Content uploaded by Douglas H. Clements

Author content

All content in this area was uploaded by Douglas H. Clements on Apr 29, 2014

Content may be subject to copyright.

www.ecs.org/per

1

Math in the Early Years

A Strong Predictor for Later School Success

20

13

OCTOBER

Education Reform

THE PROGRESS OF

Vol. 14, No. 5

The earliest years of a child’s education—from birth through 3rd grade—set the

foundation upon which future learning is built. In recent years, state policymakers have

emphasized the need to improve children’s reading skills early on because a lack in this

essential skill is a strong predictor of low student performance and increased high school

dropout rates. By 2012, a total of 32 states plus the District of Columbia had policies in

statute aimed at improving 3rd-grade literacy, with 14 of those states requiring retention

of students on the basis of reading proficiency. While the emphasis on reading proficiency

is critical, research shows that the development of mathematics skills early on may be an

even greater predictor of later school success. Early knowledge of math not only predicts

later success in math, but also predicts later reading achievement even better than early

reading skills.

Young children have a surprising capacity to learn substantial mathematics, but most

children in the U.S. have a discouraging lack of opportunities to do so. Too many

children not only start behind, but they also begin a negative and immutable trajectory in

mathematics, with insidious long-term effects. These negative effects are in one of the most

important subjects of academic life and also affect children’s overall life course.

The good news is that programs and curricula

designed to facilitate mathematical learning from

the earlier years, continued through elementary

school, have a strong positive effect on these

children’s lives for many years thereafter.

Starting early—in preschool—with high-quality

mathematics education, creates an opportunity

for substantial mathematical learning in the

primary years that builds on these foundational

competencies.

This issue of The Progress of Education Reform

reveals five surprising findings about the

importance of early math learning, and provides

implications and recommendations for state policy.

What’s Inside

Surprise 1: Math’s predictive power

Surprise 2: Children’s math potential

Surprise 3: Educators underestimate

children’s potential

Surprise 4: Math intervention for all

Surprise 5: How children think about

and learn math

Written for ECS by Drs. Douglas H. Clements and Julie Sarama (http://du.academia.edu/DouglasClements)

www.ecs.org/per

2

Surprising Research Findings

Surprise 1: There is predictive power in early mathematics

Mathematical thinking is cognitively foundational1, and

children’s early knowledge of math strongly predicts their

later success in math.2 More surprising is that preschool

mathematics knowledge predicts achievement even into high

school.3 Most surprising is that it also predicts later reading

achievement even better than early reading skills.4 In fact,

research shows that doing more mathematics increases oral

language abilities, even when measured during the following

school year. These include vocabulary, inference, independence,

and grammatical complexity.5 Given the importance of

mathematics to academic success in all subjects6, all children

need a robust knowledge of mathematics in their earliest years.

Surprise 2: Given opportunities to learn, young children possess an informal knowledge of mathematics that is amazingly broad,

complex, and sophisticated7

When children ‘play,’ they are often doing much more than that. Preschoolers can learn to invent solutions to solve

simple arithmetic problems, and almost all of them engage in substantial amounts of pre-mathematical activity

in their free play.8 In fact, early childhood programs that include more mathematics have increased higher-level

free play, all of which promotes self-regulation and executive function. Through higher-level play, children explore

patterns, shapes, and spatial relations; compare magnitudes; and count objects. Importantly, this is shown to be true

regardless of the children’s income level or gender.9 These explorations through play are pre-mathimatical. It is high-

quality education that can help all children utilize their inherent skills in order to truly mathematize.10 However, if

high-quality mathematics education does not start in preschool and continue through the early years, most children

are trapped in a trajectory of failure.11

Surprise 3: Teachers vastly underestimate what their children know and can learn12

In numerous countries, professionals in multiple educational roles vastly

underestimate beginning students' abilities.13 One study showed that groups

of teachers, teacher trainers, and counselors who worked with preschoolers

underestimated the mathematical competencies of these very same students

when they entered kindergarten.14 For example, more than 80% of the

students could count out nine marbles, but the adults’ estimates were from

20% to 50%. More than 40% of the students could subtract 10 – 8 without

objects, but all adults estimated less than 10%. If teachers and those who

work with teachers underestimate what students already know and can learn,

they will not present appropriate, challenging mathematics activities.

