Math Education, elementary

[WellSpyder]

Some common responses are usually versions of 180 + 18 + 18, or 240 - 12 - 12. A few students still do the algorithm (ignoring instructions). A few students might do 180 + 36 but not realize it was the algorithm. Since I make all students wait until all students indicate they have come up with an answer, this causes my more inventive students to come up with less obvious ways like: 225 - 45 + 36 (15^2 - 3*15 + 3*18).

I went for 12^12 + 6*12 = 144 + 0.5*144. Not trying to come up with something different, just the easiest way that came to mind to tackle the problem. (I'm really not sure why I did 6*12 by division rather than multiplication! Nor why I used something that looks like base 12 arithmetic rather than the base 10 approaches you mention....)

[Zelandakh]

I was hoping that you would reply..Your estimates surprise me in two ways. I am skeptical that the numbers are that large. But also, problem 1 is first because I thought it would be the easiest. You can visualize a clock and see that in half an hour it will be 10:05 and then add an hour.

I was hoping Elianna would reply too and was similarly surprised by her answers and in the same way. I also considered #1 to be the easiest and thought the percentages would be significantly lower. If 90% of 12 year olds can answer #2 and #3 correctly then any talk about dropping standards is to be taken with a pinch of salt.

 

The push to teach maths concepts rather than learning rote methods is one that has gathered pace in recent years internationally. There are also often many more classes on discovering patterns and relationships than people of my (or Ken's) generation would recognise. That said, just recently there has been a renewed interest in a more traditional approach in some places, driven primarily from the excellent performance of China's education system.

 

Finally, I absolutely do use the 23+24 approach for mental arithmetic and my generation learned both ways, pen and paper subtraction and mental arithmetic short-cuts. The 18x12 I would do the "normal" way though, with either 120+96 or 180+36. The direct alternatives involving (20-2), (10+2) or both are not faster for me, although those that use this method will tell you that it is with a little practice and, for example, I do like the "difference of 2 squares" method where one calculates 99*101 as 100^2-1 and 98*102 as 100^2-4.

 

As for calculators, the one piece of advice I give everyone is always to do a rough calculation in your head at the same time. If the result you get is a factor of 10 or more out from that then re-enter the numbers and check your working. Aside from that, they help to save lots of the drudgery. Understanding is certainly much more important!

[billw55]

Students complain about the amount of explaining I require them to do. In other words, it's not enough for them to be able to solve for x in 3x + 15 =75; They must be able to explain why each step is mathematically valid, and be able to critique other methods of solving (as in recognizing correctness/noncorrectness) and be able to explain to others faults in their reasoning. Further, they must demonstrate ability to use this in modeling. So for example, I might require them to create a word problem that this equation would solve (and of course the classical given situations, come up with equations to help solve them). (I actually don't teach this math, I just wanted to use an easily understood example.)

But now you have spent perhaps half an hour on 3x+15=75. In my experience one of teachers' top complaints is not enough instruction time. Certainly they cite this when opposing standardized testing. So is this a wise use of time? As an alternative, how about using that half hour to drill them on perhaps two dozen such equations? Which approach would actually get them proficient at basic algebra faster? I'm not arguing one way or the other. I'm open to discussion. But I know how I learned, and it was good enough to get me through 30 credits of math in college.

[kenberg]

More thoughts about Elianna's thoughts.

 

With the clock problem it had slipped my mind that clocks with faces have become passe. Becky and I sometimes joke about it, wondering (and I really am not sure of the answer here either) if kids know what it means to traverse a circular track counter-clockwise. I can see why they might not. So, at the very least, my idea that you "just visualize the clock to see that if it is 9:35 now then it will be 10:05 in a half hour" might not be as obvious as I thought.

But it still seems natural to do this by first seeing what time it will be half an hour from now and then adding on the number of hours. Half an hour after 9:35 it will be 10:05, and an hour later it will be 11:05. If, instead I asked for the time five and a half hours later then they would have to deal with "what time is it five hours after 10 o'clock?" A little trickier.

 

The possibility of kids growing into adulthood without being able to do such things is a little unsettling. And my guess is that if they can't do this when they are 12, they won't be able to do it when they are 20 either.

 

My guess, just a guess, about Common Core is that like practically everything else it depends on how it is implemented. Most things can be done well, most things can be done poorly.

 

 

A few words about home schooling.

First, just emotionally, I come from the totally opposite extreme. I regard my childhood as being happy overall. But my mother tried to teach me to play the piano. That was not one of the happy parts. Parental teaching does not always go well. Not at all.

Second, it is often not practical. Take a divorced mother with four kids and a full time job. I know one. She is going to home school?

Third, I have seen it close up. Sometimes it works, sometimes it is a disaster.

