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About ClemsonDana

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  1. @Farrar, I assumed that the arithmetic ones were being discussed because long division and various regrouping strategies were discussed a lot and the OP is talking about what she's done with her 6 year old. My younger, who usually refuses to do the traditional mutliplication method, breaks it down to FOIL (32 x 14 is 30 x 4 + 2 x 10 +....), which I figured also fell under the 'algorithm' description even though it's basic multiplication. I could have misunderstood, though...
  2. This thread has been interesting because I didn't give a lot of thought to not explaining the algorithm. When I talk about a new math concept with my kids, I come at it from whatever direction I think will make sense to them. For my older, much elementary math was just teaching the algorithms so that kiddo could do the work quickly and understood how to represent it, because they were already pretty good at mental math. It's my work with younger that makes me think about how the idea of 'playing with math' is likely to apply more broadly (such as with the kids that I help in an afterschool program). Those kids, and to some extent my younger kiddo, don't have a lot of interest in playing with math. At home, we use manipulatives or anything else that will help with understanding, but playing with math would only happen under duress, at which point it's not really play, it's just teaching a different way. My younger grasps most math fairly intuitively and is easy to teach (and my afterschool kids could stand to take a break for a month and just work with manipulatives), but it seems to work best to teach the algorithm and make sure that it is understood. As for when people use the algorithms, I'll agree that I rarely used them in math in college, but I used them all the time in the years that I did lab work. We could, of course, use calculators, but rather than go to your desk to find it when you were at the bench (or vice versa) it was often just as quick to add the 5 2-3 digit numbers or do simple multidigit multiplication or long division by hand. Taking recipes for reagents, calculating how to make a 0.4 M solution, or looking at various mixes needed for reactions and then scaling them up or down was something that was done many times throughout the day.
  3. I used it some when my kids were younger. I'm pretty sure that I didn't follow the grade level recommendations, but it's been several years and I'm not sure. I liked that it was all in one book (I currently use an old-school textbook so we have to also use a notebook to write in) and that there were other skills like alphabetizing as part of the work. We do co-op one day/week so I only wanted 4 days of spelling, not 5. Most days were divided into 2 sections, so I would look through the exercise for the week and cross out whichever 2 sections that I didn't want to do.
  4. Our co-op sign-ups are next week, so I had to figure out what we wanted to do there, so I've got tentative plans for both kids now. LA co-op Composition class MCT level 5 free reading of good literature from the big stack that I put together each year Math AOPS counting and probability (I think we'll do this first semester) AOPS Intermediate Algebra Life of Fred of some sort - we do this on busy days when we need an AOPS break Language Latin 2 (using Cambridge book 3) at co-op Social studies K-12 HO book 3 as spine, done at home other resources as needed/wanted Write periodic papers about what we've learned to assess learning and practice writing Science Introductory chemistry at home (may use LOF or a more traditional book) We may do some physics Science Olympiad topics - we won't know those until October Other Scratch Coding (online class) Fencing, chess, and cooking (fun co-op classes) Bible Taking a class on stories in the scriptures at co-op - it's with high schoolers and should prompt good discussion Extracurriculars baseball and basketball in season, with homeschool or local school/travel teams scouts church/youth
  5. I wasn't an engineer (I was in biochemistry) but that was totally normal for almost all classes in my major. We had some faculty explain that they liked to have a large grade distribution, but to get that they needed to make tests hard or very long so that everybody didn't cluster at a 90. It's a different philosophy from what I use when I design tests (which is 'meet a certain standard and you get an A'), but it's common. Averages were typically in the 50s, but ranged from the 20s to the 80s. If you consistently scored above the average, you knew that you at least had a B, but other than that, we had no idea what our final grade would be. I also had to adjust to thinking that it's about the learning, not about the grade - even with a B or C, you know a lot more at the end of the semester than at the start.
