Attitude and Perception: A Case of a Mediating Approach to Teaching and
Learning Mathematics*
Hamide Dogan-Dunlap, Melinda Ramos and Mo Pak
University of Texas at El Paso
hdogan@utep.edu
The initial findings of an ongoing study are provided and discussed to support the argument that it
might be possible to make changes on preservice teachers’ attitude toward and perception of mathematics
through carefully designed activities such as the approach outlined in the paper. These changes may result
in increased participation in mathematics learning leading to higher achievement.
Low self-esteem and math phobia in mathematics learning result in confused thinking,
disorganization, avoidance behavior, and passivity (Conte, 1991; McDonald, 1989; Zentall&
Zentall, 1983). Students’ attitude, perception and beliefs have a strong influence on students’
evaluation of their own ability, and on their willingness to engage in math tasks (Garofalo and
Lester, 1985; Garofalo, J., 1989; NCTM, 1989). For instance, a student considering mathematics
as a bunch of symbols and procedures may choose to memorize facts, and not make the effort to
understand the “whys.” Furthermore, a student with the negative perception of the role of
mathematics in his/her future profession may be less motivated to participate in mathematics
activities (Pintrich and et al. 1993).
Preliminary results from a set of 2001-2002 pre-questionnaires administered in
mathematics content courses for pre-service teachers at a four-year university provide similar
findings. Many of our preservice teachers, the majority are Hispanic and female, come to us with
negative attitude and high anxiety toward the subject. This is not, however, unique to our
students. There have also been other works reporting similar behaviors and emotions displayed by
the America’s preservice teachers (Battista, 1994, Smith, 1964, Ambraso????). Our preservice
teachers were asked to provide their perception and a definition of mathematics on the
questionnaires. Their responses on the pre-questionnaires reflect more of a subject that is all
about symbols, notations, equations, formulas and procedures that are to be memorized, and a
perception opposite to the one that supports the role and the importance of mathematics in K-4
teaching. Even though our preservice teachers show the potential to learn mathematics, high math
anxiety and the pessimistic beliefs they hold divert attention of many from content learning to
self-esteem issues, which consequently deteriorate their cognitive processes (Mandler, 1989;
McDonald, 1989; Tobias, 1993). The following extract of a preservice teacher’s response from a
pre-questionnaire reveals the emotions and beliefs of many of our preservice teachers:
math is a fear I have not been able to conquer; the fear of math has put a block on my
brain; doesn't like math because I feel very dumb when after so many yrs I still don't
comprehend it.
It is clear that there is a need to address the attitudinal, belief and anxiety issues before
expecting participation in mathematics activities. Many educators have made arguments in favor
of the role of mediating learning activities in making changes on some aspects of students’
emotional, attitudinal and belief factors (Fennema, 1989; Gray, 2001; McDonald, 1989). A set of
mediating activities as part of a pedagogical approach, An Integrated, Collaborative, Field-Based
Approach to Teaching and Learning Mathematics (see figure 1), has emerged as a result of
discussions between math and education faculty in order to address some aspects of attitudinal
and emotional as well as perceptional factors our preservice teachers hold, and consequently
enhance their mathematical knowledge. It has been expected that a high confidence in ability to
do mathematics will result in a positive attitude, thus an increase in motivation. Cyclically, a
positive change in attitude and increase in motivation will result in a higher confidence and selfesteem. In the long term, preservice teachers with enhanced content knowledge and higher
confidence will graduate highly motivated, mathematically literate students.
Our approach has been integrated into the existing field based block courses consisting of
three subjects taken in a cohort setting. Two of these courses are the Pedagogy of Teaching and
Learning, and the Mathematics Methodology at Elementary and Middle School Levels. The third
one is a Mathematics Content course. In the past these courses have been taught in isolation with
little to no collaboration between the education and the mathematics faculty. The students have
complained about the inconsistent teaching practices.
Elementary school
and mentor teacher
Math Project
Practice-micro lesson
Math Content
Math Methods
Micro-Teaching
Final Presentation
Reflection
Micro-Lesson
Pedagogy
Figure 1. Diagram of an integrated, collaborative, field-based approach to teaching mathematics.
Outline of the Approach
The approach consists of activities developed to support the cycle of Learn, Practice, and Teach.
It requires the integration of the three subjects, and the collaboration between the university
faculty and the local area schools. The following outlines the features of the integrated
collaborative field based approach to teaching and learning mathematics:
 Mathematics is to be the common theme for the three courses.
 Education and mathematics faculty are to collaborate to integrate the three courses
through common assignments and activities.
 Students are to advance their content knowledge through inquiry-based, collaborative
group activities with the guidance and the support of the content and the math method
teacher. Through collaborative and guided group works, students are to investigate,
conjecture, discover and generalize, and as a result further their procedural and
conceptual understanding of mathematical concepts (Gray, 2001).
 With the guidance of the three block faculty members, primarily the methodology
instructor, preservice teachers are to develop micro-lessons on the math content learned.
 Students are to practice their micro-lessons during the math content and methods hours,
and receive feedback from their instructors and classmates.
 Students are to teach their micro-lessons in an elementary classroom in the presence of
the university faculty and the in-service mentor teacher whose classroom is visited.

Students are to receive constructive feedback from their instructors and the in-service
mentor teacher on their microteaching on issues ranging from content mathematics to
classroom management.
