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  • Miah
    replied
    Re: Math 7

    Originally posted by Colomama View Post
    Waving! We're park rangers too.
    Sorry, he is not a park ranger. He wanted to be, at the state level, in Arkansas. He never got through all the math (though he did finish college algebra eventually) and ended up with nothing to show for it but debt. He's a nuclear security guard now, which is a good living that doesn't require algebra. He had plenty of discipline. His last two years in high school he boxed, did marching band, and worked full time. Some people are just apt for a different type of discipline.

    Sometimes I feel like we leave too many people behind. I've always told my kids that college isn't for everyone and there is no shame in trade schools, military service, etc. That if they ever change their minds when they are older it'll still exist and if they have to work harder at that point at least they'll know it's what they really want.

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  • Miah
    replied
    Re: Math 7

    The idea that math involves discipline and rigor and should be pursued because those are good for you (discipline and rigor are good for you, I wish either had been required of me in school), might be where I am disconnected with this. High school math was not an issue of rigor and discipline for me. I enjoyed them because they were so easy that I could finish the homework during the lesson and then read novels the rest of the class. The teacher would change up the standard assignments sometimes because I would do a week's worth to give me more goof off time. So for me I see an easy class I took not at all seriously with near perfect grades that didn't get used again.

    Which is actually a part of why I homeschool. I was bored out of my mind in school, but they wouldn't let me advance. It was a tiny rural school that didn't have a single program for advanced students other than detention for boredom induced behaviors. Memoria's program is so different from that in quality and content, but I had mostly been focused on what the Latin, literature, classical and Christian studies were bringing to the table as so different that I wasn't seeing the math as the same value. It's something to think about even if my kids seem to take after me in math.

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  • Aquila
    replied
    Re: Math 7

    Maria, I think the Barbie said something like, "Math is tough." It was pulled from the shelves because there was such a backlash. Come over one day and we will rework the talking Barbie so she speaks in the affirmative for math. Then we can play it over and over again during those tough math school days. What else are we going to do when it is this cold here? It is relentless this winter.

    I'll race you to the library to see if the book, "Beauty for truths sake" is available! That is a beautiful quote by Leibniz. I may write it out and place it above the piano.

    As for my math 'instructor' he will be added to the 'why I chose to homeschool' list. As a teenager it is hard to hear these things because you aren't given the tools to question properly. And so Anita, I agree with your reasoning as to why more women aren't in mathematics.

    There are so many good tidbits of information on this thread and a lot of great insight. It is inspiring. I haven't heard someone speak of mathematics and the mind of God in a long time.

    Leave a comment:


  • Girlnumber20
    replied
    Re: Math 7

    Originally posted by Anita View Post
    Painting. Singing. Performing arts. Climbing mountains. Are these things “useful”? They’re not utilitarian at all. At worst, they’re a waste of time. At best, they elevate the soul higher. “Useful” is animal. Truth and Beauty are Human.

    I got a good education in this though educating my own children. We had a chapter study in catechism that discussed how people and animals are different precisely because we have souls and animals do not. The distinctions are some of what I listed above as well as things like laughter. Laughter isn’t utilitarian. But life without it? Purgatory.
    I've long been intrigued with the idea of mathematics as something very beautiful. It's an idea I've heard expressed in many places. I want to be able to see that. And I hope so much my kids will get to the point that they can see that, because I know it is true and I know I'm missing something... the world is so full of a number of things...

    Catherine was there really a Barbie that said "I hate math?"
    Last edited by Girlnumber20; 02-05-2018, 04:38 PM.

