If 3/8 of a number is 6, then what is 7/8 of the number? A number of years ago*, I was sitting near my daughter who was practicing for the SAT (exam used for admissions to many colleges in the U.S.). Looking over her shoulder, I decided I would use the model drawing method (sometimes… Read More »
Do you notice when things you use are badly designed? Or do you think that you just need to pay more attention to learn what to do? My local library has an automated kiosk where people pay for parking spaces. New users must study the machine to figure out what to do. Even people who… Read More »
“Design is a funny word. Some people think design means how it looks. But of course, if you dig deeper, it’s really how it works. The design of the Mac wasn’t what it looked like, although that was part of it. Primarily, it was how it worked. To design something really well, you have to… Read More »
In elementary school math, students learn how to change a mixed fraction to an improper fraction. Here is a tip or trick that teachers may use in their instruction: The visual diagram cues the student to multiply: 5 x 1 = 5. Then the student adds: 5 + 2 = 7. This series of steps… Read More »
Merrie, a fourth grader, is confronted with the following question: If Henry ate 1/3 of 3 pizzas, how much did he eat? Merrie draws this picture to help her solve the problem: Merrie’s drawing shows 3 pizzas divided into thirds. She shades 1/3 of 1 of the pizzas. Why does Merrie think of the problem… Read More »
“In science, they just call things different names that you have to learn. You could call something a blooky-blook, or you could call it a mooky-mook. It doesn’t matter. They’re just a bunch of names!” “Laura,” a fourth grader The Big Picture A good story captures our attention and imagination. We want to learn more… Read More »
How often are better educational materials and methods used in schools?. Look behind advertisements, accepted wisdom, and even credentials of expertise to take a long, hard look at the nitty-gritty details — the nuts and bolts* — of what happens in lessons and how well all children are learning. This website shows examples of what… Read More »
Robotic vs. Human Uses of Working Memory? A simple example illustrates the importance of working memory for particular academic tasks. Try adding 3 and 9 in your head. That was probably easy for you. Now try adding 33 and 99. That was probably more difficult. Finally, try adding 333 and 999. This is quite challenging… Read More »
In the Middle Ages knowledge of the complete table was considered a substantial feat of memory reserved for the truly expert. Graham Flegg, Numbers: Their History and Meaning, p. 106 In another post, I suggested some questions as part of a thought experiment about what is needed to teach well. In this post, let’s consider… Read More »
Thought Experiment* How would you teach if you wanted someone: to learn something new? to enjoy and be engaged in your lesson? to remember the most important information and skills without a lot of reteaching and confusion? Do we need big, new, nationwide programs? Do we need a few tweaks to what we’re already doing?… Read More »