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is there an ideal pace for working ahead of your student in math?


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@Garga I think maybe you did this?

I am working ahead of my son in Alg II, and I find that if I wait too long between my learning "sessions" then I have to retrace steps and familiarize myself again with the section.  Lately the way I have been doing it is spending several hours in one sitting working on the math, and then hit it again a week later. it's not ideal but I have not been successful working every day on it thus far. I am probably 2-3 weeks ahead of my son at this point.  I am sort of simultaneously wanting to just keep working so that I can be done and move on to next year's math and not wanting to get too far ahead of him due to having to re-review the section to refresh my memory.  Maybe there is some sort of happy medium? Review briefly the night before but work ahead otherwise? What has worked for you all?  TIA!

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When I took over my son's math education in second grade, I did something similar to what you are doing.  I would preview his material a day or two ahead and then teach him the material.  My system worked fine through pre-alg, but fell apart at alg. 1.  I did not have the time or desire to remaster algebra, and being ahead of him a few pages did not make me an effective teacher.   There was no way that i could get through calculus with him.   I started out sourcing math with online classes and occasional tutors.  He got a great math education, without me being stressed out about it. 

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15 hours ago, cintinative said:

  I am sort of simultaneously wanting to just keep working so that I can be done and move on to next year's math and not wanting to get too far ahead of him due to having to re-review the section to refresh my memory.  Maybe there is some sort of happy medium? Review briefly the night before but work ahead otherwise? What has worked for you all? 

It has been my experience that for best teaching it is good to be several years ahead in math to have the "bigger picture" and know which skills and concepts will be relevant later in which context. I then only had to go back briefly whenever the kids had questions and look at the specific problem and maybe review one or two details.
That, of course, is not implemented on the short term. But I think working ahead whenever possible will give you more perspective. If you actually master the material, you won't need to review much.
I do not think being a couple of lessons ahead or learning alongside is an efficient way to teach math because many concepts solidify through the continued application and practice over the course of several weeks/months, and the student will benefit from a teacher who has already gone through that process.

Edited by regentrude
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This only worked for us through what I had previously learned (College Algebra/ Trig, so Precalculus). The last two years I mainly watched videos from Derek Owens in the morning for what dd was learning later in the day (Clausen Tech has those for your book, I think).

I also hired a "tutor/ math buddy" for Precalc knowing exactly what regentrude says above- I didn't know what I didn't know. The tutor was homeschool mom who had been a math teacher. She didn't tutor dd in the conventional sense, but they talked about math, and she answered tricky grading questions. Dd was also working on some competition-type math at the time, so sometimes that's all they did.

This was fairly inexpensive because the tutor didn't need to prep anything- she just showed up and talked with dd and was also just starting to tutor one-on-one, making dd a bit of a guinea pig.

 

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I did this with mine for a couple of reasons, and found that my best pacing was actually a year or so ahead. I did still have to review a couple of days in advance for the student, but the review was super helpful for ME in solidifying and connecting concepts.

When mine hit pre-calc, I arranged a barter-tutor situation for pre-calc and all levels of Calc.

Reasons this made sense for us: 1. I had multiple kids and calculated the time investment was worth it (it was). 2. I could not afford high-end tutors for all of high school for all kids. 3. Even though we met with occasional frustration, my kids (and I!) learned how to power through, seek resources, work backwards, and DO the math.  4. We had excellent textbooks. 5. This was the kids' choice, even when I pointed out and confessed my own inadequacies.

Not saying it would work for all, just where our situation had us. It was hard work, but grew into one of the treasures of our journey over the years.

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18 hours ago, cintinative said:

@Garga I think maybe you did this?

I am working ahead of my son in Alg II, and I find that if I wait too long between my learning "sessions" then I have to retrace steps and familiarize myself again with the section.  Lately the way I have been doing it is spending several hours in one sitting working on the math, and then hit it again a week later. it's not ideal but I have not been successful working every day on it thus far. I am probably 2-3 weeks ahead of my son at this point.  I am sort of simultaneously wanting to just keep working so that I can be done and move on to next year's math and not wanting to get too far ahead of him due to having to re-review the section to refresh my memory.  Maybe there is some sort of happy medium? Review briefly the night before but work ahead otherwise? What has worked for you all?  TIA!