  6. I'm not actually convinced that we can teach algebra to everybody if we just prep them well enough...and even if it's true, it may not be the best use of time. It's like saying 'pretty much everybody could learn to pull themselves up on the rope climb if they just practice enough' or 'everybody can learn to listen to music and hear what time signature it's in if they just put in some time'. It's probably true, but not the best use of time. I'd rather people put effort into doing a mix of exercise that they'll continue over the long term, and listening to and learning to appreciate different types of music. I sometimes think that problems arise when people who are good at something are the ones who determine what should be achievable for everybody. Sometimes it's really hard to understand how somebody can have so much difficulty with something that you can do without thinking. I still don't understand how my husband can't hear the difference between a musical piece in 3:4 time vs 4:4 time, but he can't. One of the fascinating things in Temple Grandin's book was her discussion of algebra. She can't do it. She's into brain scanning, and says that the part of the brain that does that sort of thinking isn't well developed in her. If they hadn't let her sub geometry for algebra in college, she would have dropped out. She's very self aware and willing to work, but you can't do what you can't do. We can make the argument that she's an extreme case, but I think that there are a lot of people who have difficulty with specific types of thinking. We have to decide if those are required for a high school diploma...and, if they are, we have to decide whether a high school diploma is a reasonable requirement for employment. This is on my mind because I was chatting with another mom at my kid's karate class - she teaches high school biology and was showing me the newest version of the state-specific book and looking at the format for the test that I had just given. Our local school uses block scheduling (100 min of each class each day for one semester instead of 50 min/day for a whole year). The special ed or remedial students need more time, so they do the standard bio material for one block each day for the whole year... and they still struggle. Well, of course they do. My more advanced students have to work to think through DNA replication and how the leading and lagging strands work and how to get both going 5' to 3'. I love teaching this and think it's really cool. It will be helpful for students as they sit on juries and need to understand PCR use in forensics, or we as a society make decisions about the use of CRISPR or GMOs. That being said...there is so much biology to learn, and for struggling students, I'd rather them learn pretty much anything else - more about organ systems (which, being more concrete, is easier for most students), practical nature study-type identification of local flora and fauna, applied botany through nature and gardening - than spend months on something that they can learn enough keywords about to pass the test but never actually understand. I think that for many students, advanced math falls in the same category.
  7. There was a time when I would have answered that everybody needed some subset of the standard math path, and my own kids will have both taken algebra in middle school because they'll be ready for it at that point. That being said...when my parents (who graduated from public schools in a large southern city in the 1960s) were in school, only the smartest made it to Algebra 2. I'm not even sure that both of them took geometry. I'm pretty sure that it was possible to graduate from high school without algebra, taking a 'consumer/practical math' pathway. And, when I was in high school, I tried to help a couple of friends get through algebra. I don't know if the problem was lack of background preparation or lack of ability to do abstract thinking, but they got nothing from the class even if they did manage to squeak by with a passing grade. I know that one of them is now a truck driver, a job that my algebra-adept self would struggle to do but which friend probably couldn't get without a high school diploma that requires passing algebra. Interestingly, this same friend took accounting and business math and did well at the high school versions of those classes...I'm pretty sure that they would have been better served by taking a statistics class than an algebra class. I think that one of the questions that we have to ask is whether a high school diploma should signify some sort of college-prep-readiness. In some states, the licensing for things like cosmetology or a commercial drivers license seems to be linked to having a high school diploma. It seems unreasonable to say that the requirement to be a cosmetologist is that one must pass a college-prep high school program, when the student is clearly indicating that they have chosen a profession that doesn't require a college degree. I would agree that people who know algebra use it to simplify everyday calculations, that facility with algebra can be beneficial (and often develop with practical experience) in folks in trades like construction, but I also think that it is reasonable to say that some people will never use it. I once had a fascinating conversation with some of my high school upperclassmen about what classes should be required. One said that he thought that students should have to learn something, and obviously there's a base set of info required for specific fields, but he felt (and I agree) that students are better off learning something outside of the proscribed plan than learning the normal things poorly.
  8. Perfect squares, mental math, and prime numbers. Strangely, my kid who claims to not like math loves the 'Balance Benders' puzzles from Critical Thinking Company and loved doing mental subtraction a la Singapore math (which taught that to subtract 19 from 35, you took 10 from the 30, subtracted 9, then added the 1 back to the 5, then you subtracted 10 from the remaining 20). I had dreaded teaching this sort of subtraction to this particular child, but they loved it. Kid who was super good at math at an early age doesn't enjoy the puzzle-style books as much, but at some point extrapolated knowledge of perfect squares into what they thought might be a rule about how to identify the next number in a series (don't remember if it was a square or a cube)..they turned out to be right, but it took my husband a page of math to prove it. Kiddo said that they pondered perfect squares as they were falling asleep. Lesson for me - you never know what will catch their fancy.
  9. We've traveled across time zones since the kids were tiny, staying anywhere from a week to a month. Usually we adapt fairly quickly to something close to local time. We've done it in both directions - we lived in NM when the kids were little and visited family in the southeast, and once we moved to the southeast we visited NM most years. We usually wind up maybe an hour off from normal, but with the change in activities compared to our usual at home schedule I'm not sure that the time zones make too much difference. We seem to be highly influenced by light, so getting up when it's really dark, or sleeping through a lot of light, usually doesn't happen.