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  • Anita
    replied
    Re: Math 7

    Originally posted by Maria2 View Post
    I think there are many many things that we learn or aspire to learn that aren't at all useful. They might just be beautifully useless, and all the more valuable for all of that. What "use" is music, after all? But I think that you absolutely need subject matter to learn with- and math seems like the ideal thing to hone in on when it comes to training the brain to think. Sometimes I have a crazy thought and I wonder if it really matters at all, *what* you learn- as long as you are learning, and in the process, learning how to learn, and being challenged to go ever higher?
    But I still think higher math is crucial. I ended up studying music, an area where I thought, higher math would not be needed- I had a terrible time with advanced theory and harmony. And there are "glitches" in my music ability to this day that I suspect have to do with the area of the brain that never learned how to think "that way." I always suspected that if I had studied high school math, it would have been easier because I bet I would have known how to learn that material. But it gets real hard to change the way you are wired when you are my age, lol!
    Painting. Singing. Performing arts. Climbing mountains. Are these things “useful”? They’re not utilitarian at all. At worst, they’re a waste of time. At best, they elevate the soul higher. “Useful” is animal. Truth and Beauty are Human.

    I got a good education in this though educating my own children. We had a chapter study in catechism that discussed how people and animals are different precisely because we have souls and animals do not. The distinctions are some of what I listed above as well as things like laughter. Laughter isn’t utilitarian. But life without it? Purgatory.

    Leave a comment:


  • pickandgrin
    replied
    Re: Math 7

    Originally posted by Maria2 View Post
    Sometimes I have a crazy thought and I wonder if it really matters at all, *what* you learn- as long as you are learning, and in the process, learning how to learn, and being challenged to go ever higher?
    I would draw a distinction between learning/studying cumulative subjects versus non-cumulative subjects. But yes, the 'ever higher' is a good call. It's like "further up and further in."

    Perhaps you music people will enjoy this--it's quoted in Beauty for Truth's Sake:

    Music is the pleasure the human mind experiences from counting without being aware that it is counting. Gottfried Leibniz

    If you want to look into "number" more, I heartily recommend Stratford Caldecott's book on the quadrivium, Beauty for Truth's Sake. Wow. What a book.

    Leave a comment:


  • Girlnumber20
    replied
    Re: Math 7

    I think there are many many things that we learn or aspire to learn that aren't at all useful. They might just be beautifully useless, and all the more valuable for all of that. What "use" is music, after all? But I think that you absolutely need subject matter to learn with- and math seems like the ideal thing to hone in on when it comes to training the brain to think. Sometimes I have a crazy thought and I wonder if it really matters at all, *what* you learn- as long as you are learning, and in the process, learning how to learn, and being challenged to go ever higher?
    But I still think higher math is crucial. I ended up studying music, an area where I thought, higher math would not be needed- I had a terrible time with advanced theory and harmony. And there are "glitches" in my music ability to this day that I suspect have to do with the area of the brain that never learned how to think "that way." I always suspected that if I had studied high school math, it would have been easier because I bet I would have known how to learn that material. But it gets real hard to change the way you are wired when you are my age, lol!

    Leave a comment:


  • pickandgrin
    replied
    Re: Math 7

    Originally posted by Anita View Post
    Einstein loved Math because he said it brought him closer to the mind of God. There is order to the universe. That, to me, is almost as high as mysticism gets. If Math can bring you to eternity’s threshhold, then you do yourself a disservice if you do not at least try to go.
    Truly! I remember the day we found the surface area of a bead in calculus. It's one of my only memories of that entire year of math. Since that year, I have never found (nor needed to find) the surface area of a bead, but wow--I remember that moment. I was like C. S. Lewis with his brother's little make-shift garden on a tin lid. It awoke something of the numinous in me.

    ***chill bumps***
    Last edited by pickandgrin; 02-05-2018, 07:57 PM.

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  • Anita
    replied
    Re: Math 7

    Originally posted by pickandgrin View Post
    What interesting conversations you all are having here! I got through (barely!) high school AP Calculus and remember a direct corollary between two things: homework and skill. When I did my homework, I did fine in math. When I stopped doing my homework, I crashed and burned. Most of Calculus was crash and burn, but I did not fail! Sometimes that is a win in my book.

