Does a math teacher really affect how students learn and if so does it affect future years of math learning?
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Sadly, YES. I believe more so in math than any other subject. The concept of answers being either right or wrong, is in itself a rather frightening concept - especially if you get a few wrong. I think students are most susceptible to teacher influence in the primary grades: those teachers set the tone for all future math learning in several ways. First, if the student does not learn the basic math facts well and develop a strong basic number sense their math future is greatly imperiled. Too many of today's students reach HS with poor arithmetic skills; they can't perform the four basic functions with whole numbers--never mind decimals, fraction and mixed numbers. This can be overcome, but worse, they arrive at HS with a strongly professed dislike and hatred of mathematics. They are convinced that they can't do math, never have and never will be able to. And I don't care how good a math teacher you are...it is very difficult to break through those two problems and lead a student to become reasonably proficient at math. It does not help that many elementary school teachers also hate math. I did an informal survey of several hundred pre-service elementary teachers asking them why they decided to go into elementary education instead of HS. Nearly every single one of them replied "Because I don't have to take any more math!" They did know that I was a math teacher, but it was their first response. Not a single one of them listed love of children at that age.
I also believe that they can. Math teacher, like every other teacher, each has his or her own way or method to teach math. Let us face it, math considered a challenging subject for most students. However, the teacher's role is to simplify and deliver math subjects for students so they could practice and implement mathematical problems.
Each math teacher has his own believes of what method might works when it comes to a certain subject. For me, for example, I usually starts by presenting the problem, then introduce the subject related to the problem. This way, I believe, students will make sense of the problem and realize the importance of the subject.
Of course they can. They don't always do so, and certain teachers may effect certain students and not others, but here is one example of how they might do so:
Much of my own experience with Math and much of what I've seen runs on the assumption that you learn the method, memorize it, and then you can "plug in" different numbers and still get the right answer.
I don't think this is a really effective way of doing it, if you consider the fact that it in some ways prevents students from focusing on the underlying concepts and a deeper knowledge of why we solve things certain ways.
But if a teacher were able to break out of that mold and do those things, I think they could really affect not only the student's math career in school but also their understanding of and appreciation for math as a discipline or way of looking at the world.
The previous posts were quite strong. I think that the question makes the assumption that math is unique in that teachers can inspire a love of learning within the discipline or also inspire an insurmountable amount of fear and dread regarding it. Certainly, this could be said of any discipline. Yet, I would say that given the penchant for precision and detail that is required in math, the notion that something is either "right" or "wrong, and that the numerous amount of theorems, steps, and procedures needed to successfully complete upper level math problems, a strong and connecting teacher is essential. I have always seen math as a realm where students can become lost so very easily, and to ensure that they are always sticking to the path of solutions, a good math teacher who not only understands content, but where student mistakes can happen is essential to future success in my mind. A teacher who can guide math students can help lay the groundwork for future success for math is a unique discipline where knowledge one year has a direct impact in the following years. For example, if a student "didn't get" the study of the U.S. Constitution, they can probably get it later on down the road. The 9th Amendment will speak of enumerated rights in middle school as well as high school. It won't change. Yet, if a student is lost in math early, it makes future learning difficult. For instance, if a student does not get the method of how to reduce fractions, work in pre-Algebra and Algebra becomes really tough. A good math teacher is one who can recognize the particular area of investigation and be able to prepare students for how this will play out later on down the road of math scholarship.
I can only answer this through experience - I was always a very good student - but math was difficult for me. The teachers who understood the subject so well that they could deviate from the book and teach the entire concept always managed to confuse me more. It was the teachers who went right with the book - showed several examples doing the same process over and over who best helped me understand.
That said - the one "by-the-book" math teacher I had as a freshman, in a fit of frustration with my friend one day asked, "Come on, why don't you get this? Are you just being stupid?" I was struggling with the exact same questions as the friend - and after that day I think I was just angry and too afraid to ask questions anymore... I sought help from my dad and smart kids in the class and worked really hard to make either a B or C.
The next year though (pre-calculus) I had one of those very cerebral teachers (he also taught college math) and he deviated from the book most of the time. Of course the guy wrote ALL his own tests. But I loved him. As a person, he was one of my favorite teachers. Somehow I not only did pretty well in pre-calculus, but Calculus as well... and he almost convinced me to pursue math education.
I certainly think every teacher has something to do with how well students learn. Knowledge of the subject is one key - but knowledge of the students is the other. Our attitudes are sometimes our biggest hindrance to understanding, and the teacher who can get around that and actually engage students (and maybe even get them to enjoy horrible scary subjects like math) is definitely doing something right.
As an English teacher, I guess it would be easy to argue that we have more influence on students than other subjects. However, for students who go on to pursue a math-related field later in life, their math teachers must certainly provide inspiration for future endeavors. I was influenced in a negative manner by several math teachers while in high school. One of them (who taught me for two years) was so incompetent that he had to refer to the math text for even the simplest of questions. He was very uneven in his temperament as well, and I ended up with poor grades and even poorer comprehension of the subject. I did have one fine teacher in high school, and my junior college math teacher was highly capable: I ended up with better grades in college than in high school.
In a selection board if you are to call for the applicants in a ratio 1:5 and you select 20 persons out 20*5 =100, you are a bad selector for 80 percent of the candidates who are not selected. Such is the situation of any teacher. The teacher is always a person to be blamed. Whether a maths teacher is good or bad , or whether a history or a language teacher is effective or not could not be generalised. Mostly maths teacher around the world is the bane of the of the students . But you can always find a pretty number of students for whom a language teacher is bad or a history teacher is bad or like that a maths teacher. There are thousand reasons why we are unable to generate a good teacher. A highly knowledgible erudite person in any subject need not be a good teacher. I do believe an ordinary person devoted to the profession of teaching a particular subject can also inspire his students.
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