Running Head: TIER 2 KINDERGARTEN … the Efficacy of a Tier 2 Kindergarten Intervention Ben Clarke ... Results from the 2011National Assessment for Educational Progress ... report,

Running Head: TIER 2 KINDERGARTEN INTERVENTION

Examining the Efficacy of a Tier 2 Kindergarten Intervention

Ben Clarke

Christian Doabler

University of Oregon

Keith Smolkowski

Oregon Research Institute

Scott Baker

Hank Fien

Mari Strand Cary


Technical Report #1104

Center on Teaching and Learning


TIER 2 KINDERGARTEN INTERVENTION 2

Introduction

The low level of mathematics performance of U.S. students in relation to national

standards and in international comparisons has concerned educators and policy makers

and garnered increasing attention in the past decade (National Mathematics Advisory

Panel [NMAP], 2008; National Research Council [NRC], 2001; Schmidt, Houang, &

Cogan, 2002). Results from the 2011National Assessment for Educational Progress

(NAEP) indicate that only 40% of 4th graders were deemed at or above proficient in

mathematics and 18% were below basic (National Center for Education Statistics, 2011).

Difficulties in mathematics achievement are particularly severe for students from low

income and minority backgrounds and those with learning disabilities. Signs of long-term

difficulty in mathematics appear early. Specifically, significant differences in student

knowledge can be reliably assessed at school entry on measures ranging from counting

principles and number knowledge to more complex understandings of quantities,

operations, and problem solving (Griffin, Case, & Siegler, 1994; Jordan, Kaplan, &

Locuniak, 2007). Longitudinal research suggests that students who perform poorly in

mathematics at the end of kindergarten are likely to continue to struggle throughout

elementary school (Bodovski & Farkas, 2007; Duncan et al., 2007; Hanich, Jordan,

Kaplan, & Dick, 2001; Morgan, Farkas, & Wu, 2009). Using a nationally representative

sample of students from the Early Childhood Longitudinal Study-Kindergarten Cohort

(ECLS-K), Morgan et al. (2009) found that students who were in the lowest 10th

percentile at entrance and exit from kindergarten (considered an indicator of a learning

disability in mathematics – MLD) had a 70% chance of remaining in the lowest 10th

percentile five years later. Their overall mathematics achievement in fifth grade remained


2 standard deviation units below students who did not demonstrate a MLD profile in

kindergarten. These data as well as Duncan et al.’s (2007) recent meta-analysis of

longitudinal research on the development of mathematics proficiency argue strongly for

the importance of a successful start in mathematics. Unless these differences are

addressed at entry into kindergarten, they are likely to persist and become more difficult

to remediate over time as students exit kindergarten without a solid foundation upon

which to build an increasing complex understanding of mathematics (Geary, 1993;

Jordan, Kaplan, & Hanich, 2002; Lyon et al., 2001; Morgan et al., 2009).

Recognizing that mathematics trajectories are established early in school and

kindergarten represents a critical transition from informal to formal mathematics, our

research group developed and evaluated ROOTS, a 50-lesson (Tier 2) kindergarten math

intervention. The purpose of this technical report is to summarize results from an initial

randomized controlled trial (RCT) study on the efficacy and efficiency of ROOTS. In this

report, we present an overview of the ROOTS curriculum, study design, methodology

and results focusing on the impact of ROOTS on kindergarten student math outcomes.

