Chapter 3

Knowledge graph

Knewton-powered courses are linked by the Knewton knowledge graph, a cross-disciplinary graph of academic concepts. The knowledge graph takes into account these concepts, defined by sets of content and the relationships between those concepts. Knewton recommendations steer students on personalized and even cross-disciplinary paths on the knowledge graph towards ultimate learning objectives based on both what they know and how they learn. The more content that teaches or assesses each concept that is added to the system, the more precise the adaptive course experience becomes.

When visualized, the knowledge graph can provide a sense of a student’s potential flow through the course material.

Within the knowledge graph, concepts have prerequisite relationships that contribute to defining a student’s path through the course. Special relationships that define content as either “instructional” or “assessment” determine what kind of content to deliver to students at any given point.

Continuous, as opposed to single-point adaptivity

A single-point adaptive learning system evaluates a student’s performance at one point in time, and from there determines the type of instruction she receives. An example of single-point adaptivity would be a course that includes a diagnostic exam, the results of which determine subsequent course content, with little or no further data mining and personalization.

Knewton’s continuously adaptive learning system, on the other hand, constantly mines student performance data, responding in real time to a student’s activity on the system. Upon completion of a given activity, the system directs the student to the next activity. For example, when a student struggles with a particular set of questions, Knewton will know where that particular student’s weaknesses lie in relation to the concepts assessed by those questions and can deliver content to increase the student’s proficiency on those concepts. In this way, Knewton’s continuously adaptive system provides each student with a personalized syllabus at every moment.

The following are specific examples of approaches that allow Knewton to offer truly continuously adaptive learning:

Spaced reinforcement

In contrast with massed reinforcement, the standard method of drilling which requires students to apply new concepts or skills in a short period of time until they demonstrate mastery, spaced reinforcement (also referred to as distributed reinforcement) is a learning method in which new concepts or skills are absorbed while previously-taught concepts and skills are reinforced. Because new material is introduced incrementally and woven into familiar material, spaced reinforcement typically occurs over an extended period of time. Spaced reinforcement allows Knewton recommendations to help students build their skills in a cumulative way and retain understanding once it is gained.

Retention & learning curves

The Knewton recommendation engine needs to be able to take the degradation or diminishment of skill (or forgetting) into account. That is, it needs to be able to detect such occurrences and provide actionable recommendations as a result.

Inspired by Hermann Ebbinghaus’ work on memory retention and learning curves, Knewton data scientists have used exponential growth and decay curves to model changes in student ability while learning and forgetting. These curves are governed by the following premise: each time students are exposed to content associated with a given topic, they receive a “bump” in their virtual ability level for a topic; likewise, if they are not exposed to some other topic, they likely “forget” that topic over time. The forgetting curve itself that governs rate of retention is roughly described by the following formula:

where R is memory retention, S is the relative strength of memory, and t is time.

By integrating this curve into engine validation efforts, Knewton data scientists can capture the way a student’s knowledge waxes and wanes, depending on how and when she is exposed to content. Ultimately, the process allows Knewton data scientists to test the algorithms that govern a student’s flow through the course.

Student learning profile

With Knewton, students can maintain a continuously updated learning profile that contains information on what the student knows and how she learns best. The profile is progressive, which means it keeps getting smarter the longer the student remains on the platform.

For instance, if a student who has already taken a Knewton-powered course enrolls in another, the course starts “warm” with that student’s data (as opposed to starting “cold” with no data). The course takes into account the student’s recently mastered concepts and skills and unique trajectory through the material, and uses this knowledge to maximize student learning continuously from that point forward. Once enough data is collected, the platform will uncover patterns in the student’s learning, such as blind spots, modality and medium preferences, and granular strengths and weaknesses. The more often a student uses Knewton-powered courses, the more effective the platform becomes at serving up targeted learning material.

In this way, the Knewton Adaptive Learning Platform works to minimize unproductive feelings of frustration and confusion and build student skills in a natural way over time. More fundamentally, it provides penetrating insight into students’ own understanding of the material — what they truly grasp and don’t grasp, their misunderstandings and misconceptions. Students develop a deeper, more nuanced understanding of their learning style and strengths and weaknesses, helping them to maximize their academic potential.

The implications of all this are straightforward: student engagement can be strengthened if academic work is imbued with a sense of continuity. Nothing is more dissatisfying to students than feeling like the challenges they face are essentially arbitrary and culminate in nothing. The Knewton learning profile answers the student need for continuity and meaning by affording students a sense of long-term investment in the learning process.

Network effects

The more students who use the Knewton platform, the more powerful it becomes — the more refined the relationships between content and concepts and the more precise the recommendations. For each student learning each individual concept, the system finds a population of extremely similar students who have already learned that concept. It then asks, “Who among those similar students learned that concept the best, and what did they do that worked so well?” The system then allows this proven effective learning path to inform the student’s learning path going forward. In this sense, a student experiencing a particular challenge (for example, spatial skills as they relate to math word problems) need not be limited by the fact that no one else in her class is experiencing the same difficulty. The Knewton Adaptive Learning Platform is able to take the combined data of millions of other students to help each student learn every single concept she ever encounters.

Network effects are a natural consequence of the knowledge graph and the models Knewton uses to determine its recommendations. In isolation, each student’s response to each question is only a tiny scrap of information, but when propagated through the entire system and understood in context, the value of that information is amplified tremendously. Every student action and response around each content item increases the system’s understanding not only of the student and the content item, but also, by extension, of all the content in the system and all the students in the network.