*Written by Jamie Martin of Simple Homeschool and Steady Mom*

Two weeks ago I began a short series on math by explaining how our family decided to approach this subject in a non-traditional way.

If you missed that post, I’d recommend reading it first before continuing this one.

Today I want to continue by serving up more math inspiration. **Several “out of the box” math links follow, which I hope will help you come to your own unique conclusion on this topic.**

Many of these fueled our personal decision on when and how to teach math.

You can read the entire post I reference by clicking on the title link. I’ve also written a short overview as well as included excerpts. Enjoy!

#### Just Do the Math by David Albert

*David Albert shares the story of 9-12 year-olds who learned all K-6 math in just 20 hours of study. He also shares his belief that an average teen who is actually motivated to learn math, and wasn’t held back by math anxiety, can learn all the K-12 math that he hasn’t naturally picked up in life in approximately eight weeks of study. *

“So, do the math. If you figure the actual math time at 30 hours a year for 8 years (accounting for the wasted time in the early years), it totals 240 hours. Lo and behold – if, at age 15 or so, you wanted to learn all the math K-12, weren’t inhibited by math anxiety, and were willing to spend 30 hours a week at it, it would take you…8 weeks!”

#### A Mathematician’s Lament by Paul Lockhart

*In this 25 page article (later expanded into the book above), research mathematician Paul Lockhart makes the case that math is an art form, and that the way we currently study it prevents kids from falling in love with and seeing it through the lens of imagination that the other arts inspire. *

“If I had to design a mechanism for the express purpose of destroying a child’s natural curiosity and love of pattern-making, I couldn’t possibly do as good a job as is currently being done–I simply wouldn’t have the imagination to come up with the kind of senseless, soul-crushing ideas that constitute contemporary mathematics education.”

“You want to train them to calculate 427 plus 389? It’s just not a question that many eight-year-olds are asking. For that matter, most adults don’t fully understand decimal place-value arithmetic, and you expect third graders to have a clear conception? Or do you not care if that understand it? It is simply too early for that kind of technical training. Of course it can be done, but I think it ultimately does more harm than good. Much better to wait until their own natural curiosity about numbers kicks in.”

#### Research on the Teaching of Math @ Trivium Pursuit

*This article shares (in thorough detail) how math has been taught historically through the ages–a fascinating study! The author then suggests waiting until around age ten to begin formal math lessons.*

“So to wait until age ten to teach arithmetic is actually, from an historical perspective, to advocate an “early start.” It is only from a decidedly modern perspective that waiting until age ten would appear to be a “late start.”

“Depending upon the child, upon the method, and upon the subject matter covered, there exists the potential for developmental harm from the formal teaching of arithmetic before age ten.”

“Small children cannot understand many arithmetic concepts at an early age. We can teach them to perform the process, but we cannot make them understand the concepts. The child “learns” to hate “learning.” The child’s understanding develops along the wrong lines. He may actually develop mental “blocks” to arithmetic – actual physiological blocks in the brain.”

How can someone actually begin the formal teaching of math at age ten?

Laurie Bluedorn suggests one possibility in her follow up article to the above – **Delayed Formal Math Approach:**

“At age ten we start the child in formal math with a 6th grade math textbook. I give the child two math grids, and they are allowed to use them when doing their math lessons.”

At age eleven I take away the addition/subtraction grid. The child should have the addition/subtraction facts memorized by then. If I think that he doesn’t have them memorized then we would drill on them till he does have them memorized. At age twelve I take away the multiplication/division grid.”

#### Louis P. Benezet’s study…as told in Free-Range Learning

*In 1929 Louis P. Benezet, the Superintendent of Manchester, New Hampshire schools, tried an experiment within his system. He trialed having some of his classes wait until seventh grade to introduce formal math study. Before that time he encouraged naturally occurring math learning in the classroom, but had teachers make reading, writing, and reasoning the focus in the early years. *

“I feel that it is all nonsense to take eight years to get children through the ordinary arithmetic assignment of the elementary schools. What possible need has a ten-year-old child for knowledge of long division? The whole subject of arithmetic could be postponed until the seventh year of school, and it could be mastered in two years’ study by any normal child.”

“Due to pressure from some school principals, children were started on a math book in the second half of sixth grade. All sixth-grade children were tested. By spring of that year, all the classes tested equally. In other words, those children exposed to traditional math curricula for part of the sixth-grade year had mastered the same skills as those who had spent years on drills, times tables, and exams.”

#### What we do in our family

*Adorable Elijah (9) just happened to crawl into a cardboard box when Mommy was working on this post–it can be dangerous having a mom who’s a blogger!*

In some ways it’s difficult to explain exactly what we do in our family–because it is, has been, and no doubt will continue to be completely different for each child. There’s no formula, but we have followed the advice mentioned above about waiting to introduce formal math.

