As educators, we have always known that math anxiety is a very real problem for many students. Math anxiety is also a very real problem for some teachers. The problem of math anxiety “becomes acute when the person most afraid of numbers and equations is standing in front of the classroom trying to teach the subject” (Campbell, 2006).

1. Denise Flick
Denise Flick teaches Grade 7, and is the K-7 Numeracy Coordinator
with School District #20 (Kootenay- Columbia).
Teacher Math Anxiety and Lack of
Conceptual Understanding
Math Makes Sense. This is the title of a new elementary math series recently
launched in Canada. The title was chosen to indicate to prospective users
(teachers and districts) that here at last was a resource that would encourage
and support teachers’ efforts to teach for deeper mathematical understanding.
Educators would be persuaded and instructed to teach math, using pedagogy
that would support the constructivist theory of learning and students would
understand concept before procedure and algorithm. Quality would be valued
above quantity. Engagement in mathematical activity would be the goal.
Hallelujah!
The books were delivered. Handsome teacher guides complete with CDs
accompanied the student texts. Colourful boxes of manipulatives beckoned
the teacher to open, organize and store in equally colourful bins, the wonderful
array of geoboards, pattern blocks, pentominoes, and tiles. One teacher was
heard to remark, “I arrived in September and boxes of math books and supplies
were waiting in my classroom. It was just like Christmas!”
It was not long before Christmas morning euphoria succumbed to Boxing
Day disillusionment. Soon teachers were heard to remark and snicker, “Hah!
Math Makes Sense? This Math Makes No Sense. There’s not enough practice.
I can’t spend that much time teaching patterning. The classroom is too noisy.
There is too much discussion and not enough drill. ”
What was the problem? How could a program that had promised so much
hope so quickly become a source of ridicule?
Yes, the program was different. No longer could a teacher present a concept,
demonstrate, assign practice questions and return to her seat to mark the
daily spelling work. The teacher was now required to circulate and facilitate
as students engaged in exploration of newly introduced concepts and then
attempted to connect new learning to previous knowledge. The teacher had
to deeply understand the concepts so that she might facilitate discussion. The
teacher had to possess mathematical knowledge above and beyond the grade
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2. level being taught. The teacher had to field questions that she did not always
have the answers for and adjust the pace and content of the lesson to suit the
individual needs of students.
Wait! This wasn’t right! Is not the teacher supposed to be all knowing? Is
not the teacher supposed to be in charge of the lesson? Is not the teacher the
sage on the stage and not the guide on the side? A review of all provincially
sanctioned resources soon confirmed that all recommended resources were
now enabling the educator to organise, present and deliver math instruction in
a like manner. Oy-vey!
The sad reality was that this math did not make sense. It did not make sense to
many of the teachers attempting to teach it.
Elementary school teachers are required to be all and know all. Language,
science, art, physical education, music and yes, mathematics are subjects
in which we are to be competent, knowledgeable, and proficient. Very few
individuals are so multi-talented that they can easily and effectively provide
for their students all the necessary components of a well-rounded education. I
know that I feel inadequate when teaching French. My knowledge and ability
are lacking. Others in my schoolhouse profess to be unable to carry a tune and
as a result go to great lengths to avoid teaching music and devote limited time
to musical endeavours in their classrooms.
Is it not just as likely that some individuals experience the same feelings
of inadequacy or anxiety when teaching math? Is it not true that in some
classrooms, math is the first class to be shortened or skipped when an assembly
is called or when a poster contest needs to be completed?
As educators, we have always known that math anxiety is a very real problem
for many students. Math anxiety is also a very real problem for some teachers.
The problem of math anxiety “becomes acute when the person most afraid of
numbers and equations is standing in front of the classroom trying to teach the
subject” (Campbell, 2006).
