The best students December 7, 2011
Posted by mareserinitatis in education, geology, math, teaching, younger son.Tags: animals, cub scouts, geology, math, younger son
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At teacher conferences a few weeks ago, my son’s teacher mentioned that she was going to be taking a short period during the day to break kids into two groups. One group needed some help with some of the more basic concepts in math, while the others seemed fairly advanced.
I got very excited, and I asked if I could come in and do some fun math stuff with the advanced group. She said she’d appreciate it because then she could focus on the other kids who needed more help with things.
Yesterday was my first shot at this. It’s only about 20 minutes of seat time once a week (along with about an hour of prep, considering I have to bring in materials). I worked with a group of six, and it was fun.
That’s the one thing about teaching college versus elementary school kids: college kids never get excited the same way little kids do. Of course, maybe it’s because you have to use a fundamentally different approach – more hands on – with little kids. On the other hand, I think you lose something with maturity. I have worked with a couple different cub scout groups, and they often have requirements to learn some geology for various badges. There is something amazing that happens when you put a group of 6-10 year old boys in front of rocks and other things they can touch. They’re fascinated with everything and seem to hang on your every word (when they’re paying attention). When you do the same to college kids, they just kind of shrug and proceed forth, maybe discussing the rocks with neighbors.
For these kids, I’m using a Mathworks book on how to be a zoo vet, and I decided to let each kid have their own animal as we work through the problems. Yesterday, we talked about building crates because we’re shipping our animals from one zoo to another. The kids were SO excited that they got their own animal. I tried to bring a variety: there were poison arrow frogs, king cobras, and piranhas for the boys and pandas and koalas and dolphins for the girls. I was pretty close: the two girls chose dolphins and koalas, and the boys mostly went for the dangerous animals. (One chose a polar bear, which is on the fringe between dangerous and cute and cuddly, IMO.)
Either way, they were really getting into building their crates. They were talking about the differences in sizes between all the animals, and it’s amazing all the movement and excitement and gestures that go into discussions among 7-8 year olds.
After the twenty minutes was up, I was exhausted. My comment about how college students never seem to get excited is exactly why I prefer to teach them: I can’t handle the energy level of really young kids all day long. I have to admit that I admire elementary school teachers for doing this. However, despite being exhausted, I was really tickled with their excitement and the fun we had. I’m looking forward to next week.
An appropriate challenge November 19, 2011
Posted by mareserinitatis in education, homeschooling, math, younger son.Tags: EPGY, math, perfectionism, younger son
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I’ve mentioned before that the younger son is doing math through Stanford’s EPGY program. In order to get into the program, he had to take an exam online to see if he qualified. Now that he’s enrolled, he gets weekly emails from his teacher talking about his progress. Most of the time, they say something like, “Keep up the good work.” I just tell the younger son that his math teacher is happy with his progress since he’s not real familiar with the concept of email. (Occasionally we’ll talk about some of the concepts she thinks need a bit more explanation.) I learned there’s a lot of other things he doesn’t quite understand…but I’ll get back to that in a moment.
Last month, he took a final exam to finish the grade he was working on. He didn’t pass, but he didn’t bomb it, either. He was a few points lower than the cutoff to go onto the next grade. It was a good thing, in retrospect.
The younger boy is a Perfectionist (with a capital P!), and it kills him to not do something perfectly. In fact, he refused to read until very recently because he couldn’t figure out all the words immediately. He was very disappointed when he didn’t pass the math exam and had to go back and redo some of the material. He retook the test a few days ago and got a very high grade. The lesson learned is that ‘failure’ isn’t death and doom…just means you need a bit more practice before you can go on. I think the practice did him some good as it seemed like he really got a better handle on things the second time around. I also think it helped him to see he isn’t expected to understand everything the first time he sees it. In other words, this is a good learning experience for the young perfectionist…one he would likely have not gotten in school given his grades are much higher there.
After finishing the test the second time, I showed him the email his teacher sent. I said that it was from his teacher at Stanford. I guess I’d never mentioned that bit before.
“My teacher is at Stanford?”
“Yeah, do you know what that is?”
“No.”
“It’s a big college that made the math program you’re using.”
“I didn’t pass the test the first time.”
“No, but that’s okay because it’s a hard math program. You just needed more practice. You wouldn’t be able to figure some of this stuff out unless you were pretty good at math.”
