Math Curriculum for a Math Potential Without Limits

[Sapa]

Hi everyone! I’ve been lurking for a while here but just posting for the first time! 

I know math curriculum is a common anxiety for homeschooling parents and a lot out there has already been heavily discussed on the topic (I’ve read a lot!).  Nonetheless, given my sense of the stakes, I can’t help but pose my pointed to inquiry to you sages here. My apologies for any triteness! 
 

I realize there are a ton of math curriculums that do a perfectly adequate job of getting a student up to general educational standards and making them capable test takers, and they all vary in terms of difficulty, entertainment, learning style, etc. But I also know that, setting all other considerations aside, if you want to be truly excellent at something, there is often an advantaged way of learning it, a way that teaches you to fundamentally (rather than merely functionally) understand it, and once you get to the most challenging levels, if you learned any other way, you often find yourself “un” and “re” learning to get to that next level. 
 

In choosing a math curriculum, I’d like to be sure I provide my child with an excellent foundation for progressing toward any strata of quantitative excellence he desires. I’m not interested in shortcuts for becoming an excellent test taker or anything of the like; I’d really like to help supply the right raw materials for building a mathematical mind in case my child wishes ultimately to do something that requires one. I’d never want my child to have to unlearn something I taught or have to relearn with a different approach. 
 

The problem for me is that my own math knowledge and ability is poor, so I have a true challenge assessing options. (I’m currently leaning toward Singapore Math.) With that in mind, I thought I’d reach out here for experiences or insights. For those that have raised students with a curriculum, or those of you excellent at math who can better evaluate the advantages  and drawbacks of different options, do you have any opinions on what curriculums stand out as either poor or excellent routes for developing the kind of understanding or math I’m trying to get at? 
 

So greatly appreciate any insight. Thank you! 

[wendyroo]

Singapore is a solid curriculum that teaches rigorous, conceptual math. That said, it wouldn't be my first recommendation for you. To get the most out of the program, the teacher really has to understand conceptual math. This can be helped along by reading the Home Instructors Guides, but that can be overwhelming and time consuming. There are also a lot of interchangeable/supplementary pieces to the curriculum: textbook, workbook, home instructors guide, extra practice, intensive practice, challenging word problems, process skills, fact practice, etc. Again, this can be overwhelming for a teacher who doesn't fully understand the method.

I would recommend Math Mammoth. One "worktext" (textbook plus workbook combined in one) that is written to the student. I go through Math Mammoth lessons with my very young students, but there is nothing I have to teach them...it is all clearly taught in the worktext. So you need to be a guide more than a teacher, and you can learn the concepts right along with your student.

[Clarita]

Both my kids are really little age-wise K and preschool. I suppose I'm rather mathy. I really like Singapore Math. Here's the thing though part of why I like it is because it does present many ways of solving a math problem, honestly is a bit like learning how to do the same math with a different approach. I do think this curriculum works best, especially for a parent whose math is not so strong, to take the time to read either the teacher's guide or the home educator's guide. Not only for the descriptions of the mathematical concepts or the lesson script you do with your kids, but also a lot of how to incorporate these mathematical concepts in everyday. There's even a few pages I believe in the back of the textbook that has "activities to do at home". Most of these are activities I naturally do with my kids because I see math in everything and I can't help it, but I have pointed it out to others and they were kind of blown away. 

1 hour ago, Sapa said:

 if you want to be truly excellent at something, there is often an advantaged way of learning it,

I don't think this true at all. I would probably be in the camp of not at all true for math. I think the best way is different for different students/people.  The best way of learning math is the way that works both for the student and for the teacher. I mean as much as I like Singapore Math as a curriculum, my K'er is doing Beast Academy. That's the math that speaks to him, and I'm glad there are so many good options out there these days.

 

[ScoutTN]

If your own math background is weak, choose a curriculum and work all the way through it. Then choose one with a somewhat different approach and do the same. And yet again. Read here, read books suggested here. 

[Dmmetler]

Art of Problem Solving was written by math competition winning mathematicians for the next generation of same. Beast Academy is the elementary school level version. It's not right for all kids (for some, it wouldbe complete torture), but for those who are mathy kids who thrive on challenge, it's pretty awesome. 
 