Surprise 4: All students need a math intervention

Most children benefit from a math intervention.15 As W. Steven Barnett and

others’ research has shown, it is not just the poorest children who need

interventions.16 When they enter kindergarten, most children are behind

their peers from the best-funded communities. That is, there is a significant

gap between every “quintile” and the highest 20% (see Figure 1 on following

page). Still, those in poverty need mathematics interventions the most.17

There is a three-year difference in mathematics developmental level for

students from low-resource versus high-resource communities.18

POLL RESULTS

What do parents and children say about math?

Math is very important

(parents)

Schools need to help the

brightest learn math (parents)

Children who like math before

middle school

Math is very important

(children)

I am good at math

(children)

98%

89%

55%

91%

55%

Source: Harrison Group, PROMISE research, Phase 2, June 2010, Michigan

State University.

Before her 4th birthday, Abby was given five train

engines. She walked in one day with three of them. Her

father said, “Where’s the other ones?” “I lost them,” she

admitted. “How many are missing?” he asked. “I have

one, two, three. So [pointing in the air] foooour, fiiiive ...

two are missing, four and five. [pause] No! I want these

to be [pointing at the three engines] one, three, and five.

So, two and four are missing. Still two missing, but they’re

numbers two and four.”Abby thought about counting and

numbers—at least small numbers—abstractly. She could

assign one, two, and three to the three engines, or one,

three, and five! Moreover, she could count the numbers.

That is, she applied counting ... to counting numbers!

www.ecs.org/per

3

Surprise 5: We know a lot

A lot is known about how children

think about and learn math, and

teachers can use learning trajectories

to synthesize this knowledge into

effective interventions for children.

There are books and research

available to districts that detail the

learning trajectories that can help

underlie scientific approaches to

standards, assessment, curricula,

and professional development and

provide teachers with curricula that

show effect sizes that are large and

significant.19 Two such models are

the Building Blocks curriculum and

TRIAD scale-up model (see figures

2 and 3). High-quality instruction

has meaningful effects on children’s

mathematics knowledge.20

60

55

50

45

40 Lowest

20% Second Lowest

20% Second Highest

20% Highest

20%

Middle

20%

Source: Analysis of data from the

Early Childhood Longitudinal Study, Kindergarten Class of 1998-99

(See nces.ed.gov/ecls/kindergarten.asp) by W. Steven Barnett and Milagros Nores for

the National Institute for Early Childhood Education Research.

Reading

Math

General Knowledge

When they enter kindergarten, children from lower- and middle-income families are, on average, far behind their wealthier peers in reading,

mathematics, and general knowledge. High-quality preschool could help close this gap in school readiness.

Figure 1: Closing the school-readiness gap

SCHOOL-READINESS GAP

Average Academic Ability Scores

Family Outcome by Quintile

62

56

50

44

38

PreK Pre PreK Post Kindergarten Post 1st Grade Post

TRIAD Follow Through

TRIAD

Control

TRIAD > Control, ES = .28

TRIAD FT > Control, ES = .51

TRIAD FT > TRIAD, ES = .24

Source: D.H. Clements, J. Sarama, C.B. Wolfe, and M.E. Spitler, "Longitudinal Evaluation of a Scale-up Model for Teaching

Mathematics with Trajectories and Technologies: Persistence of Effects in the Third Year,"

American Educational Research Journal

,

50(4), (2013): 812-850, doi: 10.3102/0002831212469270.

Figure 2: Mathematics achievement scores for

children using Triad Scale-up Model

www.ecs.org/per

4

Policy Implications and Recommendations

The Importance of High-Quality Curriculum and Instruction

The quality of mathematics education varies across settings but is

generally disappointing, especially in the earliest years. For example,

60% of 3-year-olds had no mathematical experience of any kind across

180 observations.21 Even if a program adapts an ostensibly “complete”

curriculum, mathematics is often inadequate, with the most commonly

used engendering no more math instruction than a control group.22

It is little surprise, then, that evaluations show little or no learning of

mathematics in these schools.23 As an example, observations of Opening

the World of Learning (OWL), which includes mathematics in its

curriculum, found that out of a 360-minute school day, only 58 seconds

were devoted to mathematics. Most children made no gains in math

skills, and some lost mathematics competence over the school year.24 Teachers often believe that they are “doing

mathematics” when they provide puzzles, blocks, and songs. Even when they teach mathematics, that content is

usually not the main focus, but is “embedded” in a fine-motor or reading activity.25 Unfortunately, evidence suggests

such an approach is ineffective.26 To ensure a program is truly effective, policymakers and school leaders must

prioritize investing in high-quality math curricula and instruction that meet the needs of all students.

