For some time now, it seems that when American education is addressed in the media, it is reported in a less than flattering light. Compared with other countries, schools in the United States are supposedly lagging behind in performance, test scores and so on. While the accuracy and relevance of such comparisons can and should be debated, there is one thing that I personally have found during my pursuit of an education degree: many people struggle with the subject of mathematics. I have witnessed college students – potential teachers – who are unable to perform basic math functions. I have also spoken with quite a few students that have problems with the subject and have formed some strong conclusions based on my observations.
I believe that schools in our country have perpetuated a cycle of sub-par math instruction that has resulted in poor math performance and a general acceptance of the fact that some people simply “can’t do math.” This unfortunate statement becomes alarming when individuals that struggle with math become elementary teachers; what quality of math instruction can be expected from teachers that have a shaky understanding of the subject themselves? However, teachers that lack a strong mathematical background are not the only problem. Some math teachers that greatly excel at the subject can be equally ineffective. If the teacher is unwilling or unable to teach the subject in a variety of ways, fails to properly assess student understanding, and does not attempt to get to know their students, the results can be as unfortunate as those from a teacher with weak math skills.
My observations were reinforced in print in the August, 2005 issue of Middle Ground: The Magazine of Middle Level Education. In that journal, University of Virginia education professor Carol Ann Tomlinson describes two classes from her middle school years that shaped not only her philosophy of education, but her overall attitude toward two subjects and more importantly, her self-esteem. Her article “Differentiating Instruction: Why Bother?” describes her seventh grade math teacher:
She was a serious math teacher. She covered math with a single-mindedness that was evident even to seventh graders. She explained the math in one way and one way only. She taught each topic one time and one time only. She used one form of assessment and one form only. She knew math, but she didn’t know about me at all.
Ms. Tomlinson goes on to describe how her suddenly found inability to “do math” damaged her self-confidence as an individual during the already difficult stage of adolescence. She also developed a profound dislike for math that has persisted into adulthood.
Thankfully, she simultaneously had an English teacher that had a completely opposite view of his students. While she acknowledges his shortcomings as a teacher, the lasting effect from her time in his class was the manner in which he got to know each student, adapting his instruction to fit their interests and abilities. Doing so kindled a great interest in literature and writing for Ms. Tomlinson, and made her realize the importance of differentiating instruction (a term that she says that she doubts anybody used at that time). By finding her talents, her English teacher showed that he wanted his students to learn and excel, while her math teacher displayed a differing attitude: “That I understood virtually nothing she was talking about was either off her radar or beyond the parameters of her interest.” This attitude was more damaging because while she felt validated in English, it could not offset the negative effects of the math class. Reading the article, it is a wonder that Ms. Tomlinson was not turned off of education completely. Instead, she discovered the reason for differentiated instruction: “Our success as teachers in helping students see themselves as competent in the subjects we teach will affect the rest of their lives.”
In addition to less than ideal instruction, much of the problem with United States math performance can be attributed to the attitudes we have toward the subject. Unlike subjects such as science, English, art and so on, answers to math problems are not open to interpretation; answers are correct or they are not. The problem with considering math in this light is that the focus has been almost completely on finding the right answer. Over the years, it seems that we have found one primary method for finding ‘the correct answer’ and that method is taught in exercises, over and over again.
American students learn how to add complex numbers in the same way, learn to multiply the same way, multiply fractions the same way and so on. Students perform these steps, in this order, get the correct answer, and repeat. The issue in teaching this way is that the focus shifts away from the thought processes needed to solve math problems. The end result becomes teachers like the woman described in Ms. Tomlinson’s article. Such a narrow view of math perpetuates attitudes like this one from a Florida school board candidate (and retired assistant principal): “one plus one still equals two.” (Solochek) Opinions like this one provide a major roadblock to the improvement of math instruction, especially when it comes from potential school board members.
