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Gil

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About Gil

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    Supreme PooBah of Learning at G.I.Z.M.O.S

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  1. 1) There is no "set" way to help a person enjoy math. Different people might have their interest hooked by different things. Of course there is always the possibility that your child is a person who, ultimately, will not like mathematics for mathematics sake in the end. If that turns out to be the case, it doesn't mean that you used the wrong curriculum, or that you used the right curriculum incorrectly or anything like that. 2) It is by far much easier and more efficient to simply augment the instruction and/or problem sets in a math book that has already been written, than to create something completely customizable. Doing math off the cuff can be done--and well--but it's not really an approach that I'd recommend unless you have the knowledge, experience, time and energy to do it well for a year+. I have 2 kids and they are very close in age and are academically capable of a lot of the same academic work. There were quite a few topics or subtopics in math that I wanted introduced or exercised in a very specific way. Other times there were topics that I wanted to introduce them to, but aren't a part of the typical scope/sequence or wouldn't have been introduced at a time that was convenient for us. By age/grade The Boys are in middle school but we've done a lot of math and I've had to "DIY" a lot of math teaching and have customized a lot of math lessons for them over the years. At various points in the mathematics curriculum/continuum, I've taught The Boys (and occassionally Tutees) using my own explanations and home made problem sets, my own explanations and 3rd-party problem sets, using 3rd-party explanations and problem sets. In my experiences it's easier to write a few lessons to explain or teach a few key concepts, and write customized problem-sets and exercises to fill specific needs than it is to write an entire math program. I really don't recommend creating a customized math curriculum by hand unless you have the knowledge, time, energy and experience to do it well. There is no need to pour that type of time and energy into this project if you run a very likely risk of producing a mediocre project. I don't want that last part to sound snide, superior or anything like that. It's just plain old logistics. If I ever wound up HSing another kid or crop of kids, I wouldn't create a customize math textbook for them. I'd use my own explanations and ready-made 3rd-party text for problem sets and exercises and just use my customized lessons/exercises where they fit.
  2. I'm pretty sure (95.8%) that Python won't run directly on Chromebook. You'll need to hop through some hoops--probably have to run a virtual machine, or use a cloud-based solution--to use Python from a Chromebook.
  3. Yes, among way too many others. 1- Yes, exactly. It's terribly sad, but it seems to be very true. This brings me back to my earlier point: The books that today's teachers learned mathematics from when they were children, were written by people who either A- didn't know to communicate this, or B- just plain old didn't know this. Because of this, I maintain that the US does not have a "teacher-education" problem when it comes to mathematics. The US has a student-education problem that is so severe, it can't be undone by 2 semesters of math-education during "Teacher-education" programs. The symbols in math are shorthand for phrases and ideas that must be explicitly verbalized and visualized. It's like teaching US Geography from a map labeled with only 2-letter abbreviations for US state names and a star where the capital is for 5+ generations. So that in the 6th generation, when people ask: Why is 'Texas' spelled "TX", or Why are all the stars the same size, even if the capital cities aren't? or Why do we have to put each capital-star in a different location? Why not just always put them in bottom-right corner of the states silhouette? Then neither teachers nor parents can answer them. Teachers will have to give them nonsensical, bull-crap explanations like: "Well, a hundred years ago a conference of US Geologists got together and standardized the spelling--that's why all the states are spelled with 2 letters." and "You'll learn why all the capital stars are the same size when you get to College." and "A long time ago, each capital star was printed in its particular spot--it's just the tradition of US maps" Only people traveled who have extensively and very mindfully, used more detailed atlases and maps, or someone with accurate intuition would realize/understand the capital star goes in a specific spot because it represents the location of the capital city with in that particular state, but many of them will still be left wondering about the 2 letter "spelling" of each state. But the crux of the matter is that TX does NOT spell Texas. TX is an abbreviation for Texas. T-E-X-A-S spells Texas, not TX.NJ is not "how you spell New Jersey" NJ is the abbreviation for New Jersey, etc... 2-When all is said and done, you're fighting multiple generations of confused ignorance, bafflement or indifference. Its a noble cause, but lately I'm just done with people. I just try and make sure that I do what I can during class, but have been very careful to drive each concept home for my own kids. 3-"Word problems" are trivial once a student has a functional level of reading and correctly interpreting strings of mathematics.
