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## The Illusion of First Discovery

Do you think we over-prompt our students? Prompting is useful to focus the classroom’s attention on one part of a problem. It also helps the teacher steer the class towards a new problem or resource.  However, prompting does not provide a shortcut to student...

## Multiple Solution Problems

Can you give us another good problem – one that’s possible please. This is a problem I give to my grade 1 students. The Fairy-Tale-King invites you to sit down in front of him…  “design for me, a magical castle with beautiful towers.” It turns out that he has enough...

## Real World vs. Abstract Problems

The last time we talked you introduced us to cipher-breaking in World War I. I always mention war if I have the opportunity, because that engages the half of the class with excess testosterone ? The link to war also connects the problem to the real world. Do all good...

## Breaking a Cipher – an example of a good problem

You were going to give us an example of a good problem. Here is a good problem for students tackling percentages, and probability. The problem takes an hour or two… This is an example of some cipher-text created from a Polybius Square. The Germans used a variant of...

## What should children learn in the mathematics classroom?

What should children learn in the mathematics classroom? How to think. Is that all? What do you mean; “Is that all?” That is everything! I would even be happy if we got rid of elementary school mathematics classrooms and replaced them with problem-tinkering...