I wish we could discuss together how ZemZem tackled the numeral 8. She was clearly the protagonist here. Her efforts were for herself, not for me or anyone else. To me this is proof of the benefit of avoiding praise. ZemZem is personally powerful, not a praise junkie. Her disposition to learn is much more important than the numeral 8. That attitude is what she will be taking forward into the rest of her life.
For those of you who have read some of my other pages, this video is a representative example of how I have learned what I am sharing at this site. I videotape something so I can look at it again and again and hold conversations with others to co-construct the meaning. I can learn lots more doing this than studying some book or journal article. The short video conveys the experience of the Andre and ZemZem with more complexity than words can convey.
Documentation and Public Investment
Great spaces for children can be created everywhere when the educators document and reflect on what happens each day. If our common resources can provide early educators with a family support wage, they will naturally evolve more effective opportunities over years of study.
I am outraged that this is not the experience of all children, especially for children like these who have had fewer opportunities and less economic choices. ZemZem’s family just arrived from Somalia, and English was new for her. Andre arrived by bus with his mom, who was unable to read or tell time, from rural Arkansas two weeks before school started in September. Unfortunately, public policies for children in the United States prevent the creation of the conditions for great schools to evolve, while billionaires gloat, push rigid constraints on early childhood opportunities, and refuse to consider the commons. The ethical choice is to offer resources for them to study their own children, construct their own understandings, and cooperatively improve their skills. In order to save this planet, all children will need to experience a democratic learning community led by professional educators who deeply listen, are comfortable with uncertainty, and engage in action research.
When children are learning to print numerals, we can offer two types of challenges. The salt boxes offer a free space for the child to draw from memory and errors disappear. The numeral boards offer practice forming the shapes with the correct stroke order, which like all drawing is essentially practice in visual motor planning.
These are 1/2 sheet practice boards inserted in page protectors, cut in half, and sealed with tape. These are damp proof writing surfaces for wet-erase pens like the Vis-a-vis. Marks are easy to wipe clean with a damp cloth or paper towel. Along with the boards and the pens, I provide small, slightly damp dishcloths in a plastic bag and wash them out every day.
On the left is an image of the printed practice sheet as it comes out of the copy machine. On the right is a colored half page.
Numeral boards PDF provides the set for you to download and print your own.
I color code the stroke order with highlighter pens. I use purple and green, so the dotted line shows through. Regular pens obscure the dotted lines. The children use black overhead projector pens (not purple or green pens!) to trace on the plastic page protector. I like purple-green stroke order cues. I think the chant “purple-green, purple-green” is fun to say and memorable.
I have found that 10 offerings to trace is enough of a challenge without becoming too repetitive. The last numeral on the top row presents only the first stroke; the green is missing. This is repeated on the 4th numeral of the lower row. The final try provides only a place to start. It is simple to check on children’s ability to write the numerals by looking at that final bit, when they choose to try it. Of course, the children can draw anything they want on the boards.
I insert the colored half sheets into clear heavy duty sheet protectors. with a piece of light card (one-dot or two-dot chipboard) cut to the same size. I put a different numeral facing the other way on the other side of the card. Then I cut the sheet protector in half and use transparent tape to seal the seam so moisture cannot get inside. I always mix up the numerals on one board, so a child simply has to flip it over to try another numeral. One full set of numeral boards uses 4 page protectors making 8 numeral boards with different numerals on each side. Zero and one are not included. Cheap. Simple. Better than anything you can buy.
I have tried many ways to do this, and this is the best. All I have to do is watch what a child does in the lower right corner to assess his or her skills in forming the numeral.
I use the half-sheet page-protector system to create pen paths for tracing as an introduction to the numeral boards and keep the cue sequence of purple green. These are easy to make at many levels of difficulty. Whether the children use them or color them or scribble over them is perfectly fine with me.
This game was invented by Donna Burk, Paula Symonds, and Allyn Snider, one of a set of games for kindergarten in the Box It and Bag It series available through the Math Learning Center. This is my recording sheet where the children trace the numerals. I have built all the Box It and Bag It games. Green Beans fits with this numeral writing topic.
Download Green Beans PDF.
Next comes choosing your beans. The tradition, started by Donna Burk, is to buy large lima beans, spread them flat on newspaper and spray paint the top side, carefully, without underside drips. I found two coats better than one. I used green paint, so I did indeed have green beans on one side and natural white on the other. You can use any color of paint. Lavender would make a game called Lavender Beans. Alternatively, you can buy plastic counters that are red and white two-sided bean shapes by clicking the image.
Once I have my bean color, I run duplicates of the master on paper of the same color — green paper for me, red for the plastic ones. I put a small stack of the sheets in a large zippered plastic bag and beans into another lidded container to organize the materials in a way the children can restore. I include six 2-ounce portion cups and six thinking pens like the Bravo! ones at the top of the page. I put all of this in a sturdy box with a rubber band around it, adding a picture of a bean on the ends of the box.
I could just put this out in a workstations container and see what happens, but I doubt the children would invent tossing nine beans. Maintaining the distinction between independent time and group time, I don’t show them during workstations time. It’s their free time to play. so I demonstrate the game to everyone at group time. I count 9 beans into a portion cup. “I am going to count nine beans into this cup. Count with me. Ready? Count. One, two, three, four, five, six, seven, eight, nine. How many? (pause) Nine. I did it. Cup of nine, This is fine. Cup of nine, This is fine.” (I have fun, too, you know.)
Aside: I can’t tell you how grateful I have been any time a master teacher has told me exactly what to say when leading a group. This way of leading counting, “count with me, ready, count, one, two…. how many? (pause 5 seconds and say the answer)” really works!
Once I have nine beans in the cup I demonstrate dumping out the set of nine and counting the colored ones, using that same counting convention. “Let’s count the green ones. Ready? Count. One, two, three, four. Four. How many? pause Four.” Then I trace that grayed-out numeral 4 in the bottom row, starting at the dot.
As you can imagine, the children, being freely at play during workstations, do whatever they want to do with the Green Beans game. It’s all fine with me. Usually, since everyone saw my demonstration at the same time, that way rises to the top. Some tend to gravitate after a time to filling in the sheet without tossing any beans at all, filling in the entire sheet to take home. Because the random toss follows a bell curve, children soon find that there are too many 4’s, 5’s and 6’s, and they turn over some of the beans to write other numerals. If only one or two children choose the game, I post a few of the papers nearby or bring one or two to a meeting time as a provocation for children to discuss what happens at that table.
I would never ask children to spend that huge amount of time filling in all of the boxes on the recording sheet, so I have been amazed at how many children choose to do it on their own.
Two More Ahead
- Mathematics Materials shares the advanced materials in number, sorting and classifying, and measurement for five- and six-year-old children, bridging to first grade.
- Planning and Rotation Scheme presents a simple system for scheduling throughout one year.