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I am quite confident in my elementary math teaching ability, but our oldest will be in highschool in just a few years. I like math, but realized it late. I only took preCalculas my senior year of college. I loved it;) My husband took lots of math....engineer, but doesn't really like math. For him its a means to an end. Anyway, I really want to teach Algebra and geometry at least myself. I planning to use the Foerster algebra and Jacobs geometry texts. How do you learn to teach upper level math well?

I'm also interested in learning Calculus, but I have a toddler and another on the way as well a homeschooling and housekeeping, so I'm not sure a college class is a great idea...

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I love math and have always been Math-y. I only took through Calculus in college, though, because I didn't need other math for my degree. I taught Algebra I, but I am really struggling through all the proofs in Geometry. We are taking Geometry through Derek Owens, and even so, it has been a struggle for us both. The proofs are a lot more than what I learned in high school Geometry. I don't have any advice, just a warning, and I would like to follow this.

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I'd work through the texts yourself now.  Both books contain excellent teaching (I had the 2nd ed of Jacobs, so not sure about other editions). 

FWIW, I worked through the books right alongside my oldest kids in order to master the material.  I can't do a decent job beyond about 1/2 way through alg 2, but I can get that far.  I am able to look through the SM and help them figure out their mistakes for the rest of alg 2 (but I am not really teaching them.)

Edited by 8filltheheart
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I am good until half way through Algebra 2 as well- and that where I am with DD2 right now.  I'm trying to study ahead on the weekends.   I'm not sure what we will do next- thinking redo this second part of Algebra 2 and then start working on college algebra bc this kid isn't taking more than that one college math class necessary for a degree!  

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9 hours ago, countrymum said:

How do you learn to teach upper level math well?

You start a few years ahead of your student and work through at least one text for each course--even if you think you remember it well.  What would be best is for you, at a minimum, to be done with geometry and Algebra 2 by the time you begin teaching Algebra 1.  Being done with precalculus would be even better.  If you end up teaching Algebra 2, having the first semester of calculus (so, the equivalent of AP Calculus AB) under your belt before starting would be most excellent.

As far as how to go about all of this learning, I used ALEKS to refresh my knowledge of Algebra 1 and geometry and Derek Owens for Algebra 2, precalculus, and calculus.  I did all of these well ahead of my student.  I also worked through the text I was actually using with my student as I was teaching.

The reason it is helpful to be a few years ahead of your student is so that you know what's coming.  In the same vein, I also think that having a solid (and recent) understanding of Algebra 1 and geometry are critical to being able to teach elementary math well.

That said, while you can't teach math well if you don't have a good grasp of the material, knowing the material isn't all that is required for good teaching.  You can tip the odds in your favor by using a text that works well for both you and your student, but no matter what, your first student is going end up being a guinea pig.  

Edited by EKS
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With the jacobs geometry we used (whichever edition number is sold by mfw is the one we used), I read the text out loud along with my middle dd and we worked through together. I used answer key for details.  Oldest didn't need me to teach the text to her. And it was better for oldest if dad went through answer key issues with her. engineering brains and math people the both of them.  I didn't work through the text more before the lesson. But there was something in reading/teaching out loud that helped me explain as needed and helped middle dd learn.

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One thing I forgot to mention--in order to grade geometry properly, you need to understand how to write proofs yourself and be able to tell when your student has written a valid proof that isn't in the answer key.  This happens very frequently.  At least it did with my kids.

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With my two oldest (and now with our youngest) we used Saxon math with the teacher CDs.  This worked well for us.  I feel like I am pretty solid with math until about 1/2 way through Algebra II, so I also was able to supplement with my explanations in addition to the teacher on the CDs.  After the Saxon Advanced Math book I did have our oldest do Derek Owens precalculus because ds was so young when he finished the Advanced Mathematics book (9th grade) and I was wondering if he needed more before he started calculus.  He aced the DO class and went on to breeze through calculus (he actually loved it!)  This worked well for our dd as well (she only took a college algebra class but found it to be very easy).  I know a lot of people dislike Saxon, but it has worked well for us.

Also, outsourcing math is a great option, as you can select a great teacher (thanks to the reviews on this board!) and the student can receive expert help when needed.  I tried to plan high school carefully so my children were only taking two outsourced classes at the most each year (except senior year was more for each of my oldest).  This way I did not overwhelm them and we stayed within our budget.     

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I agree with @EKS -- if you want to teach it well, you should learn it ahead of time. And yes, it's a great idea to learn how proofs work. They aren't really that mysterious, though 🙂 . You get a much better feel for what is and isn't a proof by writing them and having people look over them than anything else. 