    Back to the questions though--Martin is always pointing out that the questions you ask will determine the answers you get (I'm probably paraphrasing him embarrassingly here, sorry!). One of the main points of classical Christian education is that we have jettisoned the merely utilitarian questions of, "Why do I need this? What am I going to use the for? If I'll never use it, why learn it?" etc. These are the type questions that are thrown at us regarding studies like Latin, Classical Studies, and cursive every day. Our answers are usually along the lines of "this is what you need to know to be a well educated human being, prepared for any calling that is placed on your life." Instead, we could ask: "What should you study to become a well educated human being, exhibiting wisdom and virtue, and guided by charity." Or similar...You can start from what do we include?

    Now I don't hear anyone saying they want to scrap math (although I am sure you could find some student volunteers!). What I do hear being discussed is how much math, and for how long? Ultimately, we'll be making these decisions for our children because we are homeschoolers and have assumed the responsibility to direct their learning year by year. Our states have varying requirements as well that guide us. Some of us have careers that will influence our children's perception and knowledge of certain fields.

    Another way to think of it is this: what are you good at--what do you love? When you explain to someone else why they should be curious what you love, how do you describe your field? Do you wish more people knew about the thing you love and could see it with your eyes? Cindy Davis is one of our chief math-lovers around here and I love the way she responded. I think a love of _fill in the blank__ is "caught" by being around people who love it. Anita, to your rhetorical question about "what if you'd had the other teacher" for the classes in which you did so poorly--we'll never know. What we do know from your story was the ability of a teacher to bring something alive to you, to teach it well, and to teach you to the point of understanding and appreciation.

    We were listening the other day to book 3 in the Peter and the Starcatchers series, The Secret of Rundoon. There's a point when two young men who are obviously after the heart of one girl come to a place of ally-ship (a word?). They are not friends. They are competitors. The author comments on their farewell--shaking hands like two men who respect each other a lot more than they like each other. I think we miss the mark when we allow being favorably disposed to something to be the indicator of whether or not it gets a place of importance. No one enjoys discipline at the time... Even if math isn't liked, there is a certain mystery, beauty, and majesty than can be appreciated, even if it's your nemesis. I'm thinking of Anne and Euclid.

    As Martin detailed in this article, the foundation must be solid. That is primary. Getting through all the levels for the sake of getting through is not a good goal all by itself. However, the attitude we adopt towards a subject will rub off on our students. If we see the three years of high school math as an unfortunate derailment of time then they will likely reflect that back to us.

    In summary, I would say that there are some things you can only learn through long perseverance. Latin, Math, and Music are some of the best fields of play you can find for "wisdom and virtue" formation. And yes, that window of school years is the time for putting tools in the tool box. Just my two cents to add to the conversation. I appreciate the question and the ensuing discussion.

    ETA: I picked up the book Here's Looking at Euclid and have on my to-buy list his follow-up The Grapes of Math. I really enjoy books like this that get me thinking about math in new ways!
    Einstein loved Math because he said it brought him closer to the mind of God. There is order to the universe. That, to me, is almost as high as mysticism gets. If Math can bring you to eternity’s threshhold, then you do yourself a disservice if you do not at least try to go.

    Leave a comment:


  • Anita
    replied
    Re: Math 7

    Originally posted by Aquila View Post
    I had a math teacher, who used to say that women couldn't do math because of the way their brains were formed. Yes, I am not making this stuff up. When I told my mom, she came to school to tell him what she thought of his theory. I always wondered what happened to him. Maybe he went on to program those talking Barbies. Maybe you remember them? It is was the ones that said, "I hate math!"
    There is fairly solid data to back up the fact that females are roughly as adept in STEM as their male counterparts. (Roughly. Men tend to catch on faster. But women tend to catch up faster, if that makes sense.) There is also a ton of data reflecting that most female students have not historically achieved higher careers in STEM because of teachers like Mr “I Hate Math” Barbie.