  4. Pernicious is such an appropriate term. There are many pernicious terms and explanations given in elementary level mathematics textbooks. These pernicious terms and explanations serve no purpose at the moment and often cause harm down the road. Students arrive to 10th or 12th grade thinking that equations must have variables in them, because by the time that they learned and began to use the word "equation" there were variables involved. Children can be taught to not only read but also interpret mathematical symbols on a page--how to correctly interpret the numbers, operations and relationships should be taught, modeled, and practiced in the classroom all throughout the K-5 mathematics. We teach reading comprehension--I have no idea why we don't include "mathematics comprehension" in math-class. Children struggle with word problems because they have no mathematics comprehension. It's not that they don't know how to apply the concepts--its that they have no foggy idea what the concept behind the symbol even is. Better teaching will cut down on, or even prevent kids from interpreting equations as some sort of magic. Even 1st graders can successfully be taught and helped to understand what units, expressions, operations, equations and inequalities are. But not when they're taught hodge-podge style. Not when they're given pernicious explanations. Children can learn to read mathematics as soon as they are ready and able to learn and use mathematical symbols but the vast majority of them do, in fact, need to be taught how to read mathematics. There wouldn't be any need to use pernicious phrasing or explanations if people were just taught to understand the what and how of the various symbols that are used in mathematics education, as they went along.
  5. @lewelma How do the levels for the NZ tests work? I found the list of subjects and I see that they have a Digital Technology series of exams. Any idea how I can find the texts/resources that NZ schools use to prepare for those tests?
  6. You're a genius. The "create an answer key to their own test as their test" idea is a great idea. I would probably find having the evaluator there distracting, but even if I wouldn't I really don't like to put them under spot-light so I wouldn't really want the evaluator there. The Boys don't get to attend each others lectures anymore because they heckle, distract and tease one another too much and sometimes it's overwhelmingly distracting for whoever is the lecturer and I find myself glaring at the "student-brother" and trying to keep the "lecturing-brother" focused and on task. For my sake, it's easier to just have the lecture be 1-1.
  7. Ideally, I'd like to administer a test for each subject, each month. It'd make it easier for the evaluator to "see" what material they're working on and that they are progressing--even if it's not very traditional in scope/sequence. Based on their notes, summaries, and outlines, I can harvest or write enough essay questions to use on tests for history, geography, civics/government, etc based on their notes, summaries or outlines. Thanks @Junie for the tip. @Jackie I want to keep a close and native eye on their secondary language development. A large chunk of their academics are done in Spanish and the evaluator is bilingual and willing/able to assess them in both Spanish and English, and he's open to our "quirky" style of doing things. We do value his input (to an extent) so while I don't really have the urge to "test" The Boys, I think that the evaluator is being reasonable and just looking for traditional bench-marks that he can "categorize". We're better served being assessed by a bilingual, open-minded human than a well-designed and comprehensive test at this point in time. But the day that I no longer have to jump through anyones hoop is the day I jump for joy. @ClemsonDana you are a genius. I really like your idea for a language/grammar test. I think that a "Proofreading exercise" would be a good way to demonstrate understanding of several grammar concepts all at once and in a nice succinct package. Even better is I wouldn't have to change the tests composition/format month-to-month. I'll call it "mastery" and I could just keep the same format of 1) ID parts of speech, 2) proofread, 3) vocabulary dissection, and 4) define X, Y, Z -- literary types. Best of all is that with that format, all I"d have to do is swap out the passages, different vocabulary, etc each month. Seriously: you, are a genius. We don't have to test in IT/Programming--the evaluator said that he's happy to let them just demonstrate and discuss their programming projects and in the terms that they don't do anything in IT/Programming then it's fine. @RootAnn OMG you might have just struck pay-dirt with the Answer Key idea. I don't know why I didn't think of that. If they've written the math test, then their own answer key might very well be able to serve as "them completing a test." Hmm...I don't have to broadcast or announce where the test came from.
