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lewelma

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Everything posted by lewelma

  1. This is what we use here in NZ for a qualitative report writing class. Its focus is on asking good questions, figuring out how to collect data to answer it, analyzing data, graphing data appropriately, explaining bias, sampling, making inferences, understanding assumptions, planning future work,etc. The ultimate purpose is to understand what can and can't be said with the data that has been collected. 10th grade qualitative statistics workbooks include: 1.10 Multivariate data (analyzing data) 1.11 Bivariate data (analyzing data) 1.12 Chance and data (probability) 1.13 Elements of chance (experiments) These booklets published by Sigma are very very good. They are about 40 pages each and have detailed written answers. http://www.sigmapublications.co.nz/math-workbooks/ncea-level-1/ (scroll down to the bottom of the list to find the statistics) exemplars for all reports for 10th, 11th, and 12th grade units: https://www.nzqa.govt.nz/ncea/subjects/mathematics/exemplars/
  2. Yes, NZ has publishers who make cheap workbooks. I'll get the links later today.
  3. So why algebra over qualitative statistics? Go look carefully at my links and come back an tell me that they do not show a base level of education. Explain to my why algebra would be a better choice. I am not saying *math* should not be required, but I am arguing that *algebra* is the wrong choice for many many reasons.
  4. This. My list of non-algebra jobs in my previous post were all high level. They all require a high school diploma in the current American system even though they don't require algebra on the job. I did not include low-skilled jobs: dishwasher, fruit picker, cleaner, trash collector, etc.
  5. I completely agree. My point 2 of my previous point: But to say that algebra is the *best* trainer of the mind is simply false. People must be *engaged* to train the mind, so the best choice is a difficult subject that a student has some passion for.
  6. We are not talking about whether algebra is useful to learn. The question is whether algebra should be *required* for a high school diploma. Basically, should every. single. student. regardless of job interest be required to pass algebra to be employed? I say NO.
  7. My primary school teacher friend teaches 6 year olds, and is a remedial reading teacher. She does not use algebra. The builder that came to my house yesterday may be manipulating numbers in his head or on paper, but it is not in algebraic format or recognized as algebra. It is math intuition that was developed on the job in his apprenticeship that was 4 years long.
  8. Dyscalculia is a sliding scale, so where do you draw the line? Other factors: ADHD, so they can never focus long enough to get it. Poor working memory, so they can't remember what to do. Slow processing speed, so they get frustrated and lose interest. And the big one is clear career goals that do not require algebra--. so there is no reason to pursue it. And it is not all students. I have remediated one kid from not knowing 1/10 was 0.1 at age 15 to Calculus in 3 years. He is now a fine arts major. And I have also remediated a girl at age 14 who did not understand how to answer "you have 8 apples and I give you 6 more", now 3 years later she is starting algebra 2. So I know how to bring kids up, and up fast. And to motivate. But for some kids, it is just not going to work. Better to use their math time for something more productive like qualitative statistics. They feel empowered and keep going. I am currently tutoring a kid who plans to be a fashion designer, and I've convinced her to do 12th grade statistics even though she cannot do algebra. Teens are unique, and we cannot force them into little square boxes. Just an FYI, in NZ the equivalent of AP physics is a qualitative course (with just a bit of algebra). My ds who is a freshman at MIT took calculus-based, Honors physics last term with a bunch of kids who had studied calculus-based physics in school in America. He got the top grade in the MIT HONORS physics class. He told me that the math was easy; it was the concepts that were hard. And all the students who had focused on calculus-based physics in high school just didn't know physics as well as he did even though he had taken a mostly qualitative, algebra-based physics course in high school. My point is that a lot is learned without math. For a kid who struggles in math to the point of dread, there are other paths forward.
  9. In NZ, we expose students to algebra in 7th, 8th, 9th, and 10th grade. But they do not have to pass it in an integrated course to move forward in statistics or to university. They have multiple years to have it sink in. For some, it never will. I am NOT suggesting students should not be exposed. Not teaching basic algebra closes doors only if we allow it to. The math requirement to enter university in NZ is 10th grade math with or *without* algebra, and there is no math requirement in NZ in university to fulfill some distributed requirement.
