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Brad S

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  1. Glad to hear those two worked out well together. It seemed to me that Anton, or his collaborators or commenters, really understood science and that it wasn't written by someone with no experience outside math, so Anton seems like a nice complement. Spivak seems like a great next step; although you may want to get a later edition, his first edition of "basic" calculus is free online. ETA: link
  2. AP Calculus BC: Note that there are modest upcoming changes in the AP Calculus tests starting with the 2016-17. As far as I could tell, they’re probably all fine, but the Stewart and Foerster texts might be the most likely to have a shortcoming with linking definitions with findings, etc. (There is, however, a sample AP course of study which uses a combination of those two texts, so they must think they’re OK.) For developing an AP Calculus BC syllabus and course, most of the texts above would work. In addition to the text, most people use an AP test prep book, which provide practice problems, which seems to make the link between some texts and the AP test more feasible. Barron’s seems recommended the most. There are a few resources from the College Board for making sure your course matches the AP curriculum (thanks, Arcadia, for pointing me to the new ones!), and possibly to get the AP designation. The AP Calculus BC Course Planning and Pacing Guides are super long, like 70 pages or so, and I’m not sure it’s worth the effort for a home AP calculus course. But, by primary text/texts, these 2015 guides are: Hughes-Hallett, et al., Calculus: Single Variable, 6th ed.: guide Combined Foerster Calculus, 2005 plus Stewart Calculus 7th ed., 2012, guide Finney, et al., Calculus: Graphical, Numerical, Algebraic AP Edition, 4th ed., 2012 as primary text plus four other resources incl. Hughes-Hallett: guide ETA: links and crosswalk of texts to AP Calculus BC course descriptions.
  3. Note: I edited this and added some text shown in green below to reflect new findings. If reading for the first time, just ignore the color differences. I’ve been looking at potential calculus textbooks to be used mostly for individual study by an eleventh grader. A particular career path has not been chosen, but early inclinations are the natural sciences or social sciences. A bit of mathematical rigor is desired, but more for a flavor and some experience rather than preparation for a career as a mathematician. The student will have used Foerster’s Precalculus, a moderately rigorous text (IMO well below AoPS, very slightly above Brown, above Larson or Sullivan, and well above Lial) and would like to take the AP Calculus BC test after the course. There are some calculus texts listed in the pinned High School Math thread and the College Board website lists quasi-approved texts as well as detailed AP class descriptions. Of course, time was limited and these are only my opinions, but I thought some other folks might be interested. Please let me know if you have comments or questions. A one paragraph review for each book follows: Foerster Calculus, 2nd edition, 2010 The look and feel, as well as the wording, of the Foerster text seems more like a high school text (mostly a plus for Foerster in this context) and written with the AP test in mind. I couldn’t find any coverage of the rigorous epsilon-delta proofs in Foerster, although it might be there (at least the definition of limit is given in epsilon-delta form on p. 34). Foerster doesn’t seem to prove even some of the simplest theorems that many textbooks prove, including Larson. I consider that a significant negative. While proofs may not be covered on the AP calculus tests, I think that some understanding that the results of calculus have been proved with rigor, and at least a couple of examples, is pretty important. For us, that means that Foerster would only be considered if some kind of supplementation were done with another text. Throughout the book, Foerster, as many other texts published in the last 20 years, seem to cover four ways of seeing the math: verbal, algebraic, visual, and numerical points of view. The problem sets seemed of average interest and application, mostly in a physics and engineering context -- the most important evaluation is when you go to do them and how tightly they fit with the text, and I can't really assess that. Any experience with the problem sets of Foerster or other texts? In sum, I'm not as impressed with Foerster's Calculus as his Precalculus and would only use it together with another text. But the student reviews of the book on Amazon are pretty positive, so it would seem reasonable to use it together with another book. Note that the new AP Calculus BC exam, starting about 2016, has somewhat more emphasis on linking definitions with results and more emphasis on series, so Foerster's minimalist calculus approach might need to be supplemented slightly even if your only goal is to get to the minimum needed