Beast wasn't out yet when my mathy kid was that age, and Singapore provided a great foundation for AoPS and then college (and graduate level) math classes. I will say that it is a different way of thinking about teaching math (I have a K-8 license in math Ed)-I did two online teacher training courses in it, which helped quite a bit. If you just buy the workbooks and expect to do only them, it wouldbe hard to be successful. 
 

I will also say this-betweenfour kids that I've homeschooled for all or part of math, only one of the four was a good match for Singapore-AoPS-College math classes as a K-12 math pathway. You may find it isn't the best fit for your child, either.

Edited October 17, 2022 by Dmmetler

[Sapa]

These replies have been so generous and helpful. Thank you, everybody! 

4 hours ago, wendyroo said:

I would recommend Math Mammoth. One "worktext" (textbook plus workbook combined in one) that is written to the student. I go through Math Mammoth lessons with my very young students, but there is nothing I have to teach them...it is all clearly taught in the worktext. So you need to be a guide more than a teacher, and you can learn the concepts right along with your student.

Your points are well taken, and I greatly appreciate the recommendation. I’ve heard math mammoth mentioned before, and your description makes it appealing. Do you feel it’s in any way limiting relative to something like SM or BA? That is, is it less rigorous for the sake of being more accessible? 

 

3 hours ago, Clarita said:

Both my kids are really little age-wise K and preschool. I suppose I'm rather mathy. I really like Singapore Math.

Thanks a ton for your input and perspective. It really is helpful to me!  I’ve heard it mentioned before how helpful it can be, especially for the less math adept, to work through the teacher’s guide materials carefully, so this is all well taken. Thanks for the tip on the at-home activities! 
 

3 hours ago, ScoutTN said:

 

If your own math background is weak, choose a curriculum and work all the way through it. Then choose one with a somewhat different approach and do the same. And yet again.

 

Thanks a bunch for this advice. Seems like a good idea and aligns with what others have said here. Just to clarify, are you recommend I do this with my child, or alone on my own time before even venturing to work with my child (or both)?  I will dig into the reading recommendations! 
 

2 hours ago, Dmmetler said:

Art of Problem Solving was written by math competition winning mathematicians for the next generation of same. Beast Academy is the elementary school level version. It's not right for all kids (for some, it wouldbe complete torture), but for those who are mathy kids who thrive on challenge, it's pretty awesome. 

Thank you very much for this input. My son is pre k age but already show a strong proclivity for math despite zero pushing from me, which is a large part of what has prompted my concern. I want to be sure my limited math ability doesn’t limit him if his affinity sticks. 
 

Beast Academy sounds really attractive on the surface. But I’ve gotten the sense from prior discussions that BA is really only suitable for those with both grit and giftedness in math. It sounds to me like BA’s explanations don’t do as much handholding as other curriculums, so if you aren’t quick to catch on, you’re likely to fall behind. Does that match your assessment? 

[Clarita]

So I did start off with Singapore math with my oldest (BA didn't have a level 1 last year when we started Singapore level 1). One of the reasons I considered a change to BA is my son would often request to skip the explicit teaching and lesson part of Singapore and ask to go directly to the problems. One of the things I really like about Singapore math is their explicit teaching and their use of manipulatives to teach the math. BA seems to use parts of their problem sets to teach new concepts. (At least I've seen them do this in beginning level 1.)

You have time to decide whether your child would ultimate go into BA because BA doesn't have a kindergarten level and they expect kids to come with some knowledge into level 1. 

Personally I would have hated BA as a kid. I like explicit instructions more and I would not do well being thrown into solving a puzzle without proper preparation. My son (and husband) on the other hand would rather be given a problem to solve, not be able to solve it, then go back to figure out what pieces they are missing to solve the problem.

[ScoutTN]

8 hours ago, Sapa said:

 

Thanks a bunch for this advice. Seems like a good idea and aligns with what others have said here. Just to clarify, are you recommend I do this with my child, or alone on my own time before even venturing to work with my child (or both)?  

I did it well before my kids began formal school work. I chose Right Start and Abeka to have one conceptual and one more procedural. There are many good math programs and zillions of threads here about their respective strengths and weaknesses. One size does not fit all. 

 

[Clemsondana]

I don't think that there's just one right option, and many kids would do fine with any reasonable program.  I used Singapore for both of my kids, and it's one of the few curriculum choices that I think was actually a great fit for both of them, even though they are very different.  I'm pretty comfortable with math elementary math, so I wasn't worried about that aspect.