**This decision comes from our deep belief in the importance of our young children having a full and thorough Core Phase**, which does not include a focus on early academics.

Two of my three children are now in the second phase of learning, Love of Learning, and recently math emphasis has crept into our lives more regularly. But it is still highly individualized and based on each child’s needs and strengths.

I have one who is naturally gifted with numbers, who has “played” with them over the years and by doing so has picked up quite a lot. I have two children who learn very differently to the traditional classroom style and who appear to have their geniuses (at this stage) in other areas. Of course this doesn’t mean that math won’t be a part of their lives, but it means that I introduce concepts when I believe maturity and readiness are present–so I can set them up for success.

If you decide to get out of the box when it comes to math, what can you do in the early years to prepare and play with numbers instead? I’m glad you asked!

Come back next week for a list of specific resources so you can create your own math playground.

*** Update: This series is now finished! Read the third post and final post – enjoy!*

“Mathematics should be taught as art for art’s sake. These mundane “useful” aspects would follow naturally as a trivial by product. Beethoven could easily write an advertising jingle, but his motivation for learning music was to create something beautiful.”

~ Paul Lockhart

*Are there any helpful or surprising aha moments you have when reading any of the above articles? Do you find yourself feeling excited, skeptical, scared, or some other emotion while reading?*

The problem I’m having with this is that in my state, I am required to give “evidence of instruction similar to what the student would receive in the public school system” and our portfolio is reviewed twice yearly. Any ideas on how to implement a more natural approach to learning within those confines?

Hi Sarah. My reply to Sarah M is along the same lines as your comment and might be worth reading. HSLDA or the similar organization in your own state would also be a really good one to call or email for specific “translations” of what the laws truly mean and how to navigate them.

I’ve got to be honest – this is a little depressing to me. I have a 9 year old who claims to hate math (although she’s quite competent at it). In her 1st grade year (public school) and for the past two years of homeschool, it’s been one long cram-fest of math facts, concepts, basically everything I shouldn’t have done. There are tears on a regular basis. (From both of us). I feel like I’ve done it all wrong. I get the allure of this other approach to math, but 1) it seems too late and 2)I’m not sure I’d even have the courage to go that far out of the box.

So I guess my questions would be is there a middle ground? Is there any back-tracking with a kid who’s already so far down the traditional math road and hating it? And like the above commenter was asking, how does one reconcile this approach with testing/state requirements?

I’m so sorry to hear that this is depressing to you, Katie. I definitely didn’t spend hours writing this post to try and depress anyone or make them feel bad. And I most definitely would not say that a 9-year-old is past all hope and doomed to math hatred forever – so far from it. Age 9 is a perfect place to begin! I’ve addressed some of the testing/state issues in my other comments here, but I think it also comes down to searching your heart to find the solution that is right for you and your daughter in this moment.

Maybe you don’t have the courage because it isn’t right for you to go so far out of the box, and therefore you don’t need that type of courage. Or maybe you don’t have the courage just because you’re really, really scared…but deep down you know you’re supposed to step out in faith, and the courage will meet you when you’re free falling. You’re the only one who can find the answer to that, but the answer truly is there for you when you’re ready for it. Don’t worry about what you’ve done in the past – just think about what you feel you should do TODAY. Blessings on you and yours, Jamie

Thank you for your reply Jamie. I apologize for the tone of my comment, it certainly isn’t your fault that math is the way it is at our house! I appreciate all the inspiration I’ve gained from reading about your homeschool approach and I really need to stop feeling like it’s a personal indictment every time I read about others’ successful approaches to things I struggle with. Thank you for your gracious response to my questions, and again I apologize!

You’re beyond welcome, Katie! I struggle with this topic, too, (which is why I’ve never really written about math in the past five years of this blog!), and I think many people would not describe our approach as “successful” – surely not by conventional standards, at least! Yet it is the “right” approach for us, and I wanted to give voice to it in this space for those who perhaps have the feeling that they need to make a change in this area as well – to let them know it is possible.

Katie, I had an avowed math-hater until we discovered Teaching Textbooks. While not exactly out of the box, it has helped our homeschool immensely. My previous loather of arithmetic now races to the computer each morning to do math! My favorite benefit of TT is the program keeps a grade book for you. So to fulfill any state requirements isnt difficult. A bonus is that it isn’t expensive either. (Not trying to sound like a commercial, this is just what has been working for us.) For us, the traditional textbook math was not working and it was killing the love of learning in my kids. TT preserved the love of learning in math for us. Maybe it would help rekindle it in your homeschool too.

I love all those quotes, and I’m totally on board. Unfortunately where I live my kids do have to remain within grade level (mostly) for the province’s requirements. We play a LOT of games for math, but we do have to keep up with the workbooks, too.

