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Everything posted by lewelma

  1. No, these were last year admissions. DS is at MIT now. I was just comparing our experience last year with daijobu's experience this year. We had the same feeling after the EA to MIT, that he would get into at least one other elite in the regular round, especially with his stellar interviews. It was a bit of a punch to get 3 rejections all on the same day. So 100% admission on the early round (MIT, Michigan) and only 25% on the regular round (CM only). Left us wondering about many things.
  2. Don't you wonder how in the world they make decisions. Older ds was in a similar situation last year. Accepted: MIT (EA), Carnegie Mellon, University Michigan Rejected: Stanford, Harvard, Princeton My dad has hypothesized that in order to keep yields up, that elite universities might share information on EA acceptances so that regular admission to the others is less likely. ETA: I just read the other comments, and looks like others are thinking the same thing. Fascinating.
  3. Gil, I would have your boys just do the starred problems in each chapter, until they can't do them. Then as you say, back up and read that chapter. They have covered all this content through more traditional books, and I'm guessing will enjoy applying their knowledge to the tougher problems. I also think you may want to reword your question. Your kids have finished beyond Calculus, right. So it sounds like you are looking for a way to embrace the complexity of the best of AoPS, not actually to test their knowledge with tests.
  4. I don't know if I'll be a lot of help, because we have chosen to go deep rather than broad. You could learn about NZ history through Michael King's History of NZ or Te Ara online history encyclopedia, and learn about the native wild life through Biozone's ecology and evolution worktexts, but we have preferred to dig deeper into single localities through our geography research projects. By focusing on single issues, we have had the time to develop a deeper understanding, to understand multiple competing perspectives, and to embrace complexity. So it depends on what you guys want to learn. If its breadth, I'm not so helpful with resources. We are currently studying hydro power on the Waitaki River in the South Island (8 dams, 56km of canals rerouting 2 rivers, 37m increase in level of one glacier lake, 55 years to construct). We are trying to answer six questions through our research: How was it constructed? Why was it constructed there? What were the impacts on the environment? What were the impacts on the people? How have they tried to make it sustainable? What are the current best practices? These questions have focused our research efforts on topology of the area, civil engineering of dams, impact of dams on river hydromorphology, glacier processes, maori history of the area, the welfare state (it started as a make work project done with picks and shovels), ecology of the braided river system, endangered species, sustainable practices, impact on hydro to global warming (not as straight forward as you would imagine), impact on tourism, and future best practices. It has been awesome and taught us about a broad range of issues in NZ as a whole in addition to the Canterbury area. Good luck with finding something that will work for your goals!
  5. This has been such a wonderful thread. Last year the board was down for the two weeks before announcements came out. Congrats to everyone, and hoping your kids all fall in love with their final choices.
  6. Well, you know that I attended Reno in conservation biology, and I loved it! Loved the department, the professors, the community, the classes, the students, the city. I loved it all. I did finish in 1992, but still happy to answer questions. Ruth in NZ
  7. My ds is 15 and a half and still does imaginative play. He uses his tiny lego figures. I can walk in and tell him to do xyz, and he will say, 'I need 5 more minutes to finish this scenario' Many times he has expressed concern that this is not an OK activity for a high schooler, but I have reminded him that the Bronte sisters had imaginative play into the 20s, and that many novel writers use imaginative play to get inspiration for their artistic works. My son is most creative with words and has had an adult-level creative writing style since the age of 12. When he was younger, I tried to get him to be creative with drawing, or sculpting, or music. Why did I never see language as his form of creativity? I've told him to stand tall, and embrace who he is. If he likes mock battles with small figures, that is not that different than mock battles in civil war re-enactments. My attitude is do what gives you joy. Ruth in NZ
  8. square _25, I've very much enjoyed talking about this issue. Quite a fascinating discussion.
