I’d like to paint a scenario that reflects a common occurrence in classrooms nationwide. A student in an introductory algebra class — we’ll call him Stu — receives a score of 63%, a D, on his quiz from chapter 13 on adding and subtracting polynomials. The teacher — let’s call her Mrs. T — has several decades of experience under her belt and knows that if Stu simply moves on to the next topic without developing a proficient understanding of the skill of adding and subtracting polynomials, he will probably do poorly in much of the rest of the course. Having designed the quiz herself, she’s aware that it’s assessing several key objectives. Among these are:
- Be familiar with the notation for adding and subtracting polynomial functions.
- Add and subtract polynomials and polynomial functions.
- Solve perimeter word problems involving the addition or subtraction of polynomials.
- Solve other application problems that include histograms and charts by adding or subtracting polynomials.
Mrs. T is also aware that the problems on this quiz call upon and use previous skills in her course, skills she refers to as the section’s prerequisites. For example, a section from Chapter 9 introduced word problems involving perimeter, a Chapter 11 section covered how to interpret histograms and charts, a Chapter 12 topic provided a basic understanding of functions, and an earlier section in Chapter 13 covered combining like terms.
Mrs. T wants to help Stu review these prerequisite skills, so she examines her gradebook to see what scores he received in each topic. He seemed to do fairly well (over 80%) on the quiz from Chapter 9 on perimeter word problems and the quiz from Chapter 12 on functions, but he struggled (lower than 60%) with the section from Chapter 11 on interpreting histograms and charts and the earlier section in Chapter 13 on combining like terms.
Mrs. T creates a packet of review materials and puts together a remedial quiz containing questions from those sections in Chapters 11 and 13. Her hope is that after Stu has gained proficiency in the prerequisite skills, he will better understand the Chapter 13 material and be ready to re-tackle the quiz on adding and subtracting polynomials.
This sort of personalized remediation is indeed carried out by the best teachers in our schools, but it can be especially difficult if the student continues to fail in upcoming topics, and it becomes a Herculean, if not an impossible, task if the teacher has to carry it out for all the students in all her classes.
In a Knewton-powered adaptive course, the intricate scenario just outlined happens at the click of a button — thanks in part to the Knewton knowledge graph. The knowledge graph is a cross-disciplinary graph of academic concepts; within the graph, concepts have prerequisite relationships that help define a student’s path through the course.
When a student fails a topic in a Knewton-powered course, he or she is instantly remediated with prerequisite skills, prioritized on the strength of their relationships to the topic at hand and on the student’s demonstrated strengths and weaknesses. This frees Mrs. T from the administrative work of locating all prerequisite skills and correlating them with each student’s past performance. She now has more time to orchestrate classroom activities, introduce creative group work, or sit down with each student to address their misconceptions and encourage them through their frustrations.
Knewton’s knowledge graphs, carefully constructed by subject matter experts, incorporate the connections identified by experienced teachers into the course itself. Learning is by nature an extremely interrelated activity, and with a knowledge graph an adaptive platform can take full advantage of those connections when scaffolding students and guiding them toward mastery.
As more and more students progress through a Knewton course, the strength of these connections are refined over time. We may find that some prerequisite skills are rarely helpful, or only helpful to certain types of students with identified weaknesses, while others are extremely effective as skills to review before students return to a failed topic. The goal of such data-driven analytics is to mimic in real time, on a large scale, the sort of intuition a great teacher develops over his or her career.
Creating unique study plans for each student in a class would be incredibly time-consuming for teachers. By mapping each course to a continuously refined knowledge graph, Knewton does this automatically, ensuring that no student is left behind.