Our research team had previously developed and evaluated the Early Learning in

Mathematics (ELM) kindergarten core curriculum (Davis & Jungjohann, 2009). ELM

consists of 120 lessons and focuses on four key mathematics strands: (a) Number and

Operations, (b) Geometry, (c) Measurement, and (d) Vocabulary. The first three of these

map directly onto the three content domains contained in the National Council of

Teachers of Mathematics Curriculum Focal Points (NCTM, 2006), and the fourth

(vocabulary) is addressed in the NCTM Process Standards (2000). We tested the efficacy

of ELM in a RCT, randomly assigning 66 kindergartens classrooms to treatment and


control conditions. Students in the treatment condition, ELM, outperformed their control

classroom peers on two distal measures of math proficiency. ELM students significantly

outperformed control students on both the Test of Early Mathematics Ability – 3rd

Edition (TEMA; t = 2.41, p = .02) and Early Numeracy Curriculum Based Measurement

(EN-CBM; t = 1.99 p = .05). Overall Hedges g effect sizes were .13 on the TEMA and

.14 on EN-CBM (Clarke et al., 2011). In condition by risk status analyses, at-risk

students (defined as performing below the 40th percentile on the TEMA at pretest)

demonstrated the greatest treatment benefit (Clarke et al., 2011). At-risk treatment

students significantly outperformed at-risk control students on both the TEMA (t = 3.29,

p = .0017, g = .24) and EN-CBM total score (t = 2.54, p = .0138, g = .22).

The pattern of findings is important for two reasons. First, differential impact

favoring the at-risk students was aligned with our theoretical framework. In developing

ELM our objective was to create a core mathematics programs (i.e., Tier 1) that would

address the needs of the average- and high-performing students (in the analysis, students

above the 40th percentile at pretest performed the same at posttest in both ELM and

control conditions) and substantially increase the mathematics achievement of students at

risk for math difficulties (which occurred). Second, although the ELM curriculum was

beneficial to at-risk students in particular, the performance of at-risk students at the end

of the year did not match the performance of students not at risk (at pretest). In other

words, although there was differential impact by risk status, the program did not fully

eliminate the gap between at-risk and average-achieving students.

Spurred by our findings that while ELM helped reduce but not fully eliminate the

achievement gap between at-risk students and their on track peers, we developed a Tier 2


intervention, ROOTS, to be used as a supplemental program with ELM. The ROOTS

intervention was designed to focus exclusively on Number and Operations because an in-

depth understanding of the whole number system is a critical step in achieving

proficiency in more sophisticated mathematics, such as rational numbers and algebra

(Gersten et al., 2009a; NCTM, 2006; NRC, 2001, 2009). For example, authors of the IES

practice guide on effective mathematics instruction and intervention for at-risk students

observed that “individuals knowledgeable in instruction and mathematics look for [and

develop] interventions that focus on whole numbers extensively in kindergarten through

grade 5” (Gersten et al., p. 18; 2009a). Concurring, the Common Core State Standards for

Mathematics (CCSS, 2010) recommends extensive coverage of whole number concepts

and skills during kindergarten (i.e., counting and cardinality, operations and algebraic

thinking, and number and operations in base ten).

In the second study of the ELM efficacy trial (Baker et al., 2008), we explored the

value added of the intervention program, ROOTS, to accelerate the learning of students at

risk for MLD. All students randomly assigned to the treatment condition received core

instruction in ELM and at-risk students received the combination of ELM and the

ROOTS intervention. Instructional assistants delivered ROOTS to small groups of 4-5 at-

risk students during the second half of the kindergarten school year. This technical report

summarizes findings from that study.

ROOTS Intervention Overview

ROOTS is a 50-lesson kindergarten intervention program designed to develop

procedural fluency with and conceptual understanding of whole number concepts.

ROOTS is delivered by instructional assistants to small groups consisting of 4-5 students,


2 to 3 times per week, for 20 weeks during the second half of the school year. Each

ROOTS lesson is approximately 20 minutes in duration and includes 4 to 5 brief math

activities that center on whole number concepts and skills. ROOTS provides in-depth

instruction in whole number concepts by linking the informal mathematics developed

prior to kindergarten to the formal mathematics of kindergarten. Specifically, ROOTS

focuses on three key areas of whole number understanding (a) Counting and Cardinality

(b) Number Operations and (c) Base 10/Place Value. Students advance from objectives

centered on counting objects and identifying numerals to applying their knowledge of

foundational principles to number operations and the base 10 system. The specific focus

on whole number aligns with calls for more focused and coherent curricula (NCTM,

2006; NMAP, 2008), and intervention programs designed to meet the needs of students

at-risk for MLD (Gersten et al., 2009a). ROOTS Objectives and the alignment overview

between ROOTS and the Common Core State Standards (CCSS, 2010) are listed in

Appendix A (pp. A1-A10).

