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Middle/High School Math Thoughts and Ideas

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#1 Dana

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Posted 12 January 2014 - 04:33 PM

I’m starting this thread as a spin off from another discussion. Here are some comments, links, and ideas I have about math in middle school & high school. I hope others will add to it and it’ll be a useful resource.

 

Studying math (or science) isn’t like studying any other subject. You’ll read the material at a MUCH slower pace than for any other subject. Ideally, a student will read text examples with a pencil and paper and will cover up the work (fold a page in half) and try to work the problem ahead of the example, looking at the next step in the text explanation after writing what you think the next step is. Pay CLOSE attention to the EXPLANATIONS given. That’s the sort of thing I say in class as I’m doing examples.

 

I once spent about 3 hours reading 3 pages in a math text. It took me that long to really take in what was happening. Lots of scratch paper is useful! I also like doing math on unlined paper because it seems to allow me to write larger and more neatly. It’s when I start skipping too many steps that I find myself making careless errors.

 

For taking math notes, I used to have my students keep a math journal. I’m trying to attach the pdf I’d hand out with an explanation of what I was looking for. The practice problems a student does really don’t need to be kept, but a set of explanations of how to do certain problem types would be very useful for later reference.  (not working, but PM me with your email & I'll send the pdf)

 

I really liked the book Winning at Math by Paul Nolting. It’s out of print now, but it looks like some cheap used copies are available – and our library has some.


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#2 Dana

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Posted 12 January 2014 - 05:29 PM

Interact Math software (currently free online http://interactmath.com/home.aspx ) is the software that is used with MyMathLab (used by some of the technical colleges here). You can pick any textbook with a title that matches what you’re studying (Basic College Math will be prealgebra and this goes to calculus and beyond). The “Help Me Solve This” feature is excellent for getting help walking through a problem.

 

Art of Problem Solving http://www.artofproblemsolving.com/  does seriously solid math. They’ve got an elementary program they’re getting started, Beast Academy. Their high school texts are excellent. They are large since they’re written to the student and all the explanations are in the text. Their online courses will likely move too quickly for most students, but they have free online videos that are very good (I’ve not been annoyed by anything I’ve seen on them). They also have Alcumus – online problem solving practice – also very good.

 

PurpleMath has good explanations. http://www.purplemath.com/ Links are in the lessons section. I don’t like the ad changes on the page, but I do like her explanations.


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#3 Dana

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Posted 12 January 2014 - 05:44 PM

When taking any courses at the technical colleges here in SC, note that there are some strange things going on with numbering.

 

https://www.sctrac.o...25/Default.aspx

This is a site where you can see transfer agreements within the SC public colleges. This can help you find how a course taken at one school would count at another school.

You’ll notice that MAT 101 and 102 do NOT get transfer credit – they are not considered college-level courses. However, ENG 101 and 102 DO get transfer credit. This makes no sense, but it’s the current numbering system.

 

http://www.che.sc.go...tionAccess.aspx

This page from CHE (SC Commission on Higher Education) has some useful information about guidelines for college admission for SC public institutions. IF a student is looking to go to a public college, it may be smart to look at what colleges expect from entry students. At the technical colleges, we see a number of students who are trying to transfer to public colleges but are missing foundational courses (math, reading, English). I regularly see students who are “recent” high school graduates (where 3 math credits are required to graduate and Algebra I is the lowest credit allowed) in MAT 101 (which is roughly an Algebra I class). These students have typically covered the material in a prior course, but they didn’t master the material (note study tips above). Math is foundational and subsequent courses build on prior courses.


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#4 Dana

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Posted 12 January 2014 - 05:57 PM

The typical Algebra I - Geometry - Algebra II sequence may work for many students.

At the technical college, MAT 101, 102 would roughly correspond to Algebra I and II. A student who successfully completes MAT 102 can take 110 (college algebra), 120 (statistics), or some other courses that do get college transfer credit.

 

Geometry is NOT taught at the technical colleges. A geometry course gives experience with formal proofs; it shows WHY we have the rules we have and trains the brain for logical problem solving. Patty Paper Geometry (available at Rainbow Resource) is a neat program. I don't think it would be enough for a full geometry credit, but ti's pretty cool.

 

I'm very much in the college track with my son - especially since I've been teaching at the technical college since 1996.

