Mathematics Self-Efficacy of College Freshman

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Mathematics Self-Efficacy

of College Freshman

By J. M ichael Hall and Michael K. Po nton

Students lack the ability

to iden tify factors that

limit their

success

[in

mathematics].

J. Michael Hall

AssistantProfessor

Department of Mathematics and Statistics

Arkansas State University-fonesboro

P.O.Box 70

StateUniversity AR 72467

mhall@csm. astate. edu

Michael K. Ponton

Professorof E ducation

School of Education

Regent U niversity

1000 Regent University Drive

Virginia Beach, VA 23464

ABSTRACT: The purpose ofthisstudy

is to determine differences in mathematics

self-efficacy hetween students enrolled in a

developmental mathematics course and

those enrolled in a calculus course. Data

from a sample of 185 freshmen students at

a single 4-year institution using the Math-

ematics Self-Efficacy Scale are analyzed.

Results indicate that calculus students pos-

sess not only b etter mathematical sk ills hut

also a more powerful sense of self-helief in

their ahility to succeed in a college math-

ematics course. The results of this study

suggest that future teaching methodologies

should he designed specifically for students

enrolled in developmental courses that not

only develop m athematics capabilityhutalso

a self-awareness of increased capability.

Efficacy-enhancing instructional strategies

should be tested for effectiveness thereby

improvingtheteachingandlearning process

for all learners.

Students' ability to learn and succeed in

matheinatics has been a concern of educators

for many years, especially since mathematics

seems to be a determina te of not only choice

of a college major but also serves as a deter-

minant in the acquisition ofacollege degree.

Trusty and

Niles

(2003) assert that high school

students earning high school credit in rigor-

ous math courses have a much greater likeli-

hood of success in acquiring a bachelor's de-

gree than students not completing such a

course. R elated research has been con ducted

in an attempt to establish a relationship be-

tween success in mathematics courses and

success in college. For example, several stud-

ies (Campbell

Hackett, 1986; Hackett, Betz,

O'Halloran, Romac, 1990) have determin ed

tbat previous mathematics performance and

perceived ability are both key elements for

success in mathematics. Furthermore, re-

search (Dorner & Hutton, 2002; Moreno &

Muller, 1999; Hagedorn, Siadet, Fogel, Nora,

& Pascarella, 1999) indicates that, although

many courses aide students in the completion

of a college degree, mathematics is the sub-

ject most essential to students' choices in de-

termining college majors and ultimately to

success in attaining a college degree.

The num ber of students enrolling in

leges and u niversities, and co nsequently i

velopmental courses such as developm

matbematics, has continued to increase

tbe past 30 years to a level wbere 3 out o

first-time fresbman students are enrolle

such a course (Breneman & Haarlow, 1

Smittle, 2003). With the num ber of stud

requiring developmental courses grow

yearly, many colleges an d universities a re

tinuing to invest money in these course

creating additional courses, biring new

ulty, and sometimes creating new de

ments for developm ental studies. As a r

of colleges spending valuable resource

developmental coursework, many in tbe

ulty and surround ing community want a

ance that the funding for developme

courses is no t wasteful. In addition, Aren

(2003) notes tbat both legislatures and bo

of bigber education desire to make institu

more accountable for remediation of stud

Therefore, creating quality instruction in

velopmental courses has become a priori

many institutions.

At its core, developmental educa

sbould attempt to expand tbe academic s

of students. Hence, relationships between

students enrolled in developmental cou

and cognitive factors suchasself-efficacy

to be established. Research (Brenema

Haarlow, 1998; Higbee & Tbom as, 1

Stanley & Murphy, 1997; Wbeland, Kone

Butler, 2003) indicates tbat, for develop

tal mathematics students, academic self

cepts, attitudes toward success in mathe

ics, confidence in ability to learn matbe

ics, mathematics anxiety, self-efficacy,

locus of control are all variables that a

student

goals,

performances, an d attainm

in matbematics. Higbee and Thom as o

tbat for educators to be effective, they

have an understanding of bow stud

cognitively process information.

