Shelly in VA
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Posts posted by Shelly in VA
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22 hours ago, Clarita said:
There is a documentary "The Story of Maths" it's a 4 part series and the 3rd part covers Calculus. It's fun and doesn't really derive the things, but it talks about why and the progression of how we (humanity) derived the mathematics we use today.
We watched this episode this morning - very interesting!
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22 minutes ago, Clarita said:
There is a documentary "The Story of Maths" it's a 4 part series and the 3rd part covers Calculus. It's fun and doesn't really derive the things, but it talks about why and the progression of how we (humanity) derived the mathematics we use today.
I can see why someone would want to know this knee-deep in Calculus. I know for me I went through a lot of math where the bulk of the lessons you have concrete real life problems like "I have 2 apples but I need to feed 6 people. How many more apples do I need?" Calculus was the first math subject where that isn't the case. Sure I want to find the area of something, but there isn't a clear reason why I'd want to find the area under a curve which is described by some crazy function of sine, cosine and polynomials. A simplistic answer is that the real life problems aren't always trying to find the area for some jug that is the crazy function of sine, cosine, and polynomials. Generally speaking the "area" may be an abstraction of some physical properties that can be described by some crazy functions of sine, cosine and polynomials.
For example if you are doing signal processing (say auto-tuning) you are manipulating sound which can be described as a bunch of sines and cosines combined together. You aren't necessarily finding the area under the sound. integration and derivation manipulates the curves to get the auto-tuning that you want. Which then translates into the code/circuitry you build to make that happen. The answer to can't you just build it and check, is yes you can but using the math is less tedious and allows you to tell a machine how to figure out what manipulations are needed themselves and in real time.
I'll look for that documentary. Thank you for the input and for the examples of calculus applications.
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1 hour ago, lewelma said:
Give him a curve and ask him to estimate the area under it. He will naturally break it up into sub shapes and add them up. Have him cut the shape into 5 rectangles and calculate the area, then 10 rectangles, and then 20 rectangles, and he will understand that he is getting more accurate. It is then quite an easy step to a limit as x approaches 0. All my students can understand this idea quite easily and can see how you could invent it.
50 minutes ago, lewelma said:You can do the same thing with gradients, it is just a bit messier. Use an example, show him how you can estimate a gradient at a point by picking 2 points on either side and getting the gradient of that line. Then pick points closer and closer together. Keep drawing the lines on the curve until it becomes clear to him that a tangent would obviously be the most accurate. Then pick 2 numbers only 1/1000 apart and calculate the gradient. Then do it with calculus to show how accurate your estimate is. It should be clear to him that someone could have thought of this. Only after you go through this process do you bring up the proof and walk him through it.
43 minutes ago, lewelma said:The other thing I do is differentiate between 'magic' and math. The way calculus is done in high school is 'magic'. I call it 'retrofitted patterns' which are based on math that most calculus kids never internalize. I make it clear, that taking a derivative using a retrofitted pattern is not 'math', it is memorising. So when doing a question, I make them tell me if they are doing an algebra line (which is mathematical and logical) or a calculus line (which is 'magic' and memorized and nonsensical). This distinction really helps kids. They have been told all their life not to memorize math, but to really understand it. And then they are given all this stuff to memorize and they think there should be some logic to it. And without limits, the patterns are nonsensical, but diligent kids think they are supposed to be logical and so get very confused.
Thank you!
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I have AoPS and Saxon on my shelf, along with an ancient college calculus textbook of mine. As easy as CTC was to use from my perspective, I think I'm going to have to switch to a traditional paper and pencil textbook at this point.
Thank you all for the help!
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On 9/19/2023 at 8:04 PM, Not_a_Number said:
Yes, they prove it in any decent calculus text. No, they don't spend enough time on it for the proof to make sense to 98% of kids . . .
What exactly does he want to understand, @Shelly in VA? Could you ask him if there's a specific thing he's stuck on?
I have now shown him a proof, and gone through it with him. When I asked what, exactly, he is stuck on, he says that he still feels like he doesn't understand why anyone thought to do this in the first place. I'm not sure what he means by that. I can't decide if this is teen debating or a genuine question from him!
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1 hour ago, daijobu said:
I'm not sure what part of AoPS is not concise.
I've pasted below the proof for the derivative of a polynomial. It's all of 4 lines.
The AoPS calculus textbook 320 pages, much slimmer than any other standard calculus text.
(Let me know if you can't view the image below.)