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I have worked through the texts ahead of my dd, but not that far ahead.  Honestly, I would probably forget it if I attempted it years in advance.  I just stay somewhat ahead and work through as many problems in the lessons as I can, focusing on ones that look more challenging.  I then make little pencil notes in the solutions manuals about helpful hints for a problem or alternate solutions that may also be valid.  We have used CLE Algebra I, Jacobs Geometry, and are currently in Foerster's Algebra II.  All of them have been a success here.

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27 minutes ago, ALB said:

I have worked through the texts ahead of my dd, but not that far ahead.  Honestly, I would probably forget it if I attempted it years in advance.  I just stay somewhat ahead and work through as many problems in the lessons as I can, focusing on ones that look more challenging.  I then make little pencil notes in the solutions manuals about helpful hints for a problem or alternate solutions that may also be valid.  We have used CLE Algebra I, Jacobs Geometry, and are currently in Foerster's Algebra II.  All of them have been a success here.

I agree.  I didn't work ahead of my oldest at all.  I didn't have the time since I had a house full of little ones with one being autistic.   I sat and did math with him.  (I did every problem with him.)  That approach worked for us, but I had taken math through cal (AP in high school and again in college) so it was more of a refresher than actually learning it.

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I second (third?) what EKS said: in order to teach math well, you have to be ahead in the material by a few courses, not just by a few lessons, so that you are able to see the big picture and know where all this is going. (So, to teach calculus 1, I would expect a mastery of multivariable calculus and differential equations)
However, it is also possible to facilitate math learning while working alongside with your student and providing outside resources when needed; parents here have done this very successfully.

I like to make a clear distinction between the two modes. Teaching requires subject expertise beyond the material you cover, a solid grasp of the pedagogy of math, and the ability to develop or adapt materials to your student. Facilitating learning requires a mastery of the material that is the prerequisite to the content you want to learn, and it requires you to either devote as much time on task as your student while working alongside them, or to know where and when to ask for assistance from somebody else. Both can be successful, but they are really two very different things.

Edited by regentrude
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2 hours ago, ALB said:

I have worked through the texts ahead of my dd, but not that far ahead.  Honestly, I would probably forget it if I attempted it years in advance.

This is why you also work a week or so ahead as you are teaching.

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3 hours ago, regentrude said:

So, to teach calculus 1, I would expect a mastery of multivariable calculus and differential equations.

I will have to sheepishly admit to having taught calculus many times without being all that good at either of the things you mentioned 😉 . I use calculus with some frequency and I understand it well, but as someone who has largely stayed on the countable side of mathematics, I've never had to use either multivariable calculus or differential equations much. I've learned them, but I wouldn't say I have mastery of them. 

(I certainly know lots of math that's "past" calculus, but that's a different issue, I think.) 

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Agreeing with all this good advice. I'm very glad I kept algebra I in house and taught it and glad that I reviewed a year or two ahead of that myself. I didn't do the same for geometry and we scraped by, but the quality of the course suffered. I switched them to online classes for algebra II, which I had always planned on doing. I would say that it's okay to know your limit and invest in a good online class. It's also okay to keep it at home - something not enough people do these days. You get a lot out of teaching it and working with them.

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And whether you feel confident or not, another reason to outsource is to give your child the opportunity to have an experience with another teacher and have the opportunity for a letter of recommendation. I am currently outsourcing something I could teach but am choosing not to for those reasons. I think it can build confidence in kids in some situations, to be around other kids and a different teacher, and succeed (hopefully).

I would definitely work on things yourself. You can use a program like ALEKS or Khan Academy to supplement your own learning.  My high school math teacher was underqualified to teach Calculus, and I did not learn much of anything in that class. 

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16 hours ago, regentrude said:

However, it is also possible to facilitate math learning while working alongside with your student and providing outside resources when needed; parents here have done this very successfully.

People have done this successfully, but I would argue that it is always better to have a teacher available who has mastered the material herself and knows what's coming.   

I think a lot of homeschoolers start facilitating math in the high school years with good intentions.  But then the going gets tough and the parent can't keep up for whatever reason, and facilitating turns into handing the student a textbook and hoping for the best.  When the student has a problem, many parents end up curriculum hopping in an attempt to fix it, when in reality the problem isn't the curriculum but the lack of a human in the room.  

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Thanks for all the thoughts. I have been reading them and appreciate them. I am goig to try to work ahead some. I ordered Foerster Algebra 1 and 2. I'm not sure how far I'll get with a baby and toddler. I have taken through PreCalc in college and my hubby did differential equations ect. as an engineer. If I brush up enough, I want him to teach me calculus, but I'm also having to keep up with Spanish and Greek...no problem so far, but they will catch up;) Luckly my sis in law knows way more of both these then I do, and can help.

