Intro | 1 | 2 | 3 | 4
The cost would simply be too high. I realize that we need to invest on education to ensure a safe productive future. But let's put all the considerations in the previous posts aside and just look at the mathematics alone.
Here is a simple model based on school districts in my area (every year they send out newsletters outlining the budget): if we assume that the school day will be 8.5 hours per day and that there will be 200 days per year, we are asking for a ~40% increase in school time (1200 to 1700 hours). Thus teachers will have to be paid 40% more at least. As staff salaries make up as much as 60% of district budgets, the overall budget will have to increase at least 24% [.6(1.40)+.4 = 1.24] on raising instructional pay (which is necessary or else we will surely see strikes*). Enriched curricula and more programs would require more money but they are hard to model and so will be ignored here. Where does that 24% come from? Well, remember when you hated writing that check for your school tax bill? Voila the government's solution. I doubt many people would be thrilled to see their tax go up 24% or more. It doesn't matter whether the program operates on a local, state, or federal level, because in the end, the burden of generating the extra revenue will be on our shoulders.
There is one solution, though, that won't increase taxes too much. The US could practice more deficit spending, therefore increasing our debt even more. However, do we really want to increase a 14-figure debt? Keep in mind that we pay billions out of our budget just for the interest that accrues from the debt; that amount is several times higher than the entire budget for education. Moreover, can we really afford such a giant venture in a recession like this? Our economic situation demands increases in efficiency, not quantity.
For these many reasons that I've outlined for the past week, I'm convinced that a longer school day will not benefit us at all. Our culture has been built upon a 6.5 hour day, and trying to change this lifestyle will prove to be impossible.
Besides, I think that the reason for our less-than-stellar performances in test scores is more due to other reasons, primarily the long summer break and lack of motivation.
In a future post, I'll advocate the case for a modified school year.
*these strikes would be justifiable; teachers already paid quite low as it is, and increasing hours while holding pay steady would only decrease their hourly income.
Saturday, October 3, 2009
Friday, October 2, 2009
Percentages
Percent signs are everywhere in our lives. However, a lot of people are not very proficient with using them, and the next post will require some knowledge of percentages. If you already know these concepts, please feel free to skip this entirely; the next post will come out early tomorrow.
"Percent" means "out of 100". So "40 percent" means "40 out of 100". "40 percent of teenagers have had alcohol" indicates that 40 out of every 100 teenagers have had alcohol.
Mathematically, the idea is also pretty straightforward. What does "40% of a number" mean? Let this number be n. We want only 40 parts of it out of every 100. This is written as
. In decimals, it is .40n.
So, to write a percent as a decimal take the number before the percent sign and move the decimal point to the left by two places.
Examples: What is 25% of 80? 25 = 25. -> .25, .25(80) = 20.
What is 450% of 25? 4.50(25) = 11.25.
More confusing, however, is percent increase or decrease. Taxes and discounts all utilize this concept, so it is good to have a basic idea of how it works.
Say we have a 8% tax on a item worth $50. This is an 8% increase on the price. To find the final price, we take 8% of 50 and add it on to the 50 (in other words, take the 50 and add 8% of itself). This gives 50 + .08(50) = 54.
However, there is a shortcut. If we can see the above equation as 50(1) + 50(.08), then the final price is 50(1 + .08) = 50(1.08) = 54 by the distributive property. So an x% increase causes a number to be multiplied by 1+(x/100), since x% means x/100 (in other words, x parts of 100).
Percent decrease is similar. We'll look at a 20% discount off of $80. Take 20% of the 80, and subtract from the original 80. We have 80 - .20(80) = 64.
Like above, we can write 80(1)-80 (.20) = 80(1-.20) = 80(.80) = 64.
Decreasing a number by x% means multiplying it by 1-(x/100).
This simplifies percentages a lot, hopefully.
Practice, answers below: 1. Find 25% of 34, 60% of 70, and 200% of 33.
2. 64 increased by 30% is?
3. 75 increased by 20% gives?
4. 90 decreased by 30% gives?
5. 140 decreased by 70% is?