I didn’t do this—well, I did for Alg I and realized it wasn’t working. I had to outsource math. Like others have said, I discovered that I ought to have been at least a year ahead of my son in math in order to be an effective teacher. I had to know where we were going in order to properly teach the steps to get there. 

For my oldest son, he is naturally strong in math (is a math major in college now), and so our shaky year of Alg I didn’t harm him. Once I outsourced for him, he was fine working with his other teachers (myhomeschoolmathclass.com, then DerekOwens.com)

For my youngest, he’s stronger in English and weaker in math, so even though his math was outsourced, I would do the work alongside him. I’d watch the lessons and do every practice problem with him. That wa, when he had questions or I could see him floundering, I could better help him. 

But this year, he’s flying on his own. I do think my working alongside him helped him, because it taught him what it takes to learn, since he saw me actually learning alongside him and saw what it took from me to do it. 

 

But…I guess none of this answers the OPs question…

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Another vote that this doesn't work well after a point. Where that point is will depend on where you got in your own math education. The reason that I could look ahead by a week or so for Algebra I with my kids was that I have a pretty firm grasp on basic algebra. Enough that looking ahead a week and refreshing concepts worked fine. But that was my limit. When I tried to do that with geometry, I struggled. The math year was okay that year, but not great. And then when I looked at the algebra 2 options, I knew I was done. I could do much of it off the bat, but it wasn't something that came back to me with a quick review. It was going to be proper work. I outsourced.

I know a lot is made of this whole idea on this board. And I hate that so many families today think they need to outsource 3rd grade math of all bleeping things. Like, people, no, no you don't. And if you do think that, maybe home education isn't for you. But once you get to high school level math - pre-algebra and beyond - I think homeschool parents should look carefully at their skill sets and make sure they're working at a level that's enough ahead with a full grasp of the material that's several steps beyond what the student will be doing. Otherwise, it does our kids a disservice.

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I'm obviously not going to get a year ahead of him now, but I can certainly work farther ahead and just go back and review briefly before we cover the material. 

I covered a lot of math in college, so technically this is "review" but it has been a long time.  I feel confident in it, and I do think I am mastering it (again) as I go along.

I thought about using Derek Owens next year but I am a little concerned about the lack of textbook. This year my kids are taking Physics with him, and my oldest is struggling with some concepts. Since there is no textbook, there is no place to go to review additional problems and see where the confusion lies. I am fortunate that I own the texts the course is based on, but DO's sequence is different, so I am pulling out sections of Giancoli and trying to help my son. Because this class was supposed to be "outsourced" I have not been learning along with them, so I am feeling really inadequate to address the issues.  I really fear this with math.  Even if I do subcontract it, I don't know that it serves me well not to learn it also.

I think my oldest is getting the raw end of this deal because by the time my youngest takes the math, I am at least a year ahead. I need to work harder and further ahead. Thank you. 

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I've always worked as far ahead as possible. With more recent review as needed. For example, I'd complete the textbook ASAP, but re-do reviews and practice intermittently as needed. Any problems that I have trouble with, I'd take note of and review them more frequently.

 

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5 minutes ago, Farrar said:

Derek Owens has a textbook. It's a giant book you order from one of those self-printing places. And the videos can be rewatched. It's a text.

We have what he calls a textbook, except it's really not. It has some concepts, and some problems, but it's not like a traditional text where there are 50-100 problems and the prof only chooses certain ones to assign.  Everything that is there is assigned. So if you want to do more practice, there is no way to do so (with his text).  At least, that is how the physics works. We have not used him for math yet.

At least when I was in school, I would use the extra problems as a way to practice my understanding for a test. I didn't want to just do the same problems twice. I wanted to make sure I understood the concepts well enough to know how to apply them on other problems.  There is no way to do this with DO's setup currently

Edited by cintinative
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19 hours ago, cintinative said:

@Garga I think maybe you did this?

