Formative assessment

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Playing Games
Skill-Application Game Boards

• Provide students with additional opportunities to
  apply and reinforce skills learned in a fun and
  independent way.

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Playing Games

• Four different game boards
• Four motivational games
• Student-directed activities

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Playing Games
How would you differentiate this activity?
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Playing Games
Reflection and Application
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Playing Games

• What concepts could be most easily
  taught/practiced through games?
• Lets play some games!

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Solving Real-Life Problems
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Solving Real-Life Problems

• Drawing a Diagram
• Creating a Table
• Acting It Out or Using Concrete Materials
• Guessing and Checking
• Creating and Organized List
• Looking for a Pattern
• Working Backwards
• Using Simpler Numbers
• Creating a Tree Diagram
• Open-Ended Problem Solving
• Analyzing and Investigating
• Using Logical Reasoning

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Solving Real-Life Problems
Problem Solving

• One strategy each week
• Daily application to real-life problems
• Completed individually, in small groups, and as
  a whole class

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Solving Real-Life Problems
Problem Solving

• Problems on Transparencies, in Guided Practice
  Book, and on CD
• Callouts for teachers

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Solving Real-Life Problems

• Model problem uses a specific strategy.
• Groups write their own problems that require the
  strategy.

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Solving Real-Life Problems
Seven Problem-Solving Strategy Cards and
Transparencies

• Model how to teach the appropriate
  problem-solving strategy
• Connect the problem-solving lessons and Real-Life
  Problem-Solving Cards in each unit
• Full-color transparencies of both sides of each
  card

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Solving Real-Life Problems
14 Real-Life, Problem-Solving Strategy Cards and
Transparencies

• High-interest cards with real-life scenarios for
  applying problem-solving strategies
• Two problem-solving cards for each unit
• Full-color transparencies of both sides of each
  card

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Solving Real-Life Problems
Problem-Solvers Math Journal

• Extend and apply problem-solving skills and
  strategies.
• Provide extra problem-solving practice using the
  12 problem-solving strategies.
• Student materials can be ordered in sets of 10
  so you can order the level and quantities you
  need.

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Solving Real-Life Problems
Quilting Bee
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Solving Real-Life Problems
How would you differentiate this activity?
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Solving Real-Life Problems
Reflection and Application
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Solving Real-Life Problems

• Choose a problem-solving strategy from the chart
  in your handout.
• Write your own real-life word problem.
• Make sure that it is best solved using the
  strategy you chose.

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Mathematics Readers
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Product Scavenger Hunt
Can you find . . . ?

• a PowerPoint presentation
• callouts for teachers
• a problem-solving activity
• a differentiated activity
• the Teacher Resource CD

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Questions?
Thank you for coming!
Sara Johnson sjohnson_at_tcmpub.com Emily R.
Smith esmith_at_tcmpub.com