  9. I know what it is to go super concrete. Although I do use algorithmic approaches with some students, others definitely need a conceptual approach. One student in particular comes to mind. I took on this student at 14. She was homeschooled and at that time had completed MUS alpha - delta (1st through 4th grade) and had started on epsilon (fractions). She had been taught completely algorithmically, as she would not watch the videos and her mom was basically mathematically illiterate (she would count 0.1 wrong if the answers said .1). This girl could very quickly and accurately add, subtract, multiply, and divide multidigit integers with traditional algorithms, but her mom had hired me because she was struggling with fractions. I very quickly realized that there was a WAY bigger problem than her mom realized. This 14 year old could not tell me the answer to questions like "you have 8 apples and I give you 4 more, how many apples do you have?" She had NO understanding of math, at all. NONE. She could manipulate the numbers as told, but had NO idea what she was doing. Luckily she was homeschooled so there were no exams looming. I put her back into the 1st grade book (alpha) and had her redo ALL the word problems. Basically, I thought that she must have dyscalculia and started making plans for making her just functional for life rather than any sort of university entrance. At the time she was interested in being a hair dresser, and there were no entrance requirements in math for this program. Over the period of a year, from age 14-15, I had her redo all the word problems in MUS from 1st through 4th grade, and when she was done, she still could not handle them. I figured that this was a core requirement for life -- to use math for very very basic functions -- so I had her do them AGAIN, but this time mixed up. Believe it or not, her mom rewrote all of them mixed up in a notebook -- we are talking like 400 word problems. During this word problem time, she and I worked on fractions. I did my standard pizza explanation only to find out that she did not understand circles. She could recognize the shape and call it a circle, but couldn't understand the idea of splitting a circle up into equal parts by going through the center. She also couldn't understand candy bars (rectangles) split up into pieces. In the end, the only way she could understand fractions was with liquids. So I had to draw tiny little measuring cups of water to explain all fractions, and had her work in the kitchen every week with water and measuring cups for months. By the time she had finished the 1st-4th grade word problems for a second time, we were through the fractions book (MUS 5th grade), and I felt that she might just be able to handle a very simplistic word problem. She was 15. And I felt we had made good progress. But then the very unexpected happened. Her dad stated that he wanted her to take the NZ national exams in Algebra, Statistics, Geometry, Trig, and Numeracy that year! I was like WHAT?!?!?! But he would not back down, would not talk to me, and the mom caved. I argued for an extra year to try to get her up to speed in those 5 subjects. Yes in ONE extra year. ONE!!! And you know what, we did it. She earned Merits on all 5 exams the following year in 11th grade - top 35% nationally. Just stop and think about that. It was simply incredible. I came to believe 2 things: 1) she had been VERY poorly taught with the focus on algorithmic knowledge at the expense of any conceptual knowledge, and 2) she needed more time than typical to develop mathematical maturity. For some reason, her brain just woke up to math at age 16. She is now working on Algebra 2 in 12th grade, and wants to be either an economist or a data scientist. She plans to delay university for a year, get through precalc in high school, and then do Calculus in University in either of these preferred majors. My point is that different students are different. She was poorly taught -- with algorithmic techniques to memorize, as if the goal was to be a human calculator. It was the going back to conceptual basics, way way WAY back, that allowed her to transition from 1st grade math to Algebra 2 in 4 years. Without going back, there would have been no way forward.
  10. Yes, I enjoyed that chat, but I still feel like I didn't express myself well because the systems are so different. Students in NZ take the national exams for a 3-year course of study (8th, 9th, and 10th grade) during the 10th grade year (8th grade is high school here). The exams concluding this 3 year course are in Numeracy, Statistics, Geometry, Algebra, and Trig. They must pass 3 of the 5 for university entrance. Kids here are *required* to take integrated math from 8th through 10th, so all kids get a standard american algebra 1 course over 3 years. 20% will fail the algebra exam by design (the test is curved with 50K students taking it). I think in the USA, kids just get a pass on algebra in some schools without there being any decently high standards. Really really depends on the kid. Some kids need to be concrete, some abstract, some practical. I've had 15 year olds in my kitchen pouring water in measuring cups, sent 13 year olds home with toddler's blocks to build 3D shapes to understand volume, played battleship with 14 years olds to help them with coordinates for graphing, and measured different sized plates with string with 15 year olds to explain pi. But yet I have also sent kids home with flashcards to *memorize* algebra. When working with kids in a school system, success breeds success. If I can get a kid to pass who has previously been failing, it creates momentum. I often use efficient memory-style techniques in the first month of tutoring to get these first passes, and then once I have the kids on board with these immediate successes, we switch to conceptual. So there are two reasons to use an algorithmic approach. 1) because that is how a student learns (like me), or 2) because it can be the more efficient approach in the beginning and can create immediate success and momentum.