Wheland, Konet, and Butler (2003)

gest that many students attribute poor

formances in matbematics not to themse

bu t to factors out of tbeir control. Such

tors include ins tructors, time and day of c

and ins tructiona l style. At tbe same time

dents lack tbe ability to identify factors

6

Journal of Developmental Educa


2/7

and

be-

and

ck of confidence in one's ability to com plete

doexistandmay possibly

is notonly

to

external factors, such

as the

faculty

andtheir instructional style,butalso

of the mandatoryen-

1986;

Thomas, 1999) indicates that there

astigma associated with being labeledas a

Theembarrassment

in remedial mathematicsis es-

tofemalesand minorities

1990) andtheir perceptionofmath-

&Callahan, 1968). Re-

byBetzand Hackett (1983) suggests

to gain acompleteun-

of how these individualsare af-

by

such stigmas because

arebasedon the per-

ofabilitytoexcelin agiven field.

Itishypothesized in this study thatper-

incapabilitymay be one of the

tosuccessforstudents enrolledin

asdevelopmental mathematics.

incapabilityto organizeand

to produce outcomes is de-

as self-efficacy (Bandura, 1997). Per-

ofself-efficacy are de rived from four

of information: (a) personal accom-

(b) verbal persuasion, (c)vicari-

experiences,and (d)physiologi-

and

affective reactions (Bandura, 1986).

be

more specific, each

of

these sources

of

as a primary determinant

ef-

to achieve goals,and persevere through

pletionofthesegoals (Bandura, 1997;

Thu s, individu als withlow

of self-efficacy feelas if theydo not

the requisite skills necessary to per-

Human behaviorismotivatedbyantici-

inwhichthecapa-

offorethought isusedto cognize desir-

statesandselect coursesofaction

areideatedaspathsto these states. This

is

mediated

by

capability perceptio ns

thepresenceofactual capa-

1997;Zimm erman, 1990).

students may lack

all the

nec-

to perform tasks, motivation with

as amechanism through

andsuc-

the desired goals (Bandura,

1990; Zimmerman,

dura, Martinez-Pons, 1992). Conversely,

who do not feel efficacious in per-

forming tasksand lack motivation to do so

have

no

incentive

to

exert effort (Schunk

&

Pajares, 2002 ). Th eref ore , self-efficacy is a

mediating factorforacademic outco mes, cog-

nitive engagement,andperformance (Patrick

& Hicks, 1997).

Purpose

Self-efficacy hasbeen shownto be a me-

diating factor

in

human achievement across

numerous domains, thereby necessitating

re-

search that focuses attentionon the difficul-

tiesofaccomplishing tasks. Onesuch areaof

difficultyfornum erous individuals is the abil-

ity to complete a college-level mathematics

course. Being abletoestablisharelationship

between perceived ability to successfullyac-

complish mathematical tasksandclass enroll-

ment (i.e., developmentalvs. calculus) could

serve college and university programming

efforts. It would allowforthe creationofpro-

grams and instructional methods aimedat

creating self-sufficient learners capableof

making choices concerning their ability

to

complete tasksandaccomplish goals. Unfor-

tunately, there is alackof research compar-

ing the self-efficacy of developm ental stu-

dents to nondevelopmental students.

Therefore, thepurposeof this research

was

to

examine

the

differences

in the

mathematics self-efficacy of freshman

students enrolled in Developmenta l

Mathematics (Intermediate Algebra)and

CalculusI.