    But, controversially, there is also a substantial mound of study which indicates that women, classically and post-modern(ly?) do not tend to go as far in STEM because they do not stick with it as long and as consistently. The reason for this has been primarily: “children”. No one has said you *can’t* do both, they’ve just said that — the data has said that — more women aren’t PhD-chairs at MIT because they dropped out to have or rear their children.


    (Don’t shoot the messenger.)

    Leave a comment:


  • Aquila
    replied
    Re: Math 7

    I had a math teacher, who used to say that women couldn't do math because of the way their brains were formed. Yes, I am not making this stuff up. When I told my mom, she came to school to tell him what she thought of his theory. I always wondered what happened to him. Maybe he went on to program those talking Barbies. Maybe you remember them? It is was the ones that said, "I hate math!"

    Leave a comment:


  • pickandgrin
    replied
    Re: Math 7

    What interesting conversations you all are having here! I got through (barely!) high school AP Calculus and remember a direct corollary between two things: homework and skill. When I did my homework, I did fine in math. When I stopped doing my homework, I crashed and burned. Most of Calculus was crash and burn, but I did not fail! Sometimes that is a win in my book.

    Back to the questions though--Martin is always pointing out that the questions you ask will determine the answers you get (I'm probably paraphrasing him embarrassingly here, sorry!). One of the main points of classical Christian education is that we have jettisoned the merely utilitarian questions of, "Why do I need this? What am I going to use the for? If I'll never use it, why learn it?" etc. These are the type questions that are thrown at us regarding studies like Latin, Classical Studies, and cursive every day. Our answers are usually along the lines of "this is what you need to know to be a well educated human being, prepared for any calling that is placed on your life." Instead, we could ask: "What should you study to become a well educated human being, exhibiting wisdom and virtue, and guided by charity." Or similar...You can start from what do we include?

    Now I don't hear anyone saying they want to scrap math (although I am sure you could find some student volunteers!). What I do hear being discussed is how much math, and for how long? Ultimately, we'll be making these decisions for our children because we are homeschoolers and have assumed the responsibility to direct their learning year by year. Our states have varying requirements as well that guide us. Some of us have careers that will influence our children's perception and knowledge of certain fields.

    Another way to think of it is this: what are you good at--what do you love? When you explain to someone else why they should be curious what you love, how do you describe your field? Do you wish more people knew about the thing you love and could see it with your eyes? Cindy Davis is one of our chief math-lovers around here and I love the way she responded. I think a love of _fill in the blank__ is "caught" by being around people who love it. Anita, to your rhetorical question about "what if you'd had the other teacher" for the classes in which you did so poorly--we'll never know. What we do know from your story was the ability of a teacher to bring something alive to you, to teach it well, and to teach you to the point of understanding and appreciation.

    We were listening the other day to book 3 in the Peter and the Starcatchers series, The Secret of Rundoon. There's a point when two young men who are obviously after the heart of one girl come to a place of ally-ship (a word?). They are not friends. They are competitors. The author comments on their farewell--shaking hands like two men who respect each other a lot more than they like each other. I think we miss the mark when we allow being favorably disposed to something to be the indicator of whether or not it gets a place of importance. No one enjoys discipline at the time... Even if math isn't liked, there is a certain mystery, beauty, and majesty than can be appreciated, even if it's your nemesis. I'm thinking of Anne and Euclid.

    As Martin detailed in this article, the foundation must be solid. That is primary. Getting through all the levels for the sake of getting through is not a good goal all by itself. However, the attitude we adopt towards a subject will rub off on our students. If we see the three years of high school math as an unfortunate derailment of time then they will likely reflect that back to us.

    In summary, I would say that there are some things you can only learn through long perseverance. Latin, Math, and Music are some of the best fields of play you can find for "wisdom and virtue" formation. And yes, that window of school years is the time for putting tools in the tool box. Just my two cents to add to the conversation. I appreciate the question and the ensuing discussion.

