数学机器——笔记本将显示你孩子已经学习的进度。
Math Machine – A notebook will show your kid how far they have travelled

原始链接: https://kidswholovemath.substack.com/p/math-machine

过渡到书面数学需要一本专门的笔记本,而不是随意用纸。这能让孩子的作业更有价值,方便他们回顾之前的题目,追踪学习进度,并建立自信。给笔记本取个能增强其在数学学习中力量的名字,比如“数学机器!” 中等大小,带横线页面的笔记本最合适。页码编号对于索引公式和概念至关重要。确保笔记本易于重新排序,如果能稍微精美一些就更好了。 家长应该有自己的笔记本,避免干扰孩子的空间。预留前几页作为索引,并定期翻看旧笔记本以欣赏孩子的进步。笔记本将成为一种仪式,标志着数学学习时间的开始和结束。强调著名的数学家也保留笔记本,以此激励孩子。

这个Hacker News的讨论串围绕一篇提倡在儿童数学教育中使用物理笔记本的文章展开。原帖推崇笔记本作为可靠、无DRM(数字版权管理)的各种学科学习工具。评论者们就这种建议的必要性展开了辩论,一些人认为这显而易见,而另一些人则赞赏其强调如何使笔记本对孩子们有效。大家讨论了对页面的类型偏好(横线、点状、网格),一些人偏爱点状页面,因为它在结构和灵活性之间取得了平衡。一些人分享了他们使用笔记本进行数学学习的个人经验,强调了组织性和记录解题方法的重要性。也有人担心物理笔记本的长期存储问题,尤其是在住房成本不断上升的情况下。

原文

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

  1. We were throwing away paper after the math was done (and we got sentimental about it)

  2. One day, one of the kids wanted to reference a problem they had previously done, and we had already thrown away the paper

  3. 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.”

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).

Loren Graham, from MIT and Harvard University, writes in an article titled “The Power of Names: In Culture and in Mathematics

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.

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

  • 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

  • Medium number of pages

  • Large number of pages

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

  • 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.

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

联系我们 contact @ memedata.com