Study Description

The subjects

in

this study were

ran-

dom cluster samplesofintact classesen-

rolledinone of two freshman-level mathem at-

ics courses (Intermediate Algebra,N

=

375,

and CalculusI, N=400) at amedium-sized,

rural, state, research universityin theSouth-

eastfor theFall 2001 semester. Placementof

the students into eachof theclassesisbased

on American College Test (ACT)mathsub

scores. The ACT is comprised of foursec-

tions

(i.e.,

reading comprehension, mathemat-

ics, verbal,and science reasoning) eachhav-

inga rangeof scores from 0-36. Similarto

other U.S. collegesandu niversities,the Uni-

versity

of

Mississippi uses

the ACT as a

method toevaluate student abilityincourses

suchasmathem atics. CalculusI isdesigned

for engineering, physical science,and math-

ematics majors withACTmath sub scores

above25, whereas Intermediate Algebrais

takenbystudentsin nonmathematics majors

withACTmathsubscoresof 16 orless. At

the University of Mississippi Intermediate

Algebrais thecourse designation for devel-

opmental mathematics. Thesectionsofeach

class chosen to participatein thestudy were

randomly selected clusters from the total num

be rof sections offered.

Students enrolled in the class sectio

chosen for participation were approach

during

the

first month

of the

fall semes

and asked to participatein thestudy. Sin

student participation was completely volu

tary,it was explained that failure to pai'ti

pate in the study would have no effect on the

gradeorstandingin theclass.

Sample

The sample consisted

of 185

freshm

students from four sectionsofCalculus

1

a

four sectionsofIntermediate A lgebra. Oft

total 185p articipants, 80 were enrolled

CalculusI and105 were enrolled in Interm

diate Algebra (see Table 1). Eighty-fiveoft

students were male,and one hundred we

female. It should be noted that q uestionn air

completed by nonfreshman students enrolle

in eitherof thecourses werenotincluded

this sample. Withinthecourses,atotalof

males

and

37 females w ere enrolled

in

Calc

lusI, whereasa totalof 42malesand 63

males were enrolledinIntermediate A lgeb

Descriptive

Class

Calculus

I

Intermediate Algebra

Note.

Af= 185

Table

1

Dataof the

Gender

Al l

Male

Female

All

Male

Female

Sample

n

80

42

38

105

42

63

4.S.2

52.5

47.5

56.8

40.0

60.0

Instrumentation

Consistingof twosubscalesand a to

of34 items, the Mathematics Self-Effica

Scale(MSES)was originally developed in19

by BetzandHackettand contained75item

Revisedin1993for theinterestofparsimon

the current versionof the MSES contains

Mathematics Tasks subscaleand aMathema

ics Courses subscale.

The

purpose

of t

Mathematics Tasks subscale istomeasures

dent confidencein theabilitytoperforme

eryday mathematics tasks;

the

purpose

of

t

Mathematics Courses subscaleis toassesss

dent confidenceintheir abilitytoearnaB

betterin a college course that requires mat

ematical skills.

Betzand Hackett (1993) note that th

content validityfor theMSEShasbeendem

onstrated through research that validates eac

area measuredby theinstrument. They no

that there were positive correlations betwee

the MSES

and

other mathematics scales suc

as math anxiety(r

=

.56), confidenceindoi

me 28, Num ber 3, Spring 2005


3/7

mathematics (r= .66), perceived usefulness of

mathematics

r =

.47), and effectance motiva-

tion in math (r

=

.46), thus enhancing the con-

current validity of the instrument.

Results

An independent t-test was conducted to

determine if there was

a

significant difference

between the mathematics self-efficacy of stu-

dents enrolled in Intermediate Algebra and

Calculus1 as measured by the MSES. A two-

sample Kolmorgorov-Smirnov Test was con-

ducted to validate the assumption of normal-

ity. The results indicated

{p

= .580) that the

data were indeed no rmal, thereby allowing for

the use of the two-samplet-test. The mean

MSES score for the students in Intermediate

Algebra was 5.33

{SD =1.4464);

the mean

MSES score for the studen ts in C alculus I was

7.08{SD =1.1411). The results of the


4/7

continued from p age 28

tery expe riences. Additionally, creatin g an

environment that exhibits the magnificence

of mathematics and its implications to other

fields can allow students to see practical ap-

plications that may be of interest to them.

Lastly, encouraging students to ask questions

regarding mathematical operations and ap-

plications and then servingas aguide through

discussion can augment student understand-

ing that mathematics holds the key to many

fields of study and ultimately to choice of

major.