Conclusion: If someone wants to home school their kids, let them. Well, even parental rights can be overridden in extreme cases, but mostly we let them. But we need to go forward creating a good system for those who do not home school.

 

 

I am thinking to put some effort into my vote for the school board (retirement is great!). I have strong beliefs ni the absolutely crucial nature of a good school system I am much less clear as to how to bring this about.

[PassedOut]

A few words about home schooling.

 

First, just emotionally, I come from the totally opposite extreme. I regard my childhood as being happy overall. But my mother tried to teach me to play the piano. That was not one of the happy parts. Parental teaching does not always go well. Not at all.

 

Second, it is often not practical. Take a divorced mother with four kids and a full time job. I know one. She is going to home school?

 

Third, I have seen it close up. Sometimes it works, sometimes it is a disaster.

Conclusion: If someone wants to home school their kids, let them. Well, even parental rights can be overridden in extreme cases, but mostly we let them. But we need to go forward creating a good system for those who do not home school.

I agree completely with the need for excellent public schools. Growing up, I went to three different elementary schools and three different (9-12) high schools. The differences in quality among those schools was pretty surprising to me (and to my parents). The kids were great, but I have to say that my last two years in high school were much too easy, although the socializing was a joy. When I entered college, I had to buckle down right away to overtake the students who had had a stronger education all along.

 

That said, I do have personal experience with home schooling, and it was positive.

 

Our sons were all born during the 1980s and we sent them to Montessori school from age three through twelve (Atlanta has a good Montessori elementary school, with a lot of parental support). By the time they finished there, they were all voracious readers and were experienced in using their own computers. It turned out that the public schools were slowing them down. After a year, we moved back north to be nearer our aging parents and the rest of our families, and -- after a couple of long discussions, including with our sons -- decided to move forward with home schooling. We were fortunate to have a local college available willing to enroll our sons in courses that we weren't prepared to offer, such as laboratory sciences and life drawing, but our sons didn't need any pushing from us to read up on and master the other academic subjects. And all three had an easy transition to college.

 

For the good of the country though, this can't be the direction to go. Every kid needs a shot at reaching his or her full potential regardless of the resources of his or her parents, and the US needs that also to meet the challenges ahead. It seems to me that the Common Core is a very reasonable way to address this: What approach could work better?

 

And you can count me with those who feel that teaching kids creationism instead of science is a form of child abuse.

[Winstonm]

Perhaps the Finnish education model should be our aim?

 

 

There are no mandated standardized tests in Finland, apart from one exam at the end of students’ senior year in high school. There are no rankings, no comparisons or competition between students, schools or regions. Finland’s schools are publicly funded. The people in the government agencies running them, from national officials to local authorities, are educators, not business people, military leaders or career politicians. Every school has the same national goals and draws from the same pool of university-trained educators. The result is that a Finnish child has a good shot at getting the same quality education no matter whether he or she lives in a rural village or a university town. The differences between weakest and strongest students are the smallest in the world, according to the most recent survey by the Organization for Economic Co-operation and Development (OECD). “Equality is the most important word in Finnish education. All political parties on the right and left agree on this,” said Olli Luukkainen, president of Finland’s powerful teachers union.

[Winstonm]

 

And you can count me with those who feel that teaching kids creationism instead of science is a form of child abuse.

 

I have to go one step further here, and it comes from my personal experience: teaching children that religious beliefs are facts rather than faith is child abuse.

[barmar]

Totally agree. Also, if they don't understand why they are doing what they are doing, it will hurt them later in life when they need to understand the whys of more complicated things. Essentially it sounds like we want to teach children to think. Thinking is work and is hard, so the lazy child is going to try to avoid it. I would be in favor of a program that can get children to think to the best of their ability.

One of the techniques that is becoming popular is "active learning", which replaces much of the lecturing and textbook reading with group activities that require the students to solve problems. Children are naturally good at this, it's basically how they learn most of the games they play (no kid ever sat in a lecture learning how to play sports, and they pick up card and board games with only a minimal amount of explanation of the basic rules). And when they learn through an active process, they understand and retain it better.

[billw55]

While I am certainly opposed to teaching creationism in public schools, I think calling it child abuse is a large exaggeration.

[PassedOut]

Perhaps the Finnish education model should be our aim?

Actually, that would be great, but it seems to me that a lot of folks in the US would freak out at the very idea. Perhaps the politics here influence me to set my sights too low.

[mycroft]

1. Lunchtime. Frankly, my biggest problem with "the younguns" is that they don't realize that the difference between 1205 and 1207 is frequently irrelevant. One thing we lost with digital watches (which are still a neat idea).
   