The teaching and learning of mathematics has historically been concerned
with rote memorization and the carrying out of procedure. Deep understanding
of mathematical concepts has not been stressed. In the 1990s some effort to
make math more meaningful was bandied about and engaged in. To connect
math learning to real life, students were often working with pizza fractions or
favourite food graphs. Word problems were highlighted as the way to encourage
problem solving. Three birds plus two birds equals how many birds? Three
fish plus two fish equal how many fish? It was not always realized that the task
was only problem solving if there was a problem to be solved.
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3. Games were introduced to aid in the memorization of basic facts. Manipulatives
were used in an attempt to help children explain why “you carry the one.”
(Carry the one?) Teachers believed that simply asking students to explain was
sufficient to promote deep understanding. Statements were confused with
explanations. In elementary school, even high-performing math students often
had a shallow grasp of mathematical concepts. These students carried on to
secondary school and then on to university.
Is it not possible that many intelligent, yet math anxious individuals are drawn
to post secondary studies? These individuals do not continue their mathematical
studies at university and are therefore drawn to career study that does not
require additional math courses. Elementary teaching is such a career. It is
frequently the case that future elementary school teachers are required to take
only one math course. The course has little if anything to do with conceptual
understanding. The course is a methods course.
In recent years, the Western and Northern Canadian Protocol (WNCP) has
been established. This protocol comprises the western provinces (British
Columbia, Alberta, Manitoba, and Saskatchewan) as well as the territories
(Yukon, Nunavut and Northwest Territories). A coordinated math curriculum
and mandated pedagogy have been established. The number of concepts taught
at each grade level has been decreased. This decrease is intended to provide
teachers and students the opportunity for rich and full mathematical learning
of each concept covered rather than the surface study that was available
previously as teachers were pressed to cover far too many concepts in each
school year.
I would suggest that this noble effort to create the opportunity for improved
student conceptual understanding will create a new wave of math anxious
teachers. Many hesitant teachers of math had established some level of
comfort in the how and what they were teaching. But now… Math Makes
Sense, Math Everywhere, and Math Links are all commercially available
and provincially accepted resources. All these programs reflect the change in
content but more importantly, they reflect an important change in pedagogy.
The WNCP approved resources are doomed to fail miserably if the new is
taught in the old way and if our teacher-training facilities have not done what
is needed to prepare the next generation of teachers to use the next generation
of resources.
A key factor in the success of these many initiatives and instructional strategies
in elementary school mathematics is the ability of the teacher to effectively
implement the improved programs. As Krulick and Rudnick (1982) stated,
“before elementary teachers can teach problem solving, they must themselves
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4. become problem solvers.” I would suggest that before elementary teachers
can teach for deep conceptual understanding, they must themselves possess
deep conceptual understanding.
Many researchers claim that the majority of elementary school teachers are
“under prepared in mathematics, and that they also possess an ongoing case
of mathematics anxiety” (Battista, 1986; Buhlman & Young, 1982; Kelly &
Tomhave, 1985). These authors report that significant portions of elementary
school teachers possess levels of mathematics anxiety. The levels of
mathematics anxiety are enough to negatively affect their classroom teaching
practices. “The disproportionately large number of mathematically anxious
teachers at the elementary school level is often said to influence not only the
effectiveness of instruction, but may promote the early onset of mathematics
anxiety among students” (Hackworth, 1985, p. 8; Oberlin, 1982). These
authors state “that if elementary teachers are to make instruction more relevant
and exciting to their students, they must first overcome any fears or negative
attitudes that may have a negative influence on their planning and teaching.”
It is not this article’s purpose to criticize math anxious and/or concept deficient
teachers. The purpose is to emphasize the importance that needs to be placed
on the diagnosing and addressing of deficits in teachers’ mathematical content
knowledge, and to identify the mathematical beliefs and attitudes of those
who will or do work with students. It cannot be assumed that teachers are
trained to teach mathematics for deep understanding and are then able to do
so with confidence. Many may leave university lacking the skills needed to be
good teachers of mathematics. Classrooms may be home to teachers who lack
the pedagogy, content knowledge and disposition necessary to do the best job
possible for their students.
