Early numeracy: technical adequacy of select kindergarten and first grade screening measures

159 Pages·2016·2.14 MB·English

University of Iowa
Iowa Research Online
Theses and Dissertations
Spring 2012
Early numeracy: technical adequacy of select
kindergarten and first grade screening measures
Gregory Michael Feldmann
University of Iowa
Copyright 2012 Gregory Feldmann
This dissertation is available at Iowa Research Online: https://ir.uiowa.edu/etd/2869
Recommended Citation
Feldmann, Gregory Michael. "Early numeracy: technical adequacy of select kindergarten and first grade screening measures." PhD
(Doctor of Philosophy) thesis, University of Iowa, 2012.
https://doi.org/10.17077/etd.msauhm34
Follow this and additional works at:https://ir.uiowa.edu/etd
Part of theEducational Psychology Commons
EARLY NUMERACY: TECHNICAL ADEQUACY OF SELECT
KINDERGARTEN AND FIRST GRADE SCREENING MEASURES

by

Gregory Michael Feldmann

An Abstract

Of a thesis submitted in partial fulfillment of the
requirements for the Doctor of Philosophy degree in
Psychological and Quantitative Foundations
in the Graduate College of The University of Iowa

May 2012

Thesis Supervisors: Associate Professor Kristen Missall
Professor Stewart Ehly
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ABSTRACT

Because of a greater need to focus on early achievement in mathematics and
increased global competition in this area, emphasis is increasingly being placed upon
screening and monitoring of math development in early elementary to ensure progress for
all students. Although protocols for early literacy assessment exist, research of
psychometrically sound and instructionally useful early numeracy assessment methods is
still developing. Thus, the current study was undertaken to further develop and examine
early numeracy measures. In a two-year investigation, 72 kindergarten and 57 first-grade
students completed a set of existing and newly developed early numeracy curriculum-
based measurement (EN-CBM) tools. Reliability and validity of these measures were
examined both within and across years. The nature of score change across the academic
year was also analyzed.
Findings were generally similar to those published in previous EN-CBM research.
Alternate-form reliability estimates were largely adequate for screening purposes.
Although concurrent and predictive validity estimates varied as a function of screening
period and the outcome criterion, these estimates were generally moderate to strong. EN-
CBM discriminant validity evidence was mixed for the kindergarten measures but more
evident for first-grade tools. All measures demonstrated score change that was
statistically significant over time with at least moderate to large effect sizes for most
measures. Implications for EN-CBM use as screening tools are discussed. Study
limitations are presented as are suggestions for future EN-CBM research.
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Abstract Approved: __________________________________________________
Thesis Supervisor

__________________________________________________
Title and Department

__________________________________________________
Date

__________________________________________________
Thesis Supervisor

__________________________________________________
Title and Department

__________________________________________________
Date
EARLY NUMERACY: TECHNICAL ADEQUACY OF SELECT
KINDERGARTEN AND FIRST GRADE SCREENING MEASURES

by

Gregory Michael Feldmann

A thesis submitted in partial fulfillment of the
requirements for the Doctor of Philosophy degree in
Psychological and Quantitative Foundations
in the Graduate College of The University of Iowa

May 2012

Thesis Supervisors: Associate Professor Kristen Missall
Professor Stewart Ehly
Copyright by

GREGORY MICHAEL FELDMANN

2012

All Rights Reserved
Graduate College
The University of Iowa
Iowa City, Iowa

CERTIFICATE OF APPROVAL
___________________________

PH.D. THESIS
____________

This is to certify that the Ph.D. thesis of

Gregory Michael Feldmann

has been approved by the Examining Committee for the thesis
requirement for the Doctor of Philosophy degree in Psychological
and Quantitative Foundations at the May 2012 graduation.

Thesis Committee: __________________________________________________
Kristen Missall, Thesis Supervisor

__________________________________________________
Stewart Ehly, Thesis Supervisor

__________________________________________________
Robert D. Ankemann

__________________________________________________
John L. Hosp

__________________________________________________
Susan Assouline
ACKNOWLEDGMENTS

I want to thank Sam J. Bowek whose support was invaluable and work with
students is admirable. I am appreciative of the interest, patience, and support of my
immediate and extended family; I am fortunate to be your son, brother, and in-law. Jacob,
Nathan, and Lauren have made being a parent a never ending adventure. You each bring
joy to my world and to that of those around you.
Most notable and worthy of recognition is Erin. She not only allowed, but
encouraged and supported the harebrained idea of her then father-of-one husband to
return to graduate school. She had more patience and understanding than her ever
grateful, now a father-of-three, husband could have wanted.

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TABLE OF CONTENTS

LIST OF TABLES ...............................................................................................................v
LIST OF FIGURES ........................................................................................................... vi
CHAPTER 1 INTRODUCTION ...........................................................................1

Value of Mathematical Knowledge .............................................................1
International and National Analysis.............................................................2
Introduction to the Problem .........................................................................5
Curriculum-Based Measurement .................................................................6
Research Purpose .........................................................................................7

CHAPTER 2 LITERATURE REVIEW ..............................................................10

Importance of Early Mathematics Development .......................................10
Number Sense ............................................................................................12
Early Elementary Math ..............................................................................13
Content and Process Domains: Number and Operations ...............14
Essential Core Skills: Empirical Support .......................................15
Measurement of Early Academic Skills ....................................................18
Value of Early Screening ...............................................................18
Curriculum-Based Measurement: A Description ...........................20
Curriculum-Based Measurement: Early Numeracy ...................................27
Oral Counting.................................................................................31
Number Identification ....................................................................32
Quantity Discrimination.................................................................34
Missing Number.............................................................................36
Computation ...................................................................................38
Early Numeracy-CBM: Cautions and Future Directions ...........................39
Cautions .........................................................................................39
Rationale for Current Study and Future Directions .......................42
New EN-CBM Tools .....................................................................46
Research Questions ....................................................................................48

CHAPTER 3 METHODS ....................................................................................49

Participants .................................................................................................49
Instruments .................................................................................................49
Early Numeracy – Curriculum-Based Measurement .....................49
Number Identification ........................................................49
Quantity Discrimination.....................................................50
Math Computation .............................................................52
Closer Number ...................................................................53
Verbal Math .......................................................................54
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Criterion Measures .........................................................................56
Teacher Rating ...................................................................56
WIAT-2 Math Reasoning ..................................................57
Report Card ........................................................................58
Iowa Tests of Basic Skills ..................................................58
Procedures ..................................................................................................59
Data Analysis .............................................................................................61

CHAPTER 4 RESULTS ......................................................................................64

Introduction ................................................................................................64
Descriptive Statistics ..................................................................................64
Reliability ...................................................................................................65
Validity ......................................................................................................67
Relationships Among Variables ....................................................67
Concurrent Convergence ...............................................................68
Discriminant ...................................................................................70
Predictive .......................................................................................71
Developmental Sensitivity .........................................................................74

CHAPTER 5 DISCUSSION ................................................................................77

Summary and Interpretation of the Findings .............................................78
Reliability Evidence .......................................................................78
Validity Evidence...........................................................................80
Sensitivity ......................................................................................85
Implications for Practice ............................................................................87
Limitations and Considerations .................................................................89
Future Research .........................................................................................92
Summary ....................................................................................................95

APPENDIX A TABLES...............................................................................................96

APPENDIX B SAMPLE KINDERGARTEN PROBES ............................................115

APPENDIX C SAMPLE FIRST-GRADE PROBES .................................................120

APPENDIX D FIGURES ...........................................................................................126

BIBLIOGRAPHY ............................................................................................................136

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