for the new AP test. Anton, Bivens, and Davis, Calculus (Early Transcendentals), 7th edition, 2002, looks and feels like a college calculus text. I really like how Anton separates out rigorous (epsilon-delta) proofs so that they can be covered (or not) along the way; we’d probably do a few early on and then skip them later, unless DS really gets into it. I couldn’t see that Anton had better problems than Foerster. They both seemed average at first glance, mostly in a physics and engineering context. I will say that some of the Anton problems and text had what I'd consider excellent practical advice for using calculus in science, exceeding the Hughes-Hallett and Larson texts reviewed below. This edition of Anton starts with an 100-page introductory review chapter on functions, whereas Foerster starts at about the same place as Chapter 2 of Anton. If you feel like your precalculus was strong, that seems like extra text to wade through; if you feel like your precalculus was weaker or partially forgotten, that chapter might be a plus. Most texts have a brief introductory precalculus or functions chapter, some tightly integrated into the text and some more optional. The last five chapters in Anton go beyond topics covered in Foerster in this version, perhaps only multivariable calculus topics. One possible approach for us would be to use Foerster most of the way, but to get some experience with rigorous proofs in some other book, like Anton’s Chapter 2 (Limits and Continuity), Chapter 3 (The Derivative), and maybe a few other places if interest exists. After reviewing the text myself, I later read the reviews on Amazon: they weren't good; a number of reviewers said that Anton did not explain concepts well for a first-time student. This has definitely given me some pause. On the other hand, a comment below says that her (extremely talented) DS found it a useful supplement to AoPS calculus. An intriguing text upon first review is Hughes-Hallett, Gleason, McCallum, et al, Calculus (Single Variable), 3rd ed. It strikes me as concise, elegant, appropriate for high school or college, and has some nice problems across disciplines. While it has the standard background chapter on functions to start out, it’s efficient, 54 pages vs. longer in some books, and leads nicely into the next chapter on limits and derivatives; for example, chapter one provides motivation for limits and derivatives along the way, so it doesn’t seem like a waste, even though it starts out at a pretty basic level. The text does use the rigorous epsilon-delta form in the definition of the limit as part of the main text and does prove some easier results. The text seems very careful with the mathematics, and has “applications†across several disciplines. Unlike Anton, however, the text seems highly disjointed from real data, real science, and probabilistic phenomena. Anton gives a solid introductory section on modeling (Section 1.7), including deterministic and probabilistic, and gives enlightening scientific points along the way in the text; on the other hand, I couldn’t find evidence in the Hughes-Hallett text that the authors were even aware of the points in the Anton text let alone clearly conveying them. In addition to not finding these modeling and scientific points covered, I found the initial example of a function unnecessarily confusing and begging for a probabilistic explanation. Hughes-Hallett does have a clean, concise style which would seem pleasant for both high school and college students, so we have some trade-offs here. Even though it’s one of the shorter texts, the presentation of key concepts like limits and the derivative seemed to go slowly, which is a big plus. I was not able to evaluate how easy or hard the problems were nor how well they complemented the presentation, but they don’t seem like just routine calculation. For comparison in length, Hughes-Hallett is 558 pages – it has quite a bit of white space, so it’s on the shorter side; Foerster is 658 pages with some white space; Anton 788 pp. before the vectors chapter starts, and it’s pretty dense; Larson 760 pp. before vectors and it’s pretty dense too. You get more depth with Anton, but it is longer. (For comparison, AoPS has about 304 pp of fairly dense text.) ETA: While I personally still like the Hughes-Hallett text for the reasons described above, the reviews on Amazon are pretty negative, more so than for most competitor texts. The main complaints seem to be that: (1) the text doesn't explain things well to the student (hard for me to tell myself -- looks reasonable to me, but I've already learned the material); and (2) the problems are too big a jump from the text. I might still use it, but it would be with a text like Larson or Thomas readily available if DS doesn't understand it. I'd also carefully preview the problems for appropriateness. Larson, Hostetler, and Edwards Calculus, 8th ed., seems like a basic, standard text, with a feel of either a high school or college book; some problems like those marked “Writing About Concepts†seems somewhat geared to the AP exam. Many of the theorems have proofs in the text. The proofs given didn’t seem particularly hard; there were, however, a few Putnam Exam challenge problems, clearly marked as such, in the first chapter, so there’s at least some exposure there (if you get those, you probably need a different book!). The formal epsilon-delta limit definition is given (p. 52, and used on pp. 53-54), but I didn’t check the later proofs for rigor. There was a short discussion of Fitting Models to Data on pp. 31-33, but it was poor; not only wasn’t it very informative, but it even gave bad advice by saying “The closer |r| is to 1, the better the model fits the data.