Composing Table Operations

In this lesson students build on what they have already learned to formalize their understanding of the Design Recipe, and then gain fluency with using the Design Recipe.

When filtering rows or building columns, we need to write Transformer expressions. This should be done carefully! We want our results to be rock solid and accurate, especially if they’re going to be used in ways that affect the world around us.

The Design Recipe is a sequence of steps that helps us document, test out, and write Transformer expressions that let us dig deeper into our data, and analyze it more carefully. It’s important for this to be like second nature, so let’s get some practice using it.

First, we need to decide which Transformer to use: Filter, Transform, or Build. Based on the Transformer’s already-provided name, students should deduce that they will use Filter. They can then record the Transformer’s name on the line.

Next, we provide example tables. In this case, we want to know the animals' names and their species, so we write down those column names. We want to list a few different animals - at least one that is a dog, and at least one that is not - to represent the variety of animals on the table. Then we think about what our transformed table will look like:

Now, we are ready to drill down on the contents of our Transformer.

Each time students encounter a new word problem, we encourage working through it with paper and pencil, as above; the Design Recipe slows down students' thinking and encourages them to reason through each scenario fully rather than guessing haphazardly.

Students learn to diagram expressions using the Circles of Evaluation. This tool has deep roots in both Order of Operations and Function Composition, and math teachers may want to take a detour through one or both of these lessons to support those learning goals.

We already know how to filter, sort, and build columns - but what if we want to do multiple things, all at once? Sorting, Filtering and Building are powerful operations, but when they are combined they become even more powerful!

A journalist comes to the shelter who wants to write a story about a successful pet adoption — but she has a very specific set of criteria. The reporter wants to report on the adoption of an animal that weighs more than 9 kilograms (they don’t use "pounds" in Britain!).

If we use our Transformers in the wrong order (trying to filter by a column that doesn’t exist yet), we might wind up crashing the program. But even worse, the program might run but produce nonsensical results!

One way to organize our thoughts is to diagram what we want to do, using the Circles of Evaluation. The rules are simple:

1) Every Circle must have one - and only one! - Transformer type, written at the top.

2) The arguments of the Transformer are written left-to-right, in the middle of the Circle.

Values like Numbers, String, and Booleans are still written by themselves. It’s only when we want to use a Transformer that we need to draw a Circle, and write the values inside from left-to-right.

Let’s try diagraming what we need to do for the journalist, using the Circles of Evaluation. We always build first, so let’s start there. We know that our transformer needs three things: the animals table, the name of the new column "kilos" and the formula expression.

But we also need to filter by that new column, so that we only have animals weighing more than 9kg! That means we need another Circle of Evaluation. We know filter goes at the top. But what table are we using for the first argument? It can’t be the animals-table again, because that doesn’t have a "kilos" column.

3) Circles can contain other Circles!

Our first Circle of Evaluation produces a table, and that’s the one we want to use as the first input to filter!

A perk of composing Transformers is that everything is just a "view" of the original data, rather than a change made to that data. Changes can cause tables to go out of sync, resulting in hard-to-find bugs and invalid results. With Transformers, any updates made to the original dataset will flow through the composition, keeping everything in sync. Transformers can also be reused, eliminating duplicate work.

Sometimes, the hardest part of solving a problem is knowing what you want to do, rather than worrying about how to do it. For example, sometimes solving an equation is a lot easier than setting it up in the first place. Circles of Evaluation give us an opportiunity to think through what we want to do, before getting in front of the computer and worrying about how to do it.

Armed with these tools, we can do some pretty complex analysis! We can even think of data displays as another kind of table operation. What will this Circle of Evaluation produce?

Review student answers to Planning Table Operations.

Was it helpful to think about the Circles, without worrying about CODAP? Why or why not?