Qualified Instructors

Teacher certification for pre-K through 3rd-grade teachers should emphasize both knowledge of the subject

(specifically, a profound knowledge of the math taught in early and elementary years) and strengths in pedagogy. It is

only recently that some states are requiring teachers to be evaluated on fluency in literacy instruction. What we now

know is that math instruction is far more effective coming from a specialist who understands both the subject matter

and the most effective ways in which young children learn math. A successful program will be one that ensures that

early math instructors specialize in these areas. One solution may be for a school to designate a teacher in each grade

who is responsible for teaching only math to all students.

Percent of adults who cannot

compute a 10% tip

Percent who cannot compute

the interest paid on a loan

Percent who cannont calculate

miles per gallon on a trip

58%

71%

78%

Source: G.W. Phillips,

Chance Favors the Prepared Mind: Mathematics and Science

Indicators for Comparing States and Nations

(Washington, DC: American Institutes

for Research, 2007).

4.00

3.90

3.80

3.70

3.60

3.50

3.40

Control Building Blocks

Source: J. Sarama, A. Lange, D.H. Clements, and C.B. Wolfe, "The Impacts of an Early Mathematics Curriculum on Emerging Literacy and Language,"

Early Childhood Research Quarterly

, 27, (2012): 489-

502, doi: 10.1016/j.ecresq.2011.12.002.

Figure 3: Expressive oral language scores at the beginning of kindergarten for

children who used the Building Block curriculum in preschool.

www.ecs.org/per

5

Seamless Learning Trajectories

The most common argument offered for limiting investments in preschool is that the gains made are soon lost as

a child matriculates through the early primary grades. The losses primarily signify a siloed approach to education,

where each grade level and teacher holds different expectations for students, creating a learning trajectory that is not

seamless. Therefore, in order for students to benefit from math instruction in the early years, primary grade teachers

must build on early math interventions and engage students in more interesting, challenging, and substantial math

lessons as students progress through competency levels. If there are follow-through interventions in kindergarten and

the primary grades, students maintain their preschool advantages.27 This effect is highlighted in Figure 2 (page 3),

which presents a significant, positive effect on student math scores when the Triad Model is used on an ongoing basis.

Professional Development

Early math is not often emphasized in teacher preparation programs. As a result, pre-service and in-service teachers

alike lack content knowledge, such as understanding of mathematical concepts and procedures. More importantly,

they lack mathematics knowledge for teaching—how mathematical knowledge is interconnected and connected to

the real world, how a student’s thinking about mathematical content develops, and how mathematical content can be

taught in a meaningful manner.28 They suffer from negative effects, including math anxiety and a lack of confidence

in their own mathematical ability and ability to teach mathematics—beliefs that lead to undervaluing the teaching

of mathematics or prevent effective teaching.29 Therefore, professional development for early childhood mathematics

needs to address content (mathematical) knowledge, particularly mathematics knowledge for teaching, as well as

pedagogical knowledge, and affective issues.30

Conclusion

It is time to begin shifting the mindset of teachers, district leaders, and policymakers from a ‘reading only’ early

intervention strategy to one that incorporates and even emphasizes mathematical thinking and reasoning. To do

so, stakeholders should take a deep look into the current state of early math instruction beginning in preschool and

creating a seamless trajectory for math learning through the early grades. Education leaders should find ways to

maximize children’s abilities to learn by evaluating the current state of mathematics instruction within schools, based

not only on the current curricula, but also the time committed to instruction, as well as who is doing that instructing.

Most children can master the required skills early if given the chance.

Dr. Clements engages in math activites with two kindergarteners in order to help them understand

the core unit of patterns.

www.ecs.org/per

6

Endnotes

1 D.H. Clements and J. Sarama, Learning and Teaching Early Math: The Learning Trajectories Approach (New York, NY: Routledge, 2009);

D.H. Clements and J. Sarama, Early Childhood Mathematics Education Research: Learning Trajectories for Young Children (New York, NY:

Routledge, 2009).

