tag:blogger.com,1999:blog-7638578.post3054202628494150764..comments2024-03-28T18:32:57.799-07:00Comments on An Academic's Freedom: Failing by SolvingUnknownnoreply@blogger.comBlogger11125tag:blogger.com,1999:blog-7638578.post-15919775486429239922019-07-15T07:12:49.550-07:002019-07-15T07:12:49.550-07:00kanchipuram silk sarees
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They make wonderful crafts.Shuaib Ahmedhttps://www.blogger.com/profile/13245980941162760421noreply@blogger.comtag:blogger.com,1999:blog-7638578.post-18209226974734676132018-12-21T01:56:58.831-08:002018-12-21T01:56:58.831-08:00Twofold choice is so much well known these days in...Twofold choice is so much well known these days in light of the fact that once it is comprehend by anybody he begins his business in it. They can gain a great deal on the off chance that he comes to realize its fundamentals like in the event that we know to compose we can do work on <a href="http://www.thesisdefense.org/" rel="nofollow">http://www.thesisdefense.org/</a> effectively by the assistance of our reasoning. We ought to see the present need in which we are living.Anonymoushttps://www.blogger.com/profile/03122613601156402099noreply@blogger.comtag:blogger.com,1999:blog-7638578.post-15420098986197662352018-12-19T02:36:16.254-08:002018-12-19T02:36:16.254-08:00If this method is really helpful to teach mathemat...If this method is really helpful to teach mathematics to the students so that method can also be adopted by the other schools to enhance their results in order to have better ranks in <a href="http://www.personalstatementservices.org/how-our-personal-statement-writer-service-works/" rel="nofollow">read more</a> so the more students can come to the schools and can learn what is more beneficial for them.<br />mikonhttps://www.blogger.com/profile/00020457880484119572noreply@blogger.comtag:blogger.com,1999:blog-7638578.post-18375506600678837102018-12-18T07:12:42.626-08:002018-12-18T07:12:42.626-08:00Even I am confused at the moment because how can y...Even I am confused at the moment because how can you judge the life of the captain by telling the number of sheeps and the goats on the plain. How can we <a href="http://www.applicationessayprompts.com/answers-to-college-essay-prompts/college-application-personal-statement-writing-service/" rel="nofollow">check this</a> that there is the best approximate age of the captain on the ship and hwo that can be the very sure for the time being?Mdlknoreply@blogger.comtag:blogger.com,1999:blog-7638578.post-67608804888919874972012-01-25T19:41:39.530-08:002012-01-25T19:41:39.530-08:00Bhaskar,
Thank you, those are some very useful re...Bhaskar,<br /><br />Thank you, those are some very useful recommendations and suggestions. I've ordered the JUMP books and will be contacting them for their Tutor Guides.<br /><br />I do make sure I spend time on expanding his horizons and getting him interested in the larger world (astronomy nights with my telescope, field trip to see ballet, and more in the future -- I'd like to do a hike and a museum soon). But your suggestions have made me realize that I don't ask much about the goings-on in his world, and say almost nothing about life in my world. I'll make sure to incorporate those.<br /><br />Good stuff!Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-7638578.post-39294552503732311032012-01-25T00:02:27.412-08:002012-01-25T00:02:27.412-08:00Dear Anonymous,
Thank you for sharing your exp...Dear Anonymous, <br /><br /> Thank you for sharing your experience. I admire you for volunteering your time to work with this child in need. <br /><br />If you feel that a drill-based approach may be the only way to go at least for now, may I recommend taking a look at the JUMP math curriculum (jumpmath.org) if possible? It's a particularly well-thought out curriculum and you can find workbooks titled "JUMP at Home Grade x" on Amazon, for 1st to 6th grade. I recommend starting with a much lower grade to see what he gets and what he is missing from earlier grades. The core philosophy of JUMP math (which I do agree with, despite my strong advocacy of free, inquiry-driven learning in general), is that in mathematics you do have to master certain basic skills with solid understanding before going to the next steps; any gaps result in a lot of confusion. The JUMP program has a very systematic, thorough approach. In many cases, because the teachers are pressed for time to cover the curriculum at a standard pace, some students don't quite master these critical skills and the class moves on leaving them further and further behind. The JUMP philosophy tries to avoid this from ever happening.<br /><br />I have worked with inner city school children in new york and LA in the past, and it affected me deeply to see how many kids from disadvantaged backgrounds lack positive role models and exposure to richer learning experiences in their life. What you are doing for this child already and what you could do for him to expand his horizons is priceless. <br /><br />Besides working with him on his math and english, I hope you also talk to him about other aspects of your life, your interests, the kind of work you do, about people you know and what they do. Beyond helping him catch up with his classes, do tell him about and show him things that will evoke a sense of wonder about the world outside his home and school. You may also find it useful to hear him tell you about his world, and spend some time understanding what matters and is interesting to him. You may find this way some keys to help him learn and grow.Bhaskarhttps://www.blogger.com/profile/04794187138960706452noreply@blogger.comtag:blogger.com,1999:blog-7638578.post-16498056824871229272012-01-24T23:07:21.349-08:002012-01-24T23:07:21.349-08:00Bhaskar,
