07 Apr 2014 25 Comments

# How we do maths without a curriculum

Back in January I shared our maths plans for this term. Our plans are always flexible. One of the joys of not following a curriculum is that if something isn’t working we can switch topic or try a different approach.

Maths with one of my children has far exceeded my hopes and expectations this term. C(10) has matured in so many ways over the last six months, and being her maths mentor has become a real delight. She’s developed genuine enthusiasm to engage with mathematical ideas and persist with challenging problems. And she’s always willing to listen to my suggestions for improving her working methods.

We started in January reading Awesome Arithmetricks, whiteboards to hand. This worked well as a recap of addition and subtraction (with some fun interludes like this simplifying equations puzzle). Awesome Arithmetricks also explained long multiplication in a way that made sense to C(10).

## The long division question

Then we came to long division. Before she started using the standard algorithm, C(10) wanted to know how it worked. Great question, but not one which is explained in Awesome Arithmetricks. {Tangent: according to one of my favourite books about teaching maths, The Elephant in the Classroom, one of the main reasons girls do less well than boys in maths at school is because girls so often want to know “Why?”, a question there is rarely enough classroom time or teacher skill to address.}

### You don’t have to be a maths genius to teach your kids maths without a curriculum

So what did I do? I did what I always do when one of my kids asks a tricky question – I turned to google. “How does the long division algorithm work?” I found plenty of helpful websites, but – to be completely honest – I didn’t follow many any of the explanations!

I didn’t panic. You really don’t need to be a maths genius to teach your child maths without a curriculum. I’m certainly not! If I’d devoted a bit of time to understanding how the long division algorithm works I’m sure I would have got there. But I decided it would be more fun to figure it out alongside my daughter.

{*Edit*: The Cookie Factory Guide to Long Division at Let’s Play Math is a brilliant explanation of how long division works. I now understand it, yay!}

C(10) knows my attitude to learning maths. She knows that I got top maths grades up to “A” level but that I mostly learned by unquestioning memorisation, rather than fully grasping the mathematical concepts. She trusts me, not to know all the answers, but to help her discover them for herself, in a way she deeply understands.

At this stage of her maths education it would be easy for me to swot up in advance and pretend I know it all. Instead, though, I’m aiming for a long-term approach which will create a foundation of trust. A foundation which will, I hope, continue through our homeschooling days, as C(10) becomes more independent but continues to trust me as her learning mentor.

## How we approached long division

So what did we do about long division? I downloaded Math Mammoth’s Division 2 which teaches long division in several small steps, over many lessons. C(10) completes the exercises on her iPad using Notability. A side benefit is that she’s been getting lots of multiplication fact practice.

{**A tangent about learning multiplication facts**: C(10) prefers to figure out each multiplication fact when she needs it rather than rote-learn the times tables up front. I fully support this way of working because I can see how it develops her number sense. And I’m delighted that she can now instantly recall many facts thanks to having calculated them so many times. That’s seems a sensible order for learning multiplication facts.}

## Fun maths to break up the worksheets

Division 2 is great value at $5.10 for 70 pages of well-structured teaching and practice. I’m sure by the time we’ve completed it we’ll both know everything there is to know about the hows and whys of long division. But there was no way C(10) was going to work through 70 consecutive pages of division and emerge with her love of maths intact. So, we’re taking our time.

Each day I ask what she’d like to do for maths. Usually a few times a week she chooses to work on Division 2. Other times we do something different. We have plenty of resources – many of them free – to choose from. Here are some we’ve enjoyed this term.

### An unexpected treasure trove – SATs papers

This SATs-papers website contains all the past test papers sat by English schoolchildren. I usually take one look at SATs papers (especially science and English ones) and run a mile, thanking our lucky stars that we home-educate and my kids don’t have to waste their time on this kind of stuff.

But we *love* the KS2 Level 6 Maths problems. These questions are deceptively short but they all require *thinking*, and that’s why C(10) loves them. You can download as many SATs papers as you want, you just have to register (free).

### Becoming a problem solving genius

Like Primary Grade Challenge Math, Becoming a Problem Solving Genius is made up of short chapters, each of which introduces a topic in a fun way and is followed by four sets of problems which range in difficulty from “easy” to “super-Einstein”.

While we love the problems in this book, we find some of the strategies a bit formulaic. C(10) likes to have a go at the problems and then refer back to the notes when she needs a pointer. As with our multiplication facts approach, this seems to me to be the most sensible order of doing things. Instead of being told how to do something and then being tested on it, don’t we learn better once we’ve experienced a need for a piece of information or technique?