Preservice teachers are to present various aspects, captured through pictures, of their last
microteaching during the final week of the semester in order to demonstrate their ability
to integrate content, methodology and pedagogy knowledge covered through out the
semester.

120.0%
100.0%
80.0%
Pre
Post
60.0%
40.0%
Defn
Difficult
Thinking
Formulas
Life
problems
0.0%
Solve
problems
20.0%
Figure 2. Preservice teachers’ perception of mathematics from the pre and post
questionnaires administered in spring 2002.
An extra blank column between Difficult and Defn???
Results
Figure 2 outlines some of the changes on a group of preservice teachers’ perception of
mathematics after going through a block with the integrated approach. At the end of the spring
2002 semester, compared to the number of students who provided the same responses on prequestionnaire, more students stated that:
 Mathematics is used (a tool) to solve problems.
 Mathematics is helpful to understand real life problems/issues.
 Mathematics involves logical (critical) thinking and reasoning.
Fewer students agreed that:
 Mathematics is about symbols, formulas and equations.
 Mathematics is difficult.
Fewer teachers considering mathematics as a difficult subject might be interpreted as an
increasing number of preservice teachers gaining confidence in their ability to learn mathematics
and think mathematically. Moreover, the smaller quantity of students stating mathematics as
being about formulas and equations might be attributed to the increased number of those
considering the subject as something that involves thinking and reasoning but not about
memorization of meaningless formulas and equations.
Another notable result is that a higher percentage of students provided unemotional
descriptions for mathematics (we called it definition-based) compared to the percentage of those
providing definition-based descriptions at the beginning of the semester. One might infer this to
be the result of the fewer negative emotional factors displayed on preservice teachers’ post-
questionnaire responses. Students seem to reflect more negative emotions on their writings than
positive emotions. Here is a preservice teacher’s post-questionnaire response revealing a
perception of mathematics dominantly unemotional:
Math is a way of expressing, explaining, & expanding your knowledge; by doing math,
you can express how you feel, ex, if you don't understand, you may feel frustrated;…math
is a way of explaining because once you have an answer, you can explain why you came
up with that result; math expands your knowledge because understanding math can help
you become a better critical thinker.
In her response, the student is reflecting her perception of mathematics, and how this
perception determines her decision to stay even with the most frustrating problems (McDonald,
1989). Now she looks at the subject as something that requires explaining and expending her
knowledge. She seems to believe that the more mathematics she does, and understands, the better
critical thinker she becomes, which is opposite to what many believed (unimportance of learning
more and higher mathematics) at the start of the semester. These kinds of changes on our
students’ perceptions and behaviors seem to have resulted in increased participation in
mathematics activities, thus leading to an increase in mathematical knowledge. For example,
compared to other blocks, the block that went through the integrated approach in fall 2001
performed notably better at the Texas State standardized teacher certification examination.
Figure 3 summarizes scores, from the Texas State certification examination of the two
groups (control and experimental groups) of preservice teachers from fall 2001. The experimental
group, as opposed to the control group, was introduced to the integrated approach. As figure 3
depicts, the experimental group performed notably better. The proportion of those receiving 74
and above almost doubled from that of the control group. Considering that the main major
difference (not including the differences on instructors’ styles) between the two groups is the
integrated approach, one might attribute the better performance on the state certification exam to
the integrated approach. One should also note that both the control and the experimental groups
were shown to have similar mathematics background determined by the students’ responses on a
set of pre-test questions in mathematics.
State Certification exam results
60
50
%
40
exp
30
cont
20
10
0
65<
65<= , <74
74<=
Score
Figure 3. Percentage of the State Certification Examination scores for a control (N=126) and an
experimental group (N=29) for fall 2001 preservice teachers.
Conclusion
This paper discussed the preliminary results of a study documenting changes, after going through
the integrated approach, on preservice teachers’ attitudes toward and perception of mathematics.
Guided, inquiry-based and collaborative group work has helped our preservice teachers gain
confidence in their ability to learn mathematics and think mathematically. This in turn has
resulted in a change in their perception of mathematics from that of a subject being all about
symbols, equations and formulas to be memorized to a subject that requires logical thinking,
reasoning, investigation and discovery. Moreover, the micro-lessons and teaching in actual
elementary classrooms have provided opportunities for our students to experience the importance
of knowledge of higher mathematics and the conceptual understanding of elementary school
mathematics in accurately and effectively responding to a variety of questions elementary school
students may pose. These experiences have made changes on the students’ attitudes toward and
beliefs about mathematics. In essence, positive changes in behavior, emotion and perception
motivate preservice teachers to increasingly participate in math content activities, and as a result
become more confident in their ability to do mathematics. The higher confidence in turn results in
positive changes in attitude, emotion and perception.
The authors are aware of the potential effects due to the differences of the instructors’
teaching styles and personalities on the learner’s beliefs about, behaviors toward and perception
of a subject. Therefore, an additional research is advocated for a similar study eliminating
observed differences in instructors.
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Acknowledgement. Data reported on this paper was collected by the partial support of NSF-MSP
grant, and with the collaboration of two colleagues (Drs. Izquierdo and Kosheleva). The opinions
expressed on this paper are those of the authors, and do not necessarily reflect the views of the
National Science Foundation.
*A shorter version of this paper was presented at the joint meetings in 2003, Phoenix, Arizona.