Tier 2 Interventions for Mathematics

Denver Public Schools

August 2009

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Overview of Morning

• Process for identifying recommended interventions

• Supporting DPS Core Mathematics with Tier 2 Interventions

• Preview DPS recommended interventions Math Navigator: grades 2-10 ALEKS: grades 3-12 ORIGOmath: grades 1-2 Aim for Algebra (pilot): grades 8-9

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Screen of Intervention Programs• Clear directions for guided and independent

practice

• Instructional materials with adequate practice (concepts & procedures) and sufficient review (distributed, cumulative, & varied)

• Additional support for ELLs

• Identification of common misconceptions with suggestions to address them

• Mathematically correct content

• Multiple assessments (diagnostic, progress monitoring, summative) with clear guidelines for use and instructional interpretation

Research-Based Recommendations for

Mathematics Interventions• Screen all students to identify those at risk

• Focus intensely on in-depth treatment of whole numbers in K- 5 and on rational numbers in 4-8

• Provide explicit and systematic instruction (models of proficient problem solving, verbalization of thought processes, guided practice, corrective feedback, & frequent cumulative review)

• Include instruction on solving word problems

• Include opportunities for students to work with visual representations of mathematical ideas

• Devote about 10 minutes per session to building fluent retrieval of basic arithmetic facts

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Assisting Students Struggling with Mathematics: Response to

InstructionBegin with high-quality instruction and universal

screening for all students

• Core program (Everyday Mathematics, Connected Mathematics, or Discovering Mathematics)

• Instructional time as described in Best Practice documents

• Differentiated instruction within core program to support students

• Periodic assessment using tools within core program

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Universal Screening in Mathematics

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Universal Screening: Grade 3

• Current third graders Spring 2009 DPS benchmark results Standards-based progress reports with a focus

on Number Sense and Computation Diagnostic screener

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Implementing Tier 2 Interventions

• Select an intervention program

• Identify students to be served, create an order and send order (electronically) to Maggie Wolfe in ERS

• Create an intervention schedule

• Teachers delivering intervention attend central professional development

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Program Preview

• Mathematics Navigator

from America’s Choice

• ORIGOmath

from ORIGOeducation

• ALEKS—an online system

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Mathematics Navigator

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Introduction to Mathematics Navigator

• Does not repeat initial teaching• Focuses on revising misconceptions• Encourages students to approach the

mathematics from several angles• Provides learning opportunities beyond

solving problems—analyze work for errors, test validity of their work against others’ work, try multiple strategies to determine if prior knowledge holds true, and modify or invent similar problems

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Mathematics Navigator Program Design

• Targeted Concepts

• Algebraic Structure of Arithmetic

• Prior Knowledge and Misconceptions

• Language-Rich Environment

• Better Learners of Mathematics

• Instructional Support

Module Design

• 20 days for each module Module design in elementary units includes two

check-points Module design in secondary units includes a

check-point every 5 days

• Recommended instructional time: 35-45 minutes a minimum of 3 days a week in addition to core instruction

• Group size Elementary: up to 10 students Secondary: up to 30 students

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Instructional Support Overview

• Instructional guidance

• ELL Support

• Formal and Informal Assessments Diagnostic screeners Pre- and post-tests Checkpoints

Universal Screening: Grades 4-10

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Universal Screening: Grade 3

• Current third graders Spring 2009 DPS benchmark results Standards-based progress reports with a focus

on Number Sense and Computation Diagnostic screener

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Getting Started with Year

• Administer Screener

• Analyze assessment data and determine modules to implement and place order

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Getting Started with a Module

Day 1

• Administer and Score Pre-Test

• Record Pre-Test data on the Pre-Test/Post-Test Profile

• Consider Pre-Test results for individual student and for class

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Getting Started with a Session

• Skill Cards (using quick response boards)

• Skill Practice (in student book)

• Solo Work: Problem 1

• Partner Work: Problem 1

• Probing for Understanding

• Solo Work: Problem 2

• Partner Work: Problem 2

• Probing for Understanding

• Closing the Lesson

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Instructional Support within Modules

• Instructor Edition Purpose of Module Goals for the Module Day-by-Day Overview English Language Learner Considerations Types of Assessment & Record Keeping

• Chart of Rituals

• Study Cards

• Materials List

• Checkpoints

• Checkpoint Profile

• Class Profile

Mathematics Navigator in DPS

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ALEKS

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What is ALEKS?

• Assessment and LEarning in Knowledge Spaces

• Only online intervention recommended by DPS for mathematics intervention

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Features of ALEKS

• Assessment and learning with Standards-Based Content for Grades 3-12

• Monitors Student, Class, School and District Progress Toward State Standards

• Fully Bilingual – English and Spanish for Grades 3-9

• Unlimited Online Access – PC & Mac Compatible

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How Does ALEKS Work?