A central feature of the ROOTS program, established through a set of research-

based instructional design principles (Doabler et al., in press), is an explicit and

systematic approach to instruction. Mathematics intervention studies consistently

demonstrate that students at-risk for MLD learn more from explicit math instruction

compared to other approaches to instruction (Baker, Gersten, & Lee, 2002; Gersten, et

al., 2009b; Haas, 2005; Kroesbergen & Luit, 2003). Explicit and systematic instruction is

a method for teaching the “essential skills in the most effective and efficient manner

possible” (Carnine, Silbert, Kame’enui, & Tarver, 2004; p. 5). This approach

incorporates the instructional design principles that (a) facilitate overt and conspicuous


instructional interactions among teachers and students targeting key math content and (b)

increase intervention intensity required to accelerate learning for kindergartners at-risk

for MLD. For example, the lessons provide teachers with guidelines for modeling and

demonstrating what they want students to learn, and providing specific academic

feedback to students as they engage in learning activities. The program also provides

students with frequent and structured opportunities to practice learning key mathematics

concepts and content.

Methodology

Design

A randomized controlled trial was the research design used. Math achievement

data were collected from individual students, and random assignment and instructional

delivery took place at the classroom level. Classrooms were randomly assigned to

treatment or control conditions, blocking on school. Our primary analysis framework is a

group-randomized trial (Murray, 1998) with students nested within classrooms and

classrooms nested within condition. Fourteen classrooms were in the treatment condition

and 15 classrooms were in the control condition.

Participants

Full day kindergarten classrooms who participated in the ELM study were

randomly assigned to treatment or control conditions, blocking on teachers’ ELM

experience (one year or none) and school. Fourteen classrooms were in the treatment

condition (ELM+Roots) and 15 classrooms were in the control condition (ELM-only).

Time was controlled so that treatment and control classrooms provided the same amount

of daily mathematics instruction. This was accomplished by delivering the Roots


instruction during the individual, worksheet-based “math practice” portion of ELM in

treatment classrooms. Classroom teachers (treatment and control) provided whole class

ELM instruction throughout the year. Roots instruction began in January and was

provided by trained instructional assistants.

Instructional Assistants. Fourteen instructional assistants (IAs) participated in

the study, of which thirteen were female and all identified themselves as White. Three of

the IAs had college degrees and two held current teacher certifications. In this sample,

nine of the IAs had four or more years experience as an instructional assistant and all but

four of the IAs had completed college level coursework in mathematics.

Students. A list of students by classroom who had scored below the 40th

percentile on the TEMA pre-test was provided to participating teachers (n = 29) who

were asked to select 5 students from the list who they believed would benefit from a

small group math intervention. In treatment classrooms (ELM+Roots), these “Roots

students” (n=69) received all of the whole-class ELM instruction, however, three days

per week, instead of practicing that day’s ELM topics independently (i.e. math practice

worksheets), they received Roots instruction. Nominated students in control classrooms

(n = 74) served as “matched pairs.” Given that Roots was not offered in their classrooms,

they participated only in whole class ELM instruction, five days per week.