“Did you tell my teacher at Stanford that I’m good at math?”
“I’m pretty sure she knows.”
What’s kind of funny is that I don’t think he knows. That’s good, though, because it means he’s being challenged and not repeating work he already understands.
Another approach to multiplication November 14, 2011
Posted by mareserinitatis in math, teaching, Uncategorized, younger son.Tags: arithmetic, math, multiplication, teaching
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My younger boy has been working through multiplication, and the problems he’s doing are getting more difficult, so I decided it was time to start working with the dreaded memorization.
I’ve talked before about simply giving kids multiplication tables to work from. My younger son, however, seems like he’s a little better with memorization, so we took the following approach.
Most kids have a fairly easy time with learning to count by twos, threes, and fives. So that’s where you start. The other thing the child needs to know is how to add with carrying. If the child can do that, the rest of the tables are easy. Since counting by 2s and 3s is known, we’ll start with fours.
If you have a problem involving a 4, say 8 x 4, then you have them compute 8 x 2. Once they have the answer to that, have them double it. So basically, once they know all their 2s, they can easily obtain their fours. The same principle goes for 6s and 8s. For a multiplication problem involving a 6, they can either add the corresponding problem with twos three times or take the threes problem twice. Finally, for 8s, they can work from twos to fours, and then from fours to eights.
With the younger boy, this means that if he has a problem like 8×7, he first figures out 2×7. He doubles that answer to get 4×7, and then doubles it again to get 8×7. For him, adding things up goes a bit faster.
For nines, he uses the finger method: he holds down the finger that corresponds to the multiplier, moving from left to right. That is, if he has 3×9, he holds down the third finger from the left. To the left of that finger, he has the number of tens (in this case, 2), and to the right he has the number of ones (7). So the answer is 27.
So what do you do about 7s? Actually, given you have methods for everything else, the only one to memorize is 7×7. On the other hand, if you have a kid that sort of stuck when it comes to commutivity of multiplication, then another way to deal with it is that it’s the sum of the threes problem and the fours problem. (7×7 = 3×7 + 4×7 = 21 + 28 = 49)
Tens are usually pretty easy, so I’ll skip that one.
Eleven and twelve were learned by breaking them into two parts. First, take the number times ten and then take it times one (for eleven) or two (for twelve) and add the results. So 12×9 would be 10×9 plus 2×9.
I’m fairly certain this method would have never worked with my older boy. He has very poor working memory and ADHD, so I don’t think he was able to do a lot of this in his head (and was always resistant to writing it down). For him, I think using a multiplication table was a better approach. For the younger boy, though, who seems to enjoy working through problems and has a very good working memory, this has been a far more, and I might even say quicker, method.
You were paying attention! September 12, 2011
Posted by mareserinitatis in math, older son.Tags: math, older son
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My older boy came up to me last night. He was working on an algebra problem, and he said he thought the book had an error.
He was right. When I looked at the solution, it turned out they had only used some of the information given, while the other part was ignored. Turned out that if you used the other part, you got contradictory information. He could have chosen to use part of it, but looked at all of it and found an error.
“Good job!” I said. ”Obviously you were paying attention.”
He thought I was joking. I wasn’t. I’m proud of him for looking at all of the information and not making any assumptions…especially when it’s a subject he really doesn’t like and could have just written down and answer and been done with it.
Completely stunned August 24, 2011
Posted by mareserinitatis in education, gifted, math, younger son.Tags: gifted, math, school, younger son
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We were anticipating some issues with the younger boy starting school this year. Primarily, we have a problem: he’s already 2 years ahead in math. He’s been working through Stanford’s EPGY math program, somewhat irregularly over the summer, and he’s managed to move that far ahead. This has been kind of a surprise because he initially didn’t seem to be that gifted in math.
We decided to sit down with the principal and his new teacher and talk to them about alternatives. At first, it was fairly obvious they wanted him to be doing math with the other kids but then to add enrichment or even to go to another class. The problem is that he’s doing well with the EPGY program, so we’re very reluctant to end that. He also seems to be going at a much faster pace than we expected. Even now that he’s nearly two years ahead, he’s still only spent about 3 months to do about a year’s worth of math. Putting him in an advanced classroom that still moves at a slower pace is probably not going to be good for him.