I'd like to share some personal expe...Bhaskar,<br /><br />I'd like to share some personal experiences that seem marginally relevant to this post. I'm a volunteer at-home tutor for a 6th-grade boy. He and his family are refugees resettled in the US. He had insufficient schooling before coming here, and is quite behind. I spend a few hours with him once a week, helping him catch up.<br /><br />The two most important things he can be taught right now are English and math. Since his math seemed okay, I had been completely focused on English until the day he pulled out his math homework, which he had "solved."<br /><br />The page was full of fraction-comparing problems -- the goal of each of them was to compare a given pair of fractions and write down the sign representing the relationship between them (< and >, no equalities). I started going over them, and was immediately quite pleased to see that he had inserted the correct sign between 2/3 and 3/4. I asked him how he had arrived at the answer. He said 2 (in 2/3) is less than 3 (in 3/4) and 3 (in 2/3) is less than 4 (in 3/4), so 2/3 must be less than 3/4. It's quite unfortunate that his flawed reasoning led to the right answer in this particular case, because I had to struggle to convince him his method was incorrect despite producing the correct answer. I thought that the counterexample of 99/100 and 100/200 would help, that he would clearly see that 99 was almost all of 100, but 100 was only half of 200, but it didn't help -- he complained that the numbers were too large for him to work with. I had a twin struggle at this point -- to help him understand the magnitudes represented by fractions, and to disentangle the concepts of method and answer. With my limited time running out, I gave up after a while, and instead worked on drilling some mechanical rules for comparing fractions. His problem set included negative numbers as well, and there was no way I was going to be able to give him an intuitive understanding of it all. He just doesn't have enough time with me. I just hope that he learns and remembers his mechanical rules well enough to make progress in school, and over time is able to understand the meaning of what he is doing, hopefully with my continued help.<br /><br />Another incidental problem that came up was that he associated the word "answer" only with numerical results. I had to take some to explain to him that "<" can also be an answer to a problem. But he may not remember that next week.<br /><br />Oh, and as for the problems that could not be solved using his "method", he had just eyeballed them and arrived intuitively at the answers (~ 50% wrong, as expected), which makes me wonder what he's being taught in school.<br /><br />In my case at least, I know teaching by mechanics is a necessity. And I fear I will not have enough time with him to plug this stop-gap by eventually catching him up with the real meaning of what he's doing.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-7638578.post-701657764143313772012-01-17T22:04:09.090-08:002012-01-17T22:04:09.090-08:00Thanks for the thoughtful comments, David. I think...Thanks for the thoughtful comments, David. I think the other paper you are referring to was perhaps Lockhart's "A mathematician's lament" (http://www.maa.org/devlin/LockhartsLament.pdf).<br /><br />I don't disagree that practice is necessary to build skill, but I do feel strongly that it should not be made the centerpiece of the educational process, particularly at younger ages. <br /><br />Your point about the impact of early exposure to role models is fair. Parents and family do have a huge influence on a child's aspirations and ways of thinking. What can be done about this? One nice effort I've seen to address this issue is Iridescent (http://iridescentlearning.org , founded by a USC Viterbi Alumna) which organizes joint family science classes in LA for kids and their parents, many of whom have had limited experience of a good science education themselves. <br /><br />As to whether the ability to appreciate and do mathematics is utterly absent in some portion of the population, my gut feeling is that most kids have the raw potential to enjoy and achieve a significant level of proficiency in most endeavors. The key is that they have to perceive it