†(For example, a perfectly described relationship where there is error in the measured response variable can be far less than 1 and lower than the correlation coefficient of a poorly modeled phenomenon.) Some of the problems aren’t well stated either (e.g., p. 89, #60 which doesn’t start with something like “According to ___ , …†and the reader may confuse this approximation with a physical law. It may sound picky, but if we’re trying to teach good problem solving skills, it would be good to be careful. On the plus side, there are a lot of problems ranging from simple exercises to somewhat real world problems in a wide range of disciplines, color figures, and there are a number of helpful hints where students have had problems; it appears to me that they’ve probably had some helpful comments over the years with this widely used and modified text. Overall, the text seems OK but not great. We might use it as a supplement for an alternate explanation if something is unclear to DS from the main text. Later note: upon reading the reviews on Amazon, which were very positive, and the positive comment by Lisa in VA is in IT, and AK_Mom4's comment that Larson's explanations are clear, and both WTMers comments about the availability of good supplemental materials, I'm reconsidering Larson's text; while I definitely have reservations with the book, it does have a lot of fans in its ability to explain concepts to first-time calculus students, and that's indeed an important use for a textbook! Speaking of supplemental materials for Larson, there have been a number of positive comments on the Chalkdust videos: Lisa in VA is in IT (linked above), Brenda in MA, Jane Elliot, plansrme and a whole general thread on Chalkdust math videos (not cheap new, however). Stewart Calculus, 5th ed.: seems a bit more wordy. For the epsilon-delta rigorous proofs, there is a separate section (2.4), which redefines limits from an earlier section. It appears that the rigorous definition is an optional section (per Preface, p. viii, 3rd paragraph from end) and is not used in later proofs. There are also separate sections on applications in different fields, which may be useful to use in a college setting where you have people from different majors taking different classes, but for use with a high schooler with an unknown major, it just seems like more text to wade through. To me, the text seems to have a college text flavor; while not a deal breaker, by any means, I don’t consider a college flavor an advantage for a high schooler taking calculus, especially since the rigor seems less. We might use it to supplement a troublesome section here and there, but we won’t use it as our base text; I’d probably use Larson or another text as a backup reference text before Stewart, which may have been my least favorite. I prefer Hughes-Hallett, Anton, Larson or Thomas. Some reviewers on Amazon and elsewhere seemed to like Stewart but some strongly disliked it. Life of Fred Calculus looks to be one of the least mathematically rigorous. The rigorous epsilon-delta definition of a limit is left to an appendix; even Stewart has it as an optional section in the main text. If your kids love Fred and just want to get a feel for calculus, it may be a good choice. AMA has a brief review of Fred’s calculus. We’ll go with a different text. Saxon only goes through AB and probably too mundane for DS. Finney, et al., Calculus: Graphical, Numerical, Algebraic (2003). This is clearly a standard high school textbook, which seems to provide the most basic of AP Calculus BC training. While the limit is defined in epsilon-delta form, it doesn't seem to be used except for some exercises in an appendix, and I didn't find any proofs in the book. The material, including definitions, does seem carefully presented, but it's a very elementary text, and there are quite a few exercises rather than challenging problems. There is a very, very heavy use of graphing calculators to give a graphical view of functions, limits, etc. -- not necessarily bad, but I'm trying to give an idea of the type of text. While the text has a strong school text feel, it isn't plagued by excessive, distracting sidebars, at least in the edition I reviewed. The text is too basic for us, but I could see the text's usefulness to explain concepts which are not grasped via the primary text you're using. The