  8. I really like the idea of building the tests for content subjects around their notes. But re: math (and science) we have worked out this weirdish system of examining The Boys knowledge and abilities and it's very hard to condense or abbreviate. .... **blah, blah, blah** ... I have always been crappy at writing succinct assignments. Regentrude and a few other posters advised me on crafting assignments a while back. So for content subjects, I have followed that advice mostly, but I haven't gotten the nack for writing tests for like, math and science. We did a year or so of physics and we got through it, but I didn't do as good of a job as I would've liked. So I've just been focusing that teaching energy back into programming/IT for the time being. I'm not a good enough multitasker to do several subjects at high levels, so I'm planning ot direct the bulk of my teaching "chi" toward IT/tech/programming for another year or so.
  9. Of course kids genuinely have no clue what an equals sign means. The books that their teachers learned from in their own youth, were written by people who had no clear idea of what an equal sign means, or the that the numerals are fundamentally different from letters and that this should be taught explicitly and directly. Teachers and texts treat the numerals, operation symbols and relationship symbols like they are letters. Like they have just been randomly paired off with certain sounds and when you see the symbols 7 - 5 = 2, say the words "seven minus five equals 2". US texts often call equations number sentences in the K-5 levels and that's exactly what texts, teachers and the students take them to be: sentences with numbers in them. 1st graders often read many nonsensical, disjointed things during phonics like "Tom has a dog"--it's just a sentence, about some generic person named Tom and some generic "dog" that he's got. There is no greater meaning behind it, because the point is just to read common words while learning to sound ot short, CVC words. But during math lessons, when they read 2 + 5 = 7 they read "two plus five equals seven"--it's just some generic statement about "two" and "five" and "seven" and there is no greater meaning associated with it. When you see "m" say /mmm/, when you see "qu" say /kw/ so they apply the same logic to numerals and other math symbols. When they see "7" say /seven/, when you see "+" say /plus/ and when you see "=" say /equals/. There used to be a emoticon for banging your head on the wall. If we still had it, there would be a few of them in this post. It's maddening. I know someone who teaches 5th grade. This woman actually thinks that multiplication is repeated addition, couldn't come up with two models to illustrate or explain integers, doesn't "get" how every integer is also a rational number, and doesn't understand fractions. She teaches 5th graders math. The book she teachers from has 4 or 5 chapters on fractions and she has no idea what she's teaching. I just grit my teeth and say nothing, but I pity the poor kid who needs to ask for clarification in class.
  10. Aaah, possibly my favorite topic. I've snipped down the OP to focus my response since I'm short on time. I didn't get to read the rest of the thread so it's possible I'm repeating what's already been said. 1) Generations upon generations of mathematically incompetent teachers/principles/committees writing and teaching math programs for all sorts of reasons that aren't rooted in math. This is not a Teacher Training issue. Anyone who reaches prealgebra should be able to explain arithmetic thoroughly and well. The teachers weren't taught K-3 math, during their own K-8 education, so by the time that they get to the Teachers College, it's virtually too late for them. They'll typically have to BS their way through only 32 weeks of math courses (2-semesters) and by the time that you reach the Teachers College you've developed all sorts of Test-Passing strategies that have nothing to do with mathematics. If you've made it through 10 years (g3-12) of systematic math instruction by BSing it, you can likely make it through 32 weeks more. IF the 7-12 teachers are more competent, they still have a problem when students show up on the first day of class without ever having learned their basics, or understood the fundamentals so the teachers have to either teach elementary level math again and too students who've already shut themselves off to "math" or they press on and hodge-podge it as best they can through 7th-12th grade curriculum, and the kids either catch on enough to cope and pass, or they flounder, but either way, the US Math Problem is one that compounds upon itself rapidly after the 2nd grade. 