• Initial assessment determines students’ topic mastery

• Multi-colored chart generated for each student

• Student works in learning mode to master new topics

• Continual assessment aids students’ retention of new learning

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ALEKS in Action

• http://www.aleks.com/video/quick_tour

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ALEKS Course Products

• Mathematics-LV 3 (with Quick Tables) for Tier 2 Grades 3-4

• Mathematics-LV 4 (with Quick Tables) for Tier 2 Grade 5

• Mathematics-LV 5 (with Quick Tables) for Tier 2 Grade 6

• Essential Mathematics (with Quick Tables) for Tier 2 Grades 8, 9, 10

• High School Preparation for Algebra 1 for Tier 2 Grades 10, 11, 12

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Quick Tables Demonstration

• http://www.aleks.com/video/qt_quick_tour

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Assessment within ALEKS

• Initial Assessment

• Automatic Assessments

• Comprehensive Assessments

• Quizzes

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Instructional Time

• Recommend minimum of 2 ½ hours per week in

addition to core instruction

• Group size limited only by computer availability

and teacher supervision

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Sample Student Report

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Sample Student Pie Chart

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Other Important Information

• ALEKS can be used with either Windows or Mac with modifications

• Pricing will be determined by number of DPS students registered

• Professional development will be offered beginning in September

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ORIGOmath

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Universal Screening for Primary Grades

• Current second graders Standards-based progress reports with a focus

on Number Sense and Computation Diagnostic screener from ORIGOmath: pre-test

• Current first graders Standards-based progress reports with a focus

on Number Sense and Computation Diagnostic screener from ORIGOmath:

prerequisite check list

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ORIGOmath

• Encourages students to justify and share their thinking

• Provides real-life contexts to explore mathematical ideas

• Provides a carefully developed sequence of learning experiences

• Emphasizes students’ critical thinking and reasoning

• Provides opportunities for students to practice computation facts in addition to problem solving

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Teacher Sourcebook and

Student Journals

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Scope and Sequence

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EM-like Models

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One Unit for Two Weeks

• Each unit has five sessions

• Combine with Fundamentals game practice

• Recommend a two-week interval per unit

• Includes pre- and post-assessment for Grade 2

• Includes pre-requisite checklist for Grade 1 and

post-assessment

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Assessment Tools

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Thank you!

• We know your time is valuable—especially at the start of a school year.

• Hopefully, this was enlightening as to plans in DPS for the 2009-2010 school year to provide support for our teachers and students in accessing the critical skills in mathematics.

• For further information, please contact DPS Intervention Coordinator in Teaching and Learning, Mathematics/Science: Dr. Kris O’Clair.

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AIM for Algebra

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Aim for Algebra: An Algebra intervention/prep

program

• Developed by West Ed Conceptually based Standards-aligned

• Identified specific areas that most often become barriers to learning algebra

• Provides learning experiences that reinforce,

refresh, or reteach important concepts

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Increases Achievement

• Focuses on traditional barriers to success in algebra

• Uses purposeful sequencing and scaffolding of ideas

• Uses multiple strategies to reduce student misconceptions

• Uses manipulatives for hands-on learning

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Organization

Stand-alone unitsSigned Number Operations 2 weeksVariables and expressions 3-4 weeksRatio and Proportion 4 weeksPatterns 3-4 weeksThe Coordinate Plane 2-3 weeks Inequalities 4-6 weeks

Allows for flexible programming

Can be taught in any order but entire module should be taught sequentially

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Coming Soon

• Number Theory for Algebra

• Exponents

• Rational Numbers

• Proportional Reasoning

• Equations and Formulas

• Data and Probability

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Materials

Each unit includes:

• Facilitator guide Each unit is focused on three concepts or big

ideas

• Consumable student pages (packaged for groups of 10) Pre- and post-tests included Daily task sheets

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Teacher’s RoleFor each task

Purpose: helps focus the task. Launch: begins the discussion and connects to

prior learning before giving students their printed materials for the lesson

Facilitate the task: introduces task to whole group. Allows individual think time. Bring s group back together to check for understanding. Allows students to continue working on tasks individually or in groups. Circulates among groups and asks questions to help students who need guidance.

Summary: ensures students connect the task back to the stated purpose. Reinforces ideas.

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Students’ Role

Justify their solutions in the context of the tasks

Explain their thinking and reasoning to others

Make sense of other students’ explanations

Ask questions of the teacher or other students when they do not understand

Use correct mathematical vocabulary, language, and symbols in their explanation

Share their solutions and thinking with the whole class

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Pilots Available

• 8th and 9th grade “skills” classes to support core classes

• One teacher per participating school Use screener to identify and select desired unit Facilitator guide and student materials for one class

will be provided at no cost

• Results will be analyzed based on student achievement and teacher feedback

• Contact Kris O’Clair, Mathematics Intervention Coordinator, to be part of pilot this fall.

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Thank you!

• We know your time is valuable—especially at the start of a school year.

• Hopefully, this was enlightening as to plans in DPS for the 2009-2010 school year to provide support for our teachers and students in accessing the critical skills in mathematics.

• For further information, please contact DPS Intervention Coordinator in Teaching and Learning, Mathematics/Science: Dr. Kris O’Clair.

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