We went in, hoping that they’d be okay with us giving him other things to do during math time. They didn’t seem real keen on the idea, and we were really reluctant to try to have him do two sets of math each day…one at a lower level or slower pace and then an additional one that’s right for him.
When it was obvious they didn’t like the ideas we suggested, I just sat there and waited for them to come up with something. Finally, the principal said he’d be willing to help supervise him in doing some sort of independent study project of his choosing during math time.
I just about keeled over.
We went from them not wanting to pull him of math to do something else to them being willing to let him do his own independent study project?!
The principal apparently used to supervise kids where they did this type of project-based learning, and I get the feeling he misses it. And I think this would be something the younger boy would love to do.
So, despite the fact that I was feeling very uneasy about what was going to happen, I think we hit the jackpot.
Linkety Link July 31, 2011
Posted by mareserinitatis in feminism, links, math, science.Tags: feminism, links, math, science, women in science
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I came across this fascinating article on the history of research in global climate change. I am greatly amused by the fact that methods used for oil and gas exploration were later utilized to validate theories on climate change. Irony.
Anyway, it’s a fascinating read: The Discovery of Global Warming
I’ve also been remiss in not posting a link to this sooner. (As you can tell, blogging hasn’t been at the forefront of my brain.) GEARS wrote two great posts on diversification in STEM fields: Diversification In Stem Fields and On Diversification: with Dr. Anna Garry and Professor Ursula Keller.
Of course, there’s a lot going on at EngineerBlogs. I wrote a post recently titled Died-in-the-wool Engineer.
For fun, you should think about whether math should be taught in schools. (And yes, the video is a spoof.)
Touch math June 10, 2011
Posted by mareserinitatis in education, math, teaching, Uncategorized.Tags: finger counting, math, memory, touch math
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I have another rant about elementary math education, but this one is slightly different.
I am completely appalled that schools still do not teach touch math.
You probably have no idea what I’m talking about because you’ve probably never heard of it.
When I was in fourth grade, we moved to a town in rural North Dakota called New Salem. At the time, the population was 2000. Now it’s half that. If you’ve ever driven through North Dakota and seen the world’s largest Holstein cow on the side of a hill, you’ve seen New Salem. (The cow, by the way, is named Salem Sue.)
Shortly after we moved there, I was sent to get some extra help in math. In fourth grade, I was still counting on my fingers. Some people term that a math disability now. However, the way this rural school saw it, there was an easy fix. I was sent to the special ed teacher for two one-hour sessions. I was, of course, feeling very ashamed about my finger counting. She said that it’s not unusual and that she had a way to fix it. She pulled out a piece of paper with an image that looked something like this (only, back then, it was black and white because I grew up in the days before they invented color):
So what the heck is this?
It’s a way of computing addition and subtraction facts.
The dots are places where you touch the number, and the dots with rings around them are places where you touch the number twice. You’ll notice that seven has a single touch and three double touches. Basically, when a child is sitting there with a math problem in front of them, they can touch the number in the designated places, and count those touches rather than their fingers.
As I got the hang of this (which was very quickly), I started being able to see the points and make computations without touching the numbers. I started developing some visual strategies for calculations. Eventually, with practice, I ended up memorizing my math facts. I’ve written before about how math facts are better memorized through practice than rote. I think this would be another great method for teaching facts, as it obviously worked for me. In fact, you can look at the Touch Math website and see that there’s a decent amount of research showing that the strategy works well both for average children as well as those with learning disabilities.
So why isn’t it being used? I’m still surprised that teachers in a small rural school district were thinking so far ahead. I’m not sure why larger schools have not followed suit in the past 30 years, and it’s really unfortunate that so many people have not heard of it.
The math critic June 9, 2011
Posted by mareserinitatis in education, math, teaching, younger son.Tags: curriculum, EPGY, everyday mathematics, math, school
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The private school that my younger son attends uses the same math program as the Fargo Public Schools. It’s a program called Everyday Math. During the last few months, after my son switched to the school, he was actually using two math programs: the one at school as well as Stanford’s EPGY online math program.
In discussing how to move forward with the boy’s academics, my husband and I have been very impressed with the EPGY program as well as the younger son’s attitude toward it.
The school, of course, would really rather he stay in the classroom and maybe go to an upper-level classroom for his math instruction. When we were looking at options, I told the principal that I didn’t really like Everyday Math. Admittedly, I haven’t seen a lot of the program, but what I have seen bugs me.