    ETA: I picked up the book Here's Looking at Euclid and have on my to-buy list his follow-up The Grapes of Math. I really enjoy books like this that get me thinking about math in new ways!
    Last edited by pickandgrin; 02-05-2018, 02:12 PM.

    Leave a comment:


  • Anita
    replied
    Re: Math 7

    Originally posted by melaneesa View Post
    I was referring to math beyond geometry - trig and calculus. I don't think it's necessary for everyone to study those.

    I realize that makes me an oddball here. That's okay.
    Let me play devil’s advocate a little here...

    Pre-Algebra: 7th Grade — loved it. It made me feel confident that I wasn’t Math-impaired.
    Algebra I: 8th Grade — ditto (same teacher, btw).
    Geometry + Physical Science: 9th Grade — horrible Geometry teacher, horrible results. I was 14/15 and hitting puberty hard. My Math confidence hit bottom. I began to intuit that maybe there was something wrong with me. I did, however, fly through Physical Science with an excellent teacher (who is still my favorite teacher of all time).
    Algebra II + Biology: 10th Grade — I did okay in Algebra II (C+ for the year; I don’t remember who my teacher was). But I took Biology with the same excellent Science teacher and scored an A+ (and made the top 1% of state test scores). My confidence came back. But I was starting to think maybe Math was “too hard” for me.
    Trigonometry + Chemistry + Anatomy & Physiology: 11th Grade — bombed both Trig and Chem. HORRIBLY. Both teachers were way beyond me. And that year was rough, socially. I squeaked out a D in Trig and failed Chemistry. But I aced Anatomy & Physiology. Why? Same great Science teacher!
    Chemistry (again!): 12th Grade — same Chemistry teacher as 11th grade, same course, same result — although this time I managed to squeak out a D so I could graduate and not have to go to Summer school.

    When I got to college, I stayed as far away from Maths as possible and earned a Bachelor’s in English. I scanned (HEAVILY!) the Math requirements for graduation so as to not have to repeat the nightmare of high school Math. I was required to take deductive logic and college algebra (the “dummy courses”) and I, of course, had to take required Sciences for my core courses before I could take courses that were in my Major.

    Interestingly enough, I bombed college Biology and did fairly well — and enjoyed! — College Algebra. Why? The teachers! My college Biology teacher was immensely interesting but was way over my head (CREB Cycles and ATP chains, anyone?) but my College Algebra teacher was extremely patient and taught well. I remember figuring and plotting x and y and then graphing them with a certain amount of joy. It was so tidy. It was so interesting to see the shapes they made and how you could tell, by where the plot point landed, if your calculation was correct. I rather liked it!

    Now: have I formally “used” any of that information since my college days? No. But the discipline expanded my concentration, discipline, and view of mathematics and helped me relate to many more news articles and medical terms than I would be able to if I hadn’t taken those courses. Has that been worth it to me? Yes! Ask my husband how much media I have devoured on forensic medicine and epidemiology! One of my favorite writers is Oliver Sachs. And my most favorite genre is forensic mystery (figuring out whodunnit from clues left at the scene). I dare say I would not have nearly the enjoyment and the certainty of opinion on either of those subjects if I had shrugged my shoulders and said, “Meh. I’m never going to use this — why bother?” I’m far more literate (remember, I have an English degree) having taken — at least attempted! — somewhat higher Maths.

    I do wonder, though: if I had had my favorite Science teacher for Trig and Chem, would the result have been different? I think there lies the secret to successful learning and application.
    Last edited by Anita; 02-05-2018, 12:58 PM.

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  • Colomama
    replied
    Re: Math 7

    Originally posted by Miah View Post
    My husband was not algebraically inclined in high school and had to take it remedially in college. What bearing was algebra going to have for him to be a park ranger other than to keep him from being a park ranger?
    Waving! We're park rangers too. Most rangers lean towards unschooling hippie types. Finding a fellow ranger that's schooling classically is a needle in the haystack. Hi!