  11. For the kids who need to learn algorithmic skills before conceptual skills, they will work on the Merit-level problems only after mastering the Achieve-level material. But it would need to get done before the assessment. Very few of my kids can work towards excellence as abstract thinking in mathematics is quite difficult and only 10% of students nationally can earn these marks because the questions are that hard. I encourage all kids to work to the Merit level, explaining that if they only do Achieve level work then they will always be regurgitating and never do any interesting thinking. It is best to work at the Merit level in 10th grade, so that the transition to 11th grade merit level thinking is smooth. For students who struggle with algebra in 10th grade, NZ has a qualitative statistics course which encourages relational and insightful thinking in statistics without having to do abstract algebraic thinking. Students I have in 10th grade who want to work at a high level and can't do that in algebra, will choose to switch to statistics in 11th or 12th grade, so they aren't stuck at a low level all through highschool.
  12. Well, in NZ we are lucky. Grades are based on levels of thinking, not percent correct. This means that my kids have to get to an ah ha moment or a why, if they ever want to get higher than a C in math. So for Math in NZ, you get a: C (Achieve) if you can get 75% of algebraic manipulation correct, but you also get a C if you get 100% of this low level thinking correct, because you have only demonstrated low level thinking. B (Merit) if you can get 75% of word problems and relational thinking correct, but you also get a B if you get 100% correct, because your thinking is still only Merit level A (Excellence) if you show either insightful or abstract thinking in about 50% of problems on offer. And let's be clear 20-25% of students fail (Not achieve) any one national assessment by design, they are curved. These assessments are hard and require some serious study. So for my kids when I first get them, I am just trying to get them to 'Achieve' the assessments, but then as they get excited about doing better in maths, they target a Merit which means we have to go after more complex material, not just more accuracy in low level stuff. Because each assessment is separate for different units, some kids might choose to work towards an Excellence in Trig, but only a Merit in Complex Numbers, etc. They can pick and choose. But all kids I have ever met desire merits and excellences which drive our math studies beyond algorithmic thinking. Here is the link to examples of the internals assessments for 11th grade. (internals follow explicit requirements but can be adapted to the students. So context can be fertilizer if you are rural, and rugby if you are a sports school etc. Externals are all in November, done together nationally) Since many of you have commented on a lack of graphing skills, look at 2.2 Cv2 for the Graphing Exam example I am currently working on with some of my kids Here is the exemplars for Excellence, Merit, Achieve, and not Achieve student papers for this particular assessment. NZ does it very differently from the USA as you will see when you look at this test for Graphing. It is hard! Students study what you test, so if you want them to go beyond algorithmic material in algebra, you need to test it.
  13. Yes. He was fascinating! I was told he was a 'thicky' by a friend who knew him. Everything apparently just thought he was slow at everything. It all revolved around his dyslexia actually, because many dyslexics can't memorize their multiplication facts, so they have very little number sense for primary school math especially for fractions. I saw that he just couldn't see inside numbers, couldn't break them up, couldn't factor, couldn't reduce fractions etc. So we set out to memorize the multiplication facts at the age of 15. Took all summer with little flashcards I made him. I tried to convince his mom to hold him back a year in math and she said no. So 3 months after I started with a kid who did not understand fractions, decimals, or any prealgebra, he walked into the third year of the integrated math class (8th, 9th, 10th) and he was to take the algebra, geometry, trig, and statistics national exams at the end of the year. Wow, was that a year! But he did it, and moved on to algebra 2/precalc in 11th grade, and then the following year to calculus scoring the equivalent of a 4 on the AP Calculus exam. What happened with the fractions was fascinating. He simply could never leave the concrete stage, and beyond that he could not really understand the idea of a fraction at all. How is 1/6 half of 1/3? He could see it with the pizzas, but he could not understand why the smaller piece was only 1/6th. Basically, he couldn't grasp that it was 1 piece out of 6 equally sized pieces. It just made no sense. And he couldn't understand place value either, so I couldn't use decimals to explain fractions. In the end, I just abandoned the effort because we were walking into algebra the following week. So algebraic fractions were taught by rote with NO conceptual understanding at all. By removing the requirement to actually understand it conceptually, he could just memorize what to do for algebraic fractions and not get caught up in the understanding. And once he could do algebraic fractions, numerical fractions became clear. And when I say clear, it was just a instantaneous understanding once I simply pointed out the direct connection between the two.