The ultimate question becomes ‘what can we do to improve mathematics instruction in our schools?’ On a positive note, researchers and schools of education have the right idea. The mathematics education curriculum at Ivy Tech and the University of Southern Indiana in Evansville place a focus on answering the question ‘why?’ For example, instead of blindly multiplying fractions by multiplying the numerators and denominators, why does it work? Also of major importance is discussing the thought processes used in problem solving maths. Marking a problem wrong when the incorrect answer is not achieved does not teach a student anything; determining how the student arrived at the answer lets them know where they got off track, and allows the teacher to adjust the level of instruction that is necessary for the student to understand the concept.
As Carol Ann Tomlinson writes, differentiating instruction is also a major factor in improving school performance, and math classes are no exception. Like teachers of any subject, it is imperative that math teachers get to know their students and understand how they learn best. Creativity can exist in math classrooms just as it does in English, science, social studies or art classes. A creative maths teacher can use experiments that show how new math concepts work. Using drawings such as strip diagrams can help students visualize story problems, helping them to determine the proper method of solution. Teachers can often relate items of student interest to particular concept maths. Even small things such as using humor or inserting student names into story problems can make math more enjoyable and less of a ‘stuffy’ subject.
Reforming education is a difficult task. Much of this difficulty stems from getting people to agree on the most effective methods of reform. If the fact that American students are struggling in their mathematical abilities is believed to be true, it must be concluded that our typical methods of instruction – following specific steps repeatedly through daily homework practice – are ineffective. If we want to improve the ability of our students to solve problems and perform well in math, we must change the way that we teach the subject. Understanding the needs of each student - like we often do in reading instruction - can be done in math as well. Teaching concepts in multiple ways can accommodate the wider variety of learners that enter our classrooms. Teachers today have access to a wealth of resources; using these resources along with some creativity can go a long way in achieving the kind of math improvement that all of us can agree upon.
WORKS CITED
Solochek, Jeffrey S. “Pasco County schools switch to new math program.” St. Petersburg Times, August 22, 2010. Retrieved from http://www.tampabay.com/news/education/k12/pasco-county-schools-switch-to-new-math-program/1116669
Tomlinson, Carol Ann. “Differentiating Instruction: Why Bother?” Middle Ground: The Magazine of Middle Level Education, August, 2005.
I believe that schools in our country have perpetuated a cycle of sub-par math instruction that has resulted in poor math performance and a general acceptance of the fact that some people simply “can’t do math.” This unfortunate statement becomes alarming when individuals that struggle with math become elementary teachers; what quality of math instruction can be expected from teachers that have a shaky understanding of the subject themselves? However, teachers that lack a strong mathematical background are not the only problem. Some math teachers that greatly excel at the subject can be equally ineffective. If the teacher is unwilling or unable to teach the subject in a variety of ways, fails to properly assess student understanding, and does not attempt to get to know their students, the results can be as unfortunate as those from a teacher with weak math skills.
My observations were reinforced in print in the August, 2005 issue of Middle Ground: The Magazine of Middle Level Education. In that journal, University of Virginia education professor Carol Ann Tomlinson describes two classes from her middle school years that shaped not only her philosophy of education, but her overall attitude toward two subjects and more importantly, her self-esteem. Her article “Differentiating Instruction: Why Bother?” describes her seventh grade math teacher:
She was a serious math teacher. She covered math with a single-mindedness that was evident even to seventh graders. She explained the math in one way and one way only. She taught each topic one time and one time only. She used one form of assessment and one form only. She knew math, but she didn’t know about me at all.
Ms. Tomlinson goes on to describe how her suddenly found inability to “do math” damaged her self-confidence as an individual during the already difficult stage of adolescence. She also developed a profound dislike for math that has persisted into adulthood.