    I will say, my husband had to have a science related degree to apply. This required upper level math. He's now in management and routinely uses that higher level thinking and math to run his park from budgeting to big Horn sheep reproduction studies.

    I, on the other hand, have a BA not a BS. I struggled through algebra 1, failed. Sent to remedial algebra, passed. Geometry, passed. That was my high school. I studied statistics and called it good in college.

    I applied to parks through the experience side, not academics. I will say I used algebra in traffic accident reconstruction, wildfire spread, etc. I don't even know what's in algebra 2. Trig...same.

    My husband puts a heavy emphasis on higher level math. me...not so much.

    Interestingly he puts very little emphasis on latin even though he had to learn latin names and families of hundreds of Western plants and animals in college. He thinks I'm drinking he koolaid by teaching latin to the kids.

    Leave a comment:


  • Girlnumber20
    replied
    Re: Math 7

    Originally posted by Miah View Post
    I too loved algebra and trigonometry, but despised geometry. The proofs seemed so utterly pointless. One giant soul sucking waste of time. Now the useful aspects of geometry I liked. Weirdly I did enjoy basic programming languages in college. Practically speaking that pitiful 9 weeks of useful geometry has been the math (beyond basic operations) that I have used the most in life. The proofs? Forgotten instantly never to be used again.

    Has anyone ever thought about how useless high school math is in the long run? I loved math (geometry proofs aside). I had something like 109% in trig due to getting bonuses and I didn't even study. I just grokked it. I took trig and college algebra the same semester in college as coast classes...and that was the last time I ever used them. In 20 years I have never needed it. If you aren't in a few specialized professions you will never need it as an adult. Why do we stress so much and torture so many mathematically disinclined kids with it while lying to them that it will somehow turn out to be vital to every one of their adult lives? They know we are lying. My cohort certainly did.

    My kids like math, too, so following the standard path is not a problem, but it is for a lot of people. My husband was not algebraically inclined in high school and had to take it remedially in college. What bearing was algebra going to have for him to be a park ranger other than to keep him from being a park ranger? It's never really made sense to me the reverence with which algebra is held.

    I do know its a pattern of problem solving, but even second graders can solve problems using algrebra's basic method if it's stated in a word problem, which is what you actually find in everyday life. I am seriously asking. My youngest asks me these hard questions all the time and feeding him the lines I got as a kid...well it's like chumming the water for a shark. He smells that I don't believe them.

    I will be your test case. I never learned mathematics beyond basic arithmetic, say, up to about 5th-6th grade math. I can state positively that not learning algebra and higher math has very adversely affected me in my life. My college choices were very severely limited. Science classes were impossible, although I had developed a strong interest. It was a problem I constantly ran up against, over and over again, and that haunts me to this day as I struggle to teach my children, who are very interested in science and technology. Not learning higher math has placed so many unnecessary obstacles in my path, both practically and even psychologically speaking. I have gone through my life with the belief that my brain is incapable of higher level reasoning skills. I would never in a million years sentence my children to not learn algebra and higher math -to the best of their ability- to at least go through the sequence- because I know with a certainty that not learning it has affected the development of my own brain in such adverse ways, and has severely limited my own potential in life. All I can really say is that it is like having a giant hole in your brain where you absolutely know something is supposed to be. That is my two cents on the issue, for what it is worth. Not very evidence-based, I realize, it's just my own experience...

    ETA: You can't really know what you are missing unless you don't have it. If you didn't have math ability and the knowledge that comes only from "knowing" if that makes any sense- you might very well miss it, and even become an advocate for it. I'm willing to bet that you use the higher math you breezed through in ways that you may not be even aware of. To me it just seems like a beautiful gift.
    Last edited by Girlnumber20; 02-05-2018, 12:50 PM. Reason: attempt at clarity....

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