6. 40 increased by 400% is?
7. An item is discounted 10%, and there is a 10% sales tax. Do you pay more, less, or the same as the listed price?
********************
Answers:
1. .25(34) = 8.5; .60(70) = 42; 2.00(33) = 66.
2. 64(1+.30) = 64(1.30) = 83.2
3. 75(1.20) = 90
4. 90(1-.30) = 90(.70) = 63.
5. 140(1-.70) = 140(.30) = 42.
6. 40(1+4.00) = 40(5) = 200.
7. Original price = x.
Discounted 10% = .90x
Increase 10% for tax: (.90x)(1.10) = .99x,
which is less than the original price by 1%!! The common answer is that it will go back to the original price; as you can see, math proves that wrong.
"Percent" means "out of 100". So "40 percent" means "40 out of 100". "40 percent of teenagers have had alcohol" indicates that 40 out of every 100 teenagers have had alcohol.
Mathematically, the idea is also pretty straightforward. What does "40% of a number" mean? Let this number be n. We want only 40 parts of it out of every 100. This is written as
. In decimals, it is .40n.So, to write a percent as a decimal take the number before the percent sign and move the decimal point to the left by two places.
Examples: What is 25% of 80? 25 = 25. -> .25, .25(80) = 20.
What is 450% of 25? 4.50(25) = 11.25.
More confusing, however, is percent increase or decrease. Taxes and discounts all utilize this concept, so it is good to have a basic idea of how it works.
Say we have a 8% tax on a item worth $50. This is an 8% increase on the price. To find the final price, we take 8% of 50 and add it on to the 50 (in other words, take the 50 and add 8% of itself). This gives 50 + .08(50) = 54.
However, there is a shortcut. If we can see the above equation as 50(1) + 50(.08), then the final price is 50(1 + .08) = 50(1.08) = 54 by the distributive property. So an x% increase causes a number to be multiplied by 1+(x/100), since x% means x/100 (in other words, x parts of 100).
Percent decrease is similar. We'll look at a 20% discount off of $80. Take 20% of the 80, and subtract from the original 80. We have 80 - .20(80) = 64.
Like above, we can write 80(1)-80 (.20) = 80(1-.20) = 80(.80) = 64.
Decreasing a number by x% means multiplying it by 1-(x/100).
This simplifies percentages a lot, hopefully.
Practice, answers below: 1. Find 25% of 34, 60% of 70, and 200% of 33.
2. 64 increased by 30% is?
3. 75 increased by 20% gives?
4. 90 decreased by 30% gives?
5. 140 decreased by 70% is?
6. 40 increased by 400% is?
7. An item is discounted 10%, and there is a 10% sales tax. Do you pay more, less, or the same as the listed price?
********************
Answers:
1. .25(34) = 8.5; .60(70) = 42; 2.00(33) = 66.
2. 64(1+.30) = 64(1.30) = 83.2
3. 75(1.20) = 90
4. 90(1-.30) = 90(.70) = 63.
5. 140(1-.70) = 140(.30) = 42.
6. 40(1+4.00) = 40(5) = 200.
7. Original price = x.
Discounted 10% = .90x
Increase 10% for tax: (.90x)(1.10) = .99x,
which is less than the original price by 1%!! The common answer is that it will go back to the original price; as you can see, math proves that wrong.
Thursday, October 1, 2009
Longer School Day? NO - the issue of gifted students
Intro | 1 | 2 | 3 | 4
The strongest students will be hurt by longer days. Let's face it. The top 1% learn almost nothing in school. Bright students could ace the AP exams by just reading the review book. Instead, they spend time outside of class to further develop their academic interests. This is particularly prevalent in math, where numerous competitions stimulate many students' interest in non-routine math problems. Their popularity is shown in the growth of sites such as the Art of Problem Solving Forums, where students discuss these difficult problems. This is very beneficial - the problems foster creativity, problem solving, and interest in math. While the third result is slightly narrow, the first two are applicable in all disciplines.
