How We Use Math to Teach Math Better!
By: Preeti Hemant
Tags: Math, Analytics, Education, Algorithms, Learning And Development

With 90 million students spread worldwide, Prodigy Education is one of the largest educational platforms in the world.

As a math product that incentivizes learning through play, our platform keeps users engaged in the game while ensuring learning efficacy.

Every student is given a personalized learning experience, through educational algorithms built into the product. These algorithms adaptively assess students by measuring skill progression and mastery, creating an experience that matches their pace, strengths and knowledge gaps — much like a teacher would!

How are learning journeys customized for every student?

All first time users undergo a short assessment to determine their grade levels. This placement test is seamlessly integrated into the platform.

Once the placement test is complete, learners travel their own learning paths while being guided and supported by the algorithm.

A student learning path is a network of questions spanning a skill (for example, fractions) of various difficulty levels. The algorithm allows for as many learning paths as there are students.

Let’s look at a visualization of a simple learning graph:

A learning graph

Here, a student is progressing through questions of increasing difficulty under a specific topic. The algorithm expects a certain path, sees the student take a different one and adapts to this student’s skill level. It ultimately stitches a happy path through all the questions, taking the student from the lowest level of difficulty to the most challenging ones.

Learning paths for an entire class could look like the image below. Since no two students learn the same way, no two paths look the same. Our algorithm is designed to address this and take students through their own journeys, all while adhering to the curriculum and ensuring student progression.

Topic: Multiplication (each dot is a skill, each line is a student path, skills are coloured by difficulty)

How do we help students master skills in their curriculum?

A skill is mastered when the algorithm determines the student has an excellent level of understanding of the academic construct underpinning the skill. This is determined using a concept similar to counting the number of hops in the learning path.

A progressive hop indicates a jump to a more difficult question, while a regressive hop indicates jumping to an easier question. A series of all progressive hops would mean a student answered all questions correctly, in an increasing order of difficulty. A mix of progressive and regressive hops would mean a student has answered some questions incorrectly and there may be a need to switch to an easier question.

The count of progressive and regressive hops in these two situations is different and shows the mistakes a student made. This count and other related information are further processed by the algorithm to determine skill mastery.

Here is an illustration of two students mastering a skill differently. A game of Snakes and Ladders would be a good analogy to picture a student’s journey through questions.

Skill mastery: Student 1

Skill mastery: Student 2

Although both students master the skill, they do so in different amounts of time and over a different number of questions. These differences are used to measure skill progression and mastery, such as:

Proportion of questions answered correctly on the first chance

Number of questions answered incorrectly

Frequency of usage of hints

Time taken to produce an answer

Our analysis of skill mastery for different cohorts shows important patterns that further our understanding of how students learn.

Let’s consider a specific cohort, defined by grade and curriculum.

As a student’s exposure to a concept increases, the student begins to master this concept and the error rate begins to fall. Studying this pattern of learning lets us determine the time to master a skill, in terms of the number of questions.

Similar to error rate, hints usage and duration to answer a question also fall as the number of opportunities presented to a student increases.

Are all skills mastered in the same manner?

From experience, we know the answer is no. Our analysis says the same.

Some skills are simply easier to master, some are difficult, and others do not need ramping up.

The diagram below shows the ease of mastery for two skills spanning the first 10 questions answered. One skill has a gradual learning curve and the other has none.

To understand skill progression, we analyze learning journeys and examine the paths students take. Students naturally fall into groups called cohorts based on various parameters — some objective (grades, number of questions answered, etc) and some subjective (level of understanding, proficiency, etc.) Our intelligent algorithms help us find cohorts and characterize the groups based on objective and subjective parameters.

These approaches allow us to summarize large amounts of student answers and compare statistical performance differences between students, providing a set of parameters that help us describe their behaviour. We incorporate these findings to iteratively tune and improve our algorithms, so we can build learning journeys for every user. This feedback system creates a personalized experience for new incoming students.

Through continuous learning, our algorithm makes learning math better!

Where are we going from here?

Do learning paths differ for students from different grades? Are certain skills uniformly difficult or easy? Do learned skills decay or do they remain fresh?

These are some of the questions we’re exploring in our commitment to keeping our algorithms in tune with student behaviour. We look forward to sharing more on making learning a fun experience for everyone — students, teachers and parents!