J. Randy McGinnis

The Science Teaching Center

Department of Curriculum & Instruction

Room 2226K Benjamin

University of Maryland, College Park

College Park, Maryland 20742

Tad Watanabe

Department of Mathematics

Towson University

Towson, Maryland 21204

Gilli Shama

c/o MCTP

2349 Computer & Space Sciences

University of Maryland, College Park

College Park, Maryland 20742

Anna Graeber

The Center for Mathematics Education

Department of Curriculum & Instruction

Room 2226H Benjamin

University of Maryland, College Park

College Park, Maryland 20742

The preparation of this manuscript was supported in part by a grant from the National Science Foundation

(Cooperative Agreement No. DUE 9255745).

The Assessment of Elementary/Middle Level Teacher Candidates' Attitudes and Beliefs About the Nature of and the Teaching of Mathematics and Science

This session describes the use of a valid and reliable instrument (__n__*
*=486,_** =.**76) to measure teacher candidates' attitudes
and beliefs about the nature of and the teaching of mathematics and science.
The instrument, *Attitudes and Beliefs about the Nature of and the Teaching
of Mathematics and Science* , was developed for the Maryland Collaborative
for Teacher Preparation (MCTP), a National Science Foundation funded undergraduate
teacher preparation program for specialist mathematics and science elementary/middle
level teachers. Sections of the instrument that were verified by factor
analysis dealt with beliefs** **about mathematics and science
(=.7596); attitudes toward mathematics and science

(=.8070); beliefs about teaching mathematics and science (=.6900); attitudes
toward learning to teach mathematics and science (=.7889); and attitudes
toward teaching mathematics and science (=..6014). Data were obtained (total
instrument responses, __n__=1128; MCTP teacher candidates, __n__=
323) during the 1995/96 academic year from 38 mathematics, science, or pedagogy
undergraduate college classes taught in 8 higher education institutions
in Maryland. Findings from the data indicate that attitudes toward learning
mathematics and science as well as beliefs about mathematics and science
did not significantly change during the year in which the survey was administered.
The MCTP teacher candidates' beliefs about teaching mathematics and science
did improve significantly in the second semester. Other students' attitudes
toward learning to teach mathematics and science dropped in the second semester.
The difference between the MCTP teacher candidates' attitudes toward teaching
mathematics and science to other college students' attitudes decreased.
In addition to these findings, these data assist in constructing a statewide
landscape of what undergraduate teacher candidates feel and believe about
mathematics and science and the teaching of those disciplines before they
enter the methods and student teaching components of their teacher education
programs.

This paper describes the factor analysis and the use of a valid and reliable
instrument

(__n__ =486,_=.76) to measure teacher candidates' attitudes and beliefs
about the nature of and the teaching of mathematics and science. The instrument,
*Attitudes and Beliefs about the Nature of and the Teaching of Mathematics
and Science* , was developed for the Maryland Collaborative for Teacher
Preparation (MCTP), a National Science Foundation (NSF) funded undergraduate
teacher preparation program for specialist mathematics and science elementary/middle
level teachers.

The MCTP is a NSF funded statewide undergraduate program for students
who plan to become specialist mathematics and science upper elementary or
middle level teachers. Teacher candidates selected to participate in the
MCTP program are, in general, academically representative of all teacher
candidates in elementary teacher preparation programs. MCTP teacher candidates
are distinctive by expressing an interest in teaching mathematics __and__
science. Recruitment efforts have also attracted many students to the MCTP
traditionally underrepresented in the teaching force (23% of those formally
admitted come from those groups), most notably African Americans (19%) (MCTP,
1996, p. 3).

Higher education institutions involved in this project include nine of the
higher education institutions within the University of Maryland System responsible
for teacher preparation. Several community colleges also participate. In
addition, several large public school districts are active partners. The
goal of the MCTP is to promote the development of professional teachers
who are confident teaching mathematics and science using technology, who
can make connections between and among the disciplines, and who can provide
an exciting and challenging learning environment for students of diverse
backgrounds (University of Maryland System, 1993). This goal is in accord
with the educational practice reforms advocated by the major professional
mathematics and science education communities (e.g., National Council of
Teachers of Mathematics (NCTM), 1989, 1991; American Association for the
Advancement of Science (AAAS) 1989, 1993; National Research Council (NRC)
of the National Academy of Sciences, 1989, 1996). Figure 1 contains a program
overview of the MCTP.

In practice, the MCTP undergraduate classes are taught by faculty in mathematics,
science, and education who make efforts to focus on "developing understanding
of a few central concepts and to make connections between the sciences and
between mathematics and science" (MCTP, 1996, p. 2). Faculty also strive
to infuse technology into their teaching practice, and to employ a instructional
and assessment strategies recommended by the literature to be compatible
with the constructivist perspective (i.e., be student-centered, address
conceptual change, promote reflection on changes in thinking, and stress
logic and fundamental principles as opposed to memorization of unrelated
facts) (e.g., Cobb, 1988; Wheatley, 1991; Driver, 1989). Faculty lecture
is diminished and student-based problem-solving is emphasized that requires
cross-disciplinary mathematical and scientific applications.

