# What Analytics in Math Games About Fractions Can Show Us

# What Analytics in Math Games About Fractions Can Show Us

April 18, 2020

## What Aspects of Fractions Do We Struggle With Most?

We live in exciting times, in which technology offers new ways to learn about content like fractions, assess our knowledge of fractions, and study our aggregate successes and failures with these fraction exercises.

A lot of research has been done to investigate the specific misconceptions that occur when people learn about fractions. For example, in this study ^{1} on errors in fraction addition, three common mistakes were identified:

- Simply adding the tops (numerators) together and the bottoms (denominators) together is the most common mistake by students.
- For example, ½ + 3/5 would equal = 4/7

- The crossed multiplication strategy: “students multipied the numerator of one fraction by the denominator of another fraction”
- for example: 1/6 + 2/6 = 8/7

- The crossed-addition strategy: where students “added the numerator of one fraction by the denominator of another fraction”
^{1}- 1/6 + 2/6 = 8/7

Traditional learning tools such as textbooks or videos can correct these errors, but if we are to improve our collective understanding of fractions, we'll need better tools for studying the learning content itself.

## How Can We Assess Our Understanding of Fractions?

One such experimental venture can be found in this little web-based text game called 'Fractions Excerpt' I've designed to explore the aforementioned fraction problems. This game is an excerpt from a game I am currently working on. It demonstrates the potential data these sorts of games can generate.

A misunderstanding like this is addressed in ‘Fraction Experiment’ with semantic questions like:

- "I must add all the right hand side fractions together. To add two fractions together…"
- "the numerators have to be equal, because you can only add parts cut to the same size"
- "the denominators have to be equal, because you can only add parts cut to the same size"
- "the numerators have to be equal, because you can only add fractions that have the same numeric value"
- "the denominators have to be equal, because you can only add fractions that have the same numeric value"

Or with this more technical question, where the formula for fraction addition must be identified.

Games are virtual environments in which every variable is known and can be changed, and every player choice can be measured. Players are presented with information about the problem, and given a set of virtual tools with which to solve it. With analytics (anonymized of course), we gain access to an entirely new kind of dataset on how changes in the virtual environment help players learn.

This creates the possibility of optimizing these questions for players. If a particular misunderstanding is identified, why not have them go through a specially designed game section to explore that misunderstanding, in the hope of creating a 'Eureka!' moment? Which questions are most likely to generate 'Eureka!' moments, and which undermine such moments? Below I show some of the insights that can be garnered from this experiment of a math game about fractions.

## What Can Data From Math Games About Fractions Show Us?

Thanks to modern analytics, every action in a virtual environment can be measured. This holds two key benefits. The player gets instant feedback, and a detailed performance report at the end of their strengths and weaknesses within the game. Because games are challenges, they can reveal where a person's knowledge is incomplete. The measurements can also be anonymously aggregated to gain insight on the learning tools themselves. Which questions do people answer incorrectly the most? Are there any clusters of questions that players get wrong together, pointing to a specific misunderstanding in the player? What does the length of time spent on each question tell us about our understanding of fractions in math?

## What Are The Weaknesses Of Analytics Based Datasets From Math Games?

The necessary anonymity of the data does raise some questions about the data’s validity, which I explore here (coming soon). Additionally, I explore the challenge and opportunity provided by current technologies ability to collect and analyse data simultaneously here (coming soon). Both remain open problems with these live experiments. Yet the experiments are still interesting to run, however valid the data they produce is.

I do not know the full potential of what analytics and learning have to offer, but a good place to start is...

## What Kinds of Questions Can Analytics Answer?

Google Analytics is quite limited in the kinds of questions it can answer. All analysis is done by grouping measurements together, then segmenting and analyzing any differences with dimensions and metrics. One question type it can handle is, if players answer a question about their favourite colour, and I group them by their answers, do these groups have a different average final score?

I structured this game to ask 3 questions of this kind:

- Does a players favourite color have any correlation with their final score?
- Does highlighting key words influence the final score?
- Does their choice of method in adding fractions together (where 3 of the 4 options are viable), have any correlation with their final score

P.S: All data from before April 20th was just me testing the event dimensions and metrics, so it says nothing of value about learning. Though it does show the technology works at least!

#### Bibliography

1: Herani Tri Lestiana, Rejeki Sri, Setyawan Fariz, *Identifying Students’ Errors on Fractions*, (Journal of Research and Advances in Mathematics Education, ISSN: 2503-3697 / e-ISSN: 2541-2590 Vol. 1, No. 2, 131-139, July 2016)

More information about these reports can be found here