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B. Goddard
B. Goddard
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I'm a retired university math prof and I now have a retirement job teaching at a small private high school. This is my 4th year. This school teaches Algebra 1 to 8th graders. Geometry to 9th graders. Algebra 2 to 10th graders. Precalculus to 11th graders. Calculus to 12th graders. I have come to the opinion that for many students, these subjects are coming a year too soon. I'm convinced that if we'd let most students get another year through or past puberty, and develop their ability to think abstractly more, then they'd have less trouble in math all through high school.

I found this study:

https://www.nber.org/papers/w21610

which tangentially supports my opinion.

My question is: Is there other research that more directly addresses when to teach the various subjects of middle school and high school math?

My observations are: I've listened to the middle school teachers complain that they can't teach Prealgebra to 7th graders because they can't add fractions. And the 5 and 6th grade teachers complain that they can't teach adding fractions because the students don't know the multiplication table. I used to complain that college freshmen who took Calculus in high school were usually worse off than the freshmen who hadn't. By taking Calculus in high school, many students seemed to be permanently warped in a way that made Calc 2 much more difficult. My suspicion is that by ever trying to cram more stuff in earlier, things get a lighter treatment. So that students are never quite prepared for the next class. And this effect snowballs.

I don't know how many times I had a sophomore in Differential Equations in my office who had never seen Pascal's triangle or had no idea how to factor a quadratic. Or he sort of knew how, but couldn't execute. I would complain, "I wish the high schools would teach the high school math solidly, so that I can teach Calculus to students who are ready." And I'm observing the same effect in this high school.

Here in Texas, they have the STARR test. It's a monster. By studying it, we can tell that they're having 5th graders do stem-and-leaf plots and find quartiles of date. Sure, they can do it, but it's just one more thing crammed into the curriculum that distracts from learning to add fractions. And these easy things, like finding quartiles, andcan be learned by a 10th grader in one day. Why are we torturing 5th graders with it for a week? A typical STARR test problem is to show a polygon in the shape of Utah, and assign lengths to some of the sides. These lengths are all mixed numeral. The student is supposed to find the area of the polygon. So first he has to add and subtract mixed numerals to find the lengths of the other sides. Then he has to multiply some of these to get the area. So this is a multistep problem testing more than one thing. Not only is more material being ever shoved into the lower grade curriculum, but also a higher expectation of problem solving skills. I don't think most 5th graders are ready for the Utah problem.

So my question is, again, does anyone know of real research that would support my opinion? (Or negate my opinion?)

I'm a retired university math prof and I now have a retirement job teaching at a small private high school. This is my 4th year. This school teaches Algebra 1 to 8th graders. Geometry to 9th graders. Algebra 2 to 10th graders. Precalculus to 11th graders. Calculus to 12th graders. I have come to the opinion that for many students, these subjects are coming a year too soon. I'm convinced that if we'd let most students get another year through or past puberty, and develop their ability to think abstractly more, then they'd have less trouble in math all through high school.

I found this study:

https://www.nber.org/papers/w21610

which tangentially supports my opinion.

My question is: Is there other research that more directly addresses when to teach the various subjects of middle school and high school math?

My observations are: I've listened to the middle school teachers complain that they can't teach Prealgebra to 7th graders because they can't add fractions. And the 5 and 6th grade teachers complain that they can't teach adding fractions because the students don't know the multiplication table. I used to complain that college freshmen who took Calculus in high school were usually worse off than the freshmen who hadn't. By taking Calculus in high school, many students seemed to be permanently warped in a way that made Calc 2 much more difficult. My suspicion is that by ever trying to cram more stuff in earlier, things get a lighter treatment. So that students are never quite prepared for the next class. And this effect snowballs.

I don't know how many times I had a sophomore in Differential Equations in my office who had never seen Pascal's triangle or had no idea how to factor a quadratic. Or he sort of knew how, but couldn't execute. I would complain, "I wish the high schools would teach the high school math solidly, so that I can teach Calculus to students who are ready." And I'm observing the same effect in this high school.

Here in Texas, they have the STARR test. It's a monster. By studying it, we can tell that they're having 5th graders do stem-and-leaf plots and find quartiles of date. Sure, they can do it, but it's just one more thing crammed into the curriculum that distracts from learning to add fractions. And these easy things, like finding quartiles, and be learned by a 10th grader in one day. Why are we torturing 5th graders with it for a week? A typical STARR test problem is to show a polygon in the shape of Utah, and assign lengths to some of the sides. These lengths are all mixed numeral. The student is supposed to find the area of the polygon. So first he has to add and subtract mixed numerals to find the lengths of the other sides. Then he has to multiply some of these to get the area. So this is a multistep problem testing more than one thing. Not only is more material being ever shoved into the lower grade curriculum, but also a higher expectation of problem solving skills. I don't think most 5th graders are ready for the Utah problem.

So my question is, again, does anyone know of real research that would support my opinion? (Or negate my opinion?)

