I taught neuropsychological research with an emphasis on special education for 25 years. I got started in this area when I told a friend that I did not have visual imagery. Her reaction was, "How do you think?"
I think by talking to myself but she thought via mental imagery. From there I developed a theory of the causes and remediation of reading disability.
To get started, try a simple experiment. Image an animal. Now rate it from 0-10 in terms of vividness and being lifelike. Did you image with your eyes open or closed? Now image with your eyes closed if they were open or open if they were closed. Now rate the image. Did it change?
I have tried this demonstration many times and about 50% of the people image with their eyes open and a majority of them, find the image decreases in vividness when they close them. But how often do we hear the instructions: Close your eyes and imagine.....
Try this in your classroom and let's hear what you find.
A closing question: When a song runs through your head, who is doing the singing?
Introducing the Spreadsheet
By SheroseFamily Math Day and opportunites to explore the spreadsheet with student groups has convinced me that the spreadsheet is an important tool in developing an understanding of quantiy as well as our number system. Where to begin is always an issue,just as it is in every classroom.
Start with an introduction that provides a feeling of control and success. The challenge is to move to from the known to the unknown: move to the new content as quickly as possible by starting with the simplest version:
1) I like personalizing word problems. The spreadsheet can do that.
2) I like using real events in math. The spreadsheet can do that.
3) I like using materials as a discovery technique. The spreadsheet can do that?
4) I like when kids translate manipulatives into equations. The spreadsheet can do that.
I trained at the UN School to use math-manipulatives to help students see the various paterns in "mathematics". A stack of three green rods is different from a stack of yellows or reds . Each color represents a rod with a different lengths. The reds are two white cubes in length but in every otherway it is the same. The green is the same as three white or one red plus two white, etc, Students discover multiplication, division and fractions.
The spreadsheet was just as effective in introducing greater understanfing with a spreadsheet through discovery and play. Family Math day was fun because we were able to introduce children and parents simultaneously to the simplicity of the process. The kids giggled and smiled broadly as they proceeded playifully with the additive process. What if we put your age and your father's age on the left and a plus one in the box at the top: that tells us your age for next year. How about your ages in ten years: how old would each of you be? 21 years; in a hundred years? The little third graders giggled as they saw their age ranges change. They teased their parents playfully, too. We played with cookies as well as boxes of raisins.
"Can you guess my secret rule?" is a game we have played with early learners. It is fun to play the game on a spreadsheet with and without a computer. Piaget can help us deal with the variables and the issues we need to develop.
"How does the computer know my rule?" Is the question that I would consider after several opportunities to work with the "What's my secret?"
Learning to be a good observer of quantity is a slow process but the spreadsheet can pull data together to provide opportunities to learn important concepts that are hard to illustrate: How big/ tall is each building if it has a column of ten windows going from top to bottom? What information is missing? How many cookies do we need if we give each child 2, 3, 4? Use your bank books. Type in the amount that you have saved in the bank. If I give each of you ten more dollars and ten cents, how much money would your bank book indicate? Clearly, we can each demonstrate the complexity and develop an important awareness of how to work with variables that are significantly larger than the ones that they can minipulate using rods or other manipulatives.
Sheila
Math Manipulatives
By anneOne of the goals of the math section of my website is to provide paper/cardboard versions of manipulatives for students in schools where these (sometimes pricey) objects are not available. I have a page of printable fraction bars, and each months when I check the stats, I see that a lot of people check them out and hopefully print them out and use them.
Last month, the most popular subject page was the one where users can print out a hundreds chart to use with markers and count items up to 100. The thousand chart was also popular last month.
I suspect if I make a version of the Cuisionaire Rods that can be printed, I may have another useful manipulative for math learners.
It may also be useful to provide precise instructions to make the rods from wooden dowels available in hardware and craft shops, giving dimensions for each color rod.
Can you think of any other manipulatives I can include either as a paper version, or with directions how to make them from easily available simple materials? The purchased versions of such materials are often out of the reach of many skin and bones classrooms.
Anne