Math Machine
A notebook will show your kid how far they have travelled
At some point, math needs to be written down to solve it
Sometime in Elementary School or heading into Middle School, your kid will need to write out the math they are working on.
They will no longer be able to look at a problem and know the answer; they will have to write down the steps.
When our kids started doing these types of math problems, we bought inexpensive printer paper and worked on those pages.
However, at some point, we realized that
We were throwing away paper after the math was done (and we got sentimental about it)
One day, one of the kids wanted to reference a problem they had previously done, and we had already thrown away the paper
Taking their work and throwing it away made it feel like the work wasn’t “valuable”
So we got a notebook where math would be “done.”
Get a notebook where math happens
The power of having a notebook for math has become more apparent as time passes.
First, the kids can now go back to previous problems they’ve solved and see what worked and what didn’t.
Second, sentimentally, it’s incredible as a parent to see how they were writing/thinking about math six months ago, twelve months ago, and two years ago. It always pulls at my heartstrings to see how far they have come. Even things like their handwriting are still very precious to me.
Third, the kids have an index of formulas/concepts they’ve learned at the front of the book to help them keep track of what they’ve encountered. If they need to reference it later, they know exactly where the concept is in their notebook and can find exercises that they solved related to that concept.
Fourth, the notebook serves as a personal growth diary for the child, showing them how far they’ve come.
Fifth, the notebook serves as an impartial cheerleader because it shows the kids that they have solved and worked through all kinds of tricky math problems. Further, many of these problems will appear very easy when they look back. So, it helps to remind them that they can keep plugging away at a hard problem now, and eventually they’ll figure it out (and in the future, they may even find it very easy to solve).
Give the notebook a fun name
Loren Graham, from MIT and Harvard University, writes in an article titled “The Power of Names: In Culture and in Mathematics”1
A common concept in history is that knowing the name of something or someone gives one power over that thing or person. This concept occurs in many different forms, in numerous cultures—in ancient and primitive tribes, as well as in Islamic, Jewish, Egyptian, Vedic, Hindu, and Christian traditions. The strength of this belief varies, and there are certainly exceptions to it. Nonetheless, the persistence and historical continuity of the linking of naming and power are unmistakable.
So, have the kid give the notebook a name and, if possible, make it fun.
One of our kids named their math notebook “Math Machine!”
We want the kid to have power over the notebook.
We want the kid to have power over math.
What’s worked for us
We’ve gone through a bunch of iterations over the years. The things we tried changing were a) physical size, b) length, c) page markings (blank, lines, line spacing, grids, numbering), d) “fanciness”, e) ease of ordering, and f) parents’ notebook.
For size, we tried
tiny & small
These didn’t work. They got lost frequently. The problems had to be written on too many pages. The kids went through them too quickly. We had to buy a bunch of them.
medium
It was just right! It was kid-sized, small enough to fit in their small desks or bookshelves. They could carry it easily. It felt approachable. Most problems could fit into 1/2 a page at the start and then later into 1 page. If it was a long problem or many tries were made, it didn’t feel like it went on too long. It also looked like other books on their shelves, so the parents liked to think that they felt like they were creating their own book.
large
These didn’t work. They were too big to fit into their small desks or bookshelves. It was unwieldy to work on while having a laptop/iPad/book open at the same time. Too many problems could be done on one page, which somehow made it feel to them like they weren’t making progress. By the time they finished one large book it was really battered since it had taken almost a year to work through (and they were still very little, so it got bashed a bunch when taking it out to work in and when putting it away).
For pages, we tried
Small number of pages
Didn’t work. Felt like we were buying them too frequently.
Medium number of pages
Worked best. Felt like progress was being made. They could see prior problems.
Large number of pages
Didn’t work. The notebook was too thick to fit along side their other books. Too many pages also made it so that the notebook didn’t lay flat which made it harder for little hands to write in.
For page markings (blank, lines, line spacing, grids, numbering)
Blank Pages
Didn’t work. It was nice for working on handwriting skills, but keeping multi-step problems organized was harder. Once a line started sloping in one direction, it was harder for the following lines to stay straight.
Lined Pages
Worked best. Not double-spaced notebook lines, but single-spaced. Double-spaced lines worked best when the kids were very little, but they didn’t need extra height as they got older. Single-spacing also helped when parents reminded the kids to do one “thing” per line and not to skip steps.
Gridded Pages
Didn’t work. It was nice when they started graphing things, but otherwise, it just added extra markings to the page, so sometimes they would lose a negative sign, a fraction, or part of a number to the grid.
Numbering
Notebooks with page numbers become the go-to choice once the kids had to start remembering formulas/concepts/names of mathematical things. They could write the math concept name in the front of the book, and a page number where they wrote down the definition and the example problems. We learned this the hard way when the first concepts started appearing, and a bunch of math time was spent flipping through the notebook trying to find example problems and the definition of the math concepts.
For miscellaneous things, a few things we didn’t think about until we had started using notebooks:
Easily Orderable
We let the kids choose what their notebooks would look like, and they found some really fun and colorful ones. Then, when they finished those, we went back to order more, and to our horror, they were sold out, and we couldn't get them again for a few months. The kids were mad AND sad for a while after that.
Slightly fancier than a standard notebook
We were blessed to be able to afford fancier notebooks, so we bought them and found that the kids seemed to like them more than the normal notebooks.
That said, we’ve also used the most inexpensive notebooks from our local grocery store and found that as long as the kids decorated them with the notebook’s “name,” the kids’ name, and some drawings on the front, they held it in equal reverence.
Parents should have their own notebook
Occasionally, when the kid asked for help, we would write an example or explain something in their notebook. This did not go down well at all. It was their math notebook, so we had to ask for permission, which we did. Eventually, we defaulted to getting our own notebook, and that’s what has worked best.
Leave the first page or two empty to serve as an “index” for concepts/formulas to remember
As the math gets harder and the kid is required to remember a bunch of definitions/names/concepts of things, it’s helpful to have a table of contents at the beginning that links
Revisit old notebooks
It’s fun to revisit the old math notebooks with the kids from time to time to see how far they’ve come and what they used to find difficult.
I’m big into digital archiving, so I take pictures of old notebooks and save them on my computer and an online storage solution (Dropbox).
Getting the math notebook out helps form the “doing math” ritual
Getting the math notebook out has helped form our family's “doing math” ritual. It signifies that it’s time to do math and helps to prepare the mind for what’s to come.
Then, when it’s time to put away the math notebook, it helps to signify that the time is over and that the kids can move on to other things.
Rubbing Shoulders With Giants
Obviously, don’t put pressure on your math kid.
However, one of the great things about math is that many mathematical giants have a history of leaving behind their thinking and math notebooks.
Some examples you can share with your kid(s):
Have fun, and get your kid a math notebook.
That’s all for today :) For more Kids Who Love Math treats, check out our archives.
Stay Mathy!
All the best,
Sebastian Gutierrez
GRAHAM, LOREN. “The Power of Names: In Culture and in Mathematics.” Proceedings of the American Philosophical Society 157, no. 2 (2013): 229–34. http://www.jstor.org/stable/24640241.
thanks for sharing those notebooks for inspiration! Have you seen 11YO Wolfram notebook drawings https://writings.stephenwolfram.com/2016/04/my-life-in-technology-as-told-at-the-computer-history-museum/ ?
Strong disagree about the grids. Much much more valuable for lining up numbers to have vertical lines. I have NEVER seen anyone confuse a light blue grid with a pencil line.