We didn't use all of the books.  I had the home instructor's guide, and I used it in the beginning and if we ran into a problem.  It's pretty good, so using it daily might be enough if you work ahead.  Usually I'd talk them through the examples in the textbook if it was a new concept, and then they'd go straight to the workbook.  We did the tests at the end of chapters from the test book, and if I saw that they were struggling with something I'd pull the sub-tests and use those as extra practice.  I only remember doing that a couple of times.  We did a little with challenging word problems, but my kids didn't enjoy math for fun and it isn't where we chose to put our time.

My older is really mathy.  We did the Singapore pre-test before starting K, and based on it's recommendation we started with level 2.  My younger started in level 1.  We looked at Beast and neither kid particularly liked it.  Older moved straight to AoPS with some Life of Fred thrown in for fun.  For both kids, Singapore gave a good foundation and helped them to be comfortable with numbers and manipulations.  I don't think that it's the only path, but it worked well for us.  I've known others who had good luck with Miquon.  

[wendyroo]

8 hours ago, Sapa said:

Your points are well taken, and I greatly appreciate the recommendation. I’ve heard math mammoth mentioned before, and your description makes it appealing. Do you feel it’s in any way limiting relative to something like SM or BA? That is, is it less rigorous for the sake of being more accessible? 

One of my favorite parts about Math Mammoth is how versatile it is. I've had some kids who had to do every problem on every page, and other kids who cruised through only doing minimal problems in sections that they understood well. That allows me to customize the rigor, and tailor it to each child's strengths and weaknesses. I can supplement with living books, SM challenging word problems, BA, Zaccaro books, Miquon, Hands on Equations, etc.

I guess I really like Math Mammoth as a spine. If I take each child through Math Mammoth (at their own pacing doing as much or as little as they need to achieve deep, conceptual understanding and algorithmic proficiency), then I know they are building a really solid foundation. And that really, truly would be enough to give them a solid, rigorous math education. But since that is so open-and-go and requires so little of my attention, then I can focus on the icing on the math cake - the enrichment and extra challenge, which in my experience need to be implemented more carefully.

For example, my most mathy child, who is taking pre-calc as an 8th grader, never thrived in BA or AOPS as a primary math curriculum. He always needed to deep dive into a challenge for a while, and then retreat back to tried and true Math Mammoth when he started to get overwhelmed and needed time to mull over the challenging material. Whenever we tried to switch entirely to a discovery/puzzley curriculum, he would burn out, start to dislike math, and end up needed extended math breaks to regroup...at which point I would steer him back to Math Mammoth which was exactly what he needed.

[Dmmetler]

11 hours ago, Sapa said:

These replies have been so generous and helpful. Thank you, everybody! 

Your points are well taken, and I greatly appreciate the recommendation. I’ve heard math mammoth mentioned before, and your description makes it appealing. Do you feel it’s in any way limiting relative to something like SM or BA? That is, is it less rigorous for the sake of being more accessible? 

 

Thanks a ton for your input and perspective. It really is helpful to me!  I’ve heard it mentioned before how helpful it can be, especially for the less math adept, to work through the teacher’s guide materials carefully, so this is all well taken. Thanks for the tip on the at-home activities! 
 

Thanks a bunch for this advice. Seems like a good idea and aligns with what others have said here. Just to clarify, are you recommend I do this with my child, or alone on my own time before even venturing to work with my child (or both)?  I will dig into the reading recommendations! 
 

Thank you very much for this input. My son is pre k age but already show a strong proclivity for math despite zero pushing from me, which is a large part of what has prompted my concern. I want to be sure my limited math ability doesn’t limit him if his affinity sticks. 
 

Beast Academy sounds really attractive on the surface. But I’ve gotten the sense from prior discussions that BA is really only suitable for those with both grit and giftedness in math. It sounds to me like BA’s explanations don’t do as much handholding as other curriculums, so if you aren’t quick to catch on, you’re likely to fall behind. Does that match your assessment? 

Yes. AoPS was written by mathematicians who loved and excelled at competition-style problem solving for those kids. It's for the kids who need the experience of beating their head against a wall, but relatively few problems to gain mastery. 

