In Skemp’s article, he defines the differences between instrumental understanding and relational understanding, and provides several examples to demonstrate the differences, which makes the readers easier to understand the concepts. He shows he believes relational understanding is better, yet he tries to understand why others use instrumental understanding. This shows he is reflective.
According to Skemp’s article, he says “there are two kinds of mathematical mis-matches which can occur.”(4) This is such a good point I never really thought about before. After I give it some thoughts, I believe it is inevitable, and a way to reduce this is to use both instrumental and relational understanding when teaching. This leads to how often and when to use which. For the concept of relational understanding is not too complex, teach relational first. After a while, teach instrumental for students who could not understand relational, so they would not feel they are beyond and still get a sense of confident. For instance, the concept of area that we can teach how to find the area of triangles, trapezoids, etc. relational first, and then instrumentally tell students those really convenient formulas for area. By doing this, we can satisfy both group of students. And this gets more elaborate when he says “I used to think that maths teachers were all teaching the same subject, some doing it better than others. I now believe that there are two effectively different subjects being taught under the same name, ‘mathematics’.”(6) A good teacher is flexible. People often agree that relational is better, but what if a teacher teach relational all the time, but none or seldom of his students can understand it. This would just make things worse. A good teacher will teach either relational or instrumental understanding or both depending on the students he has. Skemps also mentions that relational “is easier to remember.”(9) I agree, but not always. I have some rules I learned in elementary, and I still remember them now; those rules just stick in my mind. I agree that Skemps says “relational understanding of a particular topic is too difficult,”(11) and students just could not understand them at that stage. Relational understanding might just scared them away, and they would feel overwhelming and start to dislike math. He also mentions “a junior teacher in a school where all the other mathematics teaching is instrumental.”(11) This back to beginning where a good teacher should be responsible and know what is suitable for his students, relational or instrumental, since every teacher has different kinds of students every class, every term, and every year.
According to Skemp’s article, he says “there are two kinds of mathematical mis-matches which can occur.”(4) This is such a good point I never really thought about before. After I give it some thoughts, I believe it is inevitable, and a way to reduce this is to use both instrumental and relational understanding when teaching. This leads to how often and when to use which. For the concept of relational understanding is not too complex, teach relational first. After a while, teach instrumental for students who could not understand relational, so they would not feel they are beyond and still get a sense of confident. For instance, the concept of area that we can teach how to find the area of triangles, trapezoids, etc. relational first, and then instrumentally tell students those really convenient formulas for area. By doing this, we can satisfy both group of students. And this gets more elaborate when he says “I used to think that maths teachers were all teaching the same subject, some doing it better than others. I now believe that there are two effectively different subjects being taught under the same name, ‘mathematics’.”(6) A good teacher is flexible. People often agree that relational is better, but what if a teacher teach relational all the time, but none or seldom of his students can understand it. This would just make things worse. A good teacher will teach either relational or instrumental understanding or both depending on the students he has. Skemps also mentions that relational “is easier to remember.”(9) I agree, but not always. I have some rules I learned in elementary, and I still remember them now; those rules just stick in my mind. I agree that Skemps says “relational understanding of a particular topic is too difficult,”(11) and students just could not understand them at that stage. Relational understanding might just scared them away, and they would feel overwhelming and start to dislike math. He also mentions “a junior teacher in a school where all the other mathematics teaching is instrumental.”(11) This back to beginning where a good teacher should be responsible and know what is suitable for his students, relational or instrumental, since every teacher has different kinds of students every class, every term, and every year.
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