Past experiences, often times failures, in

mathematics usually dictate student opinions

concerning their perception of personal abil-

ity in mathematics as well as their optimism

about career choices for which mathematics

is

th e

basis

of the curriculum. Therefore, with-

out confidence in mathematical ability, stu-

dents' choices of majors, and ultimately their

futures, may be limited to nonmathematical

areas. Though some students would naturally

choose to major in such an area, the point is

to broaden students' choices rather than limi-

tations. Hen ce, institutions of highe r learn-

ing and educators themselves should imple-

ment modes of instruction that develop and

enh anc e self-efficacy in grou ps of studen ts

with lagging self-concepts of mathematical

ability. Doingsowould allow studen ts to m ore

adequately gauge their actual ability, thereby

helping students to make better choices con-

cerning their future.

Because self-efficacy has been shown to

be a mediating influence on motivation and

performance (Bandura, 1997; Ponton, Horine-

Edmister, Ukeiley, & Seiner, 2001), enhanc-

ing mathematics self-efficacy should be an

important part of any effort to aid in the aca-

demic growth of students enrolled in lower-

level mathematics classes. Too often educa-

tors attempt to teach students with low math-

ematics self-efficacy in the sam e man ner by

which students thathavehigherlevelsof math-

ematics self-efficacy a re taugh t. By alterin g

instructional methodologies educators can

assist students to create more meaningful

mastery experiences in mathem atics. Ponton

et al. propose that faculty consider two sug-

gestions when attempting to design mastery

experiences for studen ts: (a) W hat exactly do

we want the students to master? and (b) How

are we going to let them know? It should be

the role ofafaculty mem ber to clearly define

for the students the importance of the ex-

plicit/implicit material, create mastery expe-

riences to enhance knowledge and skill, de-

velop modes of assessment that accurately

assess desired attainments, and highlight to

students actual increases in capability (Ponton,

et al.). Pointing out increases in capabilities

may be even more important for students in

developmental courses because, in order to

increase choices that influence life trajecto-

ries, changes in actual capability must be ac-

companied by adjustments to self-efficacy.

Future Research

With the results of this research indicat-

ing differences in levels of mathematics

self-

efficacy for students enrolled in Intermedi-

ate Algebra versus students enrolled in Cal-

culus, prospects for future research concern-

ing the m athematics self-efficacy and studen ts

enrol led in deve lopmenta l mathemat ics

courses are promising. First, specific instruc-

tional strategies need to be evaluated longi-

tudinally to determine their influence on en-

han cing self-efficacy beliefs. Second, Cassazza

(1999) has shown th at th e fastest grow ing seg-

ment of higher education is the number of

nontraditional-aged learners, and research

regarding self-efficacy should be conducted

Past experiences...usually

dictate student opinions

concerningtheir personal

ability in mathematics.

with this pop ulation . Lastly, many students

entering college are simply not prepared in

high school to be successful in college math-

ematics classrooms. Factors contrib uting to

this unprep aredness may include, but are not

limited to, the physical size and location of

the high school, mathematics courses offered

at the high school, and the highest mathemat-

ics class completed in high schoo l. Therefo re,

additional research should include the devel-

opment of instructional methodologies that

focus on increasing the mathematics self-effi-

cacy and ability of each subgroup identified

as having substandard levels of each.

Contrary to previously established re-

search (Betz & Hackett, 1983; Hackett, Betz,

O'Halloran, & Romac, 1990; Lent, Lopez,

Brown, & Go re, 1996; O'B rian, Martinez-

Pons, Kopala, 1999) suggesting that females

possess lower levels of mathem atics self-effi-

cacy than males, the findings of this study

suggest that there is little difference in the

mathematics self-efficacy between males and

females. Various factors that m ight contrib-

ute to differences in the findings include the

possibility that the females particip ating in the

study do ind eed possess higher levels of math-

ematics self-efficacy tha n the ir male counter-

pEirts. It is also possible tha t the participa t-

ing females inaccurately assessed their level

of mathematical ability, thereby necessit

additional research to determine not onl

sources of information each gender g

uses to determine self-efficacy but also to

ther establish the relationships between

der and mathematical ability.