It's not the right path for everyone and there isn't "one right way."

 

I think financial literacy is INCREDIBLY important and it doesn't fit into the typical college track.

I gave students a project once where they figured out how much buying a car would cost them - insurance, financing, maintenance, and car loan. Then they figured out how long it would take them to pay off the car and what percentage of their monthly paychecks would be going towards that car. I thought it was great for the students who did it.

 

A number of companies now give math and reading tests to potential applicants. The more solid their math foundation is, the more options they will have.

 

It's also surprising to see where knowing math helps students later. I had one student who said learning unit conversations made work that used to take her hours get done much faster. Geometry helped a student double-check figures when she was getting new carpet laid and she was able to show that she was being overcharged - enough to carpet an additional room. I'd never seen a practical application for mixture problems, but it saved a student money because his work was able to compute changes more accurately before sending samples off for chemical analysis.

 

I'm happy to answer questions about "where could this be useful later" as well - or just discuss math topics.

 

Hope some of this may be useful... use what helps & ignore what doesn't. There's no one right way.


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#5 kohlby

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Posted 22 January 2014 - 02:18 PM

Have you used AoPS Intro to Geometry?  My son just started it.  I'm a bit nervous as I've heard it's a lot more challenging than the Intro to Alg.  I was wondering if that was your students' experiences.  I'm a former high school math teacher myself and I saw math maturity being an issue at times in my students - especially in Geometry.  That's the biggest reason why I'm a little nervous about AoPS Geometry since he is a younger Geometry student than the norm.  (He's done the complete Intro to Alg book and also did Intro to Number Theory.  But he's 10).  I bought Jacobs Geometry second edition as well, for a back-up in case we find AoPS to be too overwhelming.  And for fun, we have a Zaccaro book.

If any one else is reading this, I must add in that we love Alcumus!  We haven't used the online videos for AoPS but use Alcumus frequently.  My son likes to do as much math as he can without me.  That means I need to make sure he really understands it since I'm not teaching him much of it anymore.  Alcumus will then show if he really understood it.  It allows him to do AoPS independently without sliding through anything without full understanding.  Alcumus is free, so it's a great way to try out AoPS style before you buy a book. 


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#6 MathMom

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Posted 22 January 2014 - 02:40 PM

WOW!

Only slightly kidding when I say maybe your 10 yo can tutor our 17 yo, Kohlby.

 

We're working through some of Dana's other recommendations and hope we've found a good path, but hearing more good things about Alcumus (and that it's FREE!) is great because a lot of learning is being done independently at our house as well.  I've had concerns about continuing that model because I wasn't sure how effective it was for the long-run with our daughter.

Having another source to test, re-test, review, etc with her will be great!  I'll add this to my bookmarks list as well.


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#7 Dana

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Posted 22 January 2014 - 06:01 PM

Have you used AoPS Intro to Geometry?  My son just started it.  I'm a bit nervous as I've heard it's a lot more challenging than the Intro to Alg.  I was wondering if that was your students' experiences.  I'm a former high school math teacher myself and I saw math maturity being an issue at times in my students - especially in Geometry.  That's the biggest reason why I'm a little nervous about AoPS Geometry since he is a younger Geometry student than the norm.  (He's done the complete Intro to Alg book and also did Intro to Number Theory.  But he's 10).  I bought Jacobs Geometry second edition as well, for a back-up in case we find AoPS to be too overwhelming.  And for fun, we have a Zaccaro book.

 

We haven't.

 

My son is 11 now. We went from Singapore 5 to him doing some algebra out of one of the texts I teach from. It's roughly an algebra I credit.

I've just bought AoPS Intro to Algebra & Geometry. I'm not sure how much I"ll use of them... We're doing more with texts from Elements of Mathematics. I was in the MEGSSS program when I was in middle school and we used the materials. They've got some excellent materials. Unfortunately, since they're doing teaching at some centers (not in SC though), they won't sell teacher's materials, so I'm working the texts along with my son. They also have started online courses here and here.

 

I like the books better and own them, so I can't see paying a second time for the online material, otherwise I probably would have done some with it.

 

I don't know if I'll stick with EM or do some with AoPS as well. It'll just depend on where I'm seeing challenge and interest level.