Fidelity of Implementation

Professional development. Participating IAs attended three PD workshops

focused on the ROOTS curriculum. The initial PD workshop focused on the instructional

objectives related to Lessons 1-25, the critical content of kindergarten mathematics,

small-group management techniques, and the instructional practices that have been


empirically validated to increase student math achievement (e.g., teacher provided

academic feedback). In the second and third workshops the same format was followed as

in workshop 1 but with a focus on the second half of the ROOTS curriculum, Lessons 26-

50. Workshops were 4 hours in length and organized around three principles: (a) active

participation (b) content focused, and (c) coherence. Although the empirical literature on

PD in math instruction is thin, a burgeoning base of evidence indicates these principles

can lead to improved outcomes for teachers and students (Blank & de las Alas, 2009;

Fixsen et al., 2005; Joyce & Showers, 2002; Scher & O’Reilly, 2009). On at least three

occasions, IAs also received onsite coaching from two expert teachers. Some IAs

received more than three coaching visits if the IA or coach felt more support was

warranted (e.g., when there were particularly pervasive student behavior problems or the

IA struggled with lesson implementation).

Fidelity. Online logs completed by the 14 instructional assistants (IA) who

delivered the ROOTS intervention revealed that groups generally completed all 50

ROOTS lessons during the year. Research staff observed ROOTS instruction 1-3 times

over the course of the study and rated fidelity of implementation using a 3-point rating

scale where 3 represented “full implementation,” 2 represented “partial implementation,”

and 1 was “not taught.” IAs demonstrated high fidelity scores (M = 2.92, SD = 0.06) for

the activities prescribed. Surveys were completed by the 14 ROOTS IAs as well as the 14

classroom teachers who provided whole class instruction to ROOTS students. IAs

(100%) and teachers (87.5%) reported that is was possible to provide 20 minutes of

ROOTS instruction on a regular basis. Using a 7-point Likert scale where 1 represented

“greatly benefited,” 4 represented “moderately benefited,” and 7 represented “did not


benefit.” IAs and classroom teachers reported that ROOTS students benefited

significantly from ROOTS instruction (respectively, M = 2.0, SD = 1.15; M = 2.0, SD =

1.19).

Student Measures

Test of Early Mathematics Ability-Third Edition (TEMA-3; Pro Ed, 2007).

The TEMA-3 is a norm-referenced individually-administered measure of early

mathematics for children ages 3 to 8 years 11 months. The TEMA-3 is designed to

identify student strengths and weaknesses in specific areas of mathematics. The TEMA-3

measures both formal mathematics and informal mathematics including skills related to

counting, number facts and calculations, and related mathematical concepts. Test authors

report alternate-form reliability of .97 and test-retest reliability ranges from .82 to .93.

Concurrent validity with other criterion measures of mathematics is reported as ranging

from .54 to .91.

Early Numeracy-Curriculum-Based Measurement measures (EN-CBM;

Clarke & Shinn, 2004). EN-CBM is a set of four measures based on principles of

curriculum-based measurement (Shinn, 1989). For our purposes, these measures map

onto the ROOTS objective of developing procedural fluency. Each 1-minute fluency-

based measure assesses an important aspect of early numeracy development including

magnitude comparisons and strategic counting. The EN-CBM measures have been

validated for use with kindergarten students (Chard et al., 2005; Clarke et al., 2008). Oral

Counting (OC). The OC measure requires students to orally rote count as high as possible

without making an error. Concurrent and predictive validity range from 46 to .72 with

other published standardized measures. Number Identification Measure (NI). The NI


measure requires students to orally identify numbers between 0 and 10 when presented

with a set of printed number symbols. Concurrent and predictive validity range from .62

to .65 with other published standardized measures. Quantity Discrimination Measure

(QD). The QD measure requires students to name which of two visually presented

numbers between 0 and 10 is greater. Concurrent and predictive validities range from .64

to .72. Missing Number Measure (MN). The MN measure requires students to name the

missing number from a string of numbers (0-10). Students are given strings of three

numbers with the first, middle, or last number of the string missing. Concurrent and

predictive validities range from .46 to .63.

Data Collection

All measures were individually administered to students. Trained staff with

extensive experience in collecting educational data for research projects administered all

student measures. All data collectors were required to obtain inter-rater reliability

coefficients of .90 prior to collecting data with students. Follow-up trainings were

conducted prior to each data collection period to ensure continued reliable data

collection.

