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Strategies for Mathematics Intervention

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Presented by:

Sara [email protected]

Emily R. Smith [email protected]

Today’s 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

Build a Sentence

- Use these words and numbers to make a true sentence:
- 10
- 50%
- twice
- difference

Build a Sentence

- Use these words and numbers to make a true sentence:
- 10
- equals
- 1/2
- 40

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

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

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.”

TCM Mathematics Intervention

Exploring Math

An Intervention and Reinforcement Resource

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

Targeted Mathematics Intervention

for Summer School, After School, and Other Instructional Programs

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

TCM Mathematics Intervention

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

TCM Mathematics Intervention

- Develops students’ mathematical understanding through . . .
- concrete examples
- multiple representations
- multiple algorithms

TCM Mathematics Intervention

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

Strategies to Engage Students

- Developing vocabulary
- Using manipulatives
- Solving real-life problems
- Playing games

Developing Vocabulary

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

Developing Vocabulary

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

Developing Vocabulary

Developing Vocabulary

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

Differentiation

Differentiating Activities

above

Objective

on

below

Differentiating Activities

Tiering/Leveling Activities

- Start with whole class activity
- Below grade level—Narrow the scope of the activity and make it more concrete
- English language learners—Add context to the activity and make it more concrete
- Above grade level—Increase the complexity of the activity

Differentiate through:

Content (what is taught)

Process (how it is taught)

Product (what they produce)

Differentiate because of:

Readiness

Learning styles

Interests

Differentiating Activities

Differentiating Activities

Developing Vocabulary

How would you

differentiate

this activity?

Developing Vocabulary

Reflection

and

Application

Developing Vocabulary

- Get into groups of 3–4 and develop your own differentiated vocabulary activity.
- Be ready to share this with others in five minutes.

Assessing Students

Assessment

“Assessments are learning opportunities for students and for teachers. Students can learn more mathematics, and teachers can learn more about their students—and sometimes more mathematics, as well—from all types of assessments.”

—Long 2000

Assessment

- Summative assessments
- individual
- grade-level criterion-referenced tests
- authentic assessments

- Formative assessments
- group and individual
- authentic assessments

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.

Assessment

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

Assessment

Reflection

and

Application

Assessment

Answer this question by yourself or with your “elbow partner.”

How do you assess mathematical thinking?

Using Manipulatives

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

Using Manipulatives

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

Using Manipulatives

Lesson Plans

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

Using Manipulatives

Lesson Plans

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

Using Manipulatives

Lesson Plans

- Differentiated Guided Practice for small groups

Using Manipulatives

Two-Dimensional Shapes

Using Manipulatives

How would you

differentiate

this activity?

Using Manipulatives

Reflection

and

Application

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.

Playing Games

Playing Games

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

Playing Games

Skill-Application Game Boards

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

Playing Games

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

Playing Games

How would you

differentiate

this activity?

Playing Games

Reflection

and

Application

Playing Games

- What concepts could be most easily taught/practiced through games?
- Let’s play some games!

Solving Real-Life Problems

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

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

Solving Real-Life Problems

Problem Solving

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

Solving Real-Life Problems

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

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

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

Solving Real-Life Problems

Problem-Solver’s 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.

Solving Real-Life Problems

Quilting Bee

Solving Real-Life Problems

How would you

differentiate

this activity?

Solving Real-Life Problems

Reflection

and

Application

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.

Mathematics Readers

Product Scavenger Hunt

Can you find . . . ?

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