It’s official: younger son is smarter than I am. October 3, 2013
Posted by mareserinitatis in gifted, homeschooling, math, younger son.Tags: EPGY, math, younger son
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Younger son isn’t one you’d pinpoint as being very gifted…at least I wouldn’t. I have had random people tell me that he’s quite bright, but that’s never what has come across to me. He’s very outgoing and socially conscious…VERY big on morals and ethics. Fun. Goofy. Just wants to get his homework done so he can play.
In other words, to me he seems like a perfectly normal little boy.
In math, he’s one of these kids who struggles with computation. Not as badly as some kids (*ahem* older brother *ahem*), but it is his computation that slows him down. He’s enrolled in Stanford’s EPGY program for math, which we do at home (even though the school still grumbles occasionally). I thought he’d get into the program, but I was honestly stunned at his ability to answer logic questions. I remember when he took the test, I was watching, trying to puzzle through some of the questions and he was already onto the next question. It made me realize that there’s obviously some ability there…but because of the computation issues, he struggles to express it.
When helping the younger son do some homework on percentages earlier this week, he made a very interesting comment:
When you divide an even number by an odd number, except five, you get a repeating decimal. When you divide an odd number by an even number, though, you just get a remainder.
Is that right? It sounded like it was plausible, but I’d never come across such a rule. I had to look it up.
According to Wolfram’s MathWorld, if the divisor is a multiple of two or five you get finite decimal expansion. If, however, the denominator contains a prime other than 2 or 5, you’ll get a periodic decimal expansion (i.e. repeating decimal).
So he was very close and might have been able to prove it by induction for very small n…if he knew how to do proof by induction.
It kind of stunned me, though, that he was trying to figure this out and neither Mike nor I had ever given it any thought.
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.
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.
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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