A fundamental assumption of the MCTP is that changes in pre-secondary
level mathematics and science educational practices require reform within
the undergraduate mathematics and science subject matter and education classes
teacher candidates take throughout their teacher preparation programs (NSF,
1993). A second assumption is that MCTP teacher candidates who take reformed
undergraduate mathematics, science, and method classes that are informed
by the constructivist epistemology (i.e., learners actively construct knowledge
through interaction with their surroundings and experiences, and learners
interpret these experiences based on prior knowledge) (von Glasersfeld,
1987, 1989) develop more positive attitudes and beliefs toward mathematics
and science and the teaching of those subjects.

Research interests within the MCTP fall within both the hypothesis-testing
and hypothesis-generation domains (Brause & Mayher, 1991). In the hypothesis-generation
domain, the MCTP Research Group is longitudinally documenting over a five-year
period how the MCTP teacher candidates and the MCTP faculty participate
in the MCTP program. The goal is to construct some insights that suggest
ways of how the MCTP participants are impacted by the program. Describing
and interpreting the discourse communities is one aspect of this effort
(McGinnis & Watanabe, 1996a, 1996b). Another aspect is the focus on
case studies to compelling tell the MCTP story (Roth-McDuffie & McGinnis,
1996). In the hypothesis-testing domain, the focus is on determining what
are the MCTP teacher candidates' attitudes and beliefs relevant to mathematics,
science, technology and to teaching and comparing them with the beliefs
and attitudes of non-MCTP teacher candidates. Specifically, in this domain,
these two research questions guide MCTP research:

1. Is there a difference between the MCTP teacher candidates' and the non-MCTP
teacher candidates' attitude toward:

(i) mathematics and science?

(ii) the interdisciplinary teaching and learning of mathematics and science?

(iii) the use of technology in teaching and learning mathematics and science?

2. Is there a difference between the MCTP teacher candidates' and the non-MCTP
teacher candidates' beliefs toward:

(i) the nature of mathematics and science?

(ii) the interdisciplinary teaching and learning of mathematics and science?

(iii) the use of technology in teaching and learning mathematics and science?

To obtain data to test the hypothesis-testing research questions, the
documentation of the MCTP teacher candidates' and non-MCTP teacher candidates'
attitudes and beliefs toward and about the learning of and the teaching
of mathematics and science throughout their undergraduate years was recognized
as essential to perform. In addition to regularly conducted interviews in
which faculty and teacher candidates would be asked about their attitudes
and beliefs, it was recognized that the regular use of a survey instrument
would be a necessary complementary quantitative research strategy to collect
valid and reliable data from a large number of program participants (Jaeger,
1988). The instrument would be administered to the undergraduate students
in all the MCTP classes offered throughout the state and would be used to
assist in describing their attitudes and beliefs about the nature of and
the teaching of mathematics and science. Since the majority of MCTP classes
consist of a mixture of teacher candidates and non-teacher candidates, the
instrument needed to contain items which all enrolled students gave responses
and a section which contained items only appropriate for those intending
to teach. A Likert style instrument (Likert, 1967) was considered the most
efficient under the external constraint of classroom administration.

A comprehensive review of the mathematics and science education literature
revealed no single instrument which would provide information to inform
all of the research questions. However, partial information could be provided
by existing tools that measure attitudes or beliefs towards mathematics
or science and the teaching of mathematics or science (e.g., German, 1988;
Jasalavich & Schafer, 1994; Jurdak, 1991; Moreira, 1991; Pehkonen, 1994;
Robitalille & Garden, 1989; Schonfeld, 1989; and Underhill, 1988). Therefore,
the researchers decided to craft a new instrument, *Attitudes and Beliefs
about the Nature of and the Teaching of Mathematics and Science. *Readers
interested in the documentation of the instrument's design (history and
procedures) are directed to McGinnis, Shama, Graeber, & Watanabe (1997).

Items for the instrument needed to measure constructs within the affective,
belief, and epistemological areas to inform the research questions. Items
were crafted to measure attitudes toward and beliefs about mathematics and
science, interdisciplinary teaching and learning of mathematics and science,
and the use of technology to teach and learn mathematics and science.

The notion that teachers' attitudes (or preferences) toward mathematics
influence their teaching practice has been suggested by researchers (e.g.,
Thompson, 1984). Ball (1990b) suggests that teachers' attitudes are part
of the way they understand mathematics. Therefore, it is one of the two
broad areas in which pre-service mathematics courses must address (Ball,
1990a). Likewise, researchers in science education have recognized the importance
of the affective domain in the learning and teaching of science (e.g., Simpson,
Koballa, Oliver, & Crawley, 1994) . They define attitudes toward science
as specific feelings which indicate if a person "likes or dislikes
science" (p. 213). The MCTP project's goal is that upon completion
of their undergraduate teacher preparation program, the teacher candidates
will hold positive attitudes toward the learning and the teaching of mathematics
and science. Sample paired attitude items crafted for the survey include:

*I like mathematics (science).*

*I am not good at mathematics (science) [negative].*

*I am looking forward to taking more mathematics (science) courses.*

*I enjoy learning how to use technology (e.g., calculators, computers,
etc.) in mathematics (science).*