Sarah M

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That’s a really good point, Sarah. Each of us will have to come to our own conclusion – the one that feels right for us and our families, and obviously taking into account the requirements where we live is certainly a part of that! Like most of life, we might have a certain “ideal” in mind, but life rarely matches that ideal – instead we balance it with the realistic in a glorious imperfection that becomes our beautiful life and the right childhood our kids need.

I would say, though, that I’ve noticed sometimes the laws have more flexibility than we recognize and if we really investigate them and chat with others in our area about how they have done things differently, we might stumble upon more wiggle room than we initially thought was there.

We use a more traditional math approach, and it’s had its ups and downs, for sure. It’s a tricky subject for us, and one in which I feel the least competent to offer instruction. However, I find that math is EVERYWHERE, and my kids use it, whether they know they are or not. Thanks for the encouragement to find ways to strengthen math skills in everyday life and not just to focus on worksheets!

My son had started playing Prodigy. He loves it! It’s an online math game. It reminds me of Pokemon meets math. 🙂

That sounds cool, Dede. It’s amazing to find what’s out there these days!

we just started Life of Fred and so far we are enjoying it! Much less stressful! We have a homeschool friend who is about to graduate, she doesn’t love math and her parents didn’t push it. She needs math to get into college so she learned geometry in 3 days and algebra 1 in 2 weeks. The do the math chaper in David Alberts book was the only good chaper in the book, just read the except! I am trying not to push so hard in the math department but it isn’t easy!

“She needs math to get into college so she learned geometry in 3 days and algebra 1 in 2 weeks.”

Wow, truly amazing!

Looking forward to more on this topic. It’s great timing for us. I have a 9 year old who is great with math concepts and I really pushed him ahead with Abeka (he liked doing the workbooks). Then I really slowed down and switched to Life of Fred which he loves! But I was starting to second guess myself and pulled out a 3 digit multiplication worksheet and he hated it! I’ll be looking for your next post!

Sounds like you’re right on track, Robin–following your own instincts and paying attention to your son’s signals.

First-year homeschooler here. This makes me feel torn! I’ve been leaning toward Classical but then this really speaks to me! Is there a happy middle?!

Hi Renee! For me the middle we discovered that worked for us is A Thomas Jefferson Education, still very much a classical approach but one that flows with what they call the phases of learning (as I mention in this post). You can find out more about TJEd here: http://www.tjed.org/about-tjed/

Thank you thank you and more thank you for all you continually do in my world of homeschooling!

You’re so sweet, Lynda. Thank YOU!

Hello,

Perhaps you have a suggestion. My 15 yr old son, who at one time had a quirky intuitive way with numbers and math (could glance at a pile of screws and tell you how many, learned his addition and subtraction with a base-8, his “invention” instead of a base-10 that we normally do, could calculate tips in his head) now seems to have no capacity for remembering anything math. At all. He is 15 and passes the subjects, but then “pumps and dumps” the information pretty much as soon as the lesson is over.

I am finding myself having to figure out how to get him to internalize math so it will stick (especially algebra and above). He can do arithmetic, but I have NO idea how to get him prepared for college.

Any ideas? Thank you. OH and he has a lot of math anxiety, I believe. His memorization of other facts is astounding, but remembering anything math–nada. And he lost his ability to calculate tips (again, at like age 7) in his head if he thought about it for even a second instead of just blurting out a number.

Thank you!

Sorry, I know your question was directed at Jamie, and hopefully she’ll pipe in too. I obviously am not in a position to know for sure what your son needs. But my suggestion for you to consider is a math detox, but not one where he does no math. Instead, what if he spent maybe half a year working through the art- style mathematicians’ math and falling back in love with it? Cause I have a hard time believing anyone with that much natural math ability could possibly hate it if they are given it in it’s pure form. Lockhart, who wrote one of the articles Jamie has linked to, wrote a book called “Measurement” and it coaches you through discovering math in the way his article talks about. If this were my soon you were describing, I would play around with the idea of offering time spent working in that book as an alternative to whatever other math he’s doing for a set amount of time (2 months, 6 months, a year, whatever you want). After that he continues the traditional math, but can still continue doing the Lockhart math for fun. Just something to consider. Here’s a link in case you want to look into it:

http://www.amazon.com/Measurement-Paul-Lockhart/dp/0674284380

Thanks so much for your comment and question here. I agree with Aubrey below about letting your son take some time off from math in the way that it is causing him anxiety and do a detox, maybe getting reacquainted with math as play (which it sounds as though he is gifted at, based on your description of his younger years.) I wouldn’t try to “prepare him for college” right this very moment, but I would try to prepare him for “this moment.” Does that make sense at all? Sometimes we pass our own anxiety about the future on to our kids, but what these articles in this post show is that there are many ways math can come together for a student. However, if a child loses his love of learning completely…he or she really can’t be prepared for college OR for life.