  10. Well I could be more persuasive...... I have tutored the widest range of students probably possible. From my son, who is currently at MIT taking a Graduate level math course as a Freshman, all the way to a student with dyscalculia who at 17 when I asked her to calculate 9-7, took 2 full minutes with a tally chart to get 3. So I have seen a LOT. Sure there are students who actually *can't* do algebra (like the girl I just described), there are also many students who just hate it, or who will learn it because they have to, only to forget it 6 months later. In order to say that algebra 1 is *required* for highschool, we need to do a proper analysis and not just fall back on cultural expectations. First of all, a highschool diploma is a base requirement for work today. By saying algebra 1 is required, we are saying that you cannot get a proper job without passing algebra. Let's just put that out there. Next, I can name seven people I know personally who use algebra, and they include an IT specialist, a high school teacher, a geophysicist, a CEO, civil engineer, and 2 computer scientists. Now here is the list of jobs of people I know personally who don't use algebra: minister, primary school teacher, counselor, artist, the associate concertmaster of the NZ symphony orchestra, builder, forester, preschool teacher, professional organizer, lawyer, writer, roofer, secretary of the prostitute's collective, UN aid worker, department of conservation project manager, outdoor educator, bed and breakfast owner, lifestyle farmer, TV producer, law librarian, community organizer, political activist, plumber, restaurant owner, valuer, museum curator, owner of car dealership, music teacher, professor in old testament, chef, and dog trainer. These are my friends and family. They do NOT use algebra, even basic algebra. We need a *good* reason that these people *have* to pass algebra in order to be employed and to contribute to society and provide for their families. In order to say that algebra is required to be employed, we must do more than just say it is useful, or beautiful, or foundational, or good for the mind, or needed so kids aren't limited in the future. We must say that it is *better* than something else that could take its place. 1) Useful and foundational : well, clearly it is both useful and foundational for people going into fields that require it, but it is simply neither useful or foundational for the list of all the jobs mentioned above. 2) Good for the Mind: There are many things that will train the mind. Latin, philosophy, technical drawing, to name a few. But to say that algebra is the *best* trainer of the mind is simply false. People must be engaged to train the mind, so the best choice is a difficult subject that a student has some passion for. 3) Beautiful: To say that algebra should be required because it is beautiful undermines the definition of beauty. Just go look into the philosophy of aesthetics to see what all the possibilities are. 4) Limiting students' options without it: Only. because. we. make. it. so. If we designed it, students who decide on a more mathy career later in life could learn the required math later in life. I am doing this with two 17 year olds -- they are currently learning algebra 1. (One has decided that instead of a hair dresser, she wants to be an economist; the other is applying to American universities and must take the SAT. Neither have passed algebra. ) So yes, lacking algebra will delay entry into certain fields of study, but to say we require *all* people to take algebra even if they hate it, in order to make sure that those few who change their minds aren't too far behind, is very unfair to the ones who suffer. I see the sufferers. I see them cut, rip their fingernails off, burn their hands, abuse alcohol, take illegal drugs, drop out of school. These students suffer when required to do something they hate. Children have rights and to limit their future employment by holding their diploma hostage to algebra is ridiculous. Finally, I believe strongly that algebra takes time away from more valuable learning for many students. Qualitative statisitics is where we need to send these kids. It is useful and foundation to many many careers and to being an informed citizen. It allows you to understand what you read and hear about studies in health, culture, food, politics, and current issues. It allows you to consider if the study is biased or the sample is not reflective of the population. It allows you to think critically about how studies are designed and what they can actually tell us. It is way more useful than a year of algebra half learned. My 9-7 dyscalculia girl passed 12th grade statistics including the quantitative units (see exemplars in my previous post) because she could use a calculator. She continued all the way through high school in statistics because she believed it was valuable. She gained entrance into university *without* passing algebra, and is now studying political science and Maori. Students like her and those who simply hate algebra, will quit math the moment they can. When other options are on offer, they will take mathematical courses for longer into their school careers. Requiring algebra for those who hate it does not help them. They learn to dread math and forget anything they ever learned the moment they are allowed. I will stand by my firm believe that Algebra should NOT be a requirement for a highschool diploma. Ruth in NZ
