A couple of years ago, Kelly Spoon decided to experiment with her assessment practices.
Several instructors in the mathematics department at San Diego Mesa College, where she is a professor, had begun to explore how to integrate standards-based grading (an approach that assesses students on how well they master content) into the way they that teach calculus.
They sat down and figured out what knowledge the students needed to acquire and to what extent they needed to demonstrate their competence. Not long after, Spoon began changing the way he handled proofs in a calculus class he taught. Traditionally, Spoon says, grading practices for this course tend to emphasize students' performance on a limited number of tests. There may be a midterm, a final, and some other opportunities for students to demonstrate what they have learned. The problem with this approach, he points out, is that if a student scores 50 percent on an early exam, sometimes that doesn't seem recoverable and they put in less effort for the rest of the semester or drop out of class.
You have also changed your approach to grading in other classes and now offer more frequent assessments, provide opportunities to retake exams or quizzes, and place greater emphasis on incorporating accommodations into your class. For example, for a class scheduled for two and a half hours, you make sure your exams are only one hour long. That way, students who need extra time won't have to approach her to ask. Over time, he found that making these adjustments encouraged his students to stick with the course if they had a rocky start.
Spoon has found that the changes also allow him to hold students to a higher standard when it comes to explaining mathematical concepts, an approach that builds on pressure to focus more on critical thinking in classrooms. Because there are more opportunities to demonstrate what they have learned, she can push them to be more precise in the way they communicate about math.
Spoon's experiment coincided with research into how instructional practices influence student achievement.
Entry courses, such as statistics, algebra, or precalculus, serve as a portal to educational achievement and possible careers in science, technology, engineering, and mathematics. Students can be thrown off track by poor performance in these courses, which has spurred interest in reform.
Especially for black and Latino students in entry courses, instructional practices are often the most crucial determinant of whether they will succeed or fail, according to a new report.
A feeling of belonging'
While there has been some qualitative research focused on the role of teachers and universities in student success, there have not been many quantitative studies, according to Mina Dadgar, founder of Education Equity Solutions, an organization associated with universities. Instead, she says, researchers have focused on other factors when it comes to postsecondary courses, such as student preparation or demographics.
TO study published in September by Dadgar's organization explored the experiences of 22,827 students at four California community colleges between 2020 and 2022. The report added to empirical evidence that mathematics teachers' grading and evaluation practices are the most important factor. important thing that affects whether students passed or failed these courses.
The report also recommended instructional practices that its authors believe can reduce racial disparities in outcomes in early mathematics courses, such as offering students more opportunities to improve, providing personalized feedback, ensuring equitable accommodations are offered, and encouraging a sense of belonging for students.
There is a perception among math teachers that entry-level classes are increasingly difficult to teach, says Susan Bickerstaff, senior research associate at the Community College Research Center. Some professors report that students who take these courses have more diverse prior math experiences, she says.
A decade ago, some of the students in these courses may not have encountered a college mathematics course. But a lot of work has been done to ensure that fewer students are diverted from college mathematics and into earlier developmental courses, she says.
But the pool of students who have access to college-level math has expanded, Bickerstaff maintains. So any challenges that arise with this are a good problem to have, she says, also noting that having a more diverse group of students in a given class increases the need to provide more support for high-quality teaching.
Lost in translation
Some of the obstacles students face in mathematics do not directly have to do with understanding the material.
Student motivation, sense of belonging and self-efficacy are important, Bickerstaff says. But you need to figure out how to support that in the mathematical context, so it's important to provide tools to teachers, she adds.
Part of that challenge, he says, is providing teachers with very specific examples that can guide the implementation of better instructional principles.
For teachers like Spoon, that means moving from research knowledge to action in the classroom. So far, Spoon reports the changes are encouraging. Her students already seem to be getting better results, although she will continue to think about possible improvements.
But the experimentation process is not simple.
Like Spoon, Tammi Marshall, interim dean of mathematics, science and engineering at Cuyamaca College, has also made some changes and is now championing new approaches to instruction and assessment.
But when he initially realized that his old tactics may have steered some students away from the careers they wanted, it was painful. She went through a period of mourning, she says. She meditated on past students whose life paths she believes she unintentionally thwarted.
When an instructor learns that they may have caused difficulties, it can be a lot to take in: “It's hard for me to hear that I caused harm,” Marshall says.
So ultimately, these ideas need to be expressed delicately to teachers, he maintains.