order of most of the texts seems pretty standard, except for some including transcendental functions earlier vs. some later, so some cross-use of texts isn't out of the question. MIT Open Courseware looks like a good possibility, but DS prefers a book rather than lecture focus. We might try it with an early topic and see how it works. Strang also has a calculus text available for free download on the MIT Open Courseware site. I have not had a chance to review it yet, but his Linear Algebra and Its Applications text was my favorite math text as an undergraduate. My prof. (admittedly) was a terrible teacher, but I had no problem learning the material from the text, and I've heard that his calculus text is clear and direct too. At the same MIT OCW site, Dr. Strang has a series of videos "to show ways calculus is important in our lives." AoPS (Patrick) Calculus, 2nd ed. (2012) would merit serious consideration for folks who’ve successfully used AoPS’s courses in the past. While the AoPS text doesn’t prove as many results as Spivak or Apostol, it is a rigorous course, and seems comparable in rigor to Hughes-Hallett or Anton, all being solid books. In tone and style, AoPS strikes me as distinctly high school like, even appropriate for a prepared early high school student. If your DC thrives on AoPS, it seems like a great choice. It has that math competition preparation flavor, but I didn’t see a lot of real-world application in AoPS except in a highly mathy sort of way; Hughes-Hallett has problems using the context of a variety of disciplines, which would be more appealing to my more science-oriented DS, although they are still pretty artificial IMO; Anton goes beyond that and really enhances scientific understanding of the uses of calculus in experimental sciences (the actual problems seem mostly physics and engineering). I think Anton provides the best combination of rigor and promotion of use of calculus in non-math settings, but it is a bit longer and has more of a college feel. Larson has a number of proofs and a number of real-world examples, across many disciplines, but I’m not sure they’re as tightly integrated into the presentation as in Anton nor promote the same level of understanding. A lot of text choice has to do with how clear the explanations are in practice, and I don’t have experience on that with these 21st Century texts. Your experiences with using calculus texts to explain concepts would be appreciated! ETA: some of the links and the Finney text review. Some later notes shown in green and will be discussed in a later post. The review of Thomas' Calculus below was added in response to a question by Mike: Thomas' Calculus: Early Transcendentals 12th edition (2010) based on the original work by George Thomas as revised by Weir and Hass. There are many editions of Thomas' Calculus and this one is intended as a college course either for those with high school calculus or without. (For example, the text University Calculus by the same authors is a streamlined version meant for those who took calculus in high school, so it's outside the scope of this review. The next text to be reviewed is an older, explicitly high school text by George Thomas.) Thomas' Calculus seems to be at about the same level as Anton; there's perhaps more theory in Thomas' text but there's a good amount of rigor in Anton, and probably more than Thomas, if you select it, and Anton seems to have a significantly greater depth of practical problems. Thomas' Calculus 12 ed. appears rigorous, although it does not prove every result -- none of the texts except perhaps Spivak and Apostol do, but that's not what we or most high school students want anyhow. Thomas' has a lot of exercises, both simple and medium in difficulty. Thomas' seems like a good book, although I like Anton better for deeper applied problems and seemingly more flexibility with the theory. The most important thing, however, is how well the text explains concepts to the new learner, and, unfortunately, I can't say for sure. I'll just say it's worth considering. Thomas Elements of Calculus and Analytic Geometry 2nd edition (1976) is an adaptation of George Thomas' calculus for high school students, by George Thomas himself. It looks like a 1970s high school textbook. Transcendental functions are covered late in the book, which I'm not a fan of since it leaves less time for working with transcendental functions during the course -- this is hotly debated, which is why most textbooks nowadays have versions with late transcendentals and early transcendentals. The presentation in this relatively simple, short book does strike me as straightforward and probably fairly easy to follow. There are a few simple theorems proved. Most of the problems are simple exercises with little sense for the range of applications of calculus and not many challenging problems. In summary, I don't think this is the best choice as the core text, but it seems to have value in having around as a way of describing a problematic topic if a student is struggling.