About the time Fargo adopted the program, I was starting to homeschool the older boy. I didn’t look into the program because I’d heard it wasn’t the best. Instead, I chose to use Singapore math for the math component of his homeschooling education. That was a few years ago, so I knew that I didn’t particularly like the program, but I didn’t have any specific objections.
Before school ended, the school principal handed me a copy of the state math standards. I’m guessing he is worried I think the program doesn’t teach to the standards or that I think they aren’t following the standards – or maybe even that I don’t realize there are standards.
Since this conversation took place, I’ve spent some time researching Everyday Mathematics, and I’m now even more convinced that this is not a program I want my son using. (A good starting point is this page.)
Unlike a lot of the objections, I don’t think constructivist math is bad. The fact that they teach alternative algorithms is great. (I personally am a huge fan of lattice multiplication, and even though I don’t use it myself, my older son uses it unfailingly.) I think that learning to explore and play with math is a good thing. My objection is that it doesn’t have the kind of implementation that Singapore has. There doesn’t seem to be a logical flow, there is no textbook, and it does omit teaching some things that I DO think are important (like that pesky long division).
Let’s face it: my objection is that any math program, no matter how well written, will suffer if the person teaching it doesn’t have a decent background in math, and most elementary school teachers do not. Making a student rely solely on a teacher presentation because there is no textbook will certainly spell disaster for some students. If a student doesn’t understand during the presentation, they don’t have much recourse…and the methods used are not ones that most parents have grown up with, leaving them unable to help much.
Second, Singapore has a great progression, allowing kids to see how the concepts are connected, building from previous material. This isn’t strictly going from one concept to another, but within a concept, moving from concrete examples to abstract application. It also teaches the use of mental math – which basically means one uses shortcuts or handy rules that can be used once there is already an understanding of the concepts. This is how I view long division, and that’s why it’s a shame it isn’t taught. The algorithms presented in Everyday Mathematics may be useful as teaching the concept, but they’re, in many cases, very impractical for everyday use.
Finally, there is the jumping around. Repetition and cycling are not inherently bad things, but they can be done without a seemingly random approach. In fact, it’s much better if they’re not done randomly. The best way to retain knowledge is to attach it to something you’ve learned before. That is, it’s best to have a point of reference. By randomly approaching the topics that need to be addressed, they’re removing the foundation and sense of connectedness that should be present in a well-taught mathematics curriculum.
Those are my objections, at least. I’m not sure how to approach this with the school, or whether I even should. I am considering seeing if they have some sort of curriculum committee where I could be involved. I’m also contemplating letting the principal know that there is a lot of controversy surrounding this curriculum, including extremely poor evaluations in other states like California and Texas. I feel fortunate that we have good reason to keep my son on the EPGY program, but I feel bad for the other kids who are learning math in such a haphazard way.
First grade, all over again May 27, 2011
Posted by mareserinitatis in education, gifted, homeschooling, math, younger son.Tags: emotional scaffolding, gifted, gifted education, teaching
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Some of you know that we ended up switching the younger boy to a new school mid-year. We weren’t sure how the new arrangement would work out, so we also decided to enroll him in EPGY’s math program. I really like program, and one reason is that they introduce basic algebra very early on. He is already comfortable with using variables, and understands some basic concepts, like substitution. He was doing great until a couple days ago. Then we encountered sum and difference equations.
a+b=10
a-b=0
Actually, this particular example was fairly easy for him. You know that if the difference is zero, the values of a and b have to be the same. The problem is when you end up with a difference equation that looks like this:
a-b=4
That seemed to lose him fairly quickly. After struggling with it for a while, I decided it was time to use some manipulatives.
(Note to self: Do not use chocolate chips as manipulatives. If it’s hot, they’ll melt. And regardless of the temperature, the kid will be more interested in eating them than doing math with them.)
I explained that a-b=4 is the same as saying that a has 4 more chocolate chips than b. First we have to take away the extra four chocolate chips, and then a and b will share the remaining chocolate chips equally. So, in this case, they will share six chocolate chips equally, meaning a will end up with 7 and b will have 3.
He seemed to understand. He was able to solve several examples using the chocolate chips, but when we went back to doing the problems on the computer, he seemed lost. He couldn’t do them, and then pretty soon, he wouldn’t do them. I was flummoxed because he obviously understood how to do it a few moments before.
