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### Early Learning in MathematicsA Formula for Success

Kathy Jungjohann

University of Oregon

Ben Clarke and Mari Strand Cary

Pacific Institutes for Research

October 2, 2009

The research reported here was supported by the Institute of Education Sciences, U.S. Department of Education, through Grant R305K040081 to Pacific Institutes for Research. The opinions expressed are those of the authors and do not represent views of the Institute or the U.S. Department of Education.

Agenda

- Overview
- The ELM Curriculum
- Student and Teacher Measures
- Classroom Observations
- ELM in a multi-tier framework
- Future Plans

High Level of Interest in Mathematics Achievement

- National Research Council: Adding it Up
- National Council Teachers of Mathematics: Focal Points
- National Mathematics Advisory Report

Increasing recognition of the importance of mathematical knowledge

- “For people to participate fully in society, they must know basic mathematics. Citizens who cannot reason mathematically are cut off from whole realms of human endeavor. Innumeracy deprives them not only of opportunity but also of competence in everyday tasks”. (Adding it Up, 2001)

State of Mathematics

- Achievement on the NAEP trending upward for 4th/8th grade and steady for 12th grade
- Large numbers of students still lacking proficient skills
- Persistent income and ethnicity gaps
- Drop in achievement at the time algebra instruction begins
- TIMSS data indicate significant lower levels of achievement between US and other nations
- Relative standing of US is more discrepant at higher grades
- Jobs requiring intensive mathematics and science knowledge will outpace job growth 3:1 (STEM) and everyday work will require greater mathematical understanding

Meaningful Differences inMath Readiness

- Long term trajectories are established as early as kindergarten (Morgan & Farkas, 2009)
- 70% of students exiting K below the 10th %ile remain below the 10th %ile at the end of 5th grade
- Middle and high SES children come to school with much more informal instruction in numbers and quantitative concepts (Griffin, 1994)
- Children lacking these opportunities require formal explicit instruction to develop this understanding

What to do? Our approach

- Develop a kindergarten core curriculum program (ELM) based on
- Critical mathematics content
- Research based instructional design principles.
- Develop assessments tools
- Use in screening and progress monitoring
- Develop an observation system
- Identify and study variables that impact the effectiveness of ELM
- Conduct rigorous research
- Randomized Control Trials

What is the immediate and long-term impact of the ELM curriculum on the mathematics achievement of students in general ed. kindergarten classrooms?

Does the frequency and quality of teacher instructional practices affect student mathematics achievement?

Research QuestionsConceptual Framework for Early Learning in Mathematics

Development of

Mathematical

Concepts Models

Mathematics-related

Vocabulary and

Discourse

Procedural Fluency

Mathematical Models and Multiple Representations of Number

- Goal of ELM is to help children develop multiple representations of number through a focus on number sense, a construct that refers to a child’s fluidity and flexibility with using and manipulating numbers…to look at the world and make quantitative comparisons (Berch, 1998).

Procedural Fluency and Automaticity in ELM

- Automatic and effortless recall of basic math concepts frees up cognitive resources needed to focus on more complex problems
- Multiple strand instruction provides daily practice across lessons
- Children are given frequent opportunities to respond in whole class, partner, and written math practice activities
- Teacher checks for understanding integrated into lessons

Math Related Vocabulary and Discourse

- Basic concepts representing quantitative and relational concepts
- Before, next, last, after, more, how much
- Vocabulary unique to mathematics
- Equal, triangle, measure, subtract, pattern
- Opportunities to engage in classroom discourse using these words

ELM Instructional Content

- National Math Advisory Panel (2008) recommends a focused, coherent progression of mathematics learning with emphasis on proficiency with key topics
- ELM focuses on key strands rather than a broad array of mathematical content
- Numbers and Operations
- Geometry
- Measurement
- Vocabulary (NCTM Process Standard, 2000)

NCTM Curriculum Focal Points for K (2006)

Structure of the Curriculum

- Daily Calendar Lessons/Activities
- 15 minutes daily, whole class “circle” time
- Monthly booklets with objectives and application activities
- 120 Core Lessons divided into 4 quarters
- 30 minutes whole class instruction
- 15 minutes teacher directed written work
- End of quarter assessment of progress

ELM Objectives inNumbers and Operations

- Proficiency in numeration to 30.
- Count and identify numbers to 100.
- Including skip counting by 5s and 10s
- Use a variety of ways to model and represent numbers (fingers, tallies, ten frame, number line, hundreds chart, base ten blocks).
- Use multiple strategies to solve simple addition and subtraction problems.
- Develop an understandings of fractional unit “half.”