A second major component of the instrument was on beliefs. Researchers have
long noticed that beliefs have an influential impact on the learning and
teaching of mathematics and science (e.g., Schoenfeld, 1985; Silver, 1985;
Thompson, 1992). The MCTP project's goal is that upon completion of their
undergraduate teacher preparation program, the teacher candidates will hold
beliefs toward the learning and the teaching of mathematics and science
compatible with MCTP principles. These principles support mathematics and
science for all, the use of cooperative learning, the use of technology
to enhance instruction, the fundamental importance of problem-solving and
inquiry, and the view that the disciplines are human endeavors open to revision.
Sample paired belief items crafted for the survey include:

*Truly understanding mathematics (science) requires special abilities
that only some people possess [negative].*

*The use of computing technologies in mathematics (science) is an aid
primarily for slow learners [negative].*

A third major construct focused on a philosophical perspective on the learning
mathematics and science. The MCTP project is based on a constructivist epistemology.
Although there is still an on-going discussion on what a constructivist
teaching of mathematics and science is (see Simon, 1995; Steffe & D'Ambrosio,
1995; Tobin, Tippins, & Gallard, 1994), the MCTP promotes the following
aspects as three important components of a constructivist mathematics/science
classrooms: (a) students should be given opportunities to experience and
explore mathematics/science using concrete materials (b) students should
be encouraged to think and reflect about their mathematics/science understanding,
and (c) students should be given opportunities to exchange their ideas.
The MCTP project's goal is that upon completion of their undergraduate teacher
preparation program, the teacher candidates will hold beliefs toward the
learning and the teaching of mathematics and science compatible with these
epistemological perspectives. Sample paired epistemological items crafted
for the survey include:

*Students should be given regular opportunities to think about what they
have
learned in the mathematics (science) classroom.*

__Sample__

During the fall, 1995, the survey was administered to all undergraduate
students (__n__= 391) enrolled in 21 non-lecture hall MCTP content courses
offered at 8 institutions of higher learning in Maryland. The survey was
administered during course time. These courses included introductory science
content classes (biology, chemistry, physics, and general science), introductory
and intermediate mathematics classes, and one general pedagogy class designed
for prospective elementary teachers with a concentration in mathematics
or science. In addition, the survey was administered to all students (__n__=144)
enrolled in a large lecture MCTP-influenced content class (biology). Of
the students enrolled in the courses, the student response rate was 98%.
Most students who indicated they intended to teach were Caucasian women.
See Table 1 for detailed information on the sample.

__Findings__

The instrument includes two groups of items. One group consists of thirty-two
items that are to be answered by all students. The other group consists
of nine items that are to be answered only by those intending to teach.
The pre-planned sub-scales were verified on each group of items separately,
using principle-components factor-analysis, with varimax rotation.

In order to execute the factor-analysis, it is recommended that the sample
be at least 15 times the number of items, that is at least (32*15) 480 students.
The total sample of the first administration (fall 1995 pre-test) was 535
students (391+144). However, 49 respondents did not complete all items.
Therefore, the sample size for the factor analysis is 486. A sample of 486
exceeds the minimum sample size factor-analysis requirement for a 32-item
instrument.

Two to five factors were extracted from the 486 students' responses to the
first group of items, following the scree plot. Three factors were chosen,
since they offered the highest reliabilities and theoretically meaningful
dimensions. The three identified factors accounted for 32% of the total
variance. Their corresponding eigenvalues were 4.61, 2.98 and 2.57. A similar
process, on the 331 students' responses to the second group of items, yielded
two factors. The two factors account for 50% of the total variance. Their
corresponding eigenvalues were 3.04 and 1.43.

The items were classified into sub-groups by the factor on which they were
most highly loaded. The classification and loading appear in Table 2. Reliability
of each of the five sub-groups was examined by Cronbach's alpha . Four items
that lowered their group's reliability were taken out of any further analysis.
They included three mathematics items and one general item. All other items
were retained to maximize reliability. On each item the scale was converted,
so that 5 represents the most desired answered and 1 represents the least
desired answer. For each of the five groups, a variable X_{i} was
defined as the mean of scores on items in the group. The five variables
that were verified by factor analysis were the following:

Beliefs about the nature of mathematics and science, variable X_{1}

Attitudes towards mathematics and science, variable X_{2}

Beliefs about the teaching of mathematics and science, variable X_{3
}

Attitudes towards learning to teach mathematics and science, variable X_{4
}

Attitudes towards teaching mathematics and science, variable X_{5 }

Another factor that was extracted from each of the five groups is linked
to the classification of most items into pairs. Each pair included two corresponding
items, one from the mathematics discipline, and the other from the science
discipline. Paired items appear in the same row of Table 2.

__Limitation of the Survey__

The sample of this study included undergraduate students who do not intend
to teach. Therefore, the results should be viewed carefully when compared
to only teacher candidates' responses.

1*. Beliefs about the nature of mathematics and science*

The variable X_{1} measures beliefs about the nature of mathematics
and science, in a scale of 1 to 5. The first semester's pre-test X_{1}
students' mean was 3.81. MCTP students' mean was 3.98. The responses to
the variable X_{1,} reported by administration, by semester, and
by MCTP membership, are given in Table 3.

