Besides creativity, personal connections, verbalizing answers, and self-esteem, there are several other problematic areas within today's K12 instruction that I think can still be put to good use.

While requiring students to solve easy arithmetic problems in multiple ways, as Reform Math routinely does, is tedious and pointless, there can be a virtue to solving harder, multi-step problems in more than one way--not least because this is often the best way to check your answers.

Again, this depends on how hard the problems are. With hard, multi-step problems there is often work to show even for those who can perform complicated calculations in their heads, and teachers sometimes can't gauge whether students know what they're doing in such cases unless they examine this work.

While working in small groups in classrooms has all sorts of downsides (distractions and inefficiencies, confusion, unequal conctributions, opportunities for bullying, etc.) these can be avoided when the

**Multiple solutions**While requiring students to solve easy arithmetic problems in multiple ways, as Reform Math routinely does, is tedious and pointless, there can be a virtue to solving harder, multi-step problems in more than one way--not least because this is often the best way to check your answers.

**Showing your work**Again, this depends on how hard the problems are. With hard, multi-step problems there is often work to show even for those who can perform complicated calculations in their heads, and teachers sometimes can't gauge whether students know what they're doing in such cases unless they examine this work.

**Group discussions**While working in small groups in classrooms has all sorts of downsides (distractions and inefficiencies, confusion, unequal conctributions, opportunities for bullying, etc.) these can be avoided when the

*whole class*functions as a group, led, of course, by the teacher. Class-level group discussions are perhaps the best venues for brainstorming solutions to problems and sharing observations during literary analysis.**Hands-on, discovery learning**

Used in moderation and planned out carefully, hands-on learning can be an efficient way to learn certain things and remember them later--especially when it comes to science experiments. I once devised a hands-on activity for a 10th grade geometry in which students manipulate angles to discover that the angles of a triangle sum to 180 degrees.

Of course, none of these general ideas are new, and anyone who thinks that long-ago classrooms never applied them is laboring under the dry, dill & kill caricature of traditional schools promulgated by Constructivist alcolytes via the fallacy of the false dilemma.

## 5 comments:

I'm guessing that by "reversing home and school," Katherine, you might mean the idea that much of what constructivits propose as good classroom practice and essntial to children's educational progress, is actually better carried out at home. I've long been in agreement with this. When children play at home, it's great for the play to be unstructured. When they do chores, what could be more hands-on? Parents learn to intuit what types of activities/conversations/imaginitive play ios most appealing and most fruitful for their children (and I include totally uneducated parents). But tell us what you had in mind!

yes, Anonymous, that's more or less what I mean. The flipside occurs when schools ask parents to drill kids the multiplication tables.

Hands on learning has been found to be beneficial after students have built a strong base of knowledge. So, when used to reinforce existing knowledge, it works. When used to actually teach something, not only does it not work, it seems to lead to confusion.

I have read about studies that assigned people to learn about something in different ways. These people were given a pretest. Everyone was then given a post-test after their learning session. Those assigned to the hands on group often did worse on the post-test than the pretest. Those assigned to a lecture always did better on the post-test than the pre-test.

Other studies have found that hands on learning is highly effective for people who already have a strong knowledge base. Someone who is learning chemistry overtime will benefit less and less from books and lectures and more from hands on lab work. This is why medical students spend a lot of their early years learning in classrooms and later years learning in clinical settings. Attempts to put medical students into clinical settings too soon have created problems later on.

Hands on learning is neither a good nor bad idea. It is all in how it is implemented.

Hands on learning is neither a good nor bad idea. It is all in how it is implemented.And under the regime of those who are in control of education today, it's generally implemented poorly.

About the multiple solutions issue--not all solution strategies are equal, even for simple problems. If you are adding 5+6, then decomposing 6 into 5+1 so you are thinking of it as 5+5+1 is a really useful skill. Much more efficient than counting on, and worthwhile to think about even if you have 5+6 memorized (because it's an example of a useful way of looking at numbers that that helps with a lot of different mathematics topics)... But as usual, when I disagree with you about a math teaching strategy, I also do, however, agree that most (all?) of the new textbooks out there doing this are doing poorly and pointlessly. I've seen it done both well and poorly, but I'm not surprised that you've only seen it done poorly.

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