How to get a good math foundation

[BTC]

I have one child that graduated high school a few years ago, a high school junior, a 6th grader, and a 2nd grader.   I feel that I have made some mistakes with math with all of them at some point and I'm trying to avoid making any more.   My junior is all set, but it took years of trial and error (HATED Saxon, used LOF for 2 years, switched to Foerster's Algebra/Trig).    

 

My question is this:  I want to avoid all this switching/delaying with my other kids.  They are both using LOF right now, and although it's going well, there is very little practice and I'm not sure I want to continue with it after this year.  My 6th grader (VERY science oriented) picks up concepts quickly, but needs more practice.  I also want to make sure he will be ready for a challenging prealgebra program.  Then again, maybe I should stick with LOF  through high school, but supplement with something.     

 

As far as my 2nd grader goes, I will probably just keep doing LOF with her, supplementing the same way I decide to supplement with my 6th grader.   

 

Any advice is welcome.     My main concern is being sure that they don't get to college and find out they did not have the math foundation necessary.  Although I did well in high school math, up to Trigonometry, I remember very little and I don't feel that I am the best person to even evaluate whether a program is what they will need. 

 

 

Thank you

 

[Hunter]

I think a solid foundation in arithmetic is critical. And then a solid foundation in how algebra is a more abstract form of arithmetic. I only know how to teach this foundation with older texts as they are the only ones I know about that do this.

 

We are in such a rush to finish arithmetic before the student is developmentally ready to fully understand our number system and how it works.

 

The arithmetic section of Blumenfeld's How to Tutor is free and is a nice introduction to our number system.

Main site:

http://blumenfeld.campconstitution.net/Tutor.htm

Direct link to the pdf:

http://blumenfeld.campconstitution.net/Books/How%20To%20Tutor%20(Arithmetic).pdf

 

The OLDER version of Ray's Practical/Third Arithmetic actually has comprehension questions about the number system.

https://archive.org/details/practicalarithm00raygoog

 

Ray's Algebra presents the early algebra in the same exact order as the third arithmetic text, allowing the student to see the connections. Chapter 1, page 25 starts in the order of the Third/Practical arithmetic. Before that, the first pages mimic the Second/Intellectual arithmetic book.

https://archive.org/details/raysalgebrapartf00rayjrich

 

As far as I am concerned, the rest is all frosting that often distracts people from teaching the foundation which is our number system. A solid foundation prepares a student for future self-education.

 

University is different. But community colleges often have to start students at arithmetic, if they are doing any remedial at all. The students that fail the algebra parts of the test almost always also fail the arithmetic.

 

One of my sons only tested out of the arithmetic section and bombed the algebra, and it was such a startling score that I was questioned about it. The tester said he had never in all his years seen a score like that. That son studied what he wanted, and since he was double my bodyweight with a full beard and 2 jobs at just 14, I tended to let him do things his own way. I learned a lot from that kid, watching him break every rule about "high school", and am now copying some of how he tackled college, as I finally get there myself after all these years.

Edited October 29, 2017 by Hunter

[HomeAgain]

We use LoF as a supplement.  I like it, but it has some serious drawbacks in how it presents math.  For example, when borrowing and carrying, it talks about taking 'one' from the next value place, rather than stressing you are moving a ten or a hundred over to give an extra ten units.

 

There are a lot of full programs out there.  We started with MEP for the youngest (entirely free, just print), which encouraged mental skills and really thinking about what the numbers are doing.  We've since moved to Right Start to solidify some American measurements and spend a little extra time on multiplication.  If it works out for him we'll stick with it for the next three years' worth of program, if not, I have Beast Academy still in mind for him to try once he has all 4 operations down well.  Still using LoF, but Fred is a reinforcement.

 

My oldest went from a year of Saxon (hated it), to several years of Math U See.  It was easy for him, but it presented math in a way he needed it to be seen.  He transferred from that to AOPS, and then into dual enrollment/AP classes without issue.

 

Really be clear on what you are expecting from a math curriculum.  It will be the easiest way to find something that fits well for your family.

 

[kiwik]

My feeling is that to get a good maths foundation you would need more than LoF.

[letsplaymath]

You could use one of these 5-a-day practice sheets to supplement LoF or any other program. Explore the website for other practice problems and resources.