The hypothesis that MCTP students' mean is equal to the mean of the other
students was rejected using a t test, in each administration and in each
semester (see two Tail significance, in Table 3). The MCTP students' mean
was higher than the other students' mean. Considering both administrations
and both tests, the difference between MCTP student's mean to other students'
mean is 0.24.

A significant difference between pre-test mean to post-test mean was found
only on the Fall semester for the total sample. The 95% confidence interval
for this difference is 0.11 to 0.10. Therefore the drop in mean from pre-test
to post-test was limited in scope, small and did not include MCTP students.

2*. Attitudes towards mathematics and science*

The variable X_{2} measures attitudes towards mathematics and science,
in a scale of 1 to 5. First semester's pre-test X_{2} mean of all
students' was 3.39. The MCTP students' mean was 3.83. The responses to the
variable X_{2,} reported by administration, by semester, and by
MCTP membership, are given in Table 4.

The hypothesis that MCTP students' mean is equal to the mean of the other
students was rejected using a t test, in each administration and in each
semester (see two-Tail significance, in Table 4). The MCTP students' mean
was higher than the other students' mean. Considering both administrations
and both tests, the difference between MCTP student's mean to other students'
mean is 0.44.

The hypothesis that MCTP students' variance is equal to the variance of
the other students was rejected using a Levene's test, in fall semester.
The group of MCTP students is much more homogenous in its response than
the group of non-MCTP students.

The hypothesis that pre test's mean is equal to post test's mean was not
rejected using a t test, in each group of students and in each semester
(see two-Tail significance, in Table 4).

3*. Beliefs about the teaching of mathematics and science*

The variable X_{3} measures beliefs about the teaching of mathematics
and science, in a scale of 1 to 5. First semester's pre-test X_{3}
mean of all students' was 3.99. MCTP students' mean was 4.11. The responses
to the variable X_{3,} reported by administration, by semester,
and by MCTP membership, are given in Table 5.

The MCTP teacher candidates' mean was higher than the other students' mean,
in each semester and administration. The difference between MCTP students'
mean to other students' mean was not significant in the post test of fall
semester, and in the pre test of spring semester (see two-Tail significance,
in Table 5). Considering both administrations and both tests, the difference
between MCTP student's mean to other students' mean is only 0.15.

In the first semester, post test's mean was non-significantly higher than
pre test's mean, in each group of students. In the second semester, MCTP
students' mean significantly improved from pre test to post test (see two-Tail
significance, in Table 5).

4*. Attitudes towards learning to teach mathematics and science*

The variable X_{4} measures attitudes towards learning to teach
mathematics and science, in a scale of 1 to 5. The first semester's pre-test
X_{4} mean of all students' was 4.16. The MCTP students' mean was
4.59. The responses to the variable X_{4,} reported by administration,
by semester, and by MCTP membership, are given in Table 6.

The hypothesis that MCTP students' mean is equal to the mean of the other
students was rejected using a t test, in each administration and in each
semester (see two-Tail significance, in Table 6). The MCTP students' mean
was higher than the other students' mean. Considering both administrations
and both tests, the difference between MCTP student's mean to other students'
mean is 0.52.

The hypothesis that MCTP students' variance is equal to the variance of
the other students was rejected using a Levene's test, in both semesters
and in both administrations. Standard derivations of the group of MCTP students
are from 0.54 to 0.70. Standard derivations of the group of non-MCTP students
are above 0.85. These facts point out that the group of MCTP students is
much more homogenous in its response than the group of non-MCTP students.

The hypothesis that pre test's mean is equal to post test's mean was rejected
using a t test, for non-MCTP students in the spring semester (see two-Tail
significance, in Table 6). Considering both semesters, the mean of non-MCTP
students dropped significantly from 4.02 to 3.82. The mean of MCTP students,
which was originally very high, dropped slightly and insignificantly (see
Table 6).

5.* Attitudes towards teaching mathematics and science*

The fifth variable X_{5} measures attitudes towards teaching mathematics
and science, in a scale of 1 to 5. First semester's pre-test X_{5}
mean of all students' was 3.18. The MCTP students' mean was 3.51. The responses
to the variable X_{5,} reported by administration, by semester,
and by MCTP membership, are given in Table 7.

The MCTP students' mean was higher than the other students' mean, in all
administrations and in all semesters. Considering both administrations and
both tests, the difference between MCTP student's mean to other students'
mean is 0.36.

The hypothesis that MCTP students' mean is equal to the mean of the other
students was not rejected using a t test, in second administration of fall
semester (see two-Tail significance, in Table 7). A significant difference
between pre-test mean to post-test mean was found only on the fall semester
for the MCTP students. The MCTP students' mean dropped significantly. In
the same semester non-MCTP students' average increased slightly. Therefore,
the significant difference that was between MCTP students to other students,
in the beginning of the semester, disappeared. The average of all students
in both semesters grew insignificantly from pre-test to post-test (see first
line of Table number 7).

