Scala Math

I‘ve started a writing project recently that I’m having a good time working on so far. I’ve called it Scala Math (and on Twitter here) for now, because its central focus is deconstructing concepts and procedures into steps, and la scala is Italian for ‘staircase’. You can see the word at work in ‘escalator’, ‘scale’, etc. Scala is also the name of a programming language. Here are some reasons for that I found online.

Most of the projects I’ve worked on over the past few years have also been ways for me to learn new software languages or libraries. For Geometry Theorems, it was d3. For Scala, it was React—as well as the beautiful, amazing database that a normal person can actually look at and edit and it’s still a database: Airtable.

How It Works: Learn

Every Scala has a display window—where images and videos are shown—and a steps window, where you find the text of the steps, or ‘parts’. These areas are divided by a brain, which I’ll talk about below. When you land on a Scala (this one is Solving Arithmetic Sequences), the first thing shown in the display window is an image presenting a quick snippet of what will be covered. The image shows an essential question at the top. The use-case for the snippet was a student wanting a quick reminder about something they are working on, perhaps for homework, without having to search online and wade through tons of stuff that sorta-kinda matches what you want but not really.

The remainder of the section shown at left (called ‘Learn’ mode) is a series of steps (in this case, six), explained with text, audio narration, and the accompanying images that you can see appearing when clicking on each step. The dot navigation at the top shows us that we are on the first screen of this Scala.

Each step card has a button to replay the step, which can be pressed at any time while the step is active, and a button (up arrow) to go to the preceding step.

How It Works: Reflect

As you can see at the end of the video above, there is a Reflection question which calls for a short or extended text response. This is where the audio input on my cell phone comes in handy. Students’ responses are, at the moment, compared to a few ‘correct’ responses that I have written, and others have conributed to. The response which has the highest numerical match on a scale from 0 to 100 is presented as your score, and the pre-written response is presented as a suggested answer.

How It Works: Try

After the Learn phase is the Try phase, which consists of example-problem pairs (usually; for a very few cases, so far, stepped-out problems only). Or, more specifically, stepped-out problems followed by not-stepped-out problems. These look a little different from what I typically see as example-problem pairs, where the example and the problem are set side by side. Here, the problem follows the example, and the example is not provided when solving the problem. The typical sequence is shown below.

For the Try and Test phases, it’s always multiple choice, although it’s in the plan to look at other response inputs. When students are logged in, they build up (not earn; see below) points for every question. Right now, it’s just 50 points for each, though that gets cut in half and rounded up to the nearest integer for every incorrect answer. For an item with 3 choices, the lowest point total possible is 13. For an item with 4 choices, the lowest is 7.

On desktop, students can have the question read aloud via text-to-speech. As far as I know, that hasn’t yet come to mobile as a built-in feature, but I’ll keep my ears open for when it does.

How It Works: Test

Finally, there’s the Test phase. This is typically 4 to 6 questions that are of the same form as the ‘problems’ in the example-problem-pair Try phase. I’m just showing one such question in the video at the right.

When students are logged in, they can earn points by taking the test. The points are built up in both the Learn and Try phases. I have described how the points work for the Try phase above. The Learn phase is simpler: just clicking on a step builds up 100 points. At the moment, no points are tied to the Reflect question.

Once a student reaches the Test phase, the greatest number of points he or she can ‘bank’ is the number he or she has built up over the course of the Learn and Try phases. And the Test phase is fairly high stakes, in that each incorrect answer divides the total possible points to earn in half.

The stars shown on the score modal are awarded based on percent of total points earned. For the lesson shown in this post, the total that can be earned is 1700. So, approximately 560 points is 1 star (33%), 1130 points is 2 stars (66%), and 1360 points is 3 stars (80%).

Finally, to make sure this product connects knowledgeable people with students (whether they be parents or teachers or both) and guards against mindlessly pressing buttons to earn points, there is a final front-and-back activity, wherein students solve a different problem by listing the steps themselves and showing all their work.

Published by

Josh Fisher

Instructional designer, software development in K-12 mathematics education.