“It does feel like there could be a half-way house between the arithmetic and the algebra…

Could there be a page after the arithmetic where you have to say in general what you’re doing. But not type it. Have blocks of text that you can drag around that say “the width of the lot (l)”, “the width of the dividers (d)” along with numbers, brackets and arithmetic symbols. That way, perhaps with the teacher’s help, students could spell out what they were managing to do on the previous pages.
It wold be a formula, but without the big jump to just letters.”

Good idea.

I can see myself using the early pages of this with my Year 4s (3rd grade), because it’s such a clearly set out and satisfying multi-step question.

Even though we do begin some algebraic notation
http://year4atist.blogspot.fr/search/label/algebra
the formula pages are obviously too big a step up.

And I could quite happily leave it at that. But perhaps it’s useful to speculate how it could be even more brilliant…

I agree that the first pages could perhaps not all have the car parks divided into four bays. Three, five. Then there’s more implicit algebraic thinking – it is a variable.

It does feel like there could be a half-way house between the arithmetic and the algebra…

Could there be a page after the arithmetic where you have to say in general what you’re doing. But not type it. Have blocks of text that you can drag around that say “the width of the lot (l)”, “the width of the dividers (d)” along with numbers, brackets and arithmetic symbols. That way, perhaps with the teacher’s help, students could spell out what they were managing to do on the previous pages.
It wold be a formula, but without the big jump to just letters.

It’s one more step then to use the letters instead of the phrases. This would make it more accessible to children in primary/elementary – and maybe also older children too?

One other thing: I agree that it would be nice to have a metric option for those not in the US.

I would agree that it can be difficult to make interactive applets for all math topics, but it is definitely a great start. As you said, if we continue finding ways to make math meaningful for students with tools such as this one, students will be better able to make connections with algebraic representations (I believe, anyway).

When you mention that writing expressions is not a general skill, are you referring to the fact that there isn’t a set procedure or method? I think that is part of the reason why students struggle with it so much. Most of what we traditionally teach in math is procedural and based on a set number of steps whereas writing expressions involves much deeper thinking and understanding.

With an applet like this one, I would hope that students can learn to leverage their use of this applet to help them problem and write expressions in other situations.

One major drawback to the activity is how specific it is. The software cannot be used for any purpose other than learning to “write an algebraic expression that represents the appropriate width of a parking space in terms of the number of desired spaces, the width of the barriers and the total width of the lot”.

In order for this type of applet to be universally useful, one of two things has to be true (or both): 1) it is possible to make A LOT more of these to cover all of the phenomena we wish students to be able to model, or 2) learning how to write the algebraic expression in this applet facilitates a user’s ability to write expressions that represent other phenomena (without the benefit of an immediate link between the symbolic expression and its spatially tangible counterpart, to boot!)

Option 1 doesn’t seem feasible (although it could be!). I question Option 2 as well. I am finding more and more that learning how to write expressions that model phenomena is not a general skill, but instead is highly dependent on the specific phenomena you have learned to model. Even subtle changes in the details of a phenomena are sometimes enough to require more learning before a person can successfully model the new, change context.