“The procedures that teachers mention for determining grades are quite subjective,” said Andrea Rajchman, a graduate of the Master’s in Education program at Universidad ORT Uruguay.
According to what she stated during the defense of her thesis—titled “How Is Mathematics Learning Assessed in Secondary Education According to the Perceptions of Teachers and Students?”—teachers do not use the same criteria when evaluating their students.
He also explained that math teachers set “basic or minimum standards for grade promotion,” but that, in practice, they do not take these standards into account either.
To illustrate his point, he noted that, for a teacher, solving equations may be a fundamental aspect of the subject. But even if a student can’t do it, they might still pass the course.
“They’re basic skills, but they don’t even take them into account,” he said.
A relevant and timely topic
Rajchman analyzed the learning assessment practices implemented by11th-grade mathematics teachers at schools in Montevideo with varying socioeconomic levels.
In particular, she examined students' perceptions and teachers' discourse. She also analyzed students' written work and compared it with various curriculum documents.
During her thesis defense, which took place on Tuesday, June 11, 2019, at the Institute of Education, she explained that she was interested in analyzing whether practices vary depending on the high school’s socioeconomic context.
He said that people often talk about differences in student performance depending on the context. In general, this applies to all subjects, though particularly to mathematics. However, the pass rates for the subject in11th grade tend to be similar across different schools: “High schools with a lower sociocultural level have a pass rate quite similar to those with a high sociocultural level.” That is what sparked his interest in studying the topic.
For the study, Rajchman chose to conduct a mixed-methods study. The sample consisted of 10 public high schools in Montevideo, representing different socioeconomic levels: three from high-income areas, four from middle-income areas, and three from low-income areas.
The study included an analysis of 190 assessment tasks, a questionnaire administered to 165 students, and 10 semi-structured interviews with teachers.
Math = Fear and Anxiety?
What ideas or feelings are associated with math assessments? “Students’ comments are characterized by anxiety, fear, nervousness, and negative feelings such as ‘I’m going to do poorly’ or ‘I won’t be able to do it,’” said Rajchman, who found no differences across different contexts: these feelings were not related to the socioeconomic status of the schools.
In line with the national and regional literature, his research showed a positive relationship between self-concept and performance. Students who expressed beliefs such as “I’m going to do well” or “I like the subject” were the ones who earned passing grades. In contrast, those with a negative self-concept received failing grades.
But Rajchman was struck by the “discrepancy” between the views of teachers and students. The teachers referred to assessment as “part of the teaching process”; they said they linked it largely to grades and used it “to motivate students.”
“This is a wake-up call for teachers to consider the impact they have on their students when they treat assessment as part of the teaching process,” he said, adding that “it is necessary to include the assessment of learning in the agenda of the pedagogical debate.”
In his view, students observe and act based on how they are evaluated. “What we do will determine what they study or don’t study; what they do or don’t do,” he concluded.
How is the grade calculated?
“What factors do you take into account when grading your students?” Rajchman asked the teachers. Although they spoke to him about the importance of students acquiring certain skills, procedures, or mathematical concepts, he noticed that they placed much greater emphasis on behavioral factors, such as attitude, effort, and conduct.
“What’s more, when asked what factors they consider most important, they mention classwork, but also that students put in the effort, behave well, attend class, have a good attitude, and do their homework,” he added.
Nevertheless, the weight teachers assign to different factors varies depending on the context. That was one of Rajchman’s hypotheses. His research showed that in high schools with lower socioeconomic status, effort carries greater weight, while written exams have less impact.
In addition, the students were asked, “What skills or knowledge do you need to acquire to get a good grade in math?” For them, behavioral aspects are also more important, followed by studying and practicing.
In 90% of cases, students reported that effort is a factor that teachers take into account “frequently” or “very frequently” when assigning a grade. This is followed by class participation and, next, behavior.
“It’s striking that, of the three most common factors, two are behavioral and only one relates to performance,” Rajchman said. “It strikes me as odd, but it aligns with what the teachers themselves have been saying,” he clarified.
In her view, since assessments provide the information used for grading and, consequently, for promotion, it would be “desirable for them to be more closely aligned with the program objectives.”