  4. Ruth, I think you have a reasonable concern here, potentially. I don't see anything wrong with taking two years to do something, if that makes sense with other demands and scheduling issues, but I would be concerned if a pattern of missed deadlines is occurring. You may want to get more buy in from DS before setting the deadline, if he didn't buy in when the deadline was set. Or perhaps you could teach him to build in contingencies (e.g., "be done a week early to allow for illness during the semester, unforeseen events, unexpected difficulty near the end," or whatever makes sense in his case). Just a few thoughts. It does seem pretty correctable now that you've identified it.
  5. Feelings are what they are. (I think you should feel the way you feel, of course, and not change that.) Yes, I think it's fair for gifted kids to do fewer hours and achieve more if it's healthy and working. I think the efficiency is a sign the educational set up is working well. Your son is using the time wisely and apparently it's healthy for him. The "free time" is a chance to find out more of what interests him, and that's really important in life and competitive fields -- if you're not interested in the area, you're not likely to do really, really well in a competitive field. And that's before we get into being happy with what you're doing. I do think that some free time to think and explore helps prepare for life in competitive fields, at least if the time is being used productively. I would think that what your DS is doing takes a great deal of mental energy. Doing busy work to fulfill assessments is likely to drain DS's energy, interest, and creativity.
  6. Before reading the replies, I was going to say pretty much the above. It sure seems to me your older is phenomenally successful exactly as he's doing things. Why risk messing him up? For what, really? I think you're worrying unnecessarily too.
  7. No, I wouldn't expect test prep books to include the changes yet, and I'd even be careful a year (or two) from now with test prep books, but I was wondering about textbooks. An example AP Calculus BC textbook list from the College Board website is here, but it wasn't clear to me as to whether or not that's for the new standards. Fortunately, this change is fairly minor compared to some AP course changes.
  8. Does anyone know how existing textbooks match up to the new AP Calculus BC standards? I bolded the two general parts, and the second one should be relatively easy to check, but that first one seems a lot harder to check. I'm sure that the textbook companies would love for you just to buy the latest edition, but that's not feasible here. On the other hand, couldn't any loose ends be caught by using an AP Calculus test prep book at the end of the class? (I've seen a lot of good things about the Barron's prep book. Anyone have experience with it?)
  9. I didn't use Foerster for algebra 2, but at least his Precalculus book has an Instructor Guide with CD; the paper book had lesson plans broken down by day and the CD had a solutions manual. There are some other threads from the past year talking about this same topic: http://forums.welltrainedmind.com/topic/561410-has-anyone-used-kolbes-lesson-plans-for-foerster-algebra-2/ http://forums.welltrainedmind.com/topic/559304-anyone-have-a-foerster-algebra-2-schedule-to-share/ ETA: If I were to do algebra 2 again with DS, I'd probably use Foerster (or Dolciani/Richard Brown update).and KhanAcademy.org videos if videos were ever needed.
  10. I'm looking for an abridged version of Don Quijote in Spanish, something like the parts of Don Quijote recommended by SWB but in Spanish. DS read a simplified graphic novel Don Quijote de la Macha by Oceano press in late elementary school (he laughed heartily reading about crazy Don Quijote), and a short excerpt in Andrade, Marcel (ed.) Classic Spanish Stories and Plays (in Spanish), which had nice, brief introductions and vocabulary footnotes. But he could go deeper into this masterpiece of world literature. It would be ideal to have some vocabulary footnotes along the way given how vocabulary has changed over the centuries. DS is fluent in Spanish about at the level of an average Spanish or Latin American 9th grader now...if you've got a suggestion for something at a higher level, we could wait. Thanks!