Thankfully, she simultaneously had an English teacher that had a completely opposite view of his students. While she acknowledges his shortcomings as a teacher, the lasting effect from her time in his class was the manner in which he got to know each student, adapting his instruction to fit their interests and abilities. Doing so kindled a great interest in literature and writing for Ms. Tomlinson, and made her realize the importance of differentiating instruction (a term that she says that she doubts anybody used at that time). By finding her talents, her English teacher showed that he wanted his students to learn and excel, while her math teacher displayed a differing attitude: “That I understood virtually nothing she was talking about was either off her radar or beyond the parameters of her interest.” This attitude was more damaging because while she felt validated in English, it could not offset the negative effects of the math class. Reading the article, it is a wonder that Ms. Tomlinson was not turned off of education completely. Instead, she discovered the reason for differentiated instruction: “Our success as teachers in helping students see themselves as competent in the subjects we teach will affect the rest of their lives.”
In addition to less than ideal instruction, much of the problem with United States math performance can be attributed to the attitudes we have toward the subject. Unlike subjects such as science, English, art and so on, answers to math problems are not open to interpretation; answers are correct or they are not. The problem with considering math in this light is that the focus has been almost completely on finding the right answer. Over the years, it seems that we have found one primary method for finding ‘the correct answer’ and that method is taught in exercises, over and over again.
American students learn how to add complex numbers in the same way, learn to multiply the same way, multiply fractions the same way and so on. Students perform these steps, in this order, get the correct answer, and repeat. The issue in teaching this way is that the focus shifts away from the thought processes needed to solve math problems. The end result becomes teachers like the woman described in Ms. Tomlinson’s article. Such a narrow view of math perpetuates attitudes like this one from a Florida school board candidate (and retired assistant principal): “one plus one still equals two.” (Solochek) Opinions like this one provide a major roadblock to the improvement of math instruction, especially when it comes from potential school board members.
The ultimate question becomes ‘what can we do to improve mathematics instruction in our schools?’ On a positive note, researchers and schools of education have the right idea. The mathematics education curriculum at Ivy Tech and the University of Southern Indiana in Evansville place a focus on answering the question ‘why?’ For example, instead of blindly multiplying fractions by multiplying the numerators and denominators, why does it work? Also of major importance is discussing the thought processes used in problem solving maths. Marking a problem wrong when the incorrect answer is not achieved does not teach a student anything; determining how the student arrived at the answer lets them know where they got off track, and allows the teacher to adjust the level of instruction that is necessary for the student to understand the concept.
As Carol Ann Tomlinson writes, differentiating instruction is also a major factor in improving school performance, and math classes are no exception. Like teachers of any subject, it is imperative that math teachers get to know their students and understand how they learn best. Creativity can exist in math classrooms just as it does in English, science, social studies or art classes. A creative maths teacher can use experiments that show how new math concepts work. Using drawings such as strip diagrams can help students visualize story problems, helping them to determine the proper method of solution. Teachers can often relate items of student interest to particular concept maths. Even small things such as using humor or inserting student names into story problems can make math more enjoyable and less of a ‘stuffy’ subject.
Reforming education is a difficult task. Much of this difficulty stems from getting people to agree on the most effective methods of reform. If the fact that American students are struggling in their mathematical abilities is believed to be true, it must be concluded that our typical methods of instruction – following specific steps repeatedly through daily homework practice – are ineffective. If we want to improve the ability of our students to solve problems and perform well in math, we must change the way that we teach the subject. Understanding the needs of each student - like we often do in reading instruction - can be done in math as well. Teaching concepts in multiple ways can accommodate the wider variety of learners that enter our classrooms. Teachers today have access to a wealth of resources; using these resources along with some creativity can go a long way in achieving the kind of math improvement that all of us can agree upon.
WORKS CITED
Solochek, Jeffrey S. “Pasco County schools switch to new math program.” St. Petersburg Times, August 22, 2010. Retrieved from http://www.tampabay.com/news/education/k12/pasco-county-schools-switch-to-new-math-program/1116669
Tomlinson, Carol Ann. “Differentiating Instruction: Why Bother?” Middle Ground: The Magazine of Middle Level Education, August, 2005.
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