### Measuring Up: Prototypes for Mathematics Assessment

Measuring Up (free download) is another source of interesting games and problems on subjects ranging from probability to geometry.

According to its publishers, the book “features 13 classroom exercises for fourth grade students that demonstrate the dramatic meaning of inquiry, performance, communication and problem-solving as standards for mathematics education.”

Each of the 13 exercises is followed by an explanation of what it has been designed to achieve. Examples of high, medium and low level responses are also given. We just enjoy the puzzles!

### The Man Who Counted

When The Man Who Counted popped through my letterbox I briefly wondered if Amazon had sent it by mistake, or perhaps as a bonus for my generous contribution for their bottom line. When my brain finally clicked into gear I remembered coming across it on Math Mama Writes‘ list of a dozen delectable math books.

C(10) and I have only read a few chapters so far, but already we’ve found some delightful problems. (Really! The kind you have so much fun with you want to share them with friends and family.)

### Maths art

Highhill Homeschool has been sharing a wonderful series of posts based on the geometry of circles. Their most recent activity was based on Islamic Art and Geometric Design from the Metropolitan Museum of Art (yet another free download). This ties in perfectly with our forthcoming trip to Spain, where we’ll be visiting the Moorish palace, the Alhambra.

We’ve enjoyed looking at photos of the exquisite geometric designs at the Alhambra. And C(10) has found a reason to learn how to draw circles with a compass. We’re looking forward to moving onto finding geometric shapes within our circles.

Do you have any fun maths resources to share?

****

*I’m appreciatively linking up here:*

After School Link Up at Planet Smarty

Wonderful Wednesdays at Solagratia Mom

Collage Friday at Homegrown Learners

Weekly Wrap Up at Weird Unsocialized Homeschoolers

Shelly

Apr 07, 2014@ 12:40:04We’ve really been enjoying the Life of Fred series, which is literature-based and explains not only how to do things but why we need them.

Lucinda

Apr 07, 2014@ 16:25:47Hi Shelly, we really like Life of Fred, too. My son used to use them all the time, but we took a break halfway through Jelly Beans when he got a bit confused with the way they presented co-ordinate graphing. I’d like to invest in the intermediate books at some point. I seem to remember you got the complete set – are you pleased with the intermediate books, too?

Hwee

Apr 07, 2014@ 13:18:20I really like that you’ve covered so many grounds in one post — your approach, resources, and examples. It’s true that many parents feel ill equipped to assist their chidren in maths, but as you’ve rightly pointed out, the main requirement is the curiosity and willingness on the parent’s part to model how to find solutions. The aspect of trust is truly important, and one that is not often mentioned. I truly appreciate all the points you have in this post.

Lucinda

Apr 07, 2014@ 16:31:04Hwee, I seem incapable of writing short, to the point posts! How nicely you put it, though! And thank you for your very kind words, they are much appreciated.

Solagratiamom

Apr 07, 2014@ 13:45:41Love the math ideas! I would love to have you link them up at http://www.solagratiamom.com! Have a great day!

Lucinda

Apr 07, 2014@ 16:31:27Thank you! I’ll see you on Wednesday

katy

Apr 07, 2014@ 16:34:28Hello, I always enjoy your posts. How old were your children when you gave up a maths curriculum? Do you think its possible to teach everything in a fun living maths way? Or do the basics need to be taught more formally? I’ve found that the ‘drilling it in’ has to be through repetition and worksheets and is far from enjoyable, despite the concept being fun in the beginning.

Lucinda

Apr 07, 2014@ 17:09:37Hi Katy – thank you. We gave up following a single maths curriculum about a year ago when my children were 8 and 9. But I’d never managed to get them to stick to any one curriculum for long before then, anyway.

“Do you think it’s possible to teach everything in a fun living maths way?” Yes, I do think all maths can be learned in a fun way, but that doesn’t necessarily mean no drilling. Everyone’s definition of “fun” is different, but for us it means having plenty of variety. We’ve used very basic drill apps for getting the hang of subtraction with regrouping, for example. We just don’t use them for too long at a time! And Math Mammoth Division 2 contains plenty of drills, which is why we mix it up with lots of other maths activities. We especially like problems and puzzles which draw on a variety (that word again!) of maths skills. And when a problem involves a concept my daughter hasn’t come across yet, she’s in the perfect place to learn it.

For us, I think the key to inspiring a love of maths is freedom, and time – both of which we have in abundance when we’re not trying to follow a single curriculum. I used to worry about gaps, but time has shown that not to be an issue. Perhaps because we use so many different types of materials, we seem to cover everything.