2 K. Denton and J. West, Children's Reading and Mathematics Achievement in Kindergarten and First Grade (Washington, D.C., vol. 2002,

2002).

3 National Mathematics Advisory Panel, Foundations for Success: The Final Report of the National Mathematics Advisory Panel (Washington

D.C.: National Research Council, 2008); Mathematics in Early Childhood: Learning Paths Toward Excellence and Equity (Washington, D.C.:

National Academy Press, 2009); H.W. Stevenson and R.S. Newman, “Long-term Prediction of Achievement and Attitudes in Mathematics and

Reading,” Child Development, 57, 646-659, 1986.

4 G.J. Duncan, C.J. Dowsett, A. Claessens, K. Magnuson, A.C. Huston, P. Klebanov, and C. Japel, “School Readiness and Later Achievement,”

Developmental Psychology, 43(6), 1428–1446, 2007; D.C. Farran, C. Aydogan, S.J. Kang, M. Lipsey, Preschool Classroom Environments and

the Quantity and Quality of Children's Literacy and Language Behaviors, 2005; M.K. Lerkkanen, H. Rasku-Puttonen, K. Aunola, and J.E.

Nurmi, “Mathematical Performance Predicts Progress in Reading Comprehension Among 7-year-olds,” European Journal of Psychology of

Education, 20(2), 121-137, 2005.

5 J. Sarama, A. Lange, D.H. Clements, and C.B. Wolfe, “The Impacts of an Early Mathematics Curriculum on Emerging Literacy and

Language,” Early Childhood Research Quarterly, 27, 489-502, 2012, doi: 10.1016/j.ecresq.2011.12.002.

6 P.M. Sadler and R.H. Tai, “The Two High-School Pillars Supporting College Science,” Science, 317, 457-458, 2007.

7 A.J. Baroody, The Developmental Bases for Early Childhood Number and Operations Standards, 2004; B.A. Clarke, D.M. Clarke, and J.

Cheeseman, “The Mathematical Knowledge and Understanding Young Children Bring to School,” Media Education Research Journal, 18(1),

81-107, 2006; D.H. Clements, S. Swaminathan, M.A.Z. Hannibal, and J. Sarama, “Young Children’s Concepts of Shape,” Journal for Research

in Mathematics Education, 30, 192-212, 1999.

8 J. Sarama and D.H. Clements, Early Childhood Mathematics Education Research: Learning Trajectories for Young Children (New York, NY:

Routledge, 2009); H.P. Ginsburg, N. Inoue, and K.H. Seo, “Young Children Doing Mathematics: Observations of Everyday Activities,” in J.V.

Copley (Ed.), Mathematics in the Early Years (Reston, VA: National Council of Teachers of Mathematics, 1999, 88-89).

9 K.H Seo and H.P. Ginsburg, “What is Developmentally Appropriate in Early Childhood Mathematics Education?” in D.H. Clements, J.

Sarama, and A.M. DiBiase (Eds.), Engaging Young Children in Mathematics: Standards for Early Childhood Mathematics Education

(Mahwah, NJ: Erlbaum, 2004, 91-104).

10 B. Doig, B. McCrae, and K. Rowe, A Good Start to Numeracy: Effective Numeracy Strategies from Research and Practice in Early Childhood

(Canberra ACT, Australia, 2003); S. Thomson, K. Rowe, C. Underwood, and R. Peck, Numeracy in the Early Years: Project Good Start

(Camberwell, Victoria, Australia: Australian Council for Educational Research, 2005).

11 C. Rouse, J. Brooks-Gunn, and S. McLanahan, “Introducing the Issue,” The Future of Children, 15, 2005, 5-14.

12 D.H. Clements and J. Sarama, Learning and Teaching Early Math: The Learning Trajectories Approach (New York, NY: Routledge, 2009).

13 C. Aubrey, “Children’s Early Learning of Number in School and Out,” in I. Thompson (Ed.) Teaching and Learning Early Number (Philadel-

phia, PA: Open University Press, 1997, 20-29).

14 M. Van den Heuvel-Panhuizen, “Realistic Arithmetic/Mathematics Instruction and Tests,” in K.P.E. Gravemeijer, M. Van den Heuvel-

Panhuizen & L. Streefland (Eds.), Contexts Free Productions Tests and Geometry in Realistic Mathematics Education (Utrecht, The

Netherlands: OW&OC, 1990, 53-78).