themselves as "cool" and/or necessary, and have sufficient time and a great deal of freedom from too much close adult supervision for immersion in it. The near-universal appreciation of video-games among kids exposed to them, and their ability (in most cases) to speak fluently in their mother-tongue are evidence enough of this. I do believe that this potential can be "schooled-out" of kids through the combination of fear, boredom and confusion that Holt refers to. <br /><br />At the same time, I am not arguing that everyone will appreciate math to the same extent. The catch with an autonomous, exploration-driven approach to education is that there is no fundamental guarantee that a particular kid will enjoy or feel inclined to consider as "cool" or important any particular activity, be it math, writing, music, or sports. Their individual interest in any particular direction is shaped by a complex blend of chance and interaction. An education system which is organized on the principle that everyone has to learn the same amount of "material" at the same pace, is fundamentally misguided.Bhaskarhttps://www.blogger.com/profile/04794187138960706452noreply@blogger.comtag:blogger.com,1999:blog-7638578.post-83739815181527123322012-01-17T20:15:01.473-08:002012-01-17T20:15:01.473-08:00This article about the sheep and cows has made the...This article about the sheep and cows has made the news in a bunch of places. I've also seen plenty of articles and papers advocating a joyful, exploring approach to math, papers advocating that children be given the freedom to explore their natural curiosity. I forget the name of the author, but there is the paper that likens the current math education to teaching students music without ever letting them hear music or touch instruments, rather learning music theory entirely in the abstract.<br /><br />What these papers often share is a list of a few beautiful results, often combinatorial or geometric, and an explanation of how these could be taught in a way that students explore and discover them, and experience the joy from doing so. I have to admit that I have not read the Berkeley paper yet, but the articles I've seen in the past were remarkably short on how a concrete math curriculum would evolve or look like for the 10+ years that students usually study math. It's easy to be shiny and beautiful if you get to pick out the gems. But to return to the musical analogy, to become a musician who can play beautifully, you must have gone through a lot of drilling, in addition to working on seeing the beauty.<br /><br />While I don't use my fast multiplication/addition skills or various other things that were drilled into me at some point very regularly, I think that these drills often breed a notion of familiarity. You are more comfortable building on concepts that you have good skills in. Yes, it would be very useful to truly understand these topics, and I like the fact that now I do. But it would be difficult if every time you need to apply a previous skill, you kind of had to rederive it from scratch. You wouldn't get very far.<br /><br />Frankly, I have become convinced that the problem is not just in the schools; the problem seems to lie in whether children have role models who themselves enjoy exploring, learning, and understanding. Your children are extremely blessed to have parents who like to think like scientists, who enjoy the process of discovery, and who are able to admit when they don't know something, and work at finding solutions. Many/most children are not lucky. I think that children can sense very easily if their parents are scared of math, or just find curious questions annoying. If parents model a lack of curiosity, and a desire to have things follow old patterns and routines, children will often pick this up early.<br /><br />Once children arrive at school with a mindset of "I want you to tell me what I need to do," it will become much harder to implement this idea of learning by exploring. I have talked with quite a few people who genuinely felt that with regards to math, they want to be told what formula solves their problem, and how to apply it. Many people like patterns and routines. And few people genuinely see the beauty of math and mathematical discovery. You and I both try to awaken it in as many students as we can, but I think that in a lot of people, it's not dormant, it's absent. <br /><br />So I think that if implemented in practice, even from a young age, creative and exploration-driven ways of teaching math would meet with a lot more resistance from students and parents than implied by many of these writers. Schools like Shriram's probably have a lot of selection bias, in that the parents believe in exploration learning, and thus will have set very different role models to begin with. Those students may be much more inclined towards this kind of approach.<br /><br />Anyway, I felt like sharing, since I'd also thought about this question before, and am not as idealistic any more as I used to be.David Kempenoreply@blogger.com