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It’s no secret that success rates in introductory math courses are low, which leads to decreased retention rates as students fail to graduate. Furthermore, when these introductory courses are online, students face an even steeper uphill battle.

After years of research, the Department of Mathematics and Statistics at the University of Toledo found a unique approach that led to improving student success in its online trigonometry course.

Online Blended Learning

Research has shown that blended learning is the most successful delivery method. Therefore, the department established a synchronous component in each of its online courses. This means that students are required to meet in a live online classroom each week, essentially making this a blended online course but still completely online.

Moreover, this was a flipped blended online course. Students went through a module at their own pace before the synchronous session that week, starting with an introduction, a list of learning objectives, and then learning about each topic in the module by reading and watching videos. Each module incorporated spaced practice, interleaving and retrieval practice. Then when students met for class, they worked in groups to solve everyday problems using the concepts they learned from the module.

Although students were aware of the weekly meeting time before registering for the course, some of them could not meet during the specified time and were unable to attend a face-to-face section at another time. Because the activities that were completed in the synchronous sessions were designed so that they could also be completed asynchronously on a discussion board, students who were unable to meet during the specified time were still able to practice applying what they learned with their peers and get instructor feedback.

Adaptive Learning

Students often come into a math course with varying levels of knowledge, yet courses are taught at one level and one pace. To overcome this obstacle, an adaptive learning system was incorporated into the course. This system determined what students knew, what they didn’t know yet and what topics they needed to spend more time studying. This allowed students to spend their time on concepts that were the most difficult for them instead of equal time on all topics.

Additionally, the system incorporated mastery learning, so students had to prove they understood a concept before moving to the next, a crucial component to a math course in which concepts build upon one another.

Results and Tips

Based on exam scores and course evaluations, students earned better grades and had higher satisfaction than previous semesters. Not only did student success increase, but so did their affinity for mathematics, and all it took were a few changes to the course design.

To incorporate these aspects into any online course, the following tips are helpful.

1. Use a flipped model. Introductory math courses are often populated with students who have not been successful in math and struggle with the subject. With a flipped model, these students can work through the content in a learning management system at their own pace. Students can spend as much time as needed with the material to gain a full grasp on what they are learning.

Then when students meet for class, the instructor can spend the time applying the basics that students learned on their own in a way that will allow for deeper learning and an increase in students’ self-efficacy in mathematics.

2. Spaced practice, interleaving and retrieval. When students are allowed to go through material on their own time, they can spread out their learning over the course of a week instead of cramming it into one face-to-face lecture. Content in a learning management system can also be designed so that topics are interleaved with one another, which research has shown to strengthen memory.

Likewise, when students constantly practice retrieval, through topics reappearing in each module after they are introduced, their understanding and memory of concepts last far beyond the semester.

3. Incorporate adaptive learning. Adaptive learning provides the best learning experience for each student based on that student’s individual needs. It allows students to spend the majority of their time on the topics that are the most difficult for them, and it requires students to master each topic before moving to the next. Therefore, students do not lack prerequisite knowledge when learning a new concept.

4. Set up synchronous sessions. Before the semester starts, choose a day and time each week to meet synchronously using web-conferencing software. Students can connect from anywhere in the world, as long as they have a reliable, high-speed internet connection. This allows students the flexibility of taking an online course, yet they still have an opportunity to work with their peers and instructor in real time.

Do not use the sessions to lecture or introduce students to concepts. Rather, use this time to guide student practice and apply mathematical concepts to real-life scenarios.

5. Keep students engaged. The majority of students in this course said their favorite part of the modules was the videos. They were able to play the videos at variable speeds, pause, rewind and watch again. Be sure that every concept is explained in the module in words and also with a video, including several examples for students to see.

Students reported that they were more engaged when watching several short videos compared to fewer long videos. Make content relevant to the real world, and students will be more likely to want to learn.

Also, don’t be afraid to be funny! Include memes and jokes and let your students know at the beginning of every module that that module is your favorite. Humor and instructor excitement about the subject go a long way in keeping students interested in the material.

6. Make content accessible. It is essential to be fully inclusive and supportive of all learners, not just those in your course with documented disabilities. To help students succeed, be sure that all videos are captioned, content is keyboard accessible, documents are compatible with screen readers and there are limited colors and easy-to-read font types.

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