ELM Objectives in Geometry

- Identify and describe common 2 and 3 dimensional geometric shapes.
- Sort and describe objects by shape, color, size, and other attributes.
- Recognize and extend simple patterns.

ELM Objectives in Measurement

- Compare and order groups of objects with various strategies (visually, 1:1 correspondence, counting).
- Identify objects and groups that are more, less, or equal.
- Understand concepts of time, money, and measurement.
- Measure in inches, tell time to the hour, count and compare coins.
- Create and interpret graphs.

Frequent and High Quality Instructional Practices

- Key math principles and concepts are explicitly modeled followed by student application and responsive teacher feedback.
- Rich and frequent opportunities to engage in essential practice of key mathematical concepts.
- Opportunities for students to verbalize essential mathematical concepts.

Effective Instructional Delivery Strategies

- Explicit and Scaffolded Teaching
- Teacher modeling, guided practice, independent
- High student engagement
- Multiple opportunities to respond
- Teacher Feedback
- Specific positive confirmations
- Corrective feedback on errors
- Distributed Practice and Review

Monitoring Progress with End of Quarter Assessment

- Last lesson in every quarter has end of quarter check for progress
- Set up activity centers for children to rotate through while you…
- Call on children to work with you
- Combination of independent (math practice) and individual teacher assessment

Pilot ELM Study - Oregon

- Three year research/development project
- Curriculum Development 2004-2005
- Field Tested in 2005-2006
- Treatment (ELM) Classrooms: 5
- Control Classrooms: 4
- Field Tested in 2006-2007
- Treatment (ELM) Classrooms: 9
- Control Classrooms: 5

Results from Pilot Study were promising

- Results were close to statistical significance at p =.057
- ELM accounted for 35% of the variance in SESAT scores and resulted in a meaningful positive effect d =.26
- Results did not vary based on at-risk status (i.e. at risk children showed the same gains)

Efficacy Studies

- Study the effectiveness of the ELM curriculum
- Study the added benefit of a small group component to the ELM curriculum
- Continued development of assessment tools

Efficacy Study - Oregon

- Two-year research project
- ELM vs. Non-ELM
- Completed 2008-09, analysis ongoing
- 66 Classrooms (split evenly)
- ELM + Small Group vs. ELM only
- Ongoing (2009-10)
- 66 Classrooms (split evenly)

Efficacy Study – Texas

- Intended to test efficacy of ELM curriculum in different context
- Two-year research project
- ELM vs. Non-ELM
- Ongoing 2009-10
- 66 Classrooms (split evenly)
- ELM + Small Group vs. ELM only
- Next year (2010-11)
- 66 Classrooms (split evenly)

Measuring Effectiveness

- Student assessments
- Teacher measures
- Observations of math time

Student assessments

- Screening and Progress Monitoring (Early Numeracy CBM)
- Outcome Measure (Test of Early Mathematics Ability)

Early Numeracy Curriculum Based Measures (EN-CBM)

- 4 measures for K & 1st grade
- Used with all students to screen for risk status
- Measures are of short duration and timed (1 minute)
- Assess key areas of mathematical knowledge
- Potential for use in progress monitoring

EN-CBM (cont’d)

- Oral Counting

Students orally count for one minute. No student materials.