There are a dearth of longitudinal studies which strive to document the
struggles teacher candidates and others confront when participating in constructivist-based
instruction that attempts to make connections between mathematics and science.
Findings from this phase of a longitudinal study focusing on this issue
is limited. The impact of one or two courses taken during one academic year
on students' beliefs and attitudes cannot be expected in all cases to initiate
dramatic positive changes. However, the instrument proved to be useful in
providing a global picture of both MCTP teacher candidates and non-MCTP
teacher candidates. As we continue to follow the MCTP teacher candidates
throughout their college experiences with this instrument, we should be
able to test whether or not the program has any impact on their beliefs
and attitudes about mathematics and science.

In general, MCTP teacher candidates appeared to have started out with very
positive attitudes and beliefs toward mathematics and science. The fact
that MCTP teacher candidates had significantly better means on all variables
may be a reflection of the fact that students with more mathematics and
science background were actively recruited.

There are, however, some troubling trends (from the project's standpoint)
in the results reported here. For example, the means for variables X_{1}
(beliefs about the nature of math and science) significantly dropped in
the Fall semester for non-MCTP students. Also, the means for X_{4}
(attitudes toward learning to teach math and science) declined significantly
for non-MCTP students and dropped slightly for MCTP students in the MCTP
courses. One possible explanation for these "negative" results
is that the MCTP courses were indeed taught differently, with different
emphases, compared to traditional mathematics and science courses that these
participants had experienced. In some cases, students might have to struggle
to get grades they were so accustomed to getting in the past since the instruction
and assessment emphasized conceptual change over rote memorization. For
some students, this experience may have had a negative impact on their attitude
toward the subject matter. This struggle in turn, even if the students realized
that this form of instruction was superior to the ones they had experienced
themselves as students, might have led some students to realize the challenge
that lay ahead as they try to learn how to teach math and science. Individual
interviews, as well as classroom observation data, will inform this hypothesis
in more detail.

Although statistically not significant, there were some promising trends
in the results. In general, the means for MCTP teacher candidates from Spring
semester indicate general shift in the direction the project is aiming.
All variables show slight (although not statistically significant) improvement
except X_{2}, which remained constant. As we continue our study
of MCTP teacher candidates' development, we will be able to examine the
effects of MCTP courses more carefully.

Overall, the survey instrument has proven to be useful as we attempt to
landscape the paths these teacher candidates will travel during their undergraduate
years. We plan to continue surveying the MCTP teacher candidates regularly
for next three years to document the attitudinal and belief journeys they
take. The issues raised during the first semester administrations will be
addressed as we continue our study.

Within the MCTP, the survey instrument has proven useful as one tool
in our effort to landscape the attitudinal and belief paths the MCTP teacher
candidates travel during their undergraduate years. We plan to continue
administering the survey to the MCTP teacher candidates regularly as they
proceed through their undergraduate programs and begin their first years
of teaching practice. However, we are not focusing all of our attention
solely on this strategy to inform us on this important aspect of teacher
preparation. In addition to the regular administration of the survey, we
are also using complementary research strategies such as in-depth interviews
and longitudinal case studies of faculty and teacher candidates. Between
these quantitative data obtained from the survey instrument and the qualitative
date from the case studies and interviews, we believe that we will be able
to vigorously document the attitudinal and belief progression of MCTP teacher
candidates (and a comparable sample of non-MTCP teacher candidates). These
findings are anticipated to contribute to the crucial need to better understand
the impact of reform practices in undergraduate science and mathematics
teacher preparation.

Outside the MCTP, the survey instrument is offered as a valid and reliable
tool to measure teacher candidates' attitudes and beliefs about the nature
of and the teaching of mathematics and science.

The researchers within the MCTP research team would like to acknowledge
the ongoing support given to them by the MCTP Principal Investigators, Jim
Fey, Genevieve Knight, John Layman, Tom O'Haver, and Jack Taylor, and the
MCTP Executive Director, Susan Boyer. We also are very appreciative of the
participation of the many faculty, teacher candidates, and cooperating classroom
teacher participants in the MCTP research program. We would also like to
acknowledge the support to the MCTP Research Group provided by some talented
and hardworking doctoral students in mathematics education: Amy Roth-McDuffie,
Steve Kramer, Mary Ann Huntley, and Karen King.

Interested readers are invited to browse the MCTP worldwide web homepage
to access additional information concerning the project and the Research
Group's efforts (http://www.wam.umd.edu/~toh/MCTP.html).

The preparation of this manuscript was supported in part by a grant from
the National Science Foundation (Cooperative Agreement No. DUE 9255745).

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__Attitudes and Beliefs__

Below, there is a series of sentences. Indicate on your bubble sheet the
degree to which you agree or disagree with each sentence.