If you haven’t researched the phases of learning, I would take a quick peek and see if you can determine which phase your son is in (not by his age but by his characteristics): http://www.tjed.org/2011/06/homeschooling-excellence-phases-learning/ If that info resonates with you at all, you could read more about TJEd and focus on your own study for a while as you think about this issue and determine what’s right for your son.

Also have you spoken to him about his feelings about math and/or what he would like to do in this area? You might be surprised at his insight to take into consideration. The last thought that comes to mind is that Life of Fred might be something to look into when he is ready to try again. It is very unconventional, is based on using the math in real life, and goes all the way up to college levels: http://lifeoffredmath.com

I cannot wait to read these books. Thank you for the recommendations. I will say that, as a rookie homeschooler and someone who always performed well in math but battled math anxiety (still, to this day), I felt most worried about math in our homeschool. Because of this, I had several different choices for math and I rotated them through during the year, fearing gaps. My son loves numbers and he enjoyed this… until he didn’t, which was about two months ago. I backed off and I was surprised to see that he naturally does math daily. It’s as if he seeks it without me. So, yes, I could relate to this series 🙂

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I love the idea of rotating methods, Cait. I think we naturally do this in much of life (outside of school/academics), but somehow we feel as though we must pick one method for math or another subject and do it without skipping until the kids graduate! That just isn’t real life in so many other areas (and it sounds boring, anyway! =) )

Thank you for this post. I am doing alternative real life math books with my first grader, and I really need to keep hearing the confirmations that this is the best way to go. So far we have done Life of Fred, old Time Life math books, Bedtime Math, and math storybooks like the Sir Cumference adventures. We are both enjoying these together!

Sounds perfect, Katie!

This all resonates with me so much. I make sure to take it easy with math at home. We use Miquon and my daughter likes it, and I never push to do more than she wants to do. But after reading Paul Lockhart’s essay, I’ve decided to shelve the curriculum and get down and dirty with math in real life. Will definitely get his book mentioned in a previous comment, and am so glad you’ve recommended others. I’m excited to see where this takes us – I think she’s going to flourish! Just writing down all the prompts I can think of to explore together.

Excited for you, Amy!

I was a math teacher (7 – 12) and now teach college level from home and home school my kids. From watching how all ages learn, it really seems that kids especially learn best with a mix of real life application and really building number sense. But the thing I constantly have to remind myself is not to push. My son (kindergarten) did not want to work on some of the math I was trying to do with him for weeks and weeks and weeks. He would cry, he would try to get out of it, but then I let it go for a little bit (let the workbooks go) and we had some fun with numbers. When we went back to it his fluency he was really fast and he suddenly understood things that I didn’t even think he was listening to. He was finally ready to put it all together. Some things that have really helped us to keep going with this momentum is movement. He loves to learn while moving. So we do number squats to work on skip counting by 2s and leaping from lily pad to lily pad for skipping by 5s and different things like this that get him moving. And then lots of word problems in disguise to keep building on what he knows and giving it a real life application. The more I do not do in a workbook, the better he is in the workbooks and required things when we go back to them. So I think it is worthwhile to think outside the box, letting the student/child show what he/she is ready for and then it may lead to being able to keep those state requirements later on.

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Beautiful ideas, Debby. Thanks for chiming in!

I appreciate this post and you sharing some ideas that are so “out of the box” compared to the public schools (I am a former math teacher turned homeschooler)! I think you have a lot of really great ideas and I’m encouraged to see so many homeschoolers looking for creative, engaging and student-led methods of approaching math. 🙂 Blessings! ~Bethany

Thanks so much, Bethany!

Just wanted to let you know that there are math teachers out there at schools which follow the “normal” math curricula who know and agree with the info you have shared. I have found that I can reassure most kids that it is ok to not feel like they “get” math and that even though our system requires them to do it, they can follow the method for now, knowing that in time it will become something they can understand and even enjoy. Simply by changing their expectations, we can reduce their fear of math. And it is so rewarding as a teacher when one day they do get it and are excited to be able to see the patterns and puzzles within the numbers!

I was just thinking this week about how natural or is for me to approach reading this way (make it fun, wait till the child is ready, etc) but not math. Maybe it’s because I love reading and I want my kids to love reading, but I don’t necessarily “love” math. I think I fear that if I don’t follow the traditional methods, my kids will never learn it! I’m interested in looking into the resources you mentioned. 🙂

Sorry about the typos!!

Thank you!!! I was just losing sleep last night over not doing any formal math with my 8 year old yet, fearing him now far behind. We follow a Tjed philosophy and had intentionally not pushed, but major doubt and pain set in yesterday. This post just reassured me in more ways than you know!

“panic” not “pain”….auto correct, lol!

I’m so glad it helped, Alana!