Analysis

We assessed intervention effects on each of the primary outcomes with a mixed

model (multilevel) time by condition analysis (Murray, 1998). This tests differences

between conditions on change in outcomes from the fall of kindergarten (T1) to the

spring (T2). The specific model tests time coded 0 at T1 and 1 at T2, condition coded 0

for control and 1 for ROOTS, and the interaction between the two. With 29 schools, tests

of time by condition used 27 degrees of freedom. The analyses included students


identified as at risk for math difficulties across both conditions. The analysis included all

available data—whether or not students’ scores were present at both time points—to

estimate differences between assessment times and between conditions, which minimizes

the potential for bias due to missing data. The nested time by condition analysis accounts

the intraclass correlation associated with multiple students nested within the same

schools. As a test of net differences, it also provides an unbiased and straightforward

interpretation of the results (Cribbie & Jamieson, 2000, Fitzmaurice, Laird, & Ware,

2004).

Model estimation. We fit models to our data with SAS PROC MIXED version

9.1 (SAS Institute, 2009) using restricted maximum likelihood (REML), generally

recommended for multilevel models (Hox, 2002). From each model, we estimated fixed

effects and variance components. Maximum likelihood estimation for the time by

condition analysis allows the use of all available data and provides potentially less biased

results even in the face of substantial attrition, provided the missing data were missing at

random (Schafer & Graham, 2002). In the present study, we did not believe that attrition

or other missing data represented a meaningful departure from the missing at random

assumption, meaning that missing data did not likely depend on unobserved determinants

of the outcomes of interest (Little & Rubin, 2002).

The models assume independent and normally distributed observations. We

addressed the first, more important assumption (van Belle, 2008) by explicitly modeling

the multilevel nature of the data. Regression methods have also been found quite robust

to violations of normality and outliers have a limited influence on the results in a variety

of multilevel modeling scenarios (Bloom, Bos, & Lee, 1999; Donner & Klar, 1996;


Fitzmaurice et al., 2004; Maas & Hox, 2004; 2004b; Murray et al., 2006). This feature of

multilevel models also eases concerns about the use of different scoring methods used for

different measures in the analyses (e.g., raw scores, scaled scores, standard scores).

Effect sizes. To ease interpretation of effects we computed an effect size, Hedges’

g (Hedges, 1981), for each fixed effect. Hedges’ g represents an individual-level effect

size comparable to Cohen’s d (Rosenthal, Rosnow, & Rubin, 2000), except that Cohen’s

d uses the sample standard deviation while Hedges’ g uses the population standard

deviation (Rosenthal & Rosnow, 2007).

Results

Table 1 presents means, standard deviations, and sample sizes for the TEMA-3

and CBM outcomes by assessment time and condition. We addressed our research

hypotheses with the nested time by condition model defined above, focusing on tests of

gains by condition. The results indicated that students in the ROOTS condition

outperformed students in the control condition on the TEMA scaled score (t = 2.193, df =

27, p = .0371). We did not find differences on the EN-CBM measure (t = 1.354, df = 27,

p = .1870). One significant difference was found on the EN-CBM Quantity

discrimination measure (t = 2.18, df = 27, p = .038). Hedge’s g effect sizes were .37

(TEMA scaled score), .30 (EN-CBM) and .41 (Quantity Discrimination).


Table 1. Means, standard deviations and sample sizes pre and post treatment. T ROOTS Control

TEMA Scaled T1 67.8 (9.6) 70.3 (9.9)

T2 85.3 (9.5) 84.2 (12.1)

CBM Total T1 14.9 (15.8) 21.4 (22.5) T2 106.3 (39.0) 100.0 (40.8)

Quantity Discrimination T1 1.4 (3.5) 1.8 (3.7) T2 19.8 (9.4) 16.4 (8.8)

TEMA sample size T1 56 64

T2 63 62 Note. Standard deviations (SDs) presented in parentheses. Sample sizes for CBM and TEMA data differed by one to three subjects per cell—minimum sample sizes shown.


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