2. The Day of Struggle against the Great Clinton Conspiracy. (sorry, cheating - it's after November 9. Every day is the Day of Struggle against the GCC. (Sorry, cheating. Every day since at least 2002 has been the Day of Struggle against the GCC, at least on BBF.).).
   
3. Daddy, I want to go see Santa! (and the corollary, "10 days fewer than that").
   

In re: Elianna, I was going to start by being a smartarse and saying "12x18". Or less so, "9x24". But seriously:

18  12
9  24
3  72
1 216

(with a question as to why I did it that way instead of going the other way and only having to do the x3 once)

And quite seriously, I have done multiplication like this by:

2.2.3.2.3.3 = 3.3.3.2.2.2 = 27, 54, 108, 216

[Winstonm]

While I am certainly opposed to teaching creationism in public schools, I think calling it child abuse is a large exaggeration.

 

What if a Taliban fighter was teaching his beliefs to your son, then would it be child abuse?

[Winstonm]

Actually, that would be great, but it seems to me that a lot of folks in the US would freak out at the very idea. Perhaps the politics here influence me to set my sights too low.

 

From what I have learned, the Finnish have the best public schools in the world. The do not test. They do not have homework. And, if memory serves, it is illegal to have more than 20 hours a week of class time.

 

Obviously, they seem to know something we don't.

 

Edit: It is not illegal but teachers only spend 4 hours per day in the classroom, with 2 hours a day in preparation.

[akwoo]

Re: Finland.

 

I am sure that the reason that the Finnish education works so well is that teaching is a highly regarded, well paid, and selective profession in Finland. In fact, as I understand it, the Education majors are the hardest to get admitted to, and, as a minimum requirement, you must score in the top third of national exams to be allowed to study Education (and then later become a teacher).

[Kaitlyn S]

What seems interesting to me is that we are discussing teaching children as if it is a given that you will be able to spend your time teaching.

 

I have several friends and acquaintances that are teachers and every single one of them tells me that the teacher has to spend more time on discipline problems than actually teaching; they are not allowed to do anything about a disruptive child that will cause him not to be disruptive (they are allowed to yell at him but anything else would be grounds for disciplinary action against the teacher and/or a lawsuit from the parents), and yelling rarely does any good, and the disruptive children simply ignore requests for time-out or to go to the principal's office; and there are usually multiple disruptive children per class not just one.

 

Teachers who have taught college level courses where the child or his parents are paying for it actually get to teach. Their experience is that they must teach the material that should have been taught in high school but nobody got to learn anything in high school because of all the disruption from misbehaving students.

 

In another discussion board, I suggested that a solution was to segregate based on behavior so that the 80% or so of children that want to behave and learn will all be in the same schools and the students will learn. Of course, since most internet discussion boards are mostly populated with liberals, I was chastised for this suggestion, but not one single poster disputed my depiction of what goes on in a high school classroom.

[Winstonm]

When compromise is a requirement, ideas, both best and worst, get watered down. In a sense this is a safeguard, but it also ensures we are required to accept a less than the best agenda.

 

Education is an area where one could hope to find common ground, total agreement. Alas, our American Taliban will have none of that.

[hrothgar]

Of course, since most internet discussion boards are mostly populated with liberals, I was chastised for this suggestion, but not one single poster disputed my depiction of what goes on in a high school classroom.

 

Have you considered that maybe the problem is with you?

 

If I had to weigh the probabilities between:

 

1. Kaitlyn S is surrounded by a vast liberal conspiracy where ever she goes

 

2. Kaitlyn S is an idiot and posts a lot of really stupid stuff

 

I'm guessing that #2 is a hell of a lot more likely

 

(Especially since I have a lot of direct evidence that confirms #2)

[Kaitlyn S]

1. Kaitlyn S is surrounded by a vast liberal conspiracy where ever she goes

Not one of those liberals provided a solution to disruption in the classroom; they only criticized. So here's your chance, make liberals look better in my eyes and be the first liberal to let me hear a potential solution to the problem that teachers can't teach because of discipline problems and they aren't allowed to do anything.

 

Now, I get criticized a lot because I propose solutions. I'd like to see those that criticize my solutions propose reasons why my solutions are bad, and why their solutions are better. However, for that to happen, my detractors have to actually suggest some solutions. That rarely happens. Your "playbook" tells you that you don't have to provide any solutions because you can get away with keeping the status quo by simply calling those that provide solutions "racist", "stupid", "hateful", or some other derogatory term, and you think it makes you look better because you aren't any of those things but in reality you're not doing anything except attacking people with ideas.

 

Maybe diana_eve was right. The Water Cooler is a good place to stay away from.

[Kaitlyn S]

I am also curious how Elliana gets to teach is such a rarefied situation where she actually can spend time teaching and not disciplining.