Why should we be wasting more of these gifted students' time in school? They will continue to learn nothing if they are put with peers of lower ability. Public schools usually don't have enough resources to open up honors classes that challenge everyone, so their time in school will be instruction well below their intellectual ability.
Most Nobel Prize winners in the sciences are US-born citizens, and yet we seem to have one of the weakest education systems in the world. Why? One good guess is that these students develop creativity at a very young age because of our less rigid system, and while it may not have shown when they were high school students, their cultivated ability to think from different perspectives stimulated their new discoveries down the road.
Many argue that the extended-day system will help the majority of students, and therefore it will be beneficial overall. I would like to take a radical position on this. Our scientific and technological progress occurs primarily through these extremely bright and motivated individuals who go well beyond the standard curriculum. If we were to restrict their growth, we are compromising the growth of our future. In other words, a more intelligent body of students (overall) will keep our society running more smoothly and more efficiently, but allowing the smartest of them all to flourish the most will have our society moving forward. I realize that this is a little on the elitist side but I can't deny its truth; we have here something like "reaganomics" for education.
The strongest students will be hurt by longer days. Let's face it. The top 1% learn almost nothing in school. Bright students could ace the AP exams by just reading the review book. Instead, they spend time outside of class to further develop their academic interests. This is particularly prevalent in math, where numerous competitions stimulate many students' interest in non-routine math problems. Their popularity is shown in the growth of sites such as the Art of Problem Solving Forums, where students discuss these difficult problems. This is very beneficial - the problems foster creativity, problem solving, and interest in math. While the third result is slightly narrow, the first two are applicable in all disciplines.
Why should we be wasting more of these gifted students' time in school? They will continue to learn nothing if they are put with peers of lower ability. Public schools usually don't have enough resources to open up honors classes that challenge everyone, so their time in school will be instruction well below their intellectual ability.
Most Nobel Prize winners in the sciences are US-born citizens, and yet we seem to have one of the weakest education systems in the world. Why? One good guess is that these students develop creativity at a very young age because of our less rigid system, and while it may not have shown when they were high school students, their cultivated ability to think from different perspectives stimulated their new discoveries down the road.
Many argue that the extended-day system will help the majority of students, and therefore it will be beneficial overall. I would like to take a radical position on this. Our scientific and technological progress occurs primarily through these extremely bright and motivated individuals who go well beyond the standard curriculum. If we were to restrict their growth, we are compromising the growth of our future. In other words, a more intelligent body of students (overall) will keep our society running more smoothly and more efficiently, but allowing the smartest of them all to flourish the most will have our society moving forward. I realize that this is a little on the elitist side but I can't deny its truth; we have here something like "reaganomics" for education.
Wednesday, September 30, 2009
Longer School Day? NO - the homework perspective
Intro | 1 | 2 | 3 | 4
Continued, from the previous post:
The amount of time spent on homework or independent-studying would have to be reduced. If we simply leave all the learning to be done in class, we are wasting a huge amount of resources. Some students need their own time to interpret and understand the subject material; they will also be better prepared for college work if they learn to study more independently in high school. Also, in total honesty, high school classes are not much better in presenting material than college lectures. The only difference is that secondary school educators have a teaching certificate, but teaching is more of an ability than a trained task.
Most of you may remember sleeping in lectures and reading all the notes afterward. In any case, no one learns by only listening to the teacher for an hour a day. This is where homework and studying comes in. We do not want the extra time in classes to be spent on doing homework. In some other countries this is the case, but I believe that this is an incredibly large sum to be paid on a "study-hall". The time should instead focus on enriching the material or covering more subject matter.
However, homework cannot be substantially reduced (I scoff at anyone who tries to conceive of ideas to eliminate all homework), or else the students may lose all the additional instruction, thereby rendering the increased time absolutely worthless. As I said, no one learns so well in class that he or she would not need to think about the subject at home. But if we increase the school day without reducing the homework significantly, we are only raising the academic burden on the kids. Synthesize this problem with the issue of extracurricular activities mentioned in the previous post and the infeasibility of the longer school day for busier students is evident.