  11. No, I don't. America in general has designed a high school math curriculum that leaves you with the haves and the have nots. You can either DO algebra and move up through Algebra 2, precalc, or calc; or you can't and then you languish in low level courses like consumer math. There are other paths, and NZ has one of them. NZ uses integrated math in 8th, 9th, and 10th grade including geometry, algebra, and statistics. This means that although ALL students are exposed to algebra, they can pass an integrated math course and still fail algebra, and be allowed to move forward. In 10th grade, they can even stop the integrated course, switch to statistics, and avoid algebra all together starting in 10th. But in contrast to America, the lack of algebra will not stop their math progression. What this system allows then is for students who do not like algebra and math in general, to still be learning quantitative techniques, mathematical interpretation, questioning skills, etc. They don't get stuck taking a geometry and Algebra 2 class that they hate that turn them off of math forever. Instead, they can switch to a not-lower, just-different stream and focus on qualitative report writing in statistics. This course teaches kids to interpret statistical claims rather than to DO statistics. And it is NOT low level. Kids walk out of these statistics classes being able to deeply understand question formulation, sampling techniques, bias, interpretation, questionnaires, bootstrapping, distributions, probability, technical writing, rejecting hypotheses, understanding medical claims, etc, etc. The kids in these classes can be pure math haters, but because of the way it is designed, often high-level kids take both math and statistics, so there is no sense that it is a 'cabbage' class. But for the algebra-hating kids, New Zealand gives them the opportunity to take a high-level well-designed course that does not require algebra. These kids have been *exposed* to algebra for 2-3 years, but in the end they don't have to pass it to move on in statistics. If they had been forced to pass algebra, once it was done, they would quit math forever, or consider themselves "bad" at math. Instead, there is a great option here and about 1/3rd of students take it (including high level kids). Students build confidence and skills, and don't hate math because they see it is both useful and effective for answering their questions about data and life. Here are examples of the statistical reports that they can write - notice the high level required for an 'excellence'. No algebra at all required for these reports. https://www.nzqa.govt.nz/assets/qualifications-and-standards/qualifications/ncea/NCEA-subject-resources/Mathematics/91580/91580-EXP.pdf https://www.nzqa.govt.nz/assets/qualifications-and-standards/qualifications/ncea/NCEA-subject-resources/Mathematics/91583/91583-EXP.pdf These are the two quantitative exams from 2018. Notice that they are also very high level, but there is very little to no algebra required. https://www.nzqa.govt.nz/nqfdocs/ncea-resource/exemplars/2017/91585-exp-2017-excellence.pdf https://www.nzqa.govt.nz/nqfdocs/ncea-resource/exemplars/2017/91586-exp-2017-excellence.pdf
  12. Yes. My son definitely experienced this. He would spell the same word in multiple different rule-following ways in the same paragraph and not even realize it.
  13. My younger son has dysgraphia and has struggled to spell his whole life. In the first few years we did SWR which is in the same family as AAS but more academic/linguistic. This helped my son to know all the rules. The problem was that he could not apply them when he was writing. Not at all. From 9 to 12 we tried every program under the sun in hopes of finding something that would work - Sequential Spelling, Natural Speller, Spelling Wisdom, Spelling Power, even just flashcards and drill drill drill. Nothing worked. At the age of 12, we decided to abandon all spelling programs and just do dictation, but with the sole purpose to learn to spell. We started with Cat in the Hat because at age 12 he didn't know how to spell half of the top 100 words even with years of consistent spelling work. So I would dictate to him short sentences or phrases, he would type them, and I would correct the spelling word for word as he went. I taught him to "think to spell" so to mispronounce words to accentuate the proper spelling. I got him to think in terms of syllables. I got him to focus on the base word and then how to add endings. Sometimes gave a brief overview of the rule. I focused on the tricky spots - usually the vowels- by only correcting those letters only so for "street" I would say "it is the ee representation of the sound e". As he got better, I would just say 'ee'. We did this for 30 minutes per day for 3 years. We started at Cat and the Hat, then Frog and Toad, then Narnia, then we started on easy novels that he loved (typically fantasy), with finished with working on Titus Groan which is high end. He loved it. I think it was both the slow but steady progress he experienced plus his love for literature that kept him engaged. At age 15, he still mis-spells about 10-15% of words, but he is still improving. At this point the spelling is not holding back his ability to type and compose. He just turns the spell check off until he is done writing, then goes back and fixes each underlined word *without* the help of the spell check. He wants to still improve his spelling. People always say that kids who can't spell can just use spell check, but if nothing is automated, and you have to sound out every word and remember which representation is the correct one, you simply have no ability to remember what you were going to say. This lack of spelling automation was what the problem was for my son, and dictation was the only way that we could automate the spelling within the context of writing. He had to just write words in context, 1000s and 1000s of words with me correcting him word for word as he went so that he would learn from his mistakes the instant he made them. Good Luck to you. Ruth in NZ
  14. That is not the way I've heard it used. Kathy in Richmond told me when my older son was about 13, that Olympiad Geometry required more mathematical maturity than the other olympiad topics, and that often you just needed a kid to grow up a few years. This comment was in reference to a tippy top math student.