Several problems exist. One is the often inappropriate and insufficient method
and content courses offered to teachers in training. Another problem is the
scarcity of continued education in pedagogy and continued opportunity to
improve mathematical understanding and disposition for teachers already
entrusted with the mathematical education of children. At the beginning of
one’s teacher training, negative disposition in math needs to be recognized and
addressed. Within the teaching profession, a climate of trust and opportunity
needs to be developed to ensure that in-service teacher mathematics anxiety
can be admitted and effectively and respectfully addressed. Quinn, (1998)
proposed that teachers who possess poor attitudes to math are more likely
to pass those feelings on to their students. Those students may then become
teachers and the cycle continues.
22 Spring 2008

5. The teaching community must not be afraid to acknowledge that the greatest
deterrent to “good” elementary math instruction cannot be “fixed” only with
improvement in curriculum, resources and/or pedagogy. Teacher disposition,
knowledge of pedagogy and deep understanding of the subject matter must be
addressed.
Professional development is too often ineffective. Professional development
is costly and yet for this great expenditure it is infrequent, superficial, and
noncumulative. The professional development opportunities presented are not
connected to deeper learning but are more often delivered in the form of a “tune
up” by well meaning individuals in educationally themed sweaters and jewelry.
It is my wish to inspire and validate discussion among teachers, teachers in
training, school districts and teacher educators. The education profession must
first acknowledge the existence of math anxiety and ill preparedness and then
must endeavour to provide appropriate and successful methods by which this
problem can be eliminated.
Summary
North American children continue to lag behind other countries in mathematical
achievement (Trends in International Mathematics and Science Study [TIMSS],
1999). Increased testing, variation in instruction and use of math games and
manipulatives have not improved learning. Our children’s mathematical
learning will not improve until their teachers’ mathematical learning is
provided for. Universities and colleges must recognize the mathematical needs
of pre-service teachers. School boards and district personnel must recognize
the mathematical needs of the teachers that they now have in their employ.
If pre-service and in-service elementary teachers are to make instruction less
anxious for their students, they must first overcome any fears or negative
attitudes that may have a negative influence on planning and teaching.
I believe it is through the development of conceptual and pedagogical
understanding that teachers can improve their instruction of mathematics
and improve the ability of their students to think and work mathematically.
I believe that it is through personal reflection and with the support of teacher
educators, colleagues and district personnel that teachers can address their
personnel difficulties with math anxiety and can then create an atmosphere in
which all students can investigate all things mathematical in a safe, supportive,
and effective environment.
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6. Bibliography
Battista, M. (1986). The relationship of mathematics anxiety and mathematical
knowledge to the learning of mathematical pedagogy by pre-service
elementary teachers. School Science and Mathematics, 86, 10-19.
Buhlman, B. J., & Young, D. M. (1982). On the transmission of mathematics
anxiety. Arithmetic Teacher, 30, 55-56.
Campbell, G. (2006). Popping math anxiety. Retrieved October 8, 2006, from
ASU Research http://researchmag.asu.edu/stories/cresmet.html
Hackworth, R. D. (1985). Math anxiety reduction. Clearwater, FL: H & H
Publishing.
Kelly, W., & Tomhave, W. (1985). A study of math anxiety and math avoidance
in pre-service elementary teachers. Arithmetic Teacher, 32, 51-53.
Krulick, S. & Rudnick, J.A. (1982). Teaching problem solving to pre-service
teachers. Arithmetic Teacher, 29, 42-45.
Oberlin, L. (1982). How to teach children to hate mathematics. School Science
and Mathematics, 82, 261.
Quinn, R. J. (1998). The influence of mathematics methods courses on
pre-service teachers’ pedagogical beliefs concerning manipulatives.
Clearing House, 71, pp. 235-289.
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