Conclusion

Unsuccessful attempts have been

to enhan ce m athematics self-efficacy thr

t ra ining (Ru shing, 1996) . S tuden t

Rushing's treatm ent g roup were given spe

ized materials such as teacher-created vo

lary lists, individualized study guides,

journ aling materials aimed at improving

understanding of the mathematical mat

and the ir self-efficacy. Thou gh such atte

may seem futile, it must be noted that l

ing mathematics has been a lifelong stru

for many students. Thus, development

classroom implementation of new tool

learning subjects that have contin

plagued students is quite difficult and

lenging for faculty and students.

There are no easy solutions to the

plex problems th at confront stu dents wit

levels of mathe ma tics self-efficacy. How

continual attempts should be m ade at en

ing the learning exp erience for students

have been sbown to have low levels ofs

ficacy thereby enabling individuals to m

the imp ortant con cepts of mathematics

enabling them to become lifelong, self-

lated learners. To maximize their impa

students' lives, developmental courses

not only develop actual skills but also a

tive self-image of capability.

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medial/developmental education: Past,

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/would like to thank the manuscript review-

inthe article (Norman Stahl and

Boylan).

I

learned

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Idid writingit. Q

For Your Information

March 9-13

2005-National Center

for

Developmental Education's (NADE) 29 '

Annual Conference, Learning and Teaching: Above and Beyond, inAl-

buquerque, NM. Contact http://planet.tvi.edu/nade2005 orcall Jerry

Cilesat801.266.7289orBonnie Henrieat801.863.8311formore infor-

mation.

13-15, May 22-24, August 7-9, 2005-The UniversityofMissouri's Supple-

mental Instruction's (SI) continuing series ofSupervisor Workshopsin

Kansas City, MO. See ad, page 23,formore information.

25,

2005Callforproposals deadlineforCollege Reading and Learning

Association's (CRLA)38 'Annual Conference, Sailing the Tides of Tran-

sition, inLong Beach, CA. See ad, page 29,formore information.

17-20, 2005American Association for Higher Education's 2005 National

Conference onHigher Education, Courage, Imagination, Action: Rally-

ing the Trendsetters inHigher Education, atthe Atlanta Marriott Mar-

quis Hotel in Atlanta, Georgia. For more information, visit www.aahe.org

or call 202.293.6440.

April 3-5, 2005-New York College Learning Skills Association's (NYCLSA) 28 '

Annual Symposiumatthe historic Otesaga Resort HotelinCooperstown,

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14-15,

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for

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16-20, 2005National Tutoring Association's 13 ' Annual National Con-

ference, Tutors: We'reon aMission, atthe Renaissance Hotel inChi-

cago, IL. See ad, page 23,formore information.

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ter Association's (NCLCA) 20 ' Annual Conference, Honoring our Past:

Guiding ourFuture, at theWyndham Hotel indowntown Milwaukee,

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un 12-14, 2005American Association forHigher Education's 20''' Anniver-

sary Assessment Conference, Charting New Territory, atthe Sheraton

Centre, Toronto, Canada. Contact: One Dupont Circle, Suite 360 Wash-

ington DC 20036-1143, phone 202.293.6440,fax202.293.0073oremail:

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13-17, 2005-NCLCA's 2005 Summer Institute, Excellence inLearning

Center Practice andProfessionalism, at theUniversity of Wisconsin-

Parkside in Kenosha, Wisconsin. See ad, page 23,formore information.

25July 22, 2005-The National Center forDevelopmental Education's

(NCDE) 26th Kellogg Instituteforthe Training & Certification ofDevel-

opmental Educators

at

Appalachian State University

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Boone, NC.

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ad, page 19,formore information.

July

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Marketing, and Retentionat the Grand Hyatt Washington Hotel. Con-

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