Thanks for posting that image! AoPS is certainly concise, you're right. What I was trying to say was that I was not looking for an entirely new curriculum to use, just looking for one source for a proof of derivatives, if that makes sense.
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On 9/19/2023 at 12:53 PM, regentrude said:
Don't they *prove* that in any decent calculus text? Like, derive for any function the derivative through a limit of the quotient of differences? They didn't do that in his class???
I assumed they did, but after you posted the question I asked him and also looked at the CTC lessons. It turns out that no, they don't, not at all. It's pretty plug and chug, which is why he was able to do the math but now he is frustrated that he doesn't understand it. I guess it's a good thing that he is questioning it now.
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11 hours ago, regentrude said:
Does he want to know why it works, or why one would want to solve those problems? For the latter, take physics. It becomes obvious why physicists would have invented calculus - rates if change ( derivatives) and summation of tiny parts of a continuum (integral)
He wants to know why it works. He has taken a conceptual physics class (not calculus based), and he does seem to understand how calculus is used in practical applications, but he wants to understand why the math of calculus works.
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2 hours ago, Porridge said:
I don’t know if this book will help (we just put it on hold at our local library), but it looks good.
That looks interesting! I haven't seen it before. Thanks!
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Hello! My son is doing calculus through CTC math, and it is going well. He completed the differential part of the course in the spring and the plan was to cover integrals this fall. However, coming back to it after the summer, he feels like he wants to understand the "why" behind working the problems. He asked his older brother, who was a math major in college, and was told that he was asking about something that covered two semesters of college classes, lol.
My question is what to do to give him some of the theory. Is there anything concise that could possibly provide that for him? I thought about the Art of Problem Solving Calculus book or Calculus Made Easy by Thompson and Gardner, but I'm actually looking for something more concise. Although my son is a strong math student, it is probably his least favorite subject. His quest to understand the theory is suprising me, actually!
I would appreciate any input! Thank you!
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I have not, but I have a friend who is currently using it for high school. Her oldest child is a sophomore this year. If you have a specific question or concern, I can ask her about it!
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On 7/27/2022 at 4:47 PM, shawthorne44 said:
I was just looking to see if the library had that. So far I'm batting zero. But maybe it is worth an audible credit?
I listened to The Black Count this summer as an audiobook and it was fascinating! After reading it, it made me want to read The Count of Monte Cristo so I am doing it as a read aloud this year with my teen. We are calling it his junior year read, haha, as it is so long it may take us the entire year! I highly recommend The Black Count if you can find it!
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Aside from the standard application essay requests, the only time any of my older kids were asked for anything like that was as part of honors college applications, which always seem to have their own set of requirements, anyway.
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Lantern English offers 8-week writing and literature classes for a range of ages, including several Creative Writing courses. Here is a link to their Creative Writing courses for grades 6-12: https://www.lanternenglish.com/thecreativewriter.
They are very affordable, and the quarterly class option is a nice choice. My son did several of their classes last spring as a 10th grader, and overall we were happy with the classes and the feedback he received.
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We used Year 1 for ds in 9th grade and planned to use Year 2 in 10th, but its release kept getting delayed. It is finally out as of this August! Both my son and I were very happy with it in 9th grade, so he is going to work through Year 2 this year as an 11th grader. That said, I don't know that I would do two years back-to-back with an older teen. We are just starting it this week, so I don't have a feel for how much the content and/or rigor change from Year 1 to Year 2. I will say that while I don't think you could tweak the demands of the individual assignments very easily, you could scale up the course by doing all of the required reading. For instance, in Year 2, the student has the option to either read The Agony and the Ecstasy: A Biographical Novel of Michelangelo or watch the movie version.
Hope that helps!
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I have not done this, but I have used some of the resources for older kids from Music in Our Homeschool and they have been good. I don't know if anything like this is there, but it might be worth looking.
I like the idea of bringing global music into morning time to add to your human geography studies!
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On 8/18/2022 at 4:56 PM, Momto6inIN said:
I have a big list of works I consider "credit worthy" and either have read or am willing to read and discuss. They choose from that list each year of high school. If you really want to see the list, I'll share of course 😉 but don't want to junk up the thread with a big list if you're not interested.
Specifically for senior year I require the following: To Kill a Mockingbird, Hunger Games trilogy, Til We Have Faces, I Robot, Night, Animal Farm, Old Man and the Sea, Screwtape Letters, and misc speeches from Lend Me Your Ears. My reason for saving these for senior year is because they are relatively easy to read but they also require quite a bit of maturity to really get and process. Since they are easier reading, ime they are often assigned too early in high school for the student to really get the most benefit out of them. YMMV
I love the idea of having a list and letting them choose titles each year! Thanks for mentioning that. Also, you bring up a good point about finding the right age for kids to be able to process what they are reading.