- Number Identification

Teacher Measures

- Demographics / Background Survey
- Number of yrs. teaching kindergarten
- Education degrees, certifications, and math coursework
- Typical approach to math instruction
- Content Knowledge Survey
- Strong relationship between student achievement and teachers’ math knowledge
- Designed by D. Ball and colleagues to measure the mathematical knowledge required for teaching

Instructional Logs

Online submission, twice a month

Capturing one lesson

instructional time & format

math strands & sub-strands

specific skills & vocabulary

Perceptions of the ELM program and math instruction

Satisfaction with ELM program

Thoughts on PD provided

Teacher Measures (cont’d)Observations

- Conducted approximately 200 math lesson observations
- 3 per year for all classrooms (fall, winter, and spring)
- Duration ranged from 15 to 60 minutes
- 20% were double-coded to ensure our observers were reliable

Observations (cont’d)

- Goal 1: Capture mediating variables
- Frequency of instructional interactions between teachers and students
- (e.g., teacher models, practice opportunities)
- Uses CATS observation instrument
- Goal 2: Assess implementation fidelity

Coding of Academic Teacher-Student Interactions (CATS)

- Relatively simple, easy to use tool
- Code behaviors in a continual, serial fashion
- Captures instructional context and instructional interactions

CATS Context Codes

- Start and Stop Times
- Number of Students / Whole Class
- Type of Content
- Number Operations
- Geometry
- Measurement
- Calendar
- Other (non-math)
- Non-Academic Engagement (NAE)

CATS Instructional Interaction Codes

- Teacher Model
- Group Response
- Individual Response
- Covert Response
- Student Mistake
- Academic Feedback
- Error Correction
- Response Affirmation

CATS Instrument

Note. Adapted from Smolkowski & Gunn(submitted for publication)

Sample: Transcript excerpt

- Teacher: Today, we’re going to sort shapes using Attribute Blocks. This first shape is a square. A square has 4 sides of the same length [teacher points and counts sides].” (Teacher Model)
- Teacher: “Billy, how many sides does a square have?”
- Billy: “Four” (Individual Response)
- Teacher: “Sally, are the sides of a square the same?”
- Sally: “No” (Individual Response) (Mistake)
- Teacher: “Actually, the sides of a square are the same. All four sides are the same in length [teacher points to the sides]. (Acad Feedback)
- Teacher: “Sally, are the sides of a square the same?”
- Sally: “Yes” (Individual Response)
- Teacher: “OK everyone get ready to tell me the name of each shape. Everyone, what’s the name of the first shape?”
- Class: “Circle” (Group Response)
- Teacher: “Yes” (Not coded as Academic Feedback)

Sample: Coded excerpt

A whole-class activity targeting content #2 (i.e., geometry). During the activity, which lasted 5 minutes, four students were not academically engaged.

Observations (cont’d)

- Goal 1: Capture mediating variables
- Goal 2: Assess implementation fidelity
- Target adherence to specific activities of the ELM program
- Completion of each lesson activity
- Extent to which lesson matched intended delivery as specified by the ELM program

Tier 1: Components

- Screening instruments
- Core Curriculum research based or expert judgment
- Enhancements to the core curriculum

Tier 2 and 3 Components

- Progress monitoring and diagnostic assessments
- Standard protocol interventions
- Instructional design considerations

Tier 2/3 (Interventions)

- Standard protocol approach
- Students maintain in the program for a set duration of time
- I.e. Progress monitoring data collected but not used for educational decision-making
- Limit scope to critical topics
- Avoid low grade dose of the same material and same approach

Tier 2/3 Instructional Design

- Previous Syntheses on mathematics interventions
- Not LD specific (Xin & Jitendra, 1999; Kroesbergen & Van Luit, 2003; Baker, Gersten, & Lee, 2002)
- Organized on basis of dependent measure (Swanson, Hoskyn, & Lee, 1999)
- Fuchs, Fuchs, Mathes, and Lipsey (2002) meta-analysis in reading: LD vs. Low Achieving students
- LD lower performing than low achieving (d = .61)
- Discrepancy between LD and low achieving greater on timed vs. untimed measures -- (automaticity / speed of processing implications)
- LD vs. low achieving differences were greater when LD determinations based on objective measures vs. more subjective approaches (e.g., team decision making)

Future work in mathematics

- Potential Effectiveness trial of ELM (IES Goal 4)
- Development of mathematic screening and progress monitoring system (K-8)
- Plans to develop and research intervention programs
- 1st Grade Intervention with focus on whole number (IES Goal 2 grant 2009-2011)
- Rational number

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