Dice and Dominoes for Counting and Adding

I spent a lot of last week exploring Google Reader, and found this manual called Methods of Teaching Arithmetic in Primary Schools, from 1888. You can download the whole thing as a PDF for free. Anyway, I had read before in a book by Ruth Beechick that in the "old days" children did not start doing written math problems right away; the teachers would give them lots of practice with manipulatives and "real arithmetic" before they started teaching them abstract symbols.

This book from 1888 seems to confirm that, since the whole first section of the book is about teaching children to work with numbers in dot form so they can actually see what they are doing by "adding" and "taking away". It has a graphic system based on patterned dots roughly similar to dice or domino patterns. So ever since I read that book I've been looking for online dice or domino manipulatives.

I have some large foam dominoes that look a bit like this...except they are all standard black. So I've been showing these to the littlies frequently -- I keep them in the kitchen -- with the goal of getting them to recognize the shape of the number patterns immediately. They like to play with them, too. They also have been playing a fair amount with dice which of course have the same type of pattern.

Anyway, today while I was looking online for manipulatives and worksheet activities, I found this WorksheetWorks site. It is pretty neat. You can enter parameters and it will print out various counting and number concept sheets. It has dice counting flash cards and also counting with objects, and simple image-based addition.

There is a bit more about Ruth Beechick's approach to early education....here at this lovely blog. Basically, she says that in math learning, children move from:

1. Manipulative/Concrete --->
2. Image-based (still need visuals but don't need to actually handle and move the objects)---->
3. Abstract (a mental image or symbol suffices -- you internally understand the notion of threeness, or variable, or square of the hypotenuse, or whatever)

She makes the point that primary age children need the manipulatives and images because they aren't developmentally at the stage for abstract thinking. But even older learners need hands-on and visual experience when they are starting something new. You see for yourself that it's easier learning a new computer skill if you can work through it yourself, perhaps with someone showing you how, or at least with a diagram or graphic to help you.