Course Review Summer 2026: Analysis of Learning Outcomes Data

 Over the summer I am planning to do a few things to improve my course materials.

1. Review assessment data for learning outcomes in Coreq College Algebra to identify areas for improvement.
2. Set up assessment data collection so that I can enter student scores into a single spreadsheet, and see if changes I make are improving student performance. 
3. Make adjustments to in-class activities per the notes I made during the term, improving the instruction for the areas found in Part I.
4. Create homework and other assignments to replace online homework and LMS assignments. 
5. Package all course materials in binders so students have a single resource to complete coursework in. 

Over the last few days I completed Part I, and want to share some of those results here. In College Algebra I have 65 learning outcomes I assess, and have aligned instruction, homework, and assessments to these outcomes. The assessment data for the weekly assessments and the final assessment were compiled, and using a combination of Excel Power Suite and RStudio I found that the learning outcomes that students scored less than 50% on were the following. 

In looking over this list I can think of a few things to try, and in revising and creating some of my materials I can make further changes. Specific things I want to try are underlined for future scannability. 

• 10 - Students struggle with rational exponents as is, using them in solving equations requires sufficient understanding of radical notation and how they relate to rational exponents. I can increase the amount of practice of simplifying rational exponent expressions, and then of solving these types of equations. 
• 18 - In hindsight I did not do a lot with this outcome in my instruction. Including a set of thinking questions and a page of new practice questions should help, as I don't believe the concept is difficult for students, just that they did not have enough practice. 
• 19, 20, 21 - In grading the weekly assessments these outcomes were covered in, students regularly did not provide answers that made sense of what these questions were asking for. In asking for a global maximum for example, students replied with a coordinate where the global maximum was located, not the y-value of that coordinate. In asking for an interval of increase, they gave two coordinates whose x-values were where the function increased, not the interval of x-values over which the function was increasing. There seem to be a few parts to this; understanding definitions of these terms, reading comprehension, and interval notation. Student reading of the textbook before class was pretty minimal last term, so I may need to consider different ways to get them to engage with the material before class. 
• 24 - Graphing is a common theme in these outcomes (more on that later) and graphing functions using transformations is a topic students often struggle with. Mostly students are fine with horizontal and vertical translations, but struggle with compressions and stretches of functions. I may try including at least one new POGIL model having students work through more difficult equations, and increase the amount of practice for those questions. 
• 30 - In grading their work students either forget how to find the vertex of a parabola, or how to solve for the x-intercepts by setting y equal to zero and solving the resulting quadratic. Solving quadratics is already a big part of the course, and I share multiple ways of solving them. Maybe the issue is that there are so many ways to solve them, students need some time to troubleshoot how to apply them. An end of the week set of thinking questions may help them solidify when to use which method, with a graphic organizer having them sorting out which method to use. 
• 31 - The issues here are similar to 30, with the addition that students sometimes did not distinguish between the x or y variable when providing their answer. For example, if P(x) is the profit function for creating x widgets, in asking for the maximum profit students would provide the x-value that gives the maximum profit. This seems connected to 30, but also requires some reading comprehension. A targeted activity near the start of the section on functions on what inputs and outputs are, along with a quick set of questions asking students for the units of the inputs and outputs of quadratic functions may help.
• 42, 43, 44, 45 - With this number of topics, I get the sense graphs and equations of rational functions (if they are an important topic I need to keep in the class) need more time. As it is they are jammed with graphs of polynomial functions in one week, and I usually have only one day with rational functions. I would like to try moving the schedule so I have at least two days for rational functions.
• 65 - I am not surprised this is on the list, as it is the conic section I give the least amount of time to. I'd like to drop the section on treating parabolas as conics and focus my time on ellipses and hyperbolas. This will free up some time at the end of the course for review. 

In looking over these changes there are a few things I keep coming back to. I wonder if I could set thresholds or some other conditions in the data collection to indicate which of these responses I should consider. 

• If I think instruction is sufficient, then increase the amount and quality of practice questions. This includes additional application questions in POGIL-like activities, and thinking questions using the Building Thinking Classrooms framework with a graphic organizer. 
• If student responses are not aligned to what is being asked for, then increase exposure to reading of the material before class. 
• If a topic is especially difficult for students, then include more instruction and opportunity to explore the concept or computation. Alternatively, if a topic is revisited multiple times, then find multiple places to reinforce the concept. 
• If a related set of outcomes are scoring low, then increase the amount of time spent on those sections. I could also see using this information to make a radical change in how a topic is taught. 
• If a topic is 'more trouble than it's worth', then drop it. 

Lastly, in the assessment data I noted the response type to each assessment question; G for graphing, SA for short answer either computation or word response, or MC for multiple-choice. Unsurprisingly students did best on multiple-choice, however the scores for short answer and graphing questions were fairly low; 

The fact that average scores for graphing questions are about 6.1 percentage points lower than average scores for short answers isn't by itself worrisome, however with the above learning outcomes data it points to a need to support graphing skills more generally. On reflection I don't do much foundational work with students around graphing, and assume they know how to read graphs and what graphs of equations and functions mean. It may be that I need to start them off with more foundational knowledge, or at least have that as an option. If students can answer some basic graphing questions in the Assessment 0 I give on the first day, that may be an indication to not go over that foundational knowledge. 

What are you doing over the summer to prepare for the Fall? I'll share Parts II through V later over the summer, and look forward to hearing what others are planning.