Knewton-enhanced products 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.

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.

The more students who use the Knewton platform, the more refined the relationships between content and concepts and the more precise the recommendations delivered through the knowledge graph. 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 his or her class is experiencing the same difficulty. The Knewton platform is able to take the combined data of millions of other students to help each student learn every single concept she ever encounters.

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When most people use the phrase "adaptive learning," what they're really discussing is either a) single-point adaptivity, which evaluates a student's performance at one point in time in order to determine the level of instruction or material she receives from that point on, or b) adaptive testing, which determines a student's exact proficiency level using a fixed number of questions. 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.

When Knewton refers to adaptive learning, it means a system that is continuously adaptive — that responds in real-time to each individual's performance and activity on the system and that maximizes the likelihood a student will obtain his or her learning objectives by providing the right instruction, at the right time, about the right thing.

To provide continuously adaptive learning, Knewton analyzes learning materials based on a multitude of data points — including concepts, structure, and difficulty level — and uses sophisticated algorithms to recommend the perfect activity for each student, constantly. The system refines recommendations through network effects that harness the power of all the data collected for all students to optimize learning for each individual student.

Knewton's continuously adaptive learning system 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:

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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.

The Knewton platform 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.

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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-enhanced 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-enhanced courses, the more effective the platform becomes at serving up targeted learning material.

In this way, Knewton helps 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.

One of the biggest challenges facing teachers and school administrators today is the growing diversity of the students within their population. A greater diversity of students means a greater diversity of needs to consider. Some struggle because English is not their first language; others have difficulty with focus or organization. Others may be particularly weak in some area but possess unusual strengths in another.

Knewton analytics provide insight into the learning process, specifically in terms of efficacy, engagement, and knowledge retention, and help teachers ensure that diverse needs are being met. Platform analytics may discover, for instance, that a student who is weak with math word problems is struggling because he has difficulty with reading comprehension; the system can then direct the teacher to specific material on syntax and vocabulary and suggest ways that the teacher might coach the student individually in these respects. Later, the teacher may be informed that another student who understands mathematical concepts but has trouble with carelessness in arithmetic should receive feedback about how to develop stronger estimation abilities or check work once completed. The teacher can then coach that student with a precise understanding of his or her particular weaknesses.

With Knewton analytics, teachers will be able to grasp patterns in student activity and performance across the whole class or drill down into individual student profiles to determine exactly why a student is struggling. After multiple years of teaching the same course, teachers will be able to compare data from year to year. Knewton analytics will allow them to access useful information (like which students are struggling and require immediate attention) while leaving them free to interpret the results. This capacity allows teachers to better understand their curriculum, so that they can refine it from semester to semester and year to year.

Content analytics can help teachers, publishers, and administrators determine the strongest and weakest aspects of their teaching materials--and precisely what the content they are working with teaches and assesses. This ensures that content can be analyzed for fine-tuned improvements from year to year, and that students are never stuck with outdated or ineffective materials.

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