Good Teaching, Bad Results

As a new teacher, one of the most difficult questions I am faced with is how to define or what characteristics a person must have to identify them as being a good teacher. Is it as Romberg and Carpenter suggest- that a good teacher is the one who has ten different ways to say the same thing, ensuring the students “get it” sooner or later? Is it the teacher who has zero discipline issues in his/her classroom, where students sit in parallel lines facing the front of the room, showing respect for the teacher as well as fellow classmates? Or is a good teacher defined by student success on standardized testing? My definition of a good teacher includes some degree of each of the previous attributes. As a student, I labelled teachers as good if they had the ability to make learning fun. Good teachers were those who were enthusiastic about the subject matter at hand, used a variety of teaching methods and in general altered the curriculum to be relevant to our leaning environments rather than altering us to suite the curriculum.

Unfortunately, throughout our province and certainly throughout our country, many define teachers by student performance on standardized tests (more particularly CRT’s and public exams in our province). If students do well, the teacher adequately delivered the curriculum, however if students perform poorly the teacher did not adequately cover material in the curriculum. The validity of this statement was reinforced by my principal in a recent conversation in which he said, “Jennifer, if you’re looking to transfer out of your current position, the first thing the principals and department heads of other schools are going to look at is how well your students performed on standardized assessments like CRT’s and public exams.” At first I was angered by his statement. In the case of the level three students, how could I, after teaching these students for only one year, be responsible for their performance on such assessments? With the jammed packed curriculum, how could I possibly be responsible for ensuring students understood and remembered basic concepts covered in grades 7-11? After the initial anger, I realized the key to student success was to first identify previous knowledge and misconceptions students had, followed by elimination of misconceptions and finally expansion on pre-existing knowledge.

One of the issues raised by Schoenfeld in his article, is that when solving mathematics problems, students have to follow the procedure, whether it makes sense to them or not. This was very prevalent in my educational experiences. My teachers were strong believers of the “practice makes perfect” theory. They would assign large quantities of questions all of which required little to no thought on the student part. The role of the student was simply to “plug” the numbers into the appropriate formula to obtain the correct answer. We were never challenged to think whether or not our answers made sense- it was assumed if you followed the correct procedure then the correct answer would be obtained. If we were given an exercise similar to that of the army bus, as described in Schoenfeld’s article, and obtained the wrong answer, my teachers would state that the problem was “tricky” in its wording or that students made a “silly mistake” by not reading the question carefully. It should be noted that a month and a half prior to CRT’s in grade 6 and 9, teachers would spend every math class reviewing old CRT’s to ensure students did not make the same “silly mistakes” as previous students had. Which leads me to often wonder if my teachers were some of the ones who think the curriculum is too jammed packed.

Schoenfeld’s third result: Students come to believe that all problems can be solved in just a few minutes, is a statement which I have heard numerous times throughout my educational experiences. In my previous teaching experience, I’ve had numerous students who, if they can’t solve a problem in a few minutes, give up, stating that the problem is too hard. Teachers play a large role in the creation and reinforcement of such student beliefs. As mentioned in the article, teachers (myself included) are guilty of assigning a large quantity of questions focused on small chunks of subject matter and to be completed in a short amount of time. If for some reason students still do not grasp the concept at hand, we simply assign more questions. This is true not only of in-class and home work material, but also of questions on many standardized assessments. The mathematics public exam to be completed at the end of level three consists of 50 selected response questions and 10-13 constructed response questions, all of which are to be completed in one three hour sitting. Advice given by fellow colleagues in preparation of students for standardized tests including CRT’s and public exams, is to “move on” to the next question if an answer to the current question is not obtained immediately. Thus reinforcing the belief that all math problems can be solved in just a few minutes. The same is true of in-class assessments in the form of unit tests, quizzes, mid-year examinations and pop quizzes. Students have to answer a set number of questions (usually a substantial quantity) of questions in a given time period, with little or no extra time given.

Schoenfeld’s fourth belief: Students view themselves as passive consumers of other’s mathematics, is an area in mathematics in which we are shifting the paradigm. In Math 3204, students are encouraged to complete investigations which develop the underlying concept in that particular topic/unit. Rather than having the teacher state the formula, students apply previous knowledge which in turn leads to the development of appropriate formulas, theorems, etc. This provides students with the notion that math really does make sense, and has more than one application. Such a process emphasizes the importance of making connections through math not merely on rote memorization.

Schoenfeld’s article discusses valid issues surrounding teaching and learning in our public school systems. As educators we need to move away from passive education, in which we expect students to simply memorize and apply formulas, towards active learning in which student engage in discussions and development of the mathematics.