  14. Well, all of algebra. Try to teach one of MY kid conceptually why 2x+3x = 5x and x^2 times x^2 = x^4 but 2x^2 +3x^2 = 5x^2 I actually draw the x^2 as squares, and the x's as lines to help them think 2 squares plus 3 squares is 5 squares, but they really don't have ANY conceptual idea what they are doing with ANY of algebra. It is all algorithms that they memorize. i can get out a excel spread sheet and have them work with cells and formulas, but some just don't get it at all. Or try to explain to them what a two bracket factor is actually doing. I can say that it is converting from addition of terms to multiplication. I can show them with a 2 by 2 grid how it expands out. I can do it with numbers and BEDMAS and then compare to the algebraic terms. But actually the best thing to do is to have them take ONE problem and factor it, then expand it, then factor it, then expand it, over and over without looking at the previous answer. For some of my kids, they will still struggle after 10 repetitions, even though the problem is the SAME and they are just converting it back and forth. Most of my kids who struggle like this don't have dyscalculia, and in fact all but one have continued through 12th grade statistics or calculus with me. So it is not like they have a LD, they just cannot intuitively grasp algebra for years, and then it is so beautiful to watch when one day they do. Algebra here is inside integrated math, so I teach it to them at age 13, 14, and 15. For the kids who struggle, their ah ha moment is usually at 16/17, in the beginning of 11th grade.
  15. See my above post about a student who memorized how to do algebraic fractions by rote, and only then could he understand numerical fractions.
  16. Some might be saying that, but I am NOT. I am walking evidence, as are many of my students, that intuition can be developed through algorithmic drill all the way through high school and beyond. I have a PhD in Mathematical Biology, from back before it had a name. My work has been listed in some of the core new books outlining mathematical and theoretical biology as an example of an intuitive approach. But I am *definitely* a parts to whole learner, who has learned all math and mathematical science through drill. And only *after* the drill, do I develop insight. Half of my students are like me. I have tutored many students with many different learning styles. Here is one interesting example. I took one boy aged 15 from not knowing 1/10=0.1 through calculus in 3 years. Let me be clear, that is prealgebra, algebra 1, geometry, statistics, algebra 2, precalc, and calculus in 3 years including the NZ National exams (this boy is now in university in fine arts). And by the end, he had great insight, into complex numbers in particular. Insights that I did not have. Great leaps of understanding that were a joy to witness. I got him to this point by drill, and followed up with conceptual knowledge. In fact, I taught him numerical fractions through algebra. He could just not understand how fractions work, no matter how many pizzas I drew or manipulables we played with. We spent the entire summer before his 10th grade year getting through prealgebra, and he just could NOT understand fractions. But once he had drilled algebraic fractions for 3 months in 10th grade, with basically no understanding, I looped back around and taught him numerical fractions. He understood because the rote learning had created structure in his mind which made it ready for deep understanding. I completely agree. To suggest that one method of learning is superior to another is false. They each have their strengths and weaknesses. And I use many approaches with my students, all equally valid.
  17. The chief censor has banned the video and manifesto. Hate speech is allowed, but content inciting violence is not. All copies must be destroy, and policy are starting to go after the people who have disseminated them.
  18. Square_25, It would be so interesting to sit down over a cup of tea. I work with kids on the other end of the spectrum from AoPS kids. 🙂
  19. As for AoPS, my ds said that there were a lot of students that could do the work only with hints, and once they had the hints all the problem solving was gone. I have come to believe that AoPS classes only work for students who struggle to find a way through without hints. There are only 10 or so problems each week. You can only gain mastery with so few problems if you have had to think deeply about them. If instead you turn them into drill because you have hints, then you need to do a more standard approach with way more practice to master the material. Ruth in NZ
  20. I agree with Farrar, I see algorithms throughout higher level math, and my post (copied below) was in reference to high school math. When I teach students about converting complex numbers between rectangular and polar coordinates, some kids have intuition and others require drill as I describe below. When we do the loci in complex plane, some kids need to drill the steps about 10 times before gaining enough insight that I can lead them through an intuitive understanding. Others get the concept first and can intuit a way to the answer in some messy way that I only later clean up with some standard algorithms.
  21. Tomorrow I wear a headscarf.
  22. They are banning both the purchase and the ownership of these weapons, and all parts to make them, and all larger magazine/clips. There will be a buy back program. There will also be carefully regulated exemptions to the ban -- I saw the example of a farmer who needs to cull his herd. We have a bunch of 20-something workmen (builders, joiners, electricians, etc) at my apartment complex this month, and they all support it.
  23. I think, however, that the essays are critically important. DS did the common app essay first, but then learned so much about himself after writing all the other essays over the period of 5 months. His story came out over time through self reflection. He and I knew that he needed to rewrite the common app essay, but he simply ran out of time. He did not get into the elite schools that read his common app essay. MIT doesn't use it, and their essay prompts really helped him share his story.
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