I am working ahead of my son in Alg II, and I find that if I wait too long between my learning "sessions" then I have to retrace steps and familiarize myself again with the section.  Lately the way I have been doing it is spending several hours in one sitting working on the math, and then hit it again a week later. it's not ideal but I have not been successful working every day on it thus far. I am probably 2-3 weeks ahead of my son at this point.  I am sort of simultaneously wanting to just keep working so that I can be done and move on to next year's math and not wanting to get too far ahead of him due to having to re-review the section to refresh my memory.  Maybe there is some sort of happy medium? Review briefly the night before but work ahead otherwise? What has worked for you all?  TIA!

One thing that is helpful is to restate/summarize the chapter in your own words or short hand. Write and rewrite the summary until you have the "essence" of the lessons or chapter on a half-sheet of paper (or less).

Verbalize the process (say it outloud) as you write that summary.

Then write/rewrite that summary every other day. You can set an alarm on your phone as a reminder. Because it's half of a page or less, it won't take long for you to write out and summarize the essence of a whole chapter.

In this way, you can create like a Memory Work schedule for reviewing entire chapters/sections of a text within several minutes.

 

Edited by Gil
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1 minute ago, cintinative said:

We have what he calls a textbook, except it's really not. It has some concepts, and some problems, but it's not like a traditional text where there are 50-100 problems and the prof only chooses certain ones to assign.  Everything that is there is assigned. So if you want to do more practice, there is no way to do so (with his text).  At least, that is how the physics works. We have not used him for math yet.

Well, several things. One, the videos are the text. The spiral book is the work that goes with it. Two, he tells you exactly that book the course is based on so you can just buy the book. When my kid did pre-calc, the course still required the textbook, actually. Finally, are you talking about the course or the self-graded version? If you do the self-graded version, yes, you might want to assign more problems and in that case, you should just get the textbook. The course structure is basically the same, as is the style of problems. Done. But if you do that, you're not actually outsourcing. You're using the Derek Owens text to teach your kid yourself. Which is fine! If that works well - and it has for many people here - then you should try that. But getting some videos doesn't count as outsourcing in my mind any more than getting a textbook does. If you're looking at the Derek Owens course where they grade it, they will tell your kid if they need more practice and will send extra videos and so forth. This is part of the point of outsourcing. You're taking that off your plate and letting it go.

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Re: Textbooks.

Search online for "Algebra 2" or "Intermediate Algebra" and use the chapter resources on Teacher Websites by topic.

Graphing and Transforming Polynomials is the same no matter which textbook you use.

You can order older texts online 2nd hand for $3.99+ SH

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5 hours ago, regentrude said:

t has been my experience that for best teaching it is good to be several years ahead in math to have the "bigger picture" and know which skills and concepts will be relevant later in which context. I then only had to go back briefly whenever the kids had questions and look at the specific problem and maybe review one or two details.

This--which is why I was a much better math teacher for the younger one!

That said, with the first one, I did a fast run through of Algebra 1 and later on geometry with ALEKS.  I then went through whatever text we were using as far as I could myself before starting with him and then just kept going myself after we started working on it from the beginning together.  I would then do it a third time the day/weekend before we came to it in our lessons.  I started this process about a year ahead.  

With the younger one, we used Derek Owens, and I found it easy to run through his courses quickly in the weeks before school started (because I already mostly knew the material).  You can just watch the concept/introduction videos and then do the examples on your own quickly and fast forward to the answer (to be sure it was correct) then do the homework, etc, quickly.  Now that I am actually getting a degree in math, I'm seeing just how well Derek Owens (and before that Jacobs Algebra) prepared me for what was to come.  

But back to regentrude's point.  As I go further and further in math, I see more and more connections that make me a better and better teacher.  I have come to believe that all people who teach elementary math in b&m schools should have to demonstrate proficiency with algebra and geometry, anyone teaching middle school math and above should have proficiency through the first semester of calculus, anyone teaching lower high school math should have been a math major, and anyone teaching upper high school math (precalculus, calculus), should have a master's degree in math (same requirement as at a community college).