Your choices are:

A B C D E

strongly agree sort of agree not sure sort of disagree strongly disagree

There are no right or wrong answers. The correct responses are those that
reflect your attitudes and beliefs. *Do not spend too much time with
any statement. *

M | SD | N | |

1. I am looking forward to taking more mathematics courses. | 3.12 | 1.36 | 1126 |

2. I enjoy learning how to use technologies (e.g., calculators, computers, etc.) in mathematics classrooms. | 2.06 | 1.12 | 1127 |

3. I like mathematics. | 2.65 | 1.32 | 1128 |

4. In grades K-9, truly understanding mathematics in schools requires special abilities that only some people possess. | 3.79 | 1.22 | 1127 |

5. The use of technologies (e. g., calculators, computers, etc.) in mathematics is an aid primarily for slow learners. | 4.36 | .99 | 1124 |

6. Mathematics consists of unrelated topics (e.g., algebra, arithmetic, calculus and geometry). | 3.91 | 1.25 | 1127 |

7. To understand mathematics, students must solve many problems following examples provided. | 2.49 | 1.22 | 1123 |

8. Students should have opportunities to experience manipulating materials in the mathematics classroom before teachers introduce mathematics vocabulary. | 2.33 | 1.05 | 1125 |

9. Getting the correct answer to a problem in the mathematics classroom is more important than investigating the problem in a mathematical manner. | 4.08 | 1.08 | 1124 |

10. Students should be given regular opportunities to think about what they have learned in the mathematics classroom. | 1.64 | .83 | 1127 |

11. Using technologies (e.g., calculators, computers, etc.) in mathematics lessons will improve students' understanding of mathematics. | 2.26 | 1.10 | 1127 |

12. The primary reason for learning mathematics is to learn skills for doing science. | 3.32 | 1.11 | 1126 |

13. Small group activity should be a regular part of the ...classroom. | 1.71 | .90 | 1128 |

14. I am looking forward to taking more science courses. | 2.97 | 1.39 | 1127 |

15. Using technologies (e.g., calculators, computers, etc.) in science lessons will improve students' understanding of science. | 2.26 | 1.10 | 1127 |

16. Getting the correct answer to a problem in the science classroom is more important than investigating the problem in a scientific manner. | 4.17 | 1.01 | 1123 |

17. In grades K-9, truly understanding science in the science classroom requires special abilities that only some people possess. | 3.94 | 1.18 | 1123 |

18. Students should be given regular opportunities to think about what they have learned. in the science classroom | 1.54 | .75 | 1126 |

19. Science is a constantly expanding field. | 1.33 | .69 | 1124 |

20. Theories in science are rarely replaced by other theories. | 3.67 | 1.14 | 1122 |

21. To understand science, students must solve many problems following examples provided. | 2.75 | 1.18 | 1122 |

22. I like science. | 2.46 | 1.29 | 1124 |

23. I enjoy learning how to use technologies (e.g., calculators, computers, etc.) in science. | 2.04 | 1.10 | 1121 |

24. The use of technologies (e. g., calculators, computers, etc.) in science is an aid primarily for slow learners. | 4.26 | 1.05 | 1121 |

25. Students should have opportunities to experience manipulating materials in the science classroom before teachers introduce scientific vocabulary. | 2.31 | 1.13 | 1125 |

26. Science consists of unrelated topics like biology, chemistry, geology, and physics. | 3.82 | 1.30 | 1120 |

27. Calculators should always be available for students in science classes. | 2.15 | 1.09 | 1122 |

28. The primary reason for learning science is to provide real life examples for learning mathematics. | 3.15 | 1.11 | 1115 |

29. Small group activity should be a regular part
of the science classroom. | 1.51 | .80 | 1113 |

M | SD | N | |

1. I expect that the college mathematics courses I take will be helpful to me in teaching mathematics in elementary or middle school. | 1.86 | 1.12 | 922 |

2. I want to learn how to use technologies (e.g., calculators, computers, etc.) to teach mathematics. | 1.72 | 1.05 | 921 |

3. The idea of teaching science scares me. | 3.25 | 1.31 | 916 |

4. I expect that the college science courses I take will be helpful to me in teaching science in elementary or middle school. | 2.04 | 1.14 | 919 |

5. I prefer to teach mathematics and science emphasizing connections between the two disciplines. | 2.66 | 1.16 | 915 |

6. The idea of teaching mathematics scares me. | 3.28 | 1.38 | 920 |

7. I want to learn how to use technologies (e.g., calculators, computers, etc.) to teach science. | 1.88 | 1.05 | 916 |

8. I feel prepared to teach mathematics and science emphasizing connections between the two disciplines. | 3.04 | 1.18 | 913 |

Table 1

Description | Total sample | MCTP students | |

Gender: | Male | 24.8% | 13.6% |

Female | 75.2% | 86.4% | |

Ethnicity: | African-American | 24.5% | 15.2% |

Asian/Pacific Islander | 4.4% | 3.0% | |

Caucasian | 65.0% | 79.1% | |

Hispanic | 2.0% | 0.9% | |

Other | 4.1% | 1.8% | |

Number of complete college credits: | 0-30 | 32.1% | 40.5% |

31-60 | 31.2% | 29.3% | |

61-90 | 19.4% | 17.8% | |

91+ | 15.0% | 10.3% | |

post-baccalaureate | 2.3% | 2.1% | |

Major area of concentration: | Education / Mathematics | 6.8% | 8.2% |

Education / Science | 6.5% | 6.9% | |

Education / Math & Science | 13.4% | 39.6% | |

Education / Other subject(s) | 45.8% | 43.8% | |

Not in teacher certification program | 27.5% | 1.5% | |

Area of teaching certification: | elementary (grades 1-8) | 75.5%^{(1)} |
91.2% |