(Maths with my son, by the way, is a

completelydifferent story. I’ll be posting about that soon!)I was first inspired to embark on our living maths experiment after I read Let’s Play Math by Denise Gaskins. I wrote about it here. And I shared one of our early living maths weeks here – 5 Days of Living Maths.

How old are your children, Katy?

Julie

Apr 08, 2014@ 00:02:16Your living math posts are very inspirational and I’ve enjoyed many of the resources you have recommended. Thanks for the reminder of The Man Who Counted. That book was purchased for my daughter, but I think my son is now ready for it.

We purchased the entire Life of Fred Series. I really like them, but have changed the way we use them. I find them very useful in they way they display application for math, but I think they are sometimes difficult to learn from. My son flew through the A-J series, and has been stuck in fractions for almost a year. I’m doing more hands-on fraction based activities with him which usually include some examples of methods after the concept is understood. This is done in conjunction with LOF. We go really slowly and only cover about one chapter per week.

With my daughter, who learns well from traditional method memorization curriculum, I use LOF as both a review and as a way to give the math meaning. When she reads them, she already knows how to do the math, but doesn’t always understand the purpose for the math. Life of Fred is really good for application.

I’m glad you enjoyed our geometric math activities. I have more coming in the far off future.

Lucinda

Apr 10, 2014@ 16:31:52Thanks, Julie. It’s very helpful to know how you use LoF. Perhaps I will buy Fractions. I would like to know what happens to Fred next.

I shall look forward to your geometric activities.

Denise

Apr 10, 2014@ 00:01:46When you were looking for long division resources, did you try my Cookie Factory Guide to Long Division? If so, I’d love to hear where the explanation lost you. It’s hard to judge my own writing, to know when I’m making sense and when I’m taking too big of jumps or not saying things clearly, so I really value critical feedback.

Lucinda

Apr 10, 2014@ 16:35:48Denise – thank you! I should have known to try your blog first. I tried Maria’s page and a couple of others but they all skipped to the shortcut too early for me (missing out the zeros). I LOVE your explanation – very clear with lots of practical tips. Just what we needed.

Denise

Apr 10, 2014@ 18:54:09I’m glad it helped!

Phyllis at All Things Beautiful

Apr 11, 2014@ 18:31:03This is an awesome post. I am amazed at how similarly we do math! It is wonderful to see all the ideas all in one place.

Lucinda

Apr 13, 2014@ 19:27:40Thank you so much, Phyllis! I find your maths posts very inspiring.

Beth

Apr 12, 2014@ 16:51:01I am impressed. I love reading math books to the kids. One of our favorites is Sir Cumference. It helped me to know what diameter is.

Lucinda

Apr 13, 2014@ 19:32:52Thank you, Beth. We love the Sir Cumference series, too! I agree, kids’ maths books and especially stories help me understand a lot of maths too. In fact, the same is true for quite a few subjects.

Claire

Apr 13, 2014@ 19:25:44I had a sort of light bulb moment whilst reading this. You know this is my huge area of struggle with trying to find the time to teach maths to five children with completely different learning skills. Your way sounds so fluid, and yet I find it impossible to replicate with L who is the child who wants living maths.

My light bulb moment came when you said about using many different resources to learn maths. Silly I know, but I hadn’t really considered mixing text book and living maths to a degree which may suit both girls together, and even maybe including T and A to some greater or lesser degree.

I’m not sure where I’m going with our maths, but you helped clarify things I didn’t know were muddy!

Lucinda

Apr 13, 2014@ 19:48:26What a lovely comment, Clare – thank you! I’m so happy to have got into a maths groove with one of my children. My post about maths with the other won’t be quite so cohesive! The quest to find what works keeps things interesting, though. As ever – hats off to you finding ways for things to work with five children!

Solagratiamom

Apr 15, 2014@ 14:09:46Love the post! Thank you for linking up at Wonderful Wednesdays! We have truly enjoyed putting the math art into our school this year! Blessings – Colleen

Lucinda

Apr 15, 2014@ 21:26:19Thank you so much, Colleen. I love reading all your posts!

Ingi (@ingidefygravity)

Apr 21, 2014@ 06:13:42As usual, an abundance of very useful links and ideas! I might be a little bit in love with you

Lucinda

Apr 22, 2014@ 12:51:25It’s completely reciprocated, Ingi!

Rebecca

May 02, 2014@ 04:13:23You and Hwee both always have the best ideas for math. Some day I’m going to have to actually implement some instead of just reading about them

Lucinda

May 02, 2014@ 22:12:51LOL Rebecca. I like to collect ideas from my blogging friends too … you never know when they’re going to come in useful! And if maths is working in your house, I say don’t mess with it!