We're all familiar, I'm sure, with the use of worked-out examples in mathematics teaching. Worked-out examples are often used to demonstrate problem-solving processes. They generally specify the steps needed to solve a problem in some detail. After working through such examples, students are usually given the same kind of problems to work through on their own. The strategy is generally helpful in teaching students to solve problems that are the same as the examples.
Around the world, for the most part, compulsory schooling starts at 6, although some start at 7, and a very few at 5 or even younger. There is less consensus about how long compulsory education should last, but 9 years is the most common length, with 10 years running a close second.
Recently a “Framework for Success in Postsecondary Writing” came out in the U.S. This framework talked about the importance of inculcating certain “habits of mind” in students. One of these eight habits was metacognition, which they defined as the ability to reflect on one’s own thinking as well as on the individual and cultural processes used to structure knowledge.
Consider our facts about blood:
We could, as is often advised, simply turn these into why questions. And we can answer these on the basis of the connections we’ve already made:
Because they need to accommodate changes in pressure
Because they need to accommodate high pressure
I don't think anyone's going to try arguing that fruit and vegetables are not good for your health! We know they're good. But that's just general "oh, I know it's good for me" — do you know that the benefits are not only for your general health, your protection against obesity and diabetes, cancer and heart disease, but also for your brain. Actually, there's two aspects to this. An unhealthy diet (one rich in junk food, in saturated fat and sugar) is actively bad for your brain, and (the right) healthy diet is actively good for your brain.
Most people find numbers — phone numbers, personal identification numbers, dates, and so on — more difficult to remember than words. That is, of course, why businesses try to get phone numbers that correspond to some relevant word. The system whereby this is possible — the linking of certain letters to the different digits on a telephone calling pad —is a kind of coding mnemonic. Basically, coding mnemonics are systems that transform numbers into words.
It is clear that there are differences between the genders in terms of cognitive function; it is much less clear that there are differences in terms of cognitive abilities. Let me explain what I mean by that.
It's commonly understood that males have superior spatial ability, while females have superior verbal ability. Males are better at math; females at reading. There is some truth in these generalizations, but it's certainly not as simple as it is portrayed.
The most obvious presumed benefit of homework is, of course, that it will improve students' understanding and retention of the material covered. However, partly because this (most measurable) benefit has not been consistently demonstrated, it has also been assumed that homework has less direct benefits:
A fascinating article recently appeared in the Guardian, about a woman who found a way to overcome a very particular type of learning disability and has apparently helped a great many children since.
We all know that lack of sleep makes us more prone to attentional failures, more likely to make mistakes, makes new information harder to learn, old information harder to retrieve ... We all know that, right? And yet, so many of us still go to bed too late to get the sleep we need to function well. Of course, some of us go to sleep early enough, we just can’t get to sleep fast enough, or are prone to waking in the night. (Personally, I can count the times I’ve slept through the night without waking in the last fifteen years on my fingers).