Questions about maths teachers’ training in lockdown – study
These factors could result in “gaps in knowledge”, when these students graduate as teachers, according to researchers Dr Hlamulo Mbhiza, a mathematics education lecturer at the University of South Africa; and Dr Dimakatjo Muthelo, a lecturer in maths education at the University of Limpopo’s department of mathematics, science and technology education.
Their study, “COVID-19 and the quality of mathematics education teaching and learning in a first-year course” was published in the South African Journal of Higher Education, May 2022.
It presents an auto-ethnographical account of the knowledge gaps in the teaching and learning of mathematics education in a first-year education course in an online space. “It is important to note that we were both insiders and outsiders in the system as we observed our interactions and participation during lectures,” they explain.
According to the researchers, while lockdown resulted in online teaching, in South Africa specifically, students and teachers were catapulted into virtual teaching and learning situations with the majority of them having no preparation for this shift.
A lack of engagement with concepts
The major obstacles they faced in their online teaching were “the lack of availability of adequate features in the academic portal adopted” by their institutions and “limitations in writing mathematical symbols to facilitate effective explanations”.
However, only a few students interacted with them as part of the teaching and learning process, as well as asking questions and contributing to the discussion of the mathematical ideas.
They argue that the shift to online teaching of mathematics “has compromised the students’ social construction of mathematical meanings”, because they, as lecturers, did not have control over what students did during the sessions.
“The student might be logged in but not participating or not in front of the laptop to fully engage with the mathematical ideas presented during teaching.”
In line with Professor Nic Spaull’s 2013 research that indicates that it can be assumed that the majority of students come to university with knowledge gaps spanning the previous levels of schooling due to poor teaching of the subject, the researchers say: “We find the limited participation to be concerning, especially considering the goal of enabling student teachers’ epistemological access to mathematical concepts.”
In teaching the concept of the Limit of Functions (a fundamental concept in calculus), they say they expected their students to verbally, numerically, algebraically and graphically represent Limits. They should have been able to follow the same approaches to determine when a function is continuous at a point.
“For example, if a student is reading the graph and making conclusions based on the interpretations of the observations, we [can] tell if the[y] are having misconceptions or not and provide them with formative feedback to clarify their misconceptions.”
However, the reluctance of students to share their responses on the virtual teaching and learning platform or sharing their thought processes during the sessions made it difficult for them as lecturers to monitor and evaluate their conceptual and procedural understanding.
Cheating and plagiarism
Normally, getting a clear demonstration and understanding of students’ procedural fluency could be achieved through their writing assessments under “exam conditions” which are supervised.
Due to the limitations of the teaching and learning tool and lack of supervision as the students were writing tests online, it was not possible to set questions that allowed students to demonstrate their procedural fluency in the Limit of Functions.
This is due to the learning platform being configured to accept true or false, multiple choice, and single numerical-type answers to questions. “This limited an opportunity for us as lecturers to obtain data about areas of work where students faced difficulties and, in turn, constrained the identification of the areas of work that required re-teaching,” explain the researchers.
Mbhiza and Muthelo explain that the only time that they can gauge what students cannot do is when they administer tests or assignments. “Although the challenges identified from those assessments would be formatively used to improve their construction of knowledge, by then it would be too late to improve their continuous assessment marks.”
Cheating and plagiarism added fuel to the fire: a case in point is that, for the two questions that required students to evaluate the Limits of Functions earlier, they could easily plug the problem into online calculators and generate the answers without engaging in thinking processes to answer the questions.
It could be argued that, for learners to answer the questions as true or false, multiple choice, or one-word answers, they would need to first apply specific procedures to get the answers.
“However, in our case, we soon realised that the students had discovered online calculators that can perform the procedures for them and even show them the steps to solve the problems.”
Before they could administer the first test for the module, one student sent the following e-mail: “Dr, since there are literally softwares on the internet that can differentiate and integrate, practically do everything with full steps. They can compute limits to drawing graphs. Are we going to write our examination online without supervision?”
This e-mail alerted the researchers to the fact that, as mathematics teacher educators, they are faced with a quandary of ensuring that student teachers learn and own procedural skills rather than their getting correct answers through the use of external tools such as online calculators.
While students used the social media tool, WhatsApp, for collaborative learning, they also used it to cheat in real time, while writing tests via their learning management system. Furthermore, the researchers realised that students had “gathered in one place to write the assessment as we had asked them to remain online …. as they continued writing”.
The researchers continued that “Mistakenly”, some of the students were unmuted during the test, “and we heard them seeking assistance for answering specific questions among each other”.
“This further made us aware that the students were using ‘multiple streams of cheating’ in the assessment, to ensure that ‘no student was left behind’,” according to Mbhiza and Muthelo.
Without generalising, they argue that students view assessment to be for the purpose of learning and-or for learning, but to get the right answers, even without conceptual rigour and procedural fluency.
They refer to 2007 research that revealed that the present generation of students seem to hold a “fluid perspective” of what unethical behaviour entails compared with past students.
“However, in our case, we argue that online teaching and learning exacerbates academic dishonesty and lowers the academic rigour, the development and retention of mathematical knowledge in our course,” say Mbhiza and Muthelo.
They point out that the cheating students failed to recognise the traditional conceptualisation of academic dishonesty as they exchanged answers to the test questions. They refer to Neil Howe and William Strauss’s 2003 book, Millennials go to college: Strategies for a new generation on campus: Recruiting and admissions, campus life, and the classroom, that asserts that millennial generation students cannot differentiate between traditional tendencies of cheating and contemporary concepts of information morphing.
Strategies for online maths education
“Considering that these students are pre-service teachers, our concern is that they are not making efforts in learning the mathematical skills, concepts and processes to ensure that, when they are qualified as teachers, they will possess the knowledge such that they will enable their own learners’ epistemological access to mathematics knowledge.”
From their experiences, they conclude that they cannot fairly administer mathematics assessments, which include affective and cognitive aspects in an online teaching and learning environment. Their experiences highlight concerns about the quality of mathematics teachers South Africa is going to produce for the system that is argued to have poor quality and unqualified teachers.
How the students have positioned their social presence in online learning suggests that learning to own mathematical skills and knowledge is of little concern for them, as primarily, mathematics education learning entails passing without having to engage in mathematical thinking and creation of meanings during assessments.
“Although we cannot generalise our experiences of teaching mathematics education online, it is important for those involved in teaching and implementing online mathematics courses to configure strategies to uphold academic integrity and think of alternative practices for content delivery and assessment during the pandemic,” say Mbhiza and Muthelo.