I'm a retired university math prof and I now have a retirement job teaching at a small private high school. This is my 4th year. This school teaches Algebra 1 to 8th graders. Geometry to 9th graders. Algebra 2 to 10th graders. Precalculus to 11th graders. Calculus to 12th graders. I have come to the opinion that for many students, these subjects are coming a year too soon. I'm convinced that if we'd let most students get another year through or past puberty, and develop their ability to think abstractly more, then they'd have less trouble in math all through high school.

I found this study:

https://www.nber.org/papers/w21610

which tangentially supports my opinion.

My question is: Is there other research that more directly addresses when to teach the various subjects of middle school and high school math?

My observations are: I've listened to the middle school teachers complain that they can't teach Prealgebra to 7th graders because they can't add fractions. And the 5 and 6th grade teachers complain that they can't teach adding fractions because the students don't know the multiplication table. I used to complain that college freshmen who took Calculus in high school were usually worse off than the freshmen who hadn't. By taking Calculus in high school, many students seemed to be permanently warped in a way that made Calc 2 much more difficult. My suspicion is that by ever trying to cram more stuff in earlier, things get a lighter treatment. So that students are never quite prepared for the next class. And this effect snowballs.

I don't know how many times I had a sophomore in Differential Equations in my office who had never seen Pascal's triangle or had no idea how to factor a quadratic. Or he sort of knew how, but couldn't execute. I would complain, "I wish the high schools would teach the high school math solidly, so that I can teach Calculus to students who are ready." And I'm observing the same effect in this high school.

Here in Texas, they have the STARR test. It's a monster. By studying it, we can tell that they're having 5th graders do stem-and-leaf plots and find quartiles of date. Sure, they can do it, but it's just one more thing crammed into the curriculum that distracts from learning to add fractions. And these easy things, like finding quartiles, can be learned by a 10th grader in one day. Why are we torturing 5th graders with it for a week? A typical STARR test problem is to show a polygon in the shape of Utah, and assign lengths to some of the sides. These lengths are all mixed numeral. The student is supposed to find the area of the polygon. So first he has to add and subtract mixed numerals to find the lengths of the other sides. Then he has to multiply some of these to get the area. So this is a multistep problem testing more than one thing. Not only is more material being ever shoved into the lower grade curriculum, but also a higher expectation of problem solving skills. I don't think most 5th graders are ready for the Utah problem.

So my question is, again, does anyone know of real research that would support my opinion? (Or negate my opinion?)

Source Link
B. Goddard
B. Goddard
  • 491
  • 3
  • 9

Teaching math too soon in middle school and high school

I'm a retired university math prof and I now have a retirement job teaching at a small private high school. This is my 4th year. This school teaches Algebra 1 to 8th graders. Geometry to 9th graders. Algebra 2 to 10th graders. Precalculus to 11th graders. Calculus to 12th graders. I have come to the opinion that for many students, these subjects are coming a year too soon. I'm convinced that if we'd let most students get another year through or past puberty, and develop their ability to think abstractly more, then they'd have less trouble in math all through high school.

I found this study:

https://www.nber.org/papers/w21610

which tangentially supports my opinion.

My question is: Is there other research that more directly addresses when to teach the various subjects of middle school and high school math?

My observations are: I've listened to the middle school teachers complain that they can't teach Prealgebra to 7th graders because they can't add fractions. And the 5 and 6th grade teachers complain that they can't teach adding fractions because the students don't know the multiplication table. I used to complain that college freshmen who took Calculus in high school were usually worse off than the freshmen who hadn't. By taking Calculus in high school, many students seemed to be permanently warped in a way that made Calc 2 much more difficult. My suspicion is that by ever trying to cram more stuff in earlier, things get a lighter treatment. So that students are never quite prepared for the next class. And this effect snowballs.

I don't know how many times I had a sophomore in Differential Equations in my office who had never seen Pascal's triangle or had no idea how to factor a quadratic. Or he sort of knew how, but couldn't execute. I would complain, "I wish the high schools would teach the high school math solidly, so that I can teach Calculus to students who are ready." And I'm observing the same effect in this high school.

Here in Texas, they have the STARR test. It's a monster. By studying it, we can tell that they're having 5th graders do stem-and-leaf plots and find quartiles of date. Sure, they can do it, but it's just one more thing crammed into the curriculum that distracts from learning to add fractions. And these easy things, like finding quartiles, and be learned by a 10th grader in one day. Why are we torturing 5th graders with it for a week? A typical STARR test problem is to show a polygon in the shape of Utah, and assign lengths to some of the sides. These lengths are all mixed numeral. The student is supposed to find the area of the polygon. So first he has to add and subtract mixed numerals to find the lengths of the other sides. Then he has to multiply some of these to get the area. So this is a multistep problem testing more than one thing. Not only is more material being ever shoved into the lower grade curriculum, but also a higher expectation of problem solving skills. I don't think most 5th graders are ready for the Utah problem.

So my question is, again, does anyone know of real research that would support my opinion? (Or negate my opinion?)