[BTC]

Thank you for all the suggestions......I, too, have serious issues with using LOF exclusively.  I love the theory behind it, but for most people, at the very least, more practice is needed to get good at a concept.    I have been reading about CLE.   Anyone love this program?   Is it good to use then transition to a Pre Algebra from there?

 

 

Thanks

[Lori D.]

Honestly, I don't know as though there is a guaranteed way of "nailing" the "right" math program that is the "perfect" fit for a student, starting in grade 1, and that it continues to be the "best fit" all the way through high school. ;)

 

One thing that really helped us a LOT was doing TWO math programs, each from completely different viewpoints with different explanations, for as long as we we had the time to do so (up through Pre-Algebra for us) -- one as the main "spine" program, and large excerpts from the other as "supplement". We also used a lot of other math resources and supplements of various kinds throughout the elementary grades, to work with math concepts from lots of different angles.

 

For example: what we used in elementary grades for DSs:

- Miquon (spine)

- Singapore Primary (spine)

- Saxon 3 (spine) -- for DS#2 when we were still struggling to figure out what was a fit for him

and supplements:

- The Complete Book of Math (gr. 1-2) and (gr. 3-4)

- a LOT of supplement materials using manipulatives (pattern blocks, geoboards, multi-link cubes, etc.)

 

And, what we used in the late elementary/middle grades:

- DS#1 (math-minded) = Singapore Primary, then Singapore New Elementary (spine) -- Saxon (supplement)

- DS#2 (math-struggler) = MUS (spine) -- portions of: Singapore Primary; Keys to Fractions, Decimals, Percents, Hands-On Equations (supplements)

 

Programs that were not available to us (published after we were passed those grades), that I would have seriously considered for us:

- Math in Focus

- Art of Problem Solving's Beast Academy

- Math Mammoth

- Life of Fred

 

All of that really helped build math thinking and making math connections, and developing problem solving, which helped DSs to be able to see a bit more "out of the box" and get the higher math concepts when they hit high school. However, a lot really depends on the individual student's innate abilities with math, too. DS#2 here *always* struggled with math (he has some mild LDs that made math, writing, and spelling extremely difficult for him). If you have that student, then you're just going to have to be flexible, and realize it will probably take a lot of extra time, and using a lot of different resources to find what "clicks" for each of the different problem topic areas. JMO! :)

 

BEST of luck in finding what works for your family! Warmest regards, Lori D.

Edited October 30, 2017 by Lori D.

[BTC]

Thank you Lori.  Sounds like great advice!

 

 

 

[EmilyGF]

I started all my kids with RightStart but moved each out to another solid math program that fit their personality better around 3rd grade. We've ended up in Singapore/AOPS for the oldest, MEP for the second (the one who wanted no direct instruction), and Singapore for the get-it-done perfectionist. All are showing signs of understanding and liking/loving math at this point.

 

I do think some kids do better with certain programs and they ought to be accommodated. 

 

Emily

[strawberryjam]

    I have been reading about CLE.   Anyone love this program?   Is it good to use then transition to a Pre Algebra from there?

 

 

Thanks

 

 

We LOOOOOOOOVE CLE math!!!!!! We switched to CLE about 3 years ago after trying a myriad of other math curricula including LoF. CLE is everything. It is by far the best curricula of any kind that we use. We use it slightly below grade level cause I find it advanced, even more so than Singapore. But it's a totally different kind of math than Singapore so it's really not comparable. I love that it's incremental so the kids really don't forget anything. Everything is constantly reviewed, and mastered - so they really "get it". My kids also constantly get very high grades in math, usually 95-100%. It's also written to the student so I have to do very little actual teaching, they can do most of it on their own. I also love how it covers things a lot of other math curricula doesn't. Little things that are actually important, like how to say very large or very small numbers correctly for example. Could be very important especially for kids who go into the sciences or engineering.

 

ETA to add... I don't recommend CLE for grade 1. But from about grade 2.5 onwards. Before that we did a mix-up of Singapore and Miquon, more hands-on than what CLE provides for those levels. I would still do CLE but supplement for grade 1 and 2 to prevent boredom. I plan to continue with CLE till around grade 7-8 and then probably switch to Saxon for high school.

Edited October 31, 2017 by strawberryjam