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15 hours ago, CAtoVA said:
Could you give me an idea or two of what an activity/craft you might do would look like?
Sure!
Some generic projects:
- Making bookmarks (woven from felt and ribbon, Sharpie and colored pencil on wide wooden craft sticks to create scenes that coordinate with the book, paper corner bookmarks)
- Word games (one the kids especially enjoyed was Hink Pinks; here is one Hink Pinks example, but you can find them for a range of ages with a google search)
- Origami animals that coordinate with the books (wolves for Lone Wolf by Kathryn Lasky, elephants for The One and Only Ivan by Katherine Applegate)
- Library scavenger hunts - maybe less accessible than when we did this in 2019, but a fun activity
- Ice Breaker games: This or That (everyone moves to the side of the area that matches their choice of two categories, i.e. cats or dogs, pencils or pens, summer or winter, etc.), Alphabet Soup (going around the group, people name a character, event, place, or object from the book where the first person starts with A, the next with B, etc.)
For Johnny Tremain by Esther Forbes we "silversmithed" by wrapping foil around cardboard and then etched in patterns with pencils.
For Behind Rebel Lines by Seymour Reit we decoded messages using Polybius square ciphers.
For The Year of Miss Agnes by Kirkpatrick Hill we worked on learning the ASL alphabet.
I have found that googling "activity ideas for [Book Title]" or something along those lines is very helpful! I've also searched for discussion questions (specific to individual titles and also generic book talk starters).
I hope that helps!
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1 hour ago, Lori D. said:
(I also posted on your X-post on the high school board)
If you do a mix of heavier and lighter works, doing all classics could work.
You could also mix in a few last YA works for contemporary works and/or more diverse perspectives for some overall balance as they transition into higher level/harder works.
Shorter classics:
1843 - A Christmas Carol (Dickens) -- Victorian language can be a bit stiff if not used to it/a stronger reader
1865 - Alice's Adventures in Wonderland (Carroll) -- light, humorous, great for discussing word play, poem parodies, and use of language
1872 - Around the World in 80 Days (Verne) -- adventure; Victorian language may be harder for some
1886 - The Strange Case of Dr. Jekyll and Mr. Hyde (Stevenson) -- Victorian language may be harder for some
1895 - The Importance of Being Earnest (Wilde) -- light, humorous play; can discuss themes of lying, deception. character, etc.
1897 - The Invisible Man (Wells) -- pretty accessible, fast read, good discussion on ethics and power
(the Time Machine is good too, but some students needed quite a lot of background/support info to get through this one)
1901 - The Hound of the Baskervilles (Doyle) -- mystery; not a hard read; the most "spooky" or "supernatural of the Sherlock Holmes works
1903/1906 - Call of the Wild (or, White Fang) (London) -- language/sentence structure was hard for my weaker readers -- also, Naturalism and survival of the fittest, so some animals die
1949 - Farmer Giles of Ham (Tolkien) -- light, humorous mock epic; the prologue is a bit hard, but after that, it's pretty smooth sailing
1951 - The Old Man and the Sea (Hemingway) -- easy to read; adventure; ends with a melancholy mood
1953 - Fahrenheit 451 (Bradbury) - a LOT of allusions and references that had to be explained; also, the writing style is unique and it took students through the entire first of three sections to get used to it
A few YA books that my 7th/8th grade co-op class students have enjoyed discussing:
- A Long Walk to Water (Park)
- Tuck Everlasting (Babbit)
- The Cay (Taylor)
- Enchantress from the Stars (Engdahl)Thanks! Great list of shorter classics - that is very helpful!
We read A Long Walk to Water in this group a few years ago and it was a great book for discussion!
I considered Tuck Everlasting, but I worried that it would feel too young for them. It's been a few years since I read it. It's good to know that your 7th/8th grade group enjoyed it! That makes me think it could be a good choice.
Thank you!
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19 minutes ago, CAtoVA said:
Some books that are not too "academically classic" but that still provide "meat" for discussion: The Night Gardener, Small Spaces, The Giver, The Adventures of Tom Sawyer, The Tale of Despereaux, The Phantom Tollbooth.