  15. I'm a tutor, and for my students it is definitely a development thing. I've got some really smart kids - one with a scholarship for English a year early, others who are top 10% of their class, and yet they cannot do the abstract thinking required for algebra. I can teach them just the mechanical knowledge but they really have no idea what they are doing. And given that I often work with students for 3-4 full years, I can see when the light bulb goes on, and it is usually age 15. So general understanding let alone deep understanding starts in 10th grade for my kids. Luckily, we have integrated math here, so I can catch them up on 8th and 9th grade algebra in 10th grade before the national algebra exam. But with American's doing the full algebra course often in 8th grade, it just means that it will be a dumbed down version compared to previous decades so that enough students can pass. And then it will not stick, causing many kids to flounder in Algebra 2 after a year off in Geometry. My most interesting case was a student who I thought had dyscalculia as when I started with her at 14 she could not handle word problems like " you have 8 apples and 6 banannas, how many pieces of fruit do you have altogether?" I put her back in a first grade book (MUS alpha), and had her do all the word problems through 4th grade, and when it still didn't stick, I had her do them again. 2.5 years later, she is starting algebra2 having earned in the top 10% of students on the national algebra exam for 10th graders. She now is interested in being a data scientist or economist. Clearly, there was a delay in mathematical maturity. I don't expect that all schools should cater their entire program for kids like this one, but I do think that there should be a path on offer. Clearly, she would have languished in remedial math had she been in school, and then dropped out after 10th grade consumer math. Instead, she plans to take the equivalent of both AP Calculus and AP statistics next year and have a career in a mathematical field.
  16. "You only homeschool because you don't want to have to go back to work." Ah yes, I sit around on my *ss all day and read romance novels. No work involved in homeschooling.
  17. In NZ, the national assessment is called "applying algebraic procedures in solving problems" so if you solve the problem without using algebraic procedures you can't pass the test. The goal is not to get a correct answer, the goal is to learn how to apply algebraic procedures in solving problems. As to how to teach this, I'll try to write more about that later.
  18. Med schools in NZ require the equivalent of AP Stats rather than calculus.
  19. Sure. Basically, any word problem that asks you to form an equation. You can get the answer using primary school methods, but when being tested for an algebra exam, the goal is to code it into algebra so that you develop the skills required as the problems get harder. For example Amy bought two seedlings for her garden. One variety was 8cm tall when she bought it and grew at a rate of 2.5 cm per week. The other variety was 5 cm tall and grew at a rate of 3 cm each week. After a certain number of weeks the two seedlings were the same height. Form an equation to work out when the two seedlings were the same height. My students would not know that you *multiply* 2.5 by the number of weeks. So they don't know to write that term as 2.5w. So can't write the equation 8+2.5w=5+3w. Their approach would be guess and check, and if required to show their work, they would put it into a table if you were lucky. Basically, they would see it as repeated addition 8+2.5=10.5; 10.5+2.5=13, and they would just go up on each side until the two answers matched. If the word problem required 2 decimal accuracy, they would be in trouble. All of my students are particularly bad at recognizing division, as they see it as repeated addition to get up to an answer because that is easier to do in your head.
  20. My nephew is studying Arabic and Near East Studies at Princeton. He is currently on scholarship in Jordan in an immersion program.
  21. DS accepted early and lost out on an unknown scholarship from another school because he had accepted before the scholarship was awarded. If you are second on the list for a scholarship, you don't hear about it until the first person turns it down.
  22. My SIL's brother makes games for a living. Have you ever heard of Betrayal at House on the Hill? He was a English professor, but once he started making more money on royalties on his games than as a professor, he retired from teaching to make games. 🙂 It also sounds to me like he doesn't know what impresses universities, because I definitely think he could sell his passions if he wanted to. But I'm not sure he should care given that he has a school that will take him and parents who can pay. This means he can do what he loves and let the chips fall where they may.
  23. we were writing at the same time. Wasn't sure if you saw my previous post. 🙂
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