  10. @Dicentra, don't feel bad! We have, at times, come to a similar conclusion at my house. One of my kids is a good self-teacher, but if there was something that kiddo really wanted to learn but needed direct instruction to learn, I'd consider outsourcing just because I'm not sure that I could maintain the right enthusiasm while trying to fly through a subject and stay a day ahead of kiddo. Thus far it hasn't been an issue, thankfully - the subjects that have needed more parent help happen to be subjects that I know/can easily figure out. But, at some point we may hit the wrong combo of 'student is really interested, student wants to move quickly, mom has no knowledge of the topic, and student finds it difficult to self-teach this subject' and then we may be looking to outsource. And, in some families, having students watch Crash Course videos would be different if they are usually taught directly by a parent. Honestly, both of my kids will probably take a literature class at co-op in high school - I can find the protagonist and explain the symbolism, but I never understood why anybody would want to. 🙂 Give me a good metabolic pathway any day. I want for them to have a chance at learning to appreciate that sort of thing, because I doubt that they'd get any 'appreciation' even if I did a great job of teaching the content. I've had co-op parents who were completely capable of teaching biology send their kids to take my class just because I actually like it and they wanted their kid to enjoy it as much as possible.
  11. I think that there are different kinds of bullying, and this technique can be very effective with the 'Say mean things to get a reaction' bullies and also 'Say whatever pops into your head before you think' kids, who can inadvertently upset people. I don't think it would help with somebody of the 'beat up a kid and take their toy/lunch $' type, but in many classrooms that's not the most common issue. Speaking from my/my husband's childhood experiences, and also from watching our own kids, the more reactive that you are, the worse the problem with 'Get a reaction' bullies. It's why kids who cry easily can have such problems - if they cry at the first incident, then they're picked on for crying, which starts a cycle. Obviously, it would be better if the first provoking incident never happened, but kids will do wrong things and there's no way to make sure that nobody ever says something mean. So, giving kids a pose and comeback line and them being able to use it a few times might be enough to make them not be a target any more. There are going to be kids who can't defend themselves, but if the vast majority can, then they can be taught to stand up for those who can't which can avoid the whole 'teacher's pet' issue that was mentioned in the start of the article.
  12. My kids did it in or before 2nd grade, but we were using Singapore 1-3 levels above grade level. It think Singapore math does it in 3rd. I currently volunteer with some students who are doing it in 4th, which I think is when I was taught to do it. The biggest impediment seems to be knowing the multiplication/division facts well enough to do the problems. When helping, I have struggled to tell when they don't understand the problem and when they get so distracted by having to skip count to see how many times 3 goes into 28 that they forget what they're doing. I see no reason to rush teaching it - there is no advantage to students spending a lot of time being frustrated by long division - but if students know the underlying math facts, I see no reason to put it off until a particular grade.
  13. I'll put my opinion somewhere between Dicentra and 8 - I think that you can absolutely have a class done at home, but it would be much harder to be the one actually doing the direct teaching if you have advanced, enthusiastic students who want to be taught. If we decide to do a module on allergy and immunity when I teach Bio 2, I usually start off by having the students watch the Khan Academy videos on the immune system. I don't need to do that with most other topics, but there is no reason for students to slog through my 'barely better than the textbook' explanation when those videos are really good. After that, we move back to me-led discussions of papers about what is wrong with the system that we just learned about if somebody has an allergy, for example. My kids do Science Olympiad, which, as they get older, has them dig deeply into whatever topics are covered that year. The coaches don't directly know the material, but they're willing to help research it. We usually start with the kids reading through middle/high school textbooks, general interest articles and explanations online, crash course videos, etc. Then we move on to more detailed materials, khan academy, etc. Some of the kids move on to college textbooks (the students are typically grades 5-12). So, they learn a lot and are guided by the coaches, but not taught directly. If we come to something that the student doesn't understand, they ask for help from parents or coaches, and it's not uncommon for the coaches to confer with each other to figure something out. Sometimes you get topics that a coach can help with directly (I get to coach Heredity this year - my advanced degree is in genetics), but last year I coached microbiology - I knew the basics, but had to pull in other resources once we got beyond that. Whether you want to outsource the class, or just use outside resources, probably depends on your preferences and how much your kids want to be taught directly vs how much they are interested in piecing together information from different resources (or somewhat self-teaching using traditional textbooks).
  14. My reluctant one is actually a girl, and is slowly outgrowing it. We started with Island. From a content perspective, we could have started with town, but then we would have needed to wait another year. In town, there are assignments like 'write 3 paragraphs about...' or 'write 4 lines of poetry using iamb, and then 4 using trochee' that my child couldn't have done when younger - both of mine lacked the patience/stamina for that much writing. You can skip the early level (or maybe even 2 levels) if you have an older kid - I definitely wouldn't start a 6th grader with island - but he uses different poems, authors, writing examples (which often come from classic things like Bronte poems or the Gettysburg Address), etc so it's also not just the same thing over and over if you start a younger kid at Island.
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