[Winstonm]

Not one of those liberals provided a solution to disruption in the classroom; they only criticized. So here's your chance, make liberals look better in my eyes and be the first liberal to let me hear a potential solution to the problem that teachers can't teach because of discipline problems and they aren't allowed to do anything.

 

Now, I get criticized a lot because I propose solutions. I'd like to see those that criticize my solutions propose reasons why my solutions are bad, and why their solutions are better. However, for that to happen, my detractors have to actually suggest some solutions. That rarely happens. Your "playbook" tells you that you don't have to provide any solutions because you can get away with keeping the status quo by simply calling those that provide solutions "racist", "stupid", "hateful", or some other derogatory term, and you think it makes you look better because you aren't any of those things but in reality you're not doing anything except attacking people with ideas.

 

Maybe diana_eve was right. The Water Cooler is a good place to stay away from.

 

It's actually a fairly simple solution, impossible for us, as a nation, to perform. We have to eliminate poverty and elevate the lower-middle class while raising the benefits of education to a level that makes education more attractive to youth than crime. This means making people other than ourselves our priority - it will never happen.

[mike777]

I hear the term "common core" all the time in the news but not I dont know exactly what it is or how it works to answer Ken's questions. I note posters have not really explained how it works.

 

I do know that education is one field that does not give equal pay for equal work. For example many schools differ pay based on acquired education levels or seniority not equal pay for equal work. There is strong resistance by many forces to "creative destruction" the process that would allow a local school/college to be destroyed and replaced by something or ten somethings. To be fair this process would be painful to the local community but it is even more painful/harmful in allowing failed/failing schools to survive.

[Kaitlyn S]

It's actually a fairly simple solution, impossible for us, as a nation, to perform. We have to eliminate poverty and elevate the lower-middle class while raising the benefits of education to a level that makes education more attractive to youth than crime. This means making people other than ourselves our priority - it will never happen.

This may shock you, but I somewhat agree. Universal Basic Income has been discussed elsewhere and I can see the merits of it, especially when you consider that menial jobs will be automated in most of our lifetimes.

 

However, it will take a generation or two to fix this (perhaps longer because fellow conservatives are going to fight tooth and nail against free stuff, despite the fact that I don't see an alternative), meanwhile children aren't going to start behaving overnight, and culture is hard to change. So let's assume that we don't want to lose the next generation to a poor education due to behavioral issues in the classroom, please take a shot at providing a solution.

 

Note to any conservatives reading this: I have not given up my conservative ideals, but at some point, we have to be practical. That is why I would give positive rep to almost all of barmar's posts - his ideas strike me as being very practical.

[hrothgar]

Not one of those liberals provided a solution to disruption in the classroom; they only criticized. So here's your chance, make liberals look better in my eyes and be the first liberal to let me hear a potential solution to the problem that teachers can't teach because of discipline problems and they aren't allowed to do anything.

 

Now, I get criticized a lot because I propose solutions. I'd like to see those that criticize my solutions propose reasons why my solutions are bad, and why their solutions are better. However, for that to happen, my detractors have to actually suggest some solutions. That rarely happens. Your "playbook" tells you that you don't have to provide any solutions because you can get away with keeping the status quo by simply calling those that provide solutions "racist", "stupid", "hateful", or some other derogatory term, and you think it makes you look better because you aren't any of those things but in reality you're not doing anything except attacking people with ideas.

 

 

I reject the terms of your argument.

 

My proposition is supported by the quality of the arguments that you have chosen to make and their factual basis of of your posts.

You get judged by the worst of what you offer not an arbitrary example chosen by you.

You get criticized, not because you offer "solutions", rather because your intellectual foundations are wanting.

 

In much the same manner, I do not have a responsibility to make liberals or to use the vocabulary that you seem to be more familiar with, to make "libtards" look better in your eyes.

I not looking for your respect. My sense of self worth is not contingent on your validation.

[Kaitlyn S]

I hear the term "common core" all the time in the news but not I dont know exactly what it is or how it works to answer Ken's questions. I note posters have not really explained how it works.

 

I do know that education is one field that does not give equal pay for equal work. For example many schools differ pay based on acquired education levels or seniority not equal pay for equal work. There is strong resistance by many forces to "creative destruction" the process that would allow a local school/college to be destroyed and replaced by something or ten somethings. To be fair this process would be painful to the local community but it is even more painful/harmful in allowing failed/failing schools to survive.

I have heard only the negative implications. I'd be interested in hearing rational arguments from someone in favor of it.

[PassedOut]

I hear the term "common core" all the time in the news but not I dont know exactly what it is or how it works to answer Ken's questions. I note posters have not really explained how it works.

Preparing America's students for success.