Enhancing Student Learning Through Error Analysis Joan Zoellner jzoellner@clark.edu S085

Why give quizzes in class? Why not give quizzes in class? Do you allow quiz or exam corrections?

Why give quizzes in class? Myself, as a new instructor: “Aren’t quizzes just part of teaching?” “Gives me an idea of what students are understanding.” I polled my colleagues with the same questions, and these are some representative results

Why give quizzes in class? “Incentive for students to keep up to date.” “Give students experience taking tests.” “Remind students they should be doing homework, even if it isn’t collected.” I polled my colleagues with the same questions, and these are some representative results

Why not give quizzes in class? “I don’t want to use class time for quizzes.” “Many students are stressed out by quizzes.” “There is little correlation between performance on quizzes and exams.”

Why not allow corrections? “Students will pass the class due to artificially elevated grades and will not be prepared for their next class.” “Students will get in the habit of not studying before a quiz because they know they can complete corrections.”

Motivating Question Is it possible to implement a quiz and quiz correction procedure that is a valuable use of in-class time that promotes greater student learning, including a higher level of self-assessment and error analysis, but doesn’t inflate grades? I wanted a good reason to use quizzes in my own class – a strategy that would allow me to see what students were confused about, but that would still act as a formative learning experience for the students. I didn’t want to increase my work load too much, and I really wanted students to learn from their mistakes. I also didn’t want to increase student anxiety.

I think the answer is yes. I have adopted a quiz and exam correction procedure created by Lawrence Morales at Seattle Central Community College, developed based on a model used in a study done at the City University of New York. I attended a ORMATYC/WAMATYC joint conference. Lawrence Morales had been working on materials that addressed the idea of Self-Regulated learning, and how to teach this skill to students. This was one of the resources that he created, and it seemed like it was exactly what I was looking for.

Objectives Minimal in-class time requirement Minimize test-anxiety Students identify and correct their misconceptions

Objectives Students learn to self-assess their strategies and work Students revisit incorrect work Students keep up with the course material

What does the process look like for quizzes?

Problem Selection Select two problems that students frequently get wrong on assessments. Inform students why these problems were chosen – they can make the error now and correct it, rather than on a high-stakes exam. Some favorites: 6÷2∙3, 2−3(5−4), Multiply (𝑥^2+2𝑥)(𝑥−3) vs Subtract (𝑥^2+2𝑥)−(𝑥−3), Find the limit: lim┬(𝑥→1)⁡〖𝑥/(𝑥^2+4)〗, Sketch a graph of each function in the integrand and shade the region whose area is represented by the integral:∫2_0^4▒〖[(𝑥+1)−𝑥/2] 𝑑𝑥〗

Problem Selection Two problems that should take no more than 10 minutes total, if students grasp the concept. This can help students gauge how fast they will to work on exams. Some favorites: 6÷2∙3, 2−3(5−4), Multiply (𝑥^2+2𝑥)(𝑥−3) vs Subtract (𝑥^2+2𝑥)−(𝑥−3), Find the limit: lim┬(𝑥→1)⁡〖𝑥/(𝑥^2+4)〗, Sketch a graph of each function in the integrand and shade the region whose area is represented by the integral:∫2_0^4▒〖[(𝑥+1)−𝑥/2] 𝑑𝑥〗

What does the correction process look like for quizzes? Develops self-awareness, self-efficacy

What does the correction process look like for quizzes? While most students pick careless error is most cases, I like these choices

What feedback to give? Minimal marking of specific errors. Students learn how to analyze their work and find their own mistakes. You have to tell them this, or they will complain.

What feedback to give? Make them find a similar problem. This helps students learn how to classify what problems are similar to each other and require similar strategies.

How to assign credit? Even if they get one problem correct, they get no credit until they correct the other problem. Motivates them to do corrections.

How to assign credit? If their first attempt at a correction is wrong, they have to do it again. I usually ask students to come see me in my office if their first correction is wrong.

Examples of student work Original Work (Algebra 1):

Examples of student work Corrected Work: We all have bad days – this process doesn’t penalize students for them

Examples of student work Original Work (Elementary Algebra):

Examples of student work Corrected Work: Same thing for careless errors, though the process can prompt student to take action to avoid those errors in the future.

Examples of student work Original Work (Calculus 2):

Examples of student work Corrected Work: This can help students realize that they need to do more, or at least more complicated, problems to practice.

Examples of student work Original Work (Calculus 2):

Examples of student work First Attempt Corrected Work:

Examples of student work Corrected Work: It can take a couple of attempts

Benefits of this process: Students learn how to identify their own errors. Students learn to classify types of problems by looking for similar problems to the ones they got wrong.

Benefits of this process: Students address misconceptions before taking the exam. Students become more reflective about their learning process.

What does the process look like for exams? I added the part about the behaviors and strategies

Examples of student work Original Work (Algebra 1): Lack of understanding of relationship between equation and graph, arithmetic error that messes up the rest of the problem. These corrections also allow me to be more strict than I might be without them.

Examples of student work Corrected Work:

Examples of student work Corrected Work:

Examples of student work Corrected Work (Algebra 1): Students can self-identify common mistakes, and develop strategies to overcome them.

Examples of student work Exam Corrections (Intermediate Algebra):

Student observations “I thought I had prepared enough by looking over the homework and the quizzes, however those did not cover all of the material on the exam. I should have been reading through the book and also doing practice problems in the book. This is something I will be implementing for the next exam.”

Student observations “I didn’t mention it much [earlier], but my study habits are clearly not up to par. I’m only just now at that point in school where I can’t just absorb something right away and then throw logic and intuition at it. It’s becoming more and more crucial to legitimately study and practice the material.”

What about the concerns? Students will pass the class due to artificially elevated grades and will not be prepared for their next class. Students taking classes using the quiz and exam correction procedure are no more likely to pass (or fail) the course than in a regular section. Students are as likely to pass their next class as their peers from a regular section. Except Calc 1 – higher pass rate

What about the concerns? “Students will get in the habit of not studying before a quiz because they know they can complete corrections.” “A very useful part of the class were the quizzes we had because the hellish process of correcting them made us want to get a perfect score even more.”

Student observations “I found [the quiz and test corrections] helpful because it gave me a chance to look over the problems that I missed and really gain a good understanding of where I went wrong. I think it helped out a lot because in previous classes I just look at the quiz or test and set it down somewhere and forget about it.”

Student observations “I think that [correcting my errors] made me know what areas I needed to study more on and when I did the correction the correct way to solve the problem stuck more in my head.” “Not only did they improve my grade, but they actually helped me learn!”

Take Away Think of a class in which you would like to try this quiz and quiz correction format. What questions would you ask? Do they elicit common mistakes? Are they time appropriate? What feedback would you give?

Are there any questions? jzoellner@clark.edu