  11. I came across this thread as I was looking for information about calculus texts for a high schooler. Excellent threads like these maintain their relevance, and I think that some folks new to the High School Forum in the past 2-3 years might find this thread interesting. Thanks to all the posters here. Some follow-up confirming some of mathwonk's statement (which I already knew was true having run calculus help sessions many moons ago). The Mathematical Association of America put out a report in 2015 which said much of the same about the desired preparation for calculus and beyond in college, including in the Preface, p. vi, esp. paragraphs 3-5. ETA: link
  12. What are people using for calculus? We're likely to go mostly with a text as the primary means for instruction. I'd love to hear things that didn't work as well as worked. Thanks!
  13. We used Jacobs for Algebra 1 and Jacobs for Geometry (3rd ed), and had the videos for both. Dale Callahan does the videos for geometry, whereas someone else does for algebra. My son struggled at times with the algebra but geometry was a breeze; he hardly ever watched the videos for videos and hardly asked a question and did very well with Jacobs geometry; we really liked the Jacobs Geometry text and found it very clear. We used the syllabus of AskDrCallahan, including problem set, and supplemented with a few extra proofs and did the non-Euclidean geometry chapter in detail, but it would be fine to use the syllabus exactly -- except to skip the algebra review and use an algebra book for algebra review or just finish algebra 1 and/or start algebra 2 simultaneously. If I were to do it over, I think I'd use Foerster's algebra 1 and use Jacobs algebra for explanation where needed and use Khan Academy for regular review of problem sets (and the videos where needed for clarification). YMMV.
  14. Agree. Dassah: Since your daughter had Singapore 1-7a, some of Foerster's Algebra, and seems to understand pretty complicated word problems, you might be a long way toward a very successful algebra 1 outcome. It may be that some periodic review is all that's needed, along with backing up a bit to where the material is understood. I think KhanAcademy.org does a great job with efficiently reviewing (and refreshing) older concepts and that might be just what you need. Since math is so cumulative, any missed or forgotten piece along the way can cause problems. After spending a few days with KhanAcademy, you could try the current Foerster chapter or an earlier chapter where trouble started, and see if it's now clearer.
  15. I agree with splitting it out by your high school kid and younger kids. Since it appears your other two kids will be going into 6th and 8th, you could post their question in the "logic stage"/middle school section. Especially by high school, separate providers by subject are commonly used. In some states, individual classes can be taken at a local community college, sometimes for free. Best wishes. Hang in there!
  16. I agree. I think the Norton Anthology of World Literature does a good job of picking important literature from around the world. Since you've only got a semester, you might want to get the Shorter Edition Vol 2 (Vol 2 covers from about 1650 to the present); you could also get the regular (called expanded in earlier editions) Volumes E (1800-1900) and Volume F (1900-2000). If you get the Second Edition (2002) or a previous edition, called the Norton Anthology of World Masterpieces, you can pick them up for inexpensively on AbeBooks, Amazon, etc. There is also a helpful book called "Teaching With The Norton Anthology/World Literature (Shorter Second Edition)." The Norton Anthology has brief introductions of each period/region/literature type as well as about each author and work. The instructor guide mentioned about has somewhat longer introductions and we've used these instead -- they're still short, but seem more like "just right" for a high school setting.
  17. Thanks, Mark. I also really like Foerster's Precalculus problem sets. May I ask what other texts and online resources you might recommend to accompany Foerster's Calculus (or Precalculus)? Thanks.
  18. I'm not sure if this is what you want, but the price list and ordering page on the Chalkdust site is here.
  19. We weren't planning on getting any videos to accompany a text (and not Math w/o Borders videos). DS does seem to like the KhanAcademy approach, but rarely uses those videos, and I've heard of the too, although I don't know much about them. DS tends to prefer a text and, if he doesn't understand something, to pick up an alternate text. Since Chalkdust is based on the Larson and Edwards text, and Larson seems a bit too calculation focused for DS and my tastes, that doesn't seem like a good starting place for us. But if the Chalkdust calculus videos are THAT good, maybe we'll consider them if DS struggles with Plan A. Thanks.
