When considering how to approach assessment with online learning, mathematics teachers are confronted with what its purpose should be. Jean-Pierre le Roux guides us through this important journey of assessing our assessments.
One of the many consequences of the COVID-19 pandemic in South Africa, as was the case in most affected countries around the world, was that schools were forced to close to help curb the spread of the global pandemic. With teachers and students forced to stay at home, mathematics teachers were obliged to adapt their teaching and assessment practices, something that mathematics education has been advocating for decades. It did not take long before discussions around how teachers can adapt their assessment practices gained traction in the mathematics community. From my interaction with colleagues, I came to realise that the predominant challenges faced by many mathematics teachers were not only of a technological nature but also of a pedagogical nature. Let us unpack this together.
Mathematics teachers at some schools have been fortunate enough to provide learners with virtual lessons and online learning resources. Many teachers developed video lessons and online resources for students, and virtual lessons became popular to assist the students with online-learning. It, however, did not take a long time before questions were asked from teachers around assessing students in mathematics via online means. Comments and sentiments, such as “I can get my head around teaching online but not assessment” gathered momentum in the mathematics community and was a popular thread in a mathematics teaching e-mail group. From my observation, mathematics teachers are able to adjust and adapt their instructional strategies much easier than their assessment practices. Many teachers were sceptical, to say the least, of the role of assessment during this online learning phase. There is the danger of us weakening the relationship between teaching, learning and assessment because our traditional measuring instruments are no longer useable and compatible with the learning that is taking place. Focusing on mathematics assessment is essential because what mathematics teachers assess defines what these teachers value. I agree with Gert Biesta who argued that aassessments not only places value on things but emphasises what we value. It is vital to ask if we indeed measure what we value, or whether we are just measuring what we can measure easily and thus end up valuing what we can measure. There have been increasing calls, both in the classroom assessment literature and in the mathematics education literature for teachers to make changes to their assessment practices towards promoting a learning culture.
Questions from mathematics teachers asking for assistance on e-mail groups around the validity, reliability and trustworthiness of assessing students during this remote learning phase, mostly via online modes, became louder and even more desperate. Many teachers expressed the pressure they experience from school management to continue assessing as ‘normal’. Assessing as ‘normal’ is, of course, synonymous with using summative assessment instruments. I am not discrediting summative assessments, but I want to highlight that the purpose of assessment is vital to eradicate conflict between formative classroom-based assessments and summative assessments. There should be a clear distinction between using “assessment for learning”, “assessment as learning”, and “assessment of learning”. Our assessments must fulfil a greater purpose than merely collecting data in the form of marks for reporting and certification purposes. Although a classroom-based assessment may be designed and packaged as a formative (assessment for learning) or summative (assessment of learning) assessment, it is the actual methodology, data analysis, and use of the results that determine whether an assessment is formative or summative.
It interested me that the challenges faced by many mathematics teachers were not only of a technological nature but also of a pedagogical nature pertaining to their conceptions of assessment. Teachers’ conceptions of assessment are formed by an entangled network of beliefs, including beliefs of teaching and learning mathematics, beliefs of the purposes of assessment, and beliefs of the expectations and ability of their students. I argue that mathematics teachers’ conceptions of assessment will determine if they will be able to adapt or incorporate new ideas to their assessment practices. Many studies have found that mathematics teachers’ conceptions of assessment are the strongest indication of whether the teachers aligned with an assessment culture or a testing culture of assessment. A significant number of aspects shape teachers’ conceptions of assessment, which results in the teachers having either societal conceptions of assessment or pedagogical conceptions of assessment. Societal or pedagogical conceptions of assessment affect assessment practices and result in teachers having an assessment culture or testing culture of assessment.
 Even though I acknowledge the fact that there are noticeable differences between “e-learning”, “remote learning” and “distance learning”, in this article I use these terms interchangeably, and under the same umbrella.
 I use the term conception to describe general mental structures, which encompasses beliefs, meanings, concepts, propositions, rules, mental images and preferences. Beliefs, therefore, represents a subcategory of the conceptions.
Teachers will be able to adapt and incorporate new ideas to their assessment practices during this online learning phase if they have pedagogical conceptions of assessment. Pedagogical conceptions of assessment allow for assessment to be used as a tool for improving learning, and to advocate a learning-centred culture, whereas teachers’ societal conceptions will continue to create conflict when using a “testing culture” of assessment for learning purposes. An assessment culture of assessment (as opposed to a testing culture of assessment) is critical during this online learning phase to integrate learning and teaching. The assessment designed and used by the teacher must foresee the specific type of feedback and assessment data that the assessment will generate, to inform the student and teacher of the students’ progress. For teachers to have pedagogical conceptions of assessment, which aligns to an assessment culture, the qualitative and descriptive assessment feedback, as opposed to merely giving quantitative feedback (only a mark), is critically important.
Not all teachers are of course in a position to assess their students via online means. For teachers who are in such a position, technology is of course an obstacle but it should not be the biggest obstacle. There is no reason why teachers will not be able to assess their students in a manner that will promote learning if they have an assessment culture of assessment as opposed to a testing culture of assessment. There is a range of free and easily accessible resources available to support teachers to design learning and assessments via online platforms, including Google forms and Microsoft Quiz. I recently co-presented a webinar on how to design mathematics formative assessments by using Google forms and Microsoft Quiz. Yes, I will concede that technology is a hurdle for many teachers and that teachers had to be familiar with the workings of the online platforms to fully use the tools. I received more than 10 questions from mathematics teachers at schools. What separated those who could design effective formative assessments by using online platforms were not their solely their technological skills-set. Their questions exposed their conceptions of the assessment. The teachers with a testing culture of assessment tried to emulate their traditional forms of assessments into an online platform. Teachers who projected an assessment culture tried to understand how they could bring their teaching and learning closer together, and they were interested in the quality of the feedback that would be generated.
The reality is that there are many teachers who are teaching in schools where it is a near-impossible task to do online learning. The headmaster of a school which we have a working relationship with, in Cape Town, found in a survey that only just over a quarter of students have access to smart devices and that less than 5% have access to a computer. Hardware is not the only challenge, students cannot afford data, and there is llimited network coverage in some areas where students experience intermittent connection. The socio-economic make-up of this particular school is similar to thousands of schools in our country. The headmaster bemoaned the fact that even if teachers sent online resources to students, they will not be able to access it because of how expensive data is in South Africa. Students from schools situated in low-economic communities have been left in the dark. Limited to no teaching, learning and assessment have taken place since the announcement of the lockdown, which I believe will increase the inequality gap even further. Even for the students from middle-class families, data is an enormous challenge. I am aware that some of the major cell phone network providers made zero-rated learning sites available, which allowed for materials to be downloaded for free. The challenge is that the popular platforms, which teachers could use to design assessments and develop learning materials, are not zero-rated. For mathematics teachers to be able to adapt their teaching and assessment practices, it is imperative for teachers and students to have the appropriate hardware and to be able to access learning platforms.
It must be noted that although teachers are viewed as essential agents of change in the ongoing attempt to reform education, they are also significant obstacles to change and reforming education. One of the very few positive outcomes of the COVID-19 pandemic for mathematics education was that teachers had to evaluate and adapt their assessment practices. I urge every teacher who is in a position to assess their students via online means, to continuously evaluate their conceptions of assessment. The symbiotic relationship between assessment in mathematics and the learning of mathematics is of the essence during these unprecedented times, and it will require a shift in our pedagogy.
Jean-Pierre le Roux
Head of Mathematics Department,
CEDAR HOUSE SCHOOL, SA