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Another vote for "it helps to be years ahead." I'd probably try to find some way they can have contact with a human being that's way ahead of them and has a cohesive view of what they are missing and not understanding. 

As a tutor, I generally refuse to tutor things for which I don't feel like I'm years ahead. Like, could I tutor multivariable calculus? I probably could in a pinch, but I don't feel like I have a good cohesive understanding of the concepts, since they never came up in my later education. 

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27 minutes ago, Not_a_Number said:

As a tutor, I generally refuse to tutor things for which I don't feel like I'm years ahead. Like, could I tutor multivariable calculus? I probably could in a pinch, but I don't feel like I have a good cohesive understanding of the concepts, since they never came up in my later education. 

I find that there is a difference between tutoring and teaching, in that with tutoring you're generally backfilling on the fly, answering questions and doing problems that the student is having trouble with in the moment--in other words, there is no time to prep.  With teaching, you can spend the weeks (or whatever) leading up to the lesson preparing yourself.  So it's much easier (in a sense) to teach something you're rocky with than to tutor it.  This is the reason I can be at all effective with the multivariable calculus TA gig that I am doing right now.  I spend many hours doing problems every week so that when I see the students, I can help them with trouble spots.  If it had to go in cold and do the same thing?  Ha!  No way!

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46 minutes ago, EKS said:

But back to regentrude's point.  As I go further and further in math, I see more and more connections that make me a better and better teacher.  I have come to believe that all people who teach elementary math in b&m schools should have to demonstrate proficiency with algebra and geometry, anyone teaching middle school math and above should have proficiency through the first semester of calculus, anyone teaching lower high school math should have been a math major, and anyone teaching upper high school math (precalculus, calculus), should have a master's degree in math (same requirement as at a community college).

While I agree whole-heartedly with the sentiment, I absolutely disagree with the standards proposed.

What you're really saying is that teaching single variable calculus (AB and BC content) to highschool students requires a Masters Degree. That's simply not so. If we want to require a Masters in mathematics to teach Calculus in highschool, then we as a society have to be prepared to drop that course from a huge portion of schools throughout out the entire country.

The community colleges that I'm aware of allow people with a BS in the field (or a related field) to teach the remedial classes--which is the same content from about 4th grade up to 11th grade algebra. Anyone having a minor in math and some classes in instruction/pedagogy would be sufficiently prepared for teaching highschool mathematics all the way up the "advanced" highschool course of Calculus BC. A math degree should be valued and appreciated, but certainly not required to teach highschool mathematics.

Elementary math teachers being Genuinely Proficient with math taught up to 8th grade is a reasonable standard to set and one that society could (and in my opinion should) fully support. The math done at the K-8 level is pretty much calculation or algebra-based. I mean, even the geometry done before highschool is pretty much classifying shapes based on characteristics/definitions or calculating the area, perimeter or volume of  various shapes. So to be a great math teacher at the K-8 level, you don't actually need mastery of the Geometry-centric portions of highschool geometry. It wouldn't hurt, but for many it wouldn't make a difference.

 

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1 hour ago, Gil said:

While I agree whole-heartedly with the sentiment, I absolutely disagree with the standards proposed.

What you're really saying is that teaching single variable calculus (AB and BC content) to highschool students requires a Masters Degree. That's simply not so. If we want to require a Masters in mathematics to teach Calculus in highschool, then we as a society have to be prepared to drop that course from a huge portion of schools throughout out the entire country.

My experience with high school math teachers is that when they are working at the edge of their understanding, they are far less effective.  But you're right--it is unlikely that we would be able to find enough master's level folk to teach these courses.

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On the flip side, I gamely tried teaching writing and literature for my middle school students and quickly realized I was on thin ice.  I thought I could read the books ahead of my students, but (1) I'm a slow reader (2) I have read only a small handful of works of classic literature.  Seriously, I've read hardly anything.  (3) I can barely make out the plot points of these classic books, let alone any themes or other important stuff, so I was having to do additional reading in SparkNotes, which takes even more time.  (4)  I lack the general context of literature in general.  I'm reading each book for the first time in isolation. 