My first reaction was to get frustrated, and soon I was almost angry. He wasn’t even trying!
It was at that point I realized exactly what had been going on at his old school. The kid is a serious perfectionist, and being a perfectionist, his instinct is to avoid things he can’t do very easily. He’s afraid that if he can’t do them easily, he will get them wrong. And getting things wrong is not an option to a perfectionist. (Before you say what a horrible parent I am for turning my child into a perfectionist, please note that he’s been like this since he was capable of doing *anything* and that it’s extremely common in gifted children because they are not used to things being challenging.)
I realized I needed to change my tactics quickly. I immediately told him that I knew it was hard to do these problems, but that if he tried, I was sure he’d do a good job at them. I went from frustrated to empathetic in the drop of the hat. He asked if I would help him if he got stuck, and I promised I would.
And then, suddenly, he could do the problems with no help at all.
In education, this sort of practice is called “emotional scaffolding”: the idea that influencing emotions is as much a part of learning as acquiring knowledge, and for students to learn well, they may need emotional support from their teachers as well as instruction. When I had tried to talk to the teacher at younger boy’s old school about using emotional scaffolding in the classroom, her response was that she was “not a special ed teacher”. I was surprised because, to me, addressing the emotional component of learning is just as important as the content. If you have a kid who is easily intimidated by learning, then it only makes sense they may need more pep talks than the average kid. Making a kid comfortable with learning is most definitely not something confined to special ed teachers – or at least it shouldn’t be.
On the flip side, if you don’t understand the root of the behavior, it is probably very easy to assume that the child doesn’t understand the material. Addressing the emotional component of learning means you need to have a good handle on what makes a child tick – something nearly impossible when you’re dealing with 25 or 30 kids.
I think part of the reason that the younger boy is doing so well in his new classroom is that 1) we have identified the emotional issues causing the problem and 2) he had a teacher who was very willing and able to work with him and provide that emotional scaffolding. As a result, he went from having completely shut down to now working at advanced levels in all of his curriculum.
One issue in dealing with perfectionism, however, is making sure that the child is continually challenged enough to frustrate them a little, but not so much that they are bound to fail. They need to learn that working or getting help is a better way to deal with challenges than simply shutting down. And in order to be willing to confront those challenges, teachers need to be willing to both mentally challenge a child while at the same time providing emotional support.
What I saw the past few days confirmed what I thought had happened – the teacher at the old school was willing to provide the challenge, but not willing to provide any emotional support. The teacher at the new school was able to do both. For that, he will forever have my gratitude.
It is also a reminder to me that teaching material alone is not enough: the best teachers also work to keep their students motivated and interested.
Can young students learn from online classes? April 9, 2011
Posted by mareserinitatis in education, homeschooling, math, older son, teaching, younger son.Tags: automated curriculum, curriculum, EPGY, homeschooling, Johns Hopkins, online learning, trent schools
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The New York Times is covering online classes in the ‘Room for Debate’ column. It’s interesting reading the commentary from the debators because at least half of them are talking about online learning in the abstract. That is, they’ve got some ideas about what it should be like but haven’t had much experience with it.
Over the course of my kids’ schooling, we’ve experimented with a lot of different curriculum, some of which has been online. My personal opinion is that online learning is that you really can’t say much about this topic without first defining what you’re talking about. “Online learning” is very vague. Does it mean you’re talking with people online about your homework? Are you working with completely automated curriculum? Do you have feedback from a teacher? You need to know how to answer these questions before giving an informed opinion.
My first experience with ‘online learning’ was not good at all. About 7 or 8 years ago, I enrolled the older boy in an online program called “Trent Schools”. They sent ‘lessons’ on a regular basis which I later found out were simply repackaged sections from the “What Every 2nd Grader Needs to Know”. It was incumbent on me to think of how to explain these things to my son as well as work out ways to practice. Given I could’ve gotten the book and done exactly the same thing, it really wasn’t helpful at all. It sort of embodied the worst aspects of ‘online learning’ – no interaction with other students, no feedback for the student, nothing to practice, no guidance for the parent.