2) Self-education and leading by example is probably the best, most impactful thing that an interested parent/teacher can do to help their kids math education. Brush up on your mathematics skills. Make sure that you understand and can explain all the fundamental concepts in arithmetic in words, and all without fudging out or obscuring the math behind them. Spend time each week working on your own math. Work on your own problem solving skills and build those muscles for yourself. If you know what books your kids will use, solve all of the word problems in that series yourself, and make sure that you understand the soltions. Read through the explanations and decide where you will have to reword or expand in order to preserve the actual math concept or to provide clarity. Stay engaged. I personally hate to see math-lessons passed off to a computer or independent workbook because the dialogue, the back-and-forth, observing the childs progress through a problem set and showing/explaining a problem on the big board can teach the child so much about math, but it also teaches the teacher so much about the student. You can pattern match your way through so many "independent" exercises and learn nothing for it. 3) A great math education is one that works with and nurtures a childs natural number sense. Builds logically upon itself and guides the student to express and explain the mathematics back. Children should be taught so that they can participate meaningfully in a mathematical conversation. Teach them the concepts for each symbol so that they understand the quantities, operations, and relationships either before or along side the symbol for each, but seperate from their symbol. If children learn each operation concept, they should be able to apply it to word problems with minimal guidance, so problem solving exercises should be worked in from the very beginning and in my opinion, very often. I might order the basics: Number sense > Problem solving > Procedures, but I'm not sure that I'm wedded to that sequence. There is an inherent logic and "neatness" to math, that a lot of kids really appreciate. Children should be required to attain fluency with each operation. I've always thought that having 2+ students who are close in ability in the class enhanced the discussions/experiences. Teach your kids early and often the correct mathematical language, and let them know some of the common ways it's traditionally said/done wrong, so that when they see/hear it for themselves, they recognize it as wrong. (ie, they may see people throw the '=' sign in between every expression in a long line. --which makes my eyes wanna bleed--, hear the phrase "goes into" and are likely to read that multiplication is repeated addition ) But after you teach them the what, why and how of the '=' sign, or what multiplication really is, point out that it's often misused in such-and-such way, and tell them not to do it and just keep revisiting that data point so that it sinks in. Recognize and respect to role that memorization does serve in the math education, but don't over do it.
  11. Unfortunately, no. We have used textbooks in the past--so I'm not philosophically opposed to using a textbook if it fits, but currently switching to textbooks won't fit in with our plans for the coming year. (we count our school year Jan-Dec). We'll have an evaluation sometime in May or June of 2020. I am thinking that I could do 1 test a month per subject.
  12. He'd like me to include tests as a part of their portfolio.
  13. We live in a state that requires annual evaluation and we prefer to meet this requirement via portfolio evaluation, rather than state exams. Given their age/grade, our new evaluator has requested that I administer and include tests in our portfolio. We like and want to keep this evaluator, so I'm willing to try and meet this request. The evaluator strongly suggests that I test them in math, science and grammar/language, at minimum, though he'd like to see tests for other subjects too. I am not good at writing tests at all. I could just find random tests online and have The Boys take them, but those tests wouldn't line up with the rest of their portfolio at all and since this evaluator actually peruses, takes an interest in and evaluates their work, I think that would not go over well. Again, we like and want to keep this evaluator. So, if you had to write tests for your kids, how would you write them? I might be able to tweak our examination model and make it so that I can flip it around to be a test for them, but I'm not sure if it would work well for their portfolio. So maybe I should just cobble together tests from online? Thoughts?
  14. Does it have to an online/computer based game? Is there anyone who could/would sit and play an Algebra themed board/card game with her?
  15. re: 1- Welcome and enjoy the journey. re: 2- Huh, and after 6+ years of this, I thought that I'd at least be a little familiar with the struggle. 😉. re: 3- We found it helpful to copy+paste to Word, format and print the online articles for a long while. It helps to be able to mark on, write in the margins, draw illustrations, note vocabulary etc. For high-interest reading on things that they already enjoy, the Fandom Wikia has a healthy German and French version. We also used normal old Wikipedia for high interest topics, For kid-friendly articles on non fiction topics, Vikidia has a French version, but their German site is really lacking so I'd recommend Klexikon instead. You can find something in hard copy on eBay or Amazon.com with a few carefully selected phrases. You can also use the French and German versions of Amazon, but I've never ordered internationally before so I can't attest to how easy/hard it is. On the US Amazon.com site, you can filter for books by language, or you can simply search in the target language. re: 4- Good luck! It helps to learn a few key phrases in the target language so that you can find more of what you want. I guess you'll need to teach your boys the phrases for their respective languages. re: 5- Sorry, I'm not able to help with anything like that.
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