Denise Flick
      Denise Flick teaches Grade 7, and is the K-7 Numeracy Coordinator
      with School District #20 (Koote...
level being taught. The teacher had to field questions that she did not always
have the answers for and adjust the pace an...
Games were introduced to aid in the memorization of basic facts. Manipulatives
were used in an attempt to help children ex...
become problem solvers.” I would suggest that before elementary teachers
can teach for deep conceptual understanding, they...
The teaching community must not be afraid to acknowledge that the greatest
deterrent to “good” elementary math instruction...
Bibliography
Battista, M. (1986). The relationship of mathematics anxiety and mathematical
       knowledge to the learnin...
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P. 19 Teacher Math Anxiety

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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).

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  • My children use the Math makes Sense books at school and I am online doing a web search of the series as I have serious questions about the need to confuse students with a lot of uneccesary steps when teaching math concepts that have and always will be unchanged. I feel like the error of confusing this generation of learners will become apparent in the years after these children are grown as was the error to change from phonics on the previous generation of learners. Twenty something year olds are poor readers and their spelling is even worse. I am very frustrated at the gamble being played with my children's minds in regards to changing how math is taught and learned. Math is facts, facts do not change and the way they are taught should not either. Huge mistake.
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P. 19 Teacher Math Anxiety

  1. 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 Vector 19
  2. 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. 20 Spring 2008
  3. 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 Vector 21
  4. 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. 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. Vector 23
  6. 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. 24 Spring 2008

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