  20. I'm looking over options for home schooling calculus. We'd like something for 11th grade and DS would like to take the AP Calculus BC test. He finds AoPS frustrating (likes an explanation first then problems rather than trying them first as in AoPS), yet doesn't want something that's just a drill of exercises. So we're somewhere in the middle: a little beyond the minimum for the AP Calculus BC test, but not much. (FYI, I can answer questions if DS has them, but he prefers using a text.) In looking over a number of texts and reading the pinned High School Math thread on the WTM board, I'm considering Paul Foerster's Calculus and bought the text, although I'm by no means set. Here are my thoughts on some of the texts listed on the pinned thread: Anton, Davies and Bivens: This looks like a possible alternative Apostol: Too challenging given DS background in proofs and maybe too proofs focused for DS interest AoPS: Too challenging/frustrating although the text looks elegant to me when I took a quick look Larson and Edwards, Calculus of a Single Variable: Seems too calculation focused. MIT Open Courseware: Looks like a possibility but DS prefers a book rather than lecture focus Saxon: Only through AB and probably too mundane for DS. Spivak: Too challenging and too proofs focused for DS interest Stewart: Seems a bit dry and with problems too heavily physical science and engineering focused (we like more variety). I may be off the mark on some of these comments by looking at an earlier version of a text, looking at unusual problems, etc. BTW, I have several older calculus books lying around. Although it's not necessary for us to get an AP-approved syllabus, we want to be sure to cover what's needed for the test (and be aware where we're covering topics not on the test). There's a list of reviewed texts at the College Board website, and Foerster is not on it. (Actually, of the list on the pinned thread, only Anton, Larson, and Stewart are on it, but most, if not all, would basically work.) Has anyone used Foerster's Calculus basically for self-teaching? Anton? The MIT Open Courseware? Any other recommendations? Thanks!! ETA: There are upcoming apparently modest changes for AP Calculus starting with the 2016-17 school year, as described in this WTM thread linked here.
  21. OP: not sure what your colleges would want, but a general answer to where AP Spanish fits was posted at: http://forums.welltrainedmind.com/topic/588830-high-school-spanish-4-reading-list-x-post/?p=6883995 This is also covered to some extent in the post linked above; as you said, AP Spanish Lit seems quite a bit more difficult. I think the lit course is generally the course after AP Spanish Language and Culture, where it's even offered. The first AP course is more about Spanish proficiency in a culturally aware setting. The Spanish lit course seems very focused on literature, with a specific reading list, and might be reasonable to take with AP English Lit. You'd need to look at how a specific college would give credit, but AP Spanish lit does not seem to be just a more advanced version of AP Spanish Lang and Culture even though the lit class is more advanced (e.g., not like AP Calculus BC which would make AP Calculus AB redundant and unnecessary). On the other hand, since the lit. course is more difficult, some colleges might possibly give credit for both if the lit. score is high enough. You really need to check with the specific college(s) on this one.
  22. This sounds like a good idea on how to use the book. For us, DS had been in a bricks-and-mortar school the previous year and I was less in tune with his writing ability (and that DS claimed he didn't need the exercises), we mostly used it in early 9th grade as a weekly routine of: read the chapter; discuss; and write an essay of the type in the chapter. Although that may not fit others, it worked pretty well for us. DS thought the book was excellent and resonated with him. By going through it in about 10 weeks, it has allowed DS to work on more writing assignments, now with an outside tutor. We've very happy we used WWaT and found it a great way to start the year.
  23. In Jacobs Geometry 3rd edition, I think you can run it with a discovery approach but we didn't. We ran the 3rd edition as basically direct instruction without a discovery approach.
  24. You may also want to consider Harold Jacobs Geometry. We used the 3rd edition with the AskDrCallahan.com videos (rarely used the videos, however) and were very pleased with the text (although not the algebra review problems, where you could use chapter reviews with another book or start Foerster's next book slowly, concurrently, so the algebra doesn't get rusty, and the Jacobs Geometry course can probably be done in less than full time of a school year); some people have also liked Jacobs's 2nd edition. We used Foerster after Jacobs, so it's not the same order, but the combination worked fairly well for us.
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