15 D.H. Clements and J. Sarama, “Early Childhood Mathematics Intervention,” Science, 333(6045), 2011, 968-970, doi: 10.1126/

science.1204537; D.H. Clements, J. Sarama, M.E. Spitler, A.A. Lange, C.B. Wolfe, “Mathematics Learned by Young Children in an

Intervention Based on Learning Trajectories: A Large-scale Cluster Randomized Trial,” Journal for Research in Mathematics Education,

42(2), 2011, 127-166.

16 R.C. Pianta, W.S. Barnett, M.R. Burchinal, and K.R. Thornburg, “The Effects of Preschool Education: What We Know, How Public Policy Is

or Is Not Aligned with the Evidence Base, and What We Need to Know,” Psychological Science in the Public Interest, 10(2), 2009, 49-88, doi:

10.1177/1529100610381908.

17 J. Sarama and D.H. Clements, Early Childhood Mathematics Education Research: Learning Trajectories for Young Children (New York,

NY: Routledge, 2009); D.H. Clements and J. Sarama, “Early Childhood Mathematics Intervention,” Science, 333(6045), 2011, 968-970, doi:

10.1126/science.1204537.

18 B. Wright, “What Number Knowledge Is Possessed by Children Beginning the Kindergarten Year of School?” Mathematics Education

Research Journal, 3(1), 1991, 1-16.

19 D.H. Clements, & J. Sarama, Learning and Teaching Early Math: The Learning Trajectories Approach (New York, NY: Routledge, 2009); J.

Sarama, and D.H. Clements, Early Childhood Mathematics Education Research: Learning Trajectories for Young Children (New York, NY:

Routledge, 2009).

20 D.H. Clements and J. Sarama, “Early Childhood Mathematics Intervention,” Science, 333(6045), 2011, 968-970; D.H. Clements and J.

Sarama, “Rethinking Early Mathematics: What Is Research-based Curriculum for Young Children?” in L.D. English & J.T. Mulligan

(Eds.), Reconceptualizing Early Mathematics Learning, 2013, 121-147; D.H. Clements, J. Sarama, M.E. Spitler, A.A. Lange, "Longitudinal

Evaluation of a Scale-up Model for Teaching Mathematics with Trajectories and Technologies: Persistence of Effects in the Third Year,”

American Education Research Journal, August 2013, vol. 50 no. 4, 812-850; J. Sarama and D.H. Clements, “Lessons Learned in the

Implementation of the TRIAD Scale-up Model: Teaching Early Mathematics with Trajectories and Technologies,” in T.G. Halle, A.J. Metz and

I. Martinez-Beck (Eds.), Applying Implementation Science in Early Childhood Programs and Systems, (Baltimore, MD: Brookes, 2013, 173-

191); J. Sarama, D.H. Clements, C.B. Wolfe, and M.E. Spitler, “Longitudinal Evaluation of a Scale-up Model for Teaching Mathematics with

Trajectories and Technologies,” Journal of Research on Educational Effectiveness, 5(2), 2012, 105-135; J. Sarama, A. Lange, D.H. Clements,

and C.B. Wolfe, “The Impacts of an Early Mathematics Curriculum on Emerging Literacy and Language,” Early Childhood Research

Quarterly, 27, 2012, 489-502, doi: 10.1016/j.ecresq.2011.12.002.

www.ecs.org/per

7

© 2013 by the Education Commission

of the States (ECS). All rights reserved.

ECS encourages its readers to

share our information with others.

To reprint or excerpt some of

our material, please contact ECS

at 303.299.3600 or e-mail

ecs@ecs.org.

The Education Commission of the

States is a nationwide nonprofit

organization formed in 1965 to

help governors, state legislators,

state education officials, and others

to develop policies to improve the

quality of education. ECS is the only

nationwide, nonpartisan interstate

compact devoted to education at

all levels.

www.ecs.org

Past issues of

The Progress of

Education Reform

are available

on our website at:

www.ecs.org/per.

