I have been a private math tutor for the past 7 years. I have worked with a variety of students who are being taught by a variety of teachers and professors. With my students I occasionally disagree with their teacher's style or pedagogy. I currently have a student who goes to a private school in Dallas, TX. I have never disagreed with a teacher more with his teacher about pedagogy. This teacher’s name is not Mr. Smith, but I will refer to him as “Mr. Smith” because what this teacher is doing is far more important to my discussion than who this teacher is.
The first thing I noticed about Mr. Smith is that he takes two or three weeks to teach the concepts from a particular chapter. Mr. Smith then spends two to three weeks reviewing. Now to me two to three weeks is a little long to review, but I don't have a huge problem with that. What I have a problem with, is while they are reviewing Mr. Smith teaches the next chapter.
Now this might not seem like a big deal, but I hope I can help you understand that this creates a lot of confusion for a student who is learning all these concepts for the first time. Each chapter in most textbooks covers about 7 related, but different concepts or methods. So when a student sits down to take a test or quiz they have not 7, but 14 different concepts or methods that they have learned recently. I know that it is easy for students to get confused between different ideas, especially when there are 14 different ideas to sort through.
To make matters worse Mr. Smith is very particular about the way his students do their work. For example on a recent quiz my student lost half of his points on a particular question, not because he got the wrong answer, not because he did something mathematically incorrect, but because he divided by 7 instead of multiplying by 1/7. The teacher’s note said “Wrong form.” For those of you who are rusty on your Algebra, diving by 7 and multiplying by 1/7 are mathematically equivalent. In theoretical mathematics, like Abstract Algebra, there is a difference between these two operations, but this is not a class on theoretical mathematics it is a class of 7th graders trying to learn how to solve equations. I would also like to point out that occasionally Mr. Smith changes the way that he wants his students to do a particular type of problem. I don’t know if Mr. Smith would take off points for doing it the old way or not, but taking off points like this adds to the stress of taking his difficult tests and quizzes.
Yesterday, I went to work with my student because he has a test today. There were two things that he said that I couldn’t believe. First, because there were some conflicts in schedule, not all of Mr. Smith’s classes took the test on the same day. He didn’t want his classes that had one extra day to have an unfair advantage over those who didn’t, so Mr. Smith collected worksheets and other papers from his students who had an extra day. As a student, I know that studying the day before a test is one of the best times to review for a test. I can’t believe that a teacher would do anything to hinder a student who wanted to prepare more for a test.
The other thing that I couldn’t believe was that Mr. Smith said that if thought his students were struggling he would give them a harder test because they would learn better that way. Let me say that again, If Mr. Smith’s students are struggling to learn a concept, he will give them a harder test so they will learn more. This is contrary to everything that I believe about summative assessments. The end of chapter test is not the time that a teacher should be providing a learning opportunity; it is an opportunity for students to show how much they have learned. Also, from the student’s perspective, if I am struggling to learn the concepts from a chapter, receiving a difficult test and then failing that test won’t help me learn it. It will just strengthen my belief that “I can’t do math.” A belief that is already too common in our society.
It is no wonder that many of these students need private math tutors. My student’s mother believes that about half of Mr. Smith’s students have private math tutors helping them through his class. Remember, that this is a private school and these parents are already paying thousands of dollars out of their pocket for their child’s education.
If you are wondering why “Mr. Smith” has a job, it is probably because “Mr. Smith” isn’t “Mr. Smith,” it is “Dr. Smith” who has a Ph.D. from Harvard. I don’t know what it is in; my guess is Mathematics and not Education. The more I learn about this teacher and his pedagogy strengthens my belief that in our schools we need teachers who are teachers, and not content specialist. I like to think of myself as both, but I am first and foremost, I am a teacher.
My goodness! Your poor student. I can't believe it about the 1/7 vs. dividing by 7. How confusing!
ReplyDeleteI too feel for these students, who are experiencing a very different mathematics from the one I know and love.
ReplyDeleteI don't agree, however, with this distinction between "content specialist" and "teacher". I would argue that students, more than anything, need a "mathematics teacher" someone how knows a great deal about mathematics AND the learning and teaching of mathematics.
"Mr. Smith" is drawing a hard line for his students. I liked how you mentioned math beliefs... I just started a Master of Arts in Curriculum and Instruction with the emphasis in Math Ed. I am currently developing an Action Research Plan targeting student math anxiety in the middle schools. There is a survey called the Mathematics Anxiety-Apprehension Survey (MAAS) developed by T. Nelson Ikegulu. After finding a student that demonstrates anxiety I hope to use the late Albert Ellis' RET (Rational Emotive Therapy), which focuses on correcting irrational beliefs. I now realize that therapy may have to continue through the years, especially if a student has a teacher like "Mr. Smith."
ReplyDeleteThat is not a way to run a class. He seems to motivate through fear and not through encouragement. A teacher should inspire his/her students to be actively engaged in learning math. A big problem for struggling students is that they don't see the connections between different mathematical concepts. Math then becomes a subject where success is dependent upon memorizing facts or equations. In Dr. Smith's teaching he riquires students to preform a task a certain way. I would say he is limiting his student's growth. I believe that this seems to be a leading factor the disparaging scores that US math students earn on standardized tests such as the TIMSS and PISA as compared to their counter parts from different countries.
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