Frankenstein in the form of a graphic novel might be more accessible than the text for younger teens. There is a graphic novel that uses the original text but the pictures greatly assist with interpretation.
A little "dark" but could generate some good discussion: The Lord of the Flies.
I second The Call of the Wild and The Strange Case of Dr. Jekyll and Mr. Hyde.
You could also include (as a break from novels) a group of short stories such as four classic Edgar Allan Poe short stories (maybe good for around Halloween), or a group of Ray Bradbury short stories or Shirley Jackson short stories. Alternatively, (or in addition), you could read a group of short stories organized thematically or by genre, for example dystopian/sci fi stories with one story each from Arthur C. Clarke, Ray Bradbury, Kurt Vonnegut, and Ursula K. LeGuin. The themes for groupings could be endless, i.e., stories with "surprise" endings (An Occurrence at Owl Creek Bridge, The Open Window, etc.) or stories by "feminist" authors such as Kate Chopin, etc.
Do you mind sharing how you facilitate your book club? I have been thinking of doing something similar for one or both of my daughters (11 and 14 yo) but I'm not sure what it would/should "look" like. Do the teens meet in your home or is the club at a co-op? About how many kids do you think is a "good" number to have? Do you charge a fee to the parents or is this just something you "do"? How often do you meet? Is there anything required besides reading the selection (any writing or activities, etc.)? Sorry for so many questions, but I am curious. Feel free to totally ignore me, lol.
Thank you! I like the titles you mentioned and I like the idea of some of your themed groupings. I also like the idea of a group of short stories. Our past themes were an "around the world" year where we chose books from different countries/continents and a "genre" year where we had a brief discussion on key characteristics of the genre along with our book discussion. Our other years have been totally random titles, haha. Much to think about here!
I hope you are able to start a book club! I have LOVED doing this with the kids. It is so enjoyable to interact with them over books and to hear their thoughts on the things we read, and also to see them take in the opinions and input of the other kids. Here's what our book club looks like:
Meeting Place When our book club started, we met at the home of one of the members who happened to live on a farm with a lot of open outdoor space for us to meet. We would meet inside if the weather didn't cooperate, but usually we were outside. After 2 years, we shifted to meeting at a local park (that gives younger siblings a place to play) and/or a meeting room at the library, and that's what we have done ever since.
Size I find that we need at least 4-5 kids in order to get discussion, but when we have had more than 10, that doesn't work well. If the group is too large, the quieter kids don't speak up and we also start to have disruptions because it is enough kids that some start to clown around or cause distractions. For me, it is ideal if we have 6-8 kids, but it can work with slightly different numbers.
Fee I do not charge a fee. When I started, I wasn't even sure if we could get enough kids to participate, haha! At that time, I hoped that parents might take turns leading the discussion. It hasn't worked out that way, and I have considered having a nominal fee, in part because I think that would help some of the inconsistent members to be more reliable about attendance. But at this point it is still just something that I "do."
Frequency We meet monthly and our meetings last 90 minutes. I send out all of the dates at the beginning of the academic year, and we try to stick to something people can remember (this year we will meet on the 3rd Tuesday of each month).
Meeting Days The only thing the kids are required to do is to read the book before the meeting. I prep a few questions for discussion, and depending on the book, I will find some background information on the author or subject to tell the group about or an activity/game/craft that coordinates with the book for the group to work on after we finish our discussion. We start each meeting with the kids ranking the book on a scale of 1-10. They do this anonymously and I mark their votes on a number line on a clipboard so everyone can see how the group voted overall. Then we talk about the book, sometimes while eating a snack (if one of the other parents has brought something), then the kids either do an activity or just hang out until the end of the time. Our actual voting and discussion time lasts 45-60 minutes.
Book Selection Usually, I offer the kids several titles to vote on for upcoming meetings. I print a brief summary for each of 3-4 books and have the kids vote on what they want to read. I usually pick the first title of the year and then I have them vote on the next two books so that they aren't getting the titles at the last minute (except for right now when we are meeting in a few weeks and I haven't sent out a title yet, lol).
Let me know if you have any more questions! I hope you can get a group going!
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1 hour ago, Lori D. said:
If you do a mix of heavier and lighter works, doing all classics could work.
You could also mix in a few last YA works for contemporary works and/or more diverse perspectives for some overall balance as they transition into higher level/harder works.