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FWIW, I have not taught math to any of my homeschoolers past the elementary years and am somewhat surprised (and impressed) to read all these posts from people teaching themselves math. I am good at identifying curriculum and finding additional help if needed (which has only been the case for one daughter so far.) My second daughter graduated with an electrical engineering degree last year and youngest is solid in her precalc as a high school junior. I mean, you can certainly teach yourself math and that it valuable and admirable, but it’s not strictly necessary for homeschooling. 

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9 hours ago, GoodGrief3 said:

FWIW, I have not taught math to any of my homeschoolers past the elementary years and am somewhat surprised (and impressed) to read all these posts from people teaching themselves math. I am good at identifying curriculum and finding additional help if needed (which has only been the case for one daughter so far.) My second daughter graduated with an electrical engineering degree last year and youngest is solid in her precalc as a high school junior. I mean, you can certainly teach yourself math and that it valuable and admirable, but it’s not strictly necessary for homeschooling. 

Speaking only for myself here, I absolutely did not teach myself math in order to homeschool my kids. I am operating on my previous knowledge. I will say that my arithmetic skills and speed have been tremendously improved by teaching elementary school math for so many years. I used books to help me understand how to teach it, get ideas on how to explain tricky concepts — or things that are tricky when encountered for the first time. I have strong opinions about what materials I like.

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11 hours ago, countrymum said:

If I brush up enough, I want him to teach me calculus, but I'm also having to keep up with Spanish and Greek...no problem so far, but they will catch up;) Luckly my sis in law knows way more of both these then I do, and can help.

Let me know if you need any calculus troubleshooting from the forum! I like calculus 🙂 

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I was just looking at Arizona State’s Earned Admission program, and they do have several math classes. At least some of them use Gradarius, which you can also subscribe to independently. (However, they only list Algebra for independent learning.) At Arizona State, you really only seem to have to pay if you want college credit. Otherwise it’s just the $25 fee.

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On 2/12/2021 at 11:35 PM, countrymum said:

I am quite confident in my elementary math teaching ability, but our oldest will be in highschool in just a few years. I like math, but realized it late. I only took preCalculas my senior year of college. I loved it;) My husband took lots of math....engineer, but doesn't really like math. For him its a means to an end. Anyway, I really want to teach Algebra and geometry at least myself. I planning to use the Foerster algebra and Jacobs geometry texts. How do you learn to teach upper level math well?

I'm also interested in learning Calculus, but I have a toddler and another on the way as well a homeschooling and housekeeping, so I'm not sure a college class is a great idea...

I'm currently teaching Algebra 1 to my oldest, so this is my first go-round, and I'm really enjoying it so far. In addition to working ahead (definitely not by several years, yet, but I'm working faster than he is, so the gap should widen over time), I've been poking around for both good general math resources for my own education and also resources on math pedagogy. We're using Dolciani, but I'd like to have a few other textbooks on hand to compare how they treat different topics. 

Specifically on pedagogy, I found the late Grant Wiggins' critique of how algebra is usually taught helpful in reflecting on my own algebra experience (he's written about this in lots of places, here's one), and I've found some useful stuff in the archives of math teachers' blogs, though you want to be discerning about this one! Dan Meyer's seems pretty solid.

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11 hours ago, LostCove said:

I'm currently teaching Algebra 1 to my oldest, so this is my first go-round, and I'm really enjoying it so far. In addition to working ahead (definitely not by several years, yet, but I'm working faster than he is, so the gap should widen over time), I've been poking around for both good general math resources for my own education and also resources on math pedagogy. We're using Dolciani, but I'd like to have a few other textbooks on hand to compare how they treat different topics. 

Specifically on pedagogy, I found the late Grant Wiggins' critique of how algebra is usually taught helpful in reflecting on my own algebra experience (he's written about this in lots of places, here's one), and I've found some useful stuff in the archives of math teachers' blogs, though you want to be discerning about this one! Dan Meyer's seems pretty solid.

Hmmm, interesting article! Quote from it: 

"Algebra, as we teach it, is a death march through endless disconnected technical tools and tips, out of context. It would be like signing up for carpentry and spending an entire year being taught all the tools that have ever existed in a toolbox, and being quizzed on their names – but without ever experiencing what you can craft with such tools or how to decide which tools to use when in the face of a design problem." 

I agree with him about the problem but not about the solution 😉 . But he's right that algebra is highly disconnected and boring the way it's taught. And somehow, most of the textbooks are like lemmings: they do the exact same sequence as every other textbook, even if they spice it up along the way... 

Like, why does one spend so much time graphing lines in Algebra 1?? Lines are REALLY boring. And it overtrains one on lines and leaves kids shaky on the idea of graphs. Why do we do this?? 

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