 

With Singapore, I actually used a different version than most in the US do-I sourced the Shing Lee published version from Singapore vs the Mitchell Cavendish version that has been adapted for US audiences. This was completely by accident-I ordered a lot of books on Ebay and it turned out to be the Singapore version vs the US one, but my child thrived with them because there was a lot of cultural information included that made it more interesting (and the cute cartoon creatures were animals vs cartoon kids). After that point, I continued to get the books from Singapore because they worked. 

[Xahm]

I've got kids who do great with Beast Academy, but other programs do a great job, too. The most important controllable factor to having high math success, in my opinion, is having a parent/teacher/mentor who is confident and able to guide. 

I would recommend getting a Beast Academy online account for yourself and going through it now, or at least going to the free printable resources page and reading through the chapter overviews to learn about how they present various ideas. Even if it isn't right for your child, I think it would help you to see math in a new way that will make you more aware of various issues as you evaluate curricula for your child. 

[Coco_Clark]

What you are looking for is conceptual understanding, which any modern curriculum is going to provide as long as it's taught well.

In my experience, there isn't one (or two, or three) best curriculums so much as a best fit for that child.  

Over the past decade, over 6 kids plus tutoring, I've used with success:

Miquon 

Right Start 

Singapore 

Math Mammoth

Beast Academy

And that's just arithmetic.  Don't get me started on how many different Algebra programs I've used.  

For what it's worth I've also used Saxon, Life of Fred, and Teaching Textbooks with less-than-sucess, while admitting maybe it would work for someone else.  

Questions you need to ask yourself are: How hands-on can I afford to be (do you need the student pretty independent)?  How much prep time can I afford to do (do you need open and go)? Do you have a teaching style that needs to be supported (I can't stand scripts, tbh)? Does your child have a learning style that needs to be supported (hands on, visual, oral, ect)?  How important is review and repetition to the childs success?  How frustrated are they by leaps in logic, do they thrive or do they prefer explicit instruction?  Every kid/parent will be different, so each will gain true math understanding with a different program.

Edited October 18, 2022 by Coco_Clark

[lulalu]

I think the best path is to relearn (or focus on areas you are weak in). Any textbook or program will only get you so far with a teacher who doesn't understand. But with a teacher who has understanding and can explain any textbook can become conceptual and great. The teacher's understanding and knowledge is what is important. 

I would suggest reading through Knowing and Teaching Elementary Mathematics. It isn't a how to teach book, but it will give you areas where you need to improve yourself. 

Then figure out if you need visual and hands on learning or if you need to hear explanations, etc. For us the best hands on method has been c-rods and Miquon followed by Gattegno books. This has given the visual and hands on experience that my son and myself need. 

[Not_a_Number]

I'd definitely recommend either relearning or outsourcing to someone who understands the material. 

[Dmmetler]

One thing you may want to look for is classes for prospective math teachers. The community college here offers a really great sequence that goes through preschool through high school algebra 2 and geometry, with an eye towards how to teach it, but it also really offers a chance to relearn skills that have aged, or were never really understood conceptually. Ed2Go offers online courses on Singapore Mathematics-check multiple schools because at least in my state, if you take an Ed2Go class through the state U, it costs 3x taking one through the CC-for the same class with the same instructor. PBS learning media offers good classes, too-some of the self-paced ones are even free.

[Malam]

If you want to improve your own ability to teach math, check out this article, in particular Arithmetic for Parents by Aharoni along with the book Math from Three to Seven: The Story of a Mathematical Circle for Preschoolers. If you want to understand elementary math in a more rigorous way that would be relevant to teaching, try Understanding Numbers in Elementary School Mathematics by Hung-Hsi Wu. How the Brain Learns Mathematics is a book on, you guessed it, how the brain learns math.

Edited October 26, 2022 by Malam

[Clarita]

4 hours ago, Malam said:

How the Brain Learns Mathematics is a book on, you guessed it, how the brain learns math.

This is fascinating! I've only glanced through it. I did get to the part where he has you see if you can remember a bunch of numbers, then he talks about how English makes it harder than say Chinese in memorizing numbers. Anyway I recalled the numbers because I didn't memorize the sequence by name but rather I visually remembered the Arabic numerals. I don't know if he talks about that but it's interesting.

[Sapa]

I just want to thank everyone for all of the incredibly informative responses here.  Such helpful points and resources.  In addition to reviewing different curriculums like Math Mammoth, I'm now going back and giving myself a math bootcamp and reviewing recommended materials on teaching elementary math.  Feel a lot better about the path forward after all your feedback!