Shorter classics:
1843 - A Christmas Carol (Dickens) -- Victorian language can be a bit stiff if not used to it/a stronger reader
1865 - Alice's Adventures in Wonderland (Carroll) -- light, humorous, great for discussing word play, poem parodies, and use of language
1872 - Around the World in 80 Days (Verne) -- adventure; Victorian language may be harder for some
1886 - The Strange Case of Dr. Jekyll and Mr. Hyde (Stevenson) -- Victorian language may be harder for some
1895 - The Importance of Being Earnest (Wilde) -- light, humorous play; can discuss themes of lying, deception. character, etc.
1897 - The Invisible Man (Wells) -- pretty accessible, fast read, good discussion on ethics and power
(the Time Machine is good too, but some students needed quite a lot of background/support info to get through this one)
1901 - The Hound of the Baskervilles (Doyle) -- mystery; not a hard read; the most "spooky" or "supernatural of the Sherlock Holmes works
1903/1906 - Call of the Wild (or, White Fang) (London) -- language/sentence structure was hard for my weaker readers -- also, Naturalism and survival of the fittest, so some animals die
1949 - Farmer Giles of Ham (Tolkien) -- light, humorous mock epic; the prologue is a bit hard, but after that, it's pretty smooth sailing
1951 - The Old Man and the Sea (Hemingway) -- easy to read; adventure; ends with a melancholy mood
1953 - Fahrenheit 451 (Bradbury) - a LOT of allusions and references that had to be explained; also, the writing style is unique and it took students through the entire first of three sections to get used to it
A few YA books that my 7th/8th grade co-op class students have enjoyed discussing:
- A Long Walk to Water (Park)
- Tuck Everlasting (Babbit)
- The Cay (Taylor)
- Enchantress from the Stars (Engdahl)Thanks! Great list of shorter classics - that is very helpful!
We read A Long Walk to Water in this group a few years ago and it was a great book for discussion!
I considered Tuck Everlasting, but I worried that it would feel too young for them. It's been a few years since I read it. It's good to know that your 7th/8th grade group enjoyed it! That makes me think it could be a good choice.
Thank you!
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2 hours ago, 8filltheheart said:
There are so many good options. F451/Martian Chronicles, Dracula (a fav here), Little Women/Jane Eyre, I Robot/Time Machine/Invisible Man, any Sherlock, Gulliver's Travels
Not sure if you have a certain genre you prefer. But that is a general idea of some.
Thanks! I am planning to have them read Dracula in October. I hadn't considered some of the other titles you mentioned - thank you!
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Hello! For a book club that I facilitate for kids 8th grade and up, I am considering having a classics "theme" this year, but I don't want the group to be too heavy. I am looking for titles that will promote good discussion, but I want to avoid lengthy books because the kids are getting to an age where their academic reading requires a lot of time. Does anyone have any suggestions? I am thinking of titles like The Pearl (Steinbeck), Animal Farm (Orwell), and The Outsiders (Hinton). But I'm not sure... I want the group to continue to be fun and meaningful, but I don't want it to feel too academic. It is strictly a book club, not a literary class!
We have been a part of this group for several years now, and I generally give the group several titles to vote on each month. Their favorite titles have included Framed! (Ponti), A Long Walk to Water (Parks), My Side of the Mountain (George), The Green Ember (Smith), Inkheart (Funke), and City Spies (Ponti).
When they were younger, I had so many good titles to choose from! Now I am struggling with finding titles that don't feel too young but also aren't too challenging for the younger teens.
Thanks!
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Hello! For a book club that I facilitate for kids 8th grade and up, I am considering having a classics "theme" this year, but I don't want the group to be too heavy. I am looking for titles that will promote good discussion, but I want to avoid lengthy books because the kids are getting to an age where their academic reading requires a lot of time. Does anyone have any suggestions? I am thinking of titles like The Pearl (Steinbeck), Animal Farm (Orwell), and The Outsiders (Hinton). But I'm not sure... I want the group to continue to be fun and meaningful, but I don't want it to feel too academic. It is strictly a book club, not a literary class!
We have been a part of this group for several years now, and I generally give the group several titles to vote on each month. Their favorite titles have included Framed! (Ponti), A Long Walk to Water (Parks), My Side of the Mountain (George), The Green Ember (Smith), Inkheart (Funke), and City Spies (Ponti).
When they were younger, I had so many good titles to choose from! Now I am struggling with finding titles that don't feel too young but also aren't too challenging for the younger teens.
Thanks!
Semester Long Government Class Using Crash Course?
in High School and Self-Education Board
Posted
@BakersDozen Would you be able to send me your syllabus as well? Thank you! I appreciate it!