Continued, from the previous post:
The amount of time spent on homework or independent-studying would have to be reduced. If we simply leave all the learning to be done in class, we are wasting a huge amount of resources. Some students need their own time to interpret and understand the subject material; they will also be better prepared for college work if they learn to study more independently in high school. Also, in total honesty, high school classes are not much better in presenting material than college lectures. The only difference is that secondary school educators have a teaching certificate, but teaching is more of an ability than a trained task.
Most of you may remember sleeping in lectures and reading all the notes afterward. In any case, no one learns by only listening to the teacher for an hour a day. This is where homework and studying comes in. We do not want the extra time in classes to be spent on doing homework. In some other countries this is the case, but I believe that this is an incredibly large sum to be paid on a "study-hall". The time should instead focus on enriching the material or covering more subject matter.
However, homework cannot be substantially reduced (I scoff at anyone who tries to conceive of ideas to eliminate all homework), or else the students may lose all the additional instruction, thereby rendering the increased time absolutely worthless. As I said, no one learns so well in class that he or she would not need to think about the subject at home. But if we increase the school day without reducing the homework significantly, we are only raising the academic burden on the kids. Synthesize this problem with the issue of extracurricular activities mentioned in the previous post and the infeasibility of the longer school day for busier students is evident.
Tuesday, September 29, 2009
Longer School Day? NO - Extracurricular perspective
Intro | 1 | 2 | 3 | 4
Before I proceed with this rather long post, let me emphasize that I am against a longer school day, not necessarily a longer year. I will elaborate more on the school year a little later. First I'll focus on the "extracurricular" consequences of a longer day.
After-school activities will become impossible. We have such a strong culture of clubs and sports that the few hours of after-school time has become indispensable. The article mentioned that a Massachusetts program would lengthen the day to about 9 hours. If that were the case for the entire nation, then in most places school would be from 8:30 am - 5:30 pm. The students would come home at around 6:00 pm and have dinner. This seems like a good schedule because the kids' schedule would align with the parents'. An after-school program, however, would run until 7:00 pm (usually they are slightly over an hour long), which would make the scheduling much harder for many households. Dinner would have to be delayed past 7:30 pm and beyond, which is a great inconvenience. The longer day is only really feasible for elementary students, who don't often participate in after school activities anyway.
While the above case can be alleviated partially by incorporating the programs into the school day (which is not a very economically wise because it could have been done under the current system for much less money), it does not solve the problem with varsity sports. Where I live the practices are around 2-3 hours long. The training would have to start after dinner, which would be about 7:00 pm. Thus the program would end as late as 10 pm, which is ridiculous for students who have homework to do. Athletes would almost be punished for wishing to pursue the sports they want.
Extracurricular activities would ultimately have to be cut for many students. The US emphasizes these other hobbies for children more than any other country. Part of this trend stems from the college admissions process - all applicants are evaluated heavily on their involvement in non-academic activities. On the other hand, in most other countries (including the UK), the admissions are based mostly on test scores and GPA; extracurriculars are the toppings rather than the cheese.
If a lot more time were spent in school, then a student can pursue at most one of his interests. A serious instrument player or athlete will know that at least 10 hours per week of work is usually required, which translates to about 1.5 hours per day. It is inconceivable that after finishing dinner at 7 pm, a student will have the willpower to practice both the flute and hockey until well after 10 pm, especially when he or she knows that homework and another school day are waiting ahead of him.
Personally, I am involved in swimming and piano. I have spent a lot of time in both and have seen the rewards of my investment. When I did both in high school, my schedule looked like:
8:00am - 2:45pm - School
3:00pm - 5:30pm - Swim practice
5:30pm - 7:00pm - Shower, get home, dinner
7:00pm - 8:30pm - Play piano
8:30pm - 10:30pm - homework and free time
10:30pm - sleep
If you added in another two and a half hours of school, I would have to sleep at 1am, which is unreasonable. And in all this, where is the time to socialize? Some people have work or do extensive amounts of volunteering; they will find it unfeasible to balance their outside interests and their school work. Yet, such a comprehensive network of extracurricular opportunities is the strength of our flexible education system. It would be doing these students a disservice if their interests were occupied instead by more school.