I was burned on the concept, but when the older boy started attending a gifted program in Minneapolis, I was introduced to it again. The program had kids work on several of their subjects using online educational programs. Specifically, they used Rosetta Stone for foreign language and Aleks for math. The first thing I learned (and I suspected this already) is that Rosetta Stone is not great for a beginner. However, once you have a bit of a language under your belt, it may help you improve. I’d use it as a study aid, but not as a curriculum entirely in and of itself. So much of foreign language, to be really good, depends on having a teacher with a good ear who can provide you with feedback. Without that, you’re probably spinning your wheels.
The older son made little to no progress using Rosetta Stone. However, many of his classmates did, so maybe there is some aspect of this that I’m missing.
On the other hand, I’ve been hooked on Aleks. I find that funny because the same complaints I had about Rosetta Stone, another parent had about Aleks. However, for my kid, it seems to really work. The older boy did pre-algebra and algebra 1 through his old school using the program. With just that background, he received a 500-something on his SAT quantitative score last fall. When we came back to Fargo and began homeschooling again, we opted to use the same program. The older boy doesn’t always like the explanations, but he is able to do the vast majority of his math with no oversight from me. The program regularly assesses his knowledge and reviews concepts he seems to have forgotten.
And did I mention we threw him into college-level algebra and trigonometry?
The program has a large review section, so he was able to catch up on any review he needed by skipping geometry and algebra II. He has the option of taking ACE credits for the course, as well, so some colleges will say he’s met his math requirements (unless he needs to take calc – but frankly, I’m not going to deal with that one).
I admit that he needs help from a real human being sometimes, but I appreciate that he can progress at his own pace. And I can definitely tell he’s learning a lot. Even when he asks for help, it’s pretty obvious he understands what concepts are necessary for understanding the topic and is able to explain things. And given how much he really dislikes math, I think it’s amazing the progress he’s made.
The younger boy started math through Stanford’s EPGY program this year. There are two options – one where you are assigned a tutor and they provide updates to your school while the other is simply progressing through the program and assumes that the parents are overseeing the learning. The second option, open enrollment, is probably ideal if you’re homeschooling. It’s also a lot cheaper, too.
He loves the program. Given he was claiming to dislike math, I was expecting a struggle. We decided to give it a try, however, based on positive feedback from others. It’s not been a struggle: he is very willing to sit down and do a 20 minute session nightly. He treats it like a game, and it gives positive reinforcement when he gets things correct as well as giving him the opportunity to correct his mistakes when he gets things wrong. Although he’s not very far into it, I’m impressed that they’ve managed to introduce variables and complex topics like balancing equations into lower elementary math. They start out at a very basic level and step things up gradually, so the only help he’s needed from me is when we have java glitches. His favorite part is that he can progress as fast as he likes, and he likes to be able to skip problems.
In both math programs, learning is adaptive. Assessments are done more regularly in Aleks than EPGY’s program. But my overall feeling is that math is probably one of the best candidates for ‘online learning’.
In the fall, the older boy will try taking some writing classes through Johns Hopkins. As far as I’m aware, there’s not much of this that will be automated. The classes will involve either interacting with the teacher and classmates on a web-based message board, meaning students will progress as a group, or emailing with the teacher, which can result in more personalized instruction. For writing, I’m guessing this is the best format for language as it provides the feedback he needs. I’m really not sure you can use online learning in an automated format for something like this, so there’s no way you can dispense with the teacher. One huge advantage to this method, however, is the medium: the older boy struggles a lot with handwriting, but can type easily. This is far less frustrating than having to compose things by hand, as he would do in a normal classroom.
Based on these experiences, I think online learning can really benefit some kids. Even in the best case, it’s good to have an adult to help out when necessary or to set and enforce some guidelines as far as how much time is spent on the programs. If it’s done right, online learning should include regular feedback and assessment and, because it works at the kids’ pace, should be minimally frustrating.
The biggest advantages, from my perspective, are that students aren’t stuck working at the pace of those around them, slower or faster, and they can take time to master the concepts they don’t understand while skipping over those that they do. It will work better for some topics than others, but there are ways to do many different topics well in an online environment. When using this type of teaching in school, it will be important to have teachers that can deal well with an unstructured environment. If all the kids are working at their own pace, the teacher needs to be a facilitator and can’t count on prepping the night before so that they understand the material. I can see that dealing with kids working at different levels might be more difficult for classroom teachers as they may need to learn to work on several topics at once.


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