I quickly hired a couple of local English majors and outsourced anything to do with reading or writing. 

I teach math well because (1)  I've worked through ALL the AoPS books, several times over with multiple, multiple students.  (2)  I've had extensive experience with math contests both when I was high school  and now coaching math teams and prepping students for math contests.  I have the big picture of high school math and I can get in the weeds of specific problems.  

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1 hour ago, EKS said:

My experience with high school math teachers is that when they are working at the edge of their understanding, they are far less effective.  But you're right--it is unlikely that we would be able to find enough master's level folk to teach these courses.

sure, but is single-variable calculus really the edge of understanding for someone with a BS in math? Didn't they see that (likely in HS, but at least) in the first 1/2 year of their first-year in college...so they've got another 1.5 years of lower-division and then 2 years of upper-division math beyond what's in CalcBC? Wouldn't anyone with a BS STEM degree have seen single and multi-variable calculus, stats, diff-EQ, and (if they went to school in the last 20 years) LinAlg, at least? Not to mention application of this in Calc-based Physics? That seems sufficient, no?

Edited by AEC
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8 hours ago, cintinative said:

Clausen Tech, when I google it, is giving me an online pharmacy. help?

Algebra 2 (clausentech.com) BUT it looks like he took his videos down and replaced them with a link to tutoring help. There are other resources for that book there though.

The way I found that works for finding book specific videos on YouTube is to enter the exact name of the section AND the section number. You'll get things for that topic, but if you put in both the number and name, your first results will be for that book (if there are any).

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43 minutes ago, MamaSprout said:

Algebra 2 (clausentech.com) BUT it looks like he took his videos down and replaced them with a link to tutoring help. There are other resources for that book there though.

The way I found that works for finding book specific videos on YouTube is to enter the exact name of the section AND the section number. You'll get things for that topic, but if you put in both the number and name, your first results will be for that book (if there are any).

I actually have his videos linked from youtube. I thought I recognized the name.  https://www.youtube.com/watch?v=mLfVOxjCFgY&list=PL4930E37986A4C203

So far, I haven't needed them, but just in case someone does.

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9 hours ago, EKS said:

My experience with high school math teachers is that when they are working at the edge of their understanding, they are far less effective.  But you're right--it is unlikely that we would be able to find enough master's level folk to teach these courses.

I took 2 more quarters of applied Calculus than most math majors would to get my BS in electrical engineering. Don't get me wrong a math major takes many more math classes but they get into more logic stuff and other mathematical topics that I have no place talking about. So not there yet but I would feel confident today teaching through Calculus to my kids (aside from the fact they are under 6 and totally not ready for it).   

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8 hours ago, EKS said:
8 hours ago, AEC said:

sure, but is single-variable calculus really the edge of understanding for someone with a BS in math?

Apparently it can be.

Maybe you had a bad experience with someone in particular or I'm wondering if a BS in Math didn't give enough actual usage of the Calculus (less about the actual knowledge of Calculus). I did find a lot of the Calculus topics that I struggled with in high school and early college made a lot more sense once I started using it to solve real world problems. 

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I couldn’t do this well past, say, Prealgebra, and it showed. Actually as much as I hated AOPS, their set up helped us get through the first part of algebra with one kid.  So maybe the materials/texts one uses help. Math Mammoth seems to be set up similarly except of course much much more incremental (so, in terms of content, the opposite of AOPS). 

I would love nothing more than to find an actual live teacher person  who would go through Forrester Algebra with her. I don’t want to do it, and yet I love that book. 

Edited by madteaparty
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9 hours ago, RootAnn said:

As of this year, DerekOwens's PreCalc no longer uses the textbook he previously used. 

[I'm debating using him for PreCalc for my kid#3 next year. Physics is going very slowly this year with his course.]

