IMPACTful Discussions (Math Intensive): Testing Challenges in Math Intensive Courses

By Robert Cappetta posted 8 days ago

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Since the pandemic, there has been an increased focus on providing calculus classes to remote learners. In the past, distance-learning students typically completed exams at college testing centers or approved off-site locations such as public libraries or military bases. However, the significant rise in the number of remote students has made these options increasingly impractical.

In recent years, internet-based proctoring services have been used to maintain the integrity of the exams, but a quick YouTube search on “How to Cheat on Online Proctored Exams” yields several results including one video with 1.2 million views. A second concern with these systems is potential invasion of privacy. These systems require extensive monitoring that record students’ personal space. A.I. algorithms flag “suspicious behavior” that may lead to false accusations. Furthermore, Students are coerced to consent to using these tools, leading to stress and discomfort. Additionally, there are concerns about equity because some students may not have an appropriate testing space.

Calculus tests delivered using a computer-adaptive system are often graded based on whether the final answer is entered correctly, which frustrates students as minor typographical errors can result in lost points. An alternative is using online multiple-choice tests, but many calculus instructors consider these less effective than evaluating students' written work and awarding partial credit. For remote students, submitting work poses challenges, often requiring them to photograph and upload their solutions immediately after completing the exam. Unfortunately, this process can create additional opportunities for unethical sharing of information.

These testing concerns extend beyond remote learning but also affect traditional classes. In multivariate calculus, many problems are extremely long and difficult to assess in an hour-long testing session. I have given portions of these as take-home exams but evolving A.I. platforms have become increasingly efficient at delivering completely worked out solutions for these problems, making take-home test problems obsolete.

What are the solutions? Please consider participating with the Math Intensive Academic Network as we discuss these issues and more. Contact bob.cappetta@amatyc.org for more information.

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Kelly Spoon

7 days ago

Our campus doesn't offer STEM Math courses fully online, but we are lucky to be in a place where faculty have a lot of sway and our three campuses across the district are in agreement to keep Calc 1 and higher on campus. However, I'm a huge advocate for online courses because there are a lot of students who really benefit from the flexibility of the modality - students with schedule constraints like those with caretaker or work responsibilities, students with challenges making it to campus either because of physical mobility issues or transportation issues, and students who just learn better in an environment when they can control when and where they learn.

That being said, I think the solution is to think beyond the traditional exam. Traditional exams are high-stakes and typically focus on lower level skills. In online classes, I try to provide multiple ways for students to demonstrate their understanding - a written solution and a video solution or explanation to add to class repositories. Even these I will ask students to revise and resubmit if they haven't explained something fully enough for a "less prepared student to follow along." And I try to incorporate a progression of tasks that allow them to show their revised thinking - moving from a Notice & Wonder style discussion to start a section to a discussion where they have to make a visualization of how the different concepts are related. I'm doing a poor job of describing it, but a typical online unit looks like this:

Ignite: How does this week connect to what you already know? This could be a discussion with a graph or expression asking students to write down 5 things they notice and 2 they wonder about it... or it could be a Desmos/Geogebra/wtc activity that they work through introducing a new topic.
Content: Pages with text, video, and formative assessments
Lower Level Practice: Some auto-graded required questions through an LMS, not worth much, just for students to check in on their understanding.
Written Quiz: A 'quiz' submitted similar to what Michael described where students show their communication skills and feedback is provided.
Video Solution or Explanation: A secondary quiz where students need to walk through their work on a problem or two, or explain a concept from the week's material.
Discussion: A reflection on their learning from the week, maybe revisiting the Ignite or explaining which topic they are still struggling with.

My hope is that this emphasizes their own learning process and makes it less about the output - which I think is where students try to ensure they don't lose points, when that's the focus. If I'm just filling in a box for MyMathLab, there is very little human element, no partial credit, and nothing matters except the answer - there is no value to their unique thoughts or ideas. I'd probably try to do take home exams with interviews after their submissions for those topics I think are most important...

A final thought in this rambling reply... many of the things in the prompt that are viewed as negatives - "sharing of information" and "making take-home test problems obsolete" are maybe not bad things? I want my students to learn to collaborate - to defend their thinking when they are right and assess other's thinking for correctness. I want my students doing problems that are relevant in today's technology, answering things that need a human or need their thinking. I think too much of math, especially in Math-Intensive classes, focuses on the wrong thing - getting students to arrive at an answer using a traditional approach - mimicking us. When we should be focusing on the metacognition and curiosity that make math worthwhile.

Michael Caparula

7 days ago

I actually brought this up in my post for the other discussion post.

I am not a supporter of computer-based homework systems for assessments. I made-up my own, put it on the LMS and gave the students a limited time to take it, scan their work and submit it. I then graded it using a PDF annotator (like PDF Annotator) and then sent it back to them. In other words, it was very much like an in-class assessment. I would have multiple versions to keep students from mostly working together or sharing of answers.

Personally, I don't believe online classes work well in mathematics, and we need to tell our administrators this. Now, hybrid or hyflex modalities can be very effective and I am a proponent of those. We need to come to a middle ground with admin: Less online, but more hybrid/hyflex.

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