secondary mathematics (5-12) | 4.7% | 4.0% | |

secondary science (5-12) | 1.8% | 0.0% | |

other | 17.0% | 4.6% | |

Intending to teach grades: | K-3 | 39.6% | 38.9% |

4-8 | 88.1% | 51.2% | |

9-12 | 5.1% | 1.5% | |

post-secondary | 1.4% | 0.6% | |

undecided | 15.8% | 7.8% | |

Administration | Fall 1995, Pre-test | 391 | 97 |

Fall 1995, Post-test | 293 | 74 | |

Spring 1996, Pre-test | 242 | 84 | |

Spring 1996, Post-test | 202 | 68 | |

Total | 1128 | 323 |

Table 2

Description | Item index | Avg. load |

X1. Beliefs about the nature of mathematics and science | =.7596* | ||

In grades K-9, truly understanding... requires special abilities that only some people possess. | 10 | 24 | .57 |

The use of technologies in ... is an aid primarily for slow learners. | 12 | 31 | .56 |

Getting the correct answer to a problem in the ...classroom is more important than investigating the problem in a ... manner. | 16 | 23 | .55 |

The primary reason for learning ... is to ... for learning ... | 19 | 35 | .53 |

... consists of unrelated topics like ... | 13 | 33 | .48 |

To understand ..., students must solve many problems following examples provided. | 14 | 28 | .33 |

Theories in science are rarely replaced by other theories. | 27 | .41 | |

Science is constantly expanding field. | 26^{-} | .30 | |

X2. Attitudes towards mathematics and science | =.8070 | ||

I am looking forward to taking more ... courses. | 5^{-} |
21^{(2)} |
.73 |

I like ... | 7^{-} | 29^{-} |
.69 |

I enjoy learning how to use technologies in ... classrooms. | 6^{-} |
30^{-} | .68 |

X3. Beliefs about the teaching of mathematics and science | =.6900 | ||

Using technologies in ... lessons will improve students' understanding of ... | 18^{-} |
22^{-} | .55 |

Calculators should always be available for students in science classes | 34^{-} |
.51 | |

Students should be given regular opportunities to think about what they have learned in the ... classroom | 17^{-} |
25^{-} | .48 |

Students should have opportunities to experience manipulating materials in the ... classroom before teachers introduce ... vocabulary | 15^{-} | 32^{-} |
.51 |

Small group activity should be a regular part of the ... classroom. | 20^{-} |
36^{-} | .47 |

X4. Attitudes towards learning to teach mathematics and science | =.7889 | ||

I want to learn how to use technologies to teach ... | 38^{-} | 44^{-} |
.80 |

I expect that the college courses I take will be helpful to me in teaching in elementary or middle school. | 37^{-} |
41^{-} | .74 |

X5. Attitudes towards teaching mathematics and science | =.6014 | ||

The idea of teaching scares me. | 43 | 40 | .69 |

I prefer (feel prepared) to teach mathematics and science emphasizing connections between the two disciplines. | 42^{-} |
45^{-} | .56 |

Table 3

Means, Standard Derivations and t-tests for independent samples of variable X

Both administrations | Pre-test | Post-test | 2-Tail |

n | M | SD | n | M | SD | n | M | SD | sig | |

Both semesters | ||||||||||

All students | 1128 | 3.74 | .59 | 633 | 3.77 | .56 | 495 | 3.70 | .62 | .083 |

MCTP students | 332 | 3.91 | .54 | 181 | 3.92 | .51 | 142 | 3.89 | .59 | .686 |

Non-MCTP | 805 | 3.67 | .59 | 452 | 3.70 | .57 | 353 | 3.63 | .61 | .070 |

2-Tail sig | .000^{(3)} |
.000 | .000 | |||||||

Fall semester | ||||||||||

All students | 684 | 3.76 | .58 | 391 | 3.81 | .55 | 293 | 3.70 | .61 | .009 |

MCTP students | 171 | 3.93 | .55 | 97 | 3.98 | .50 | 74 | 3.86 | .61 | .188 |

Non-MCTP | 513 | 3.71 | .58 | 294 | 3.76 | .56 | 219 | 3.64 | .60 | .018 |

2-Tail sig | .000 | .001 | .006 | |||||||

Spring semester | ||||||||||

All students | 444 | 3.70 | .60 | 242 | 3.69 | .57 | 202 | 3.72 | .63 | .599 |

MCTP students | 152 | 3.89 | .54 | 84 | 3.85 | .52 | 68 | 3.93 | .57 | .405 |

Non-MCTP | 292 | 3.60 | .61 | 158 | 3.60 | .58 | 134 | 3.61 | .63 | .868 |

2-Tail Sig | .000 | .001 | .001 |

Equalities of means that are rejected by t-test are bolded.

Table 4

Means, Standard Derivations and t-tests for independent samples of variable
X_{2} that measures attitudes towards Mathematics and Science.