Before I proceed with this rather long post, let me emphasize that I am against a longer school day, not necessarily a longer year. I will elaborate more on the school year a little later. First I'll focus on the "extracurricular" consequences of a longer day.
After-school activities will become impossible. We have such a strong culture of clubs and sports that the few hours of after-school time has become indispensable. The article mentioned that a Massachusetts program would lengthen the day to about 9 hours. If that were the case for the entire nation, then in most places school would be from 8:30 am - 5:30 pm. The students would come home at around 6:00 pm and have dinner. This seems like a good schedule because the kids' schedule would align with the parents'. An after-school program, however, would run until 7:00 pm (usually they are slightly over an hour long), which would make the scheduling much harder for many households. Dinner would have to be delayed past 7:30 pm and beyond, which is a great inconvenience. The longer day is only really feasible for elementary students, who don't often participate in after school activities anyway.
While the above case can be alleviated partially by incorporating the programs into the school day (which is not a very economically wise because it could have been done under the current system for much less money), it does not solve the problem with varsity sports. Where I live the practices are around 2-3 hours long. The training would have to start after dinner, which would be about 7:00 pm. Thus the program would end as late as 10 pm, which is ridiculous for students who have homework to do. Athletes would almost be punished for wishing to pursue the sports they want.
Extracurricular activities would ultimately have to be cut for many students. The US emphasizes these other hobbies for children more than any other country. Part of this trend stems from the college admissions process - all applicants are evaluated heavily on their involvement in non-academic activities. On the other hand, in most other countries (including the UK), the admissions are based mostly on test scores and GPA; extracurriculars are the toppings rather than the cheese.
If a lot more time were spent in school, then a student can pursue at most one of his interests. A serious instrument player or athlete will know that at least 10 hours per week of work is usually required, which translates to about 1.5 hours per day. It is inconceivable that after finishing dinner at 7 pm, a student will have the willpower to practice both the flute and hockey until well after 10 pm, especially when he or she knows that homework and another school day are waiting ahead of him.
Personally, I am involved in swimming and piano. I have spent a lot of time in both and have seen the rewards of my investment. When I did both in high school, my schedule looked like:
8:00am - 2:45pm - School
3:00pm - 5:30pm - Swim practice
5:30pm - 7:00pm - Shower, get home, dinner
7:00pm - 8:30pm - Play piano
8:30pm - 10:30pm - homework and free time
10:30pm - sleep
If you added in another two and a half hours of school, I would have to sleep at 1am, which is unreasonable. And in all this, where is the time to socialize? Some people have work or do extensive amounts of volunteering; they will find it unfeasible to balance their outside interests and their school work. Yet, such a comprehensive network of extracurricular opportunities is the strength of our flexible education system. It would be doing these students a disservice if their interests were occupied instead by more school.
Monday, September 28, 2009
Longer School Day? NO - Introduction
Recently this article on Obama's education plan has caught my attention. While the plan will not affect me at all, I still do not support a longer school day for a variety of reasons.
My reasons lie in four main categories:
1. extracurricular activities
2. homework and independent study
3. crème-de-la-crème students
4. higher costs
I will discuss each separately over the next week, and will add links to each item in the list above to the appropriate post.
Overall, I believe that the longer day will fail because it simply does not conform with the current American system of education. In order to be successful, we would have to accommodate this new plan in small increments of reform. However, a rapidly developing society demands quick changes and immediate responses. A slow process of change may make no difference at all for over 15 years, while costing us millions every day.
My reasons lie in four main categories:
1. extracurricular activities
2. homework and independent study
3. crème-de-la-crème students
4. higher costs
I will discuss each separately over the next week, and will add links to each item in the list above to the appropriate post.
Overall, I believe that the longer day will fail because it simply does not conform with the current American system of education. In order to be successful, we would have to accommodate this new plan in small increments of reform. However, a rapidly developing society demands quick changes and immediate responses. A slow process of change may make no difference at all for over 15 years, while costing us millions every day.
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