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Ask Joshua: Top questions from Week 1

A little more than a week ago, we launched an experimental (and definitely semi-controversial) initiative called Ask Joshua, which allowed teachers from anywhere in the world to run ideas on new and existing for teaching by a high-schooler. While theoretically-flawed sounding, we wanted to experiment and understand what happens. We do think that students are the customers and are the best at communicating whether or not a pedagogical or curricular style worked for them. Unfortunately, over the years, we have built pretty complex models of instruction and curriculum, and have distanced ourselves from our customers. We don’t think students have all the answers, but they definitely can help us teachers ground their planning.

We were very happy to see so many questions trickling in for Joshua, and we have filtered the top ones with Joshua’a answers below:

When I was in school, I hated teachers who gave exercises without solutions…

When I decide I’ve searched for long enough just let me have the answer before I forget the problem!

Dear teachers: students also have the ability of not looking if they want to, did you know that?! =)

I suggest breaking up a set of exercises into two groups: the first consisting of easier, routine problems; the second should contain problems that require more time and creativity. Assign the first half of the problem set on the first night, and make solutions (not just answers!) available the following day so students can check their basic understanding of the material before moving to the more difficult problems. Perhaps go over one or two of these problems at the start of this class. Then make the second half of the solutions available on the day that this second problem set is due, giving students enough time to fully process and understand the problems–and hopefully solve them–before they can look at solutions.

One of the pitfalls with waiting too long is that students may forget what aspects of the problems gave them so much trouble, and as a result they will read the solutions less actively and gain less from reading them. Thus I suggest you urge students to review solutions the night following when they are due.

How to teach the concept of negative numbers. Example: -1, -2, -3 As an example of ludico mode.

Positive numbers represent the quantity of an object. Therefore a negative number represents lacking that quantity of the object.

The most practical example of this is debt. Debts are usually written as negative numbers. For instance, if you owe 9 dollars, you have -\$9.

You are subtracting something from nothing, which implies that you lack the object you need to complete a specific task. Then, as you acquire that object, you add a positive number to the negative number. When the quantity of the object you need to use up equals the quantity of the object you find/get, you end up with a net gain of 0 units of that object.