Equipping

Education Leaders,

Advancing Ideas

This issue of

The Progress of Education Reform

was made possible by a

grant from the GE Foundation. This issue was written by Doug Clements,

Kennedy Endowed Chair in Early Childhood Learning and Professor at

the University of Denver, and Julie Sarama, Kennedy Endowed Chair in

Innovative Learning Technologies and Professor at the University of Denver

For more information on this topic, contact Emily Workman, Policy Analyst,

Education Commission of the States at eworkman@ecs.org.

ECS Resources

Recent State Policies/Activities: Preschool Policies

Summaries and links to newly enrolled or enacted legislation and recently approved state board rules from

across the states. Updated weekly.

http://www.ecs.org/ecs/ecscat.nsf/WebTopicViewAll?OpenView&Start=1&Count=1000&Expand=204#204

Third Grade Reading Policies

This paper outlines state policies relating to 3rd-grade reading proficiency, including identification of,

intervention for, and retention of struggling readers in the P-3 grades. The paper provides a state-by-state

policy summary, sample statutory language, and highlights from bills enacted this year.

http://www.ecs.org/clearinghouse/01/03/47/10347.pdf

ECS Research Studies Database:

Find research studies that provide features that define high-quality learning environments for PreK-3 students:

http://www.ecs.org/rs/SearchEngine/SearchResults.aspx?faq_id=a0870000004rrIvAAI

or on what mathematics practices impact student achievement:

http://www.ecs.org/rs/SearchEngine/SearchResults.aspx?faq_id=a0870000006yt5BAAQ.

21 J.R.H. Tudge and F. Doucet, “Early Mathematical Experiences: Observing Young Black and White

Children’s Everyday Activities,” Early Childhood Research Quarterly, 19, 2004, 21-39.

22 C. Aydogan, C.Plummer, S.J. Kang, C. Bilbrey, D.C. Farran, and M.W. Lipsey, An Investigation of

Prekindergarten Curricula: Influences on Classroom Characteristics and Child Engagement, 2005;

Preschool Curriculum Evaluation Research Consortium, Effects of Preschool Curriculum Programs on

School Readiness (NCER 2008-09, 2008).

23 D.H. Clements and J. Sarama, "Effects of a Preschool Mathematics Curriculum: Summative Research on

the Building Blocks Project," Journal for Research in Mathematics Education, 38, 2007, 136-163; Head

Start Impact Study: First Year Findings (Washington, D.C.: Department of Health and Human Services,

2005).

24 D.C. Farran, M.W. Lipsey, B. Watson, and S. Hurley, Balance of Content Emphasis and Child Content

Engagement in an Early Reading First Program, 2007; K.C. Fuson, “Pre-K to Grade 2 Goals and

Standards: Achieving 21st Century Mastery for All,” in D.H. Clements, J. Sarama, and A.M. DiBiase

(Eds.), Engaging Young Children in Mathematics: Standards for Early Childhood Mathematics

Education, 2004.

25 D.H. Clements and J. Sarama, Learning and Teaching Early Math: The Learning Trajectories Approach

(New York, NY: Routledge, 2009); National Research Council, Mathematics in Early Childhood: Learn-

ing Paths Toward Excellence and Equity (Washington, D.C.: National Academy Press, 2009).

26 National Research Council, Mathematics in Early Childhood: Learning Paths toward Excellence and

Equity (Washington, DC: National Academy Press, 2009).

27 D.H. Clements, J. Sarama, C.B.Wolfe, and M.E. Spitler, “Longitudinal Evaluation of a Scale-up Model

for Teaching Mathematics with Trajectories and Technologies: Persistence of Effects in the Third Year,”

American Educational Research Journal, 50(4), 2013, 812-850, doi: 10.3102/0002831212469270.

28 D.H. Clements and J. Sarama, Learning and Teaching Early Math: The Learning Trajectories Approach

(New York, NY: Routledge, 2009).

29 J. Sarama and D.H. Clements, Early Childhood Mathematics Education Research: Learning Trajectories

for Young Children (New York, NY: Routledge, 2009).

30 D.L. Ball and H. Bass, “Interweaving Content and Pedagogy in Teaching and Learning to Teach: Know-

ing and Using Mathematics,” in J. Boaler (Ed.), Multiple Perspectives on the Teaching and Learning

of Mathematics (Westport, CT: Ablex., 2000, 83-104); A.J. Baroody, Fostering Children’s Mathematical

Power: An Investigative Approach to K-8 Mathematics Instruction (Mahwah, NJ: Erlbaum, 1998).