I have made the argument that a classroom focused on the teaching of basic skills is missing an opportunity to actually teach a child something meaningful. It might sound strange for someone in education to refrain from teaching basic skills. It is a bit misleading.
Teaching children to read and write, add and subtract are absolutely necessary to an education. No one would argue that. However, the approach one takes to teach these things are what are being bantered about. It is all about the teacher’s philosophy of education.
When a teacher walks to the front of the class and demonstrates the algorithm for adding numbers together (carry the one and all that jazz) then expects students to simply mimic what is being written on the dry erase board, then learning has stopped. Students are not increasing their capacity for learning. They are simply memorizing a meaningless algorithm in order to complete a worksheet and get a passing grade.
However, the good teacher presents information to students in a more meaningful way, before every working on any kind of algorithm. What does it mean to add, subtract, multiply or divide? What does that look like and how do we conceive that in our eye? This can be done through manipulatives – hands-on activities that facilitate learning. Students do not sit and watch the teacher and then do what he does.
Maybe the teacher is working on fractions. Each cooperative learning group of four students has two measuring cups. One measuring cup has one-half cup of oats. The other measuring cup has one-fourth cup of oats. First the students put them together and learn that one-half add one-fourth equals three-fourths cups of oats. Next the students separate the oats again and the teacher guides them in understanding how one-half add one-four equals three-fourths. All of this is done without writing down the tradition fraction addition algorithm.
The purpose is not for the student to learn to reproduce an algorithm, but to understand how fractions work. This requires a lot of up front work on the part of the teacher, but it leads to life-long learning on the part of the student.
Last night I was tutoring a neighborhood child in fifth grade. She had to do some multiplication (2,564x5 and 45x32). This fifth grader could not remember the algorithm on how to multiply numbers.
45
x32
----
5x2 = 10, so you put down the zero and carry the 1. She could not do it. She remembered doing it last year, but over the summer she had forgotten it. This is why we teach and re-teach the same material year after year after year. She had no conception of what multiplication was or how it is applied. If there is no conceptual understanding, then the algorithm is meaningless and forgettable. By the way, there are other multiplication algorithms that make more conceptual sense than the traditional carry-the-one approach.
You split the multiplication into its parts, making it easier and more conceptual. I’ll try to show you how it works.
2x5 (=10)
2x40 (=80)
30x5 (=150)
30x40 (=1200)
Then you add 1,200+15+80+10 = 1,440. Now for those of us who learned the traditional algorithm, this seems confusing. However, if you start with this algorithm, it makes more sense when combining it with the conceptual approach. In this case, the goal is not the algorithm or the right answer, but it is the idea of what multiplication is that drives the lesson. The rest of it, the algorithm and right answer will come after the conceptual lesson has been taught.
I remember days of sitting and completing math worksheets until my brain ached. Math = memorizing the times tables and accompanying algorithm. That is still true in many of today’s classrooms, and Every Child Left Behind is only exacerbating the problem. Why do worksheets when there are many other more affective activities that can be used? In part, it is because teachers want to teach the way they were taught, regardless of how effective that approach is. The path of least resistance is human nature. A classroom of worksheets gives the teacher more time for other things like grading papers. The philosophy is teacher-centered, rather than student-centered. It seems to me that a classroom should be designed for the students rather than the teacher. Go tell that to my college professors.
Teaching children to read and write, add and subtract are absolutely necessary to an education. No one would argue that. However, the approach one takes to teach these things are what are being bantered about. It is all about the teacher’s philosophy of education.
When a teacher walks to the front of the class and demonstrates the algorithm for adding numbers together (carry the one and all that jazz) then expects students to simply mimic what is being written on the dry erase board, then learning has stopped. Students are not increasing their capacity for learning. They are simply memorizing a meaningless algorithm in order to complete a worksheet and get a passing grade.
However, the good teacher presents information to students in a more meaningful way, before every working on any kind of algorithm. What does it mean to add, subtract, multiply or divide? What does that look like and how do we conceive that in our eye? This can be done through manipulatives – hands-on activities that facilitate learning. Students do not sit and watch the teacher and then do what he does.
Maybe the teacher is working on fractions. Each cooperative learning group of four students has two measuring cups. One measuring cup has one-half cup of oats. The other measuring cup has one-fourth cup of oats. First the students put them together and learn that one-half add one-fourth equals three-fourths cups of oats. Next the students separate the oats again and the teacher guides them in understanding how one-half add one-four equals three-fourths. All of this is done without writing down the tradition fraction addition algorithm.
The purpose is not for the student to learn to reproduce an algorithm, but to understand how fractions work. This requires a lot of up front work on the part of the teacher, but it leads to life-long learning on the part of the student.
Last night I was tutoring a neighborhood child in fifth grade. She had to do some multiplication (2,564x5 and 45x32). This fifth grader could not remember the algorithm on how to multiply numbers.
45
x32
----
5x2 = 10, so you put down the zero and carry the 1. She could not do it. She remembered doing it last year, but over the summer she had forgotten it. This is why we teach and re-teach the same material year after year after year. She had no conception of what multiplication was or how it is applied. If there is no conceptual understanding, then the algorithm is meaningless and forgettable. By the way, there are other multiplication algorithms that make more conceptual sense than the traditional carry-the-one approach.
You split the multiplication into its parts, making it easier and more conceptual. I’ll try to show you how it works.
2x5 (=10)
2x40 (=80)
30x5 (=150)
30x40 (=1200)
Then you add 1,200+15+80+10 = 1,440. Now for those of us who learned the traditional algorithm, this seems confusing. However, if you start with this algorithm, it makes more sense when combining it with the conceptual approach. In this case, the goal is not the algorithm or the right answer, but it is the idea of what multiplication is that drives the lesson. The rest of it, the algorithm and right answer will come after the conceptual lesson has been taught.
I remember days of sitting and completing math worksheets until my brain ached. Math = memorizing the times tables and accompanying algorithm. That is still true in many of today’s classrooms, and Every Child Left Behind is only exacerbating the problem. Why do worksheets when there are many other more affective activities that can be used? In part, it is because teachers want to teach the way they were taught, regardless of how effective that approach is. The path of least resistance is human nature. A classroom of worksheets gives the teacher more time for other things like grading papers. The philosophy is teacher-centered, rather than student-centered. It seems to me that a classroom should be designed for the students rather than the teacher. Go tell that to my college professors.
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1 comment:
Jack, had you taught my diffy-q class... I just might have made something other than an average grade.
And you speak English... which helps, too.
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