Teaching Calculus Online with Derivita

We recently presented at ArizMATYC 2020 on "Teaching Calculus Online with Derivita". We chose this topic because to say that teaching calculus is a challenge (much less online), is an understatement. From students being unprepared to lacking motivation to being faced with competing priorities that are a barrier to learning, teaching and learning calculus online is no small feat.

On top of trying to balance a job, possibly even homeschooling and dealing with other barriers, students are also struggling with trying to learn complex concepts online, especially when many of them do not have an adequate understanding of the concepts they need to be successful in calculus. 

The Rush to Calculus 

Why are our students so underprepared when they come to calculus? There are many contributing factors but it has been shown that the rush to calculus in high school may have shortchanged students on topics from algebra, geometry, trigonometry, and analytic geometry. Calculus was first added to the high school curriculum as an early example of a rigorous, college preparatory course. It soon became somewhat of an expectation and an accepted requirement for admission to top universities - regardless of the student’s major.

However, reports have found that many students who took AP Calculus in high school still ended up retaking calculus in college, with some even needing to take a lower level course. Taking calculus in high school was associated with only a 5 percentage point increase on average in calculus scores in college. The best predictor of earning a B or better in college calculus was a student earning no less than As in high school Algebra 1 & 2 and Geometry.

We know there are many challenges that both instructors and students face when it comes to calculus and we can see how that is impacting the number of STEM degrees, which directly affects our workforce. Then, throwing in the fact that most students are now having to take calculus in either a hybrid or fully online format, there are many things to consider when trying to improve the teaching of calculus online and solve some of these problems.

That leads us to the following questions:

1. How do we help those students that are underprepared when coming to calculus by identifying these knowledge gaps early (and doing something about it)? 
2. How do we keep our students engaged and motivated, especially in an online environment? 
3. How do we provide students the feedback they need in a timely manner, especially because we know with calculus, one small mistake can make the world of difference in their answers? 

Why Derivita for Calculus? 

Here’s the good news! These are the exact questions the team at Derivita have been working to solve and are continually doing so. Derivita was founded by the co-founder and co-creator of the Canvas LMS, Devlin Daley, and former Googler, Ryan Brown, to solve these problems and  tackle the issues that both students and instructors are facing in their calculus classes.

Derivita provides many capabilities including open-ended math questions, fully auto-graded questions, randomizations, multiple attempts, immediate & meaningful feedback and worked out solutions. And - this is all right from within your LMS! 

As we already mentioned, Derivita can actually do math! We’ve built our own computer algebra system that is used to evaluate student inputs. 

For example, on indefinite integral problems, we use our CAS to take the derivative of the student input to see if it matches the prompt. This then evaluates whether their answer is correct or not.

Derivita also accepts equivalent inputs on questions and even auto-grades open-ended questions. That’s how powerful it is! Student submissions are entirely auto-graded and scores are immediately added to the LMS grade book. Derivita can auto-grade everything from open-ended questions to manipulatives and graphs. 

Here is an example of an auto-graded question that accepts equivalent inputs as the answer and provides feedback to the students based on their responses.

Derivita also provides students with immediate and meaningful feedback. Derivita detects differences in properties and forms of math expressions to provide targeted feedback using the student’s own answers. This allows students to instantly reflect on their work, what they may need to adjust and keeps them engaged in their coursework as they continue to master the math concepts. 

This is an example of an open ended question that can be auto-graded. Notice that Derivita uses the student’s actual answer to provide feedback, opposed to a generic response. Another capability showing how powerful Derivita actually is!

At Derivita, we don’t simply create new features for the sake of having something new. We listen to our partners and develop features to actually solve problems that instructors and students are facing. 

When we surveyed our instructors, we found that 80% said that student engagement was the biggest challenge they are currently facing. With courses going online, one of the biggest challenges we have heard from our instructors is that they are not able to get a solid read on their students and know how their students are actually doing in their class. In the classroom, instructors were able to utilize non-verbal cues, communicate directly with the student and pick up on how their students are doing in real time. Now, online, it is difficult to assess students to see how they are comprehending the material and how they are actually progressing. 

That’s where SpotCheck comes in! We developed SpotCheck to help instructors to have the ability to assess their students in real time. It allows you to do a quick pulse check to see how your students are doing on different concepts within a synchronous environment. 

SpotCheck allows instructors to:

• Assess students in real time
• Work on problems synchronously with students
• Quickly determine knowledge gaps 
• Pulse check on students

Derivita also has an Instructor Dashboard that allows instructors to quickly see at a glance which topic may need more instruction and where there are possible knowledge gaps within their class. As we mentioned earlier, this is extremely important in a calculus class, as many students come to calculus unprepared. This dashboard allows instructors to see which problems and topics their students may have struggled with and it also allows them to work out the problem together online or in-class! 

Then, since Derivita works with any textbook, when these knowledge gaps are determined, the instructor can easily pull additional questions on any topics that their students may need additional help with and can incorporate those within their assignments until their students have mastered those foundational concepts.

At Derivita, we understand that education is quite unpredictable right now and another big challenge that educators are facing is the ability to efficiently and effectively teach math, while adapting to multiple modalities (in-class, hybrid, or online). Some have even had to switch between modalities throughout the course! As we are approaching the spring semester, many institutions are continuing with online courses, so we are working to continually expand our capabilities to deliver the tools that educators and students need the most.

Derivita can be immediately and easily adapted for any course modality and it provides the flexibility that educators and students need whether the class is face-to-face, hybrid, or online!

ArizMATYC 2020 “Teaching Calculus Online with Derivita” Presentation

Watch our 2020 ArizMATYC Presentation on “Teaching Calculus Online with Derivita” here and view the deck here!