Both administrations Pre-test
Post-test 2-Tail

n M
SD n
M SD
n M
SD sig
Both semesters
All students 1128
3.45 .90 633
3.45 .91 495
3.48 .87 .570
MCTP students 332
3.78 .76 181
3.78 .79 142
3.78 .74 .924
Non-MCTP 805
3.34 .91 452
3.32 .92 353
3.37 .89 .483 2-Tail sig
.000
^{(4)}
.000 ^{*}
.000
^{*} Fall semester
All students
684 3.40 .92
391 3.39 .93
293 3.46 .89
.369
MCTP
students 171 3.82
.72 97 3.83
.75 74 3.82
.70 .969
Non-MCTP 513
3.29 .94 294
3.25 .93 219
3.33 .91 .317 2-Tail sig
.000
^{*}
.000 ^{*}
.000
^{*} Spring semester
All students
444 3.54 .86
242 3.55 .88
202 3.52 .84
.743
MCTP
students 152 3.73
.80 84 3.73
.83 68 3.73
.77 .943
Non-MCTP 292
3.44 .88 158
3.45 .89 134
3.42 .86 .761 2-Tail Sig
.001
.016
.014

Equalities of means that are rejected by t-test are bolded.

Table 5

Means, Standard Derivations and t-tests for independent samples of variable
X_{3} that measures beliefs about the teaching of Mathematics
and Science.

Both administrations Pre-test
Post-test 2-Tail

n M
SD n
M SD
n M
SD sig
Both semesters
All students 1128
4.03 .52 633
4.01 .51 495
4.04 .53 .270
MCTP students 323
4.13 .48 181
4.09 .48 142
4.18 .47 .063
Non-MCTP 805
3.98 .53 452
3.97 .52 353
3.98 .54 .825 2-Tail sig
.000
^{(5)}
.013
.000
Fall semester
All students
684 4.02 .54
391 3.99 .54
293 4.02 .54
.573
MCTP
students 171 4.10
.48 97 4.11
.49 74 4.10
.47 .894
Non-MCTP 513
3.97 .55 294
3.96 .55 219
4.00 .57 .495 2-Tail sig
.006
.018
.153
Spring semester
All students
444 4.05 .49
242 4.03 .47
202 4.07 .51
.299
MCTP
students 152 4.16
.47 84 4.06
.47 68 4.28
.45 .004
Non-MCTP 292
3.99 .49 158
4.01 .47 134
3.97 .51 .518 2-Tail Sig
.000
.377
.000

Equalities of means that are rejected by t-test are bolded.

Table 6

Means, Standard Derivations and t-tests for independent samples of variable
X_{4} that measures attitudes toward learning to teach Mathematics
and Science.

Both administrations Pre-test
Post-test 2-Tail

n M
SD n
M SD
n M
SD sig
Both semesters
All students 892
4.11 .88 511
4.18 .85 381
4.05 .87 .025
MCTP students 323
4.46 .61 181
4.48 .64 142
4.43 .56 .387
Non-MCTP 569
3.94 .92 330
4.02 .90 239
3.83 .95 .0788 2-Tail sig
.000
^{(6)}
.000 ^{*}
.000
^{*} Fall semester
All students
548 4.10 .90
320 4.16 .88
228 4.06 .88
.199
MCTP
students 171 4.52
.57 97 4.59
.56 74 4.43
.58 .064
Non-MCTP 377
3.93 .96 223
3.97 .92 154
3.88 .95 .379 2-Tail sig
.000
^{*}
.000 ^{*}
.000
^{*} Spring semester
All students
344 4.15 .82
191 4.23 .79
153 4.05 .86
.039
MCTP
students 152 4.39
.63 84 4.36
.70 68 4.43
.54 .541
Non-MCTP 192
3.96 .91 107
4.13 .85 85
3.74 .94 .003 2-Tail Sig
.000
^{*}
.042
.000
^{*}

Equalities of means that are rejected by t-test are bolded.

Table 7

Means, Standard Derivations and t-tests for independent samples of variable
X_{5} that measures attitudes toward teaching Mathematics
and Science.

Both administrations Pre-test
Post-test 2-Tail

n M
SD n
M SD
n M
SD sig
Both semesters
All students 888
3.21 .84 507
3.19 .85 381
3.24 .82 .394
MCTP students 323
3.44 .79 181
3.44 .78 142
3.45 .80 .868
Non-MCTP 565
3.08 .83 326
3.06 .85 239
3.12 .81 .408 2-Tail sig
.000
.000
.000
Fall semester
All students
543 3.18 .85
315 3.18 .87
228 3.19 .82
.825
MCTP
students 171 3.44
.80 97 3.51
.79 74 3.34
.82 .190
Non-MCTP 372
3.07 .84 218
3.03 .86 154
3.12 .81 .306 2-Tail sig
.000
.000
.055
Spring semester
All students
345 3.26 .81
192 3.22 .81
153 3.32 .82
.290
MCTP
students 152 3.45
.77 84 3.36
.76 68 3.57
.77 .090
Non-MCTP 193
3.11 .82 108
3.12 .84 85
3.11 .80 .967 2-Tail Sig
.000
.040
.000

Equalities of means that are rejected by t-test are bolded.

**1. ^{0} Percentages from those intending
to teach, N=922.
**