Ooh, I wonder why the change? So it’s all new videos and such? DS went through his honors precalc and it was fine, I guess? Calc BC is not a joy and delight currently but 🤷‍♀️

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10 hours ago, RootAnn said:

As of this year, DerekOwens's PreCalc no longer uses the textbook he previously used. 

[I'm debating using him for PreCalc for my kid#3 next year. Physics is going very slowly this year with his course.]

I am just investigating pre calc also. I own Larson and I also own the Brown text.  I noticed Chalk Dust uses Larson, and so does Wilson Hill.  And this teacher, who is the one on the Chalk Dust videos, also has his own sort of subscription video service with virtual tutoring:  https://coolmathguy.com/math-textbooks  I was just about to do some research on here.  

Edited by cintinative
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29 minutes ago, madteaparty said:

Ooh, I wonder why the change? So it’s all new videos and such? DS went through his honors precalc and it was fine, I guess? Calc BC is not a joy and delight currently but 🤷‍♀️

Do you know what it was based on when you took it? What I am seeing on the DO site is that he no longer requires use of the text. It might still be based on the same text. @RootAnn I know he has been dropping the text book from many courses, and just incorporating whatever into the workbook/videos instead.  

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@RootAnn my oldest is having problems in the DO physics and my youngest is REALLY far behind him now. I'll be curious to hear if your dc has trouble with the Chap 5 and 6 exam. My son just didn't have the concepts down and did not do well on the test, so now we are reteaching using the Giancoli text I own. Something didn't click with him in the way these chapters were covered.

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11 hours ago, Clarita said:

So not there yet but I would feel confident today teaching through Calculus to my kids (aside from the fact they are under 6 and totally not ready for it). 

Feeling confident teaching your own children and being appropriately prepared to teach other people's children in a school setting are two vastly different things.

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3 hours ago, cintinative said:

Do you know what it was based on when you took it? What I am seeing on the DO site is that he no longer requires use of the text. It might still be based on the same text. @RootAnn I know he has been dropping the text book from many courses, and just incorporating whatever into the workbook/videos instead.  

I don’t remember but there was a textbook which I ordered and then split in half because we would be traveling for the first part of the class. DO was nice enough to send me PDFs of those chapters, though how much my own kid used the textbook (on top of the workbooks) I really have no idea. He did fine in the class, FWIW. 

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1 minute ago, cintinative said:

It still is. I think he just dropped the text.  

Yes, that's my understanding as well. That's why I said when my kid took it, it stilled used the book. I think he's been moving all his courses away from using the additional textbook. My impression from the Calculus course (which my kid is doing now) is that it's more streamlined, which is much easier for kids to actually use.

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31 minutes ago, cintinative said:

It still is. I think he just dropped the text.  

Oh my goodness--he finally did that!?!?  How wonderful!!!

ETA:  I just checked the course (I have a lifetime subscription!)--it's really true!!!

Edited by EKS
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10 hours ago, cintinative said:

@RootAnn my oldest is having problems in the DO physics and my youngest is REALLY far behind him now. I'll be curious to hear if your dc has trouble with the Chap 5 and 6 exam. My son just didn't have the concepts down and did not do well on the test, so now we are reteaching using the Giancoli text I own. Something didn't click with him in the way these chapters were covered.

I'll PM you when we get there. Someday.... (I own the Giancoli text from the first kid who took this class. She tanked the 1st semester final because she needed more on-going review after finishing material. I built it in for her during 2nd semester.)

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37 minutes ago, RootAnn said:

I'll PM you when we get there. Someday.... (I own the Giancoli text from the first kid who took this class. She tanked the 1st semester final because she needed more on-going review after finishing material. I built it in for her during 2nd semester.)

That's good to know. Maybe that is part of the problem. I am really worried about that with my youngest since he is easily seven weeks behind my oldest at this point. So by the time he takes the midterm it will be so far out that he won't remember a lot of it.  We didn't do midterms for Biology at all. 

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1 hour ago, kiwik said:

It can be really hard to get hold of texts if you are outside the US.

Could you help me understand what you mean here?  Hard to get the Sullivan text?  The fact that it was from 1996 was making it hard to get in the US as well.

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