For many years, the mathematics tests were considered as mere problems with the right answer. Students were able to solve some equations, put in numbers and get marks according to accuracy. However, due to online learning and online assessment platforms, the way that math exams are formulated and scored has changed. With this, teachers are actively concerned nowadays not only with whether or not the answer is right but also with the rationale behind the answer. This change is part of a much wider educational agenda, which aims to assess real mathematical competence, whereas teaching simply aims to regurgitate what has been memorised or is simply guessed.
Today’s online math tests not only indicate what students know and what they have done, but also how they think, analyse a problem, and apply concepts in new, out-of-the-box situations. Therefore, the final results are no longer the most important part, as the explanation, calculations, and logical processes are now just as important. Online assessments focus on the process of learning rather than the product, and thereby tap into deeper learning and the educator’s ability to determine true understanding. Being aware of this change can make it easier for students to be prepared for math tests and use the most appropriate studying technique.
Why Online Math Assessments are Changing
With the shift to digital learning, new opportunities have emerged to assess students’ learning. Conventional testing methods have been used that would encourage students to provide answers as soon as possible without having to fully understand concepts.
In the modern era, many students suffer from extreme frustration during virtual tests and even resort to using some shortcuts to achieve success, like “pay someone to take my proctored math exam“. But, with the advent of modern assessments, students are required to show actual understanding by presenting the detailed processes used in solving the problem, and conceptual understanding is much more important than getting the answer.
Teachers understand that there is more to maths than numbers. It is a cognitive/process approach to thinking, processing information and problem solving systematically. Thus, assessment approaches are changing as the focus shifts to demonstrate these more overarching skills.
The Difference Between Knowing and Understanding
You can get the right answer by guesswork, recalling the answer or even by a lucky guess at the right answer. The answer is correct, but it is not necessarily an indication of understanding.
This is a general principle that can be applied to all of the subjects. For instance, if a student looks up Take my history exam for me on the Internet and gets a passing grade, he/she will not get much idea about what they know about the historical events or their critical thinking skills (BAW, 2022).
Likewise, in maths, teachers would like to see that students know how and why a procedure works, rather than just the result of the procedure. Explanations are very detailed and clarify true learning from a coincidence.
Demonstrate how to solve the problem
Step-by-Step Reasoning Matters
The most significant modification in online math exams is that each of the steps in the process of solving a problem has to be documented. Students are frequently asked to present the formula(s) they used, to explain their mathematical decision-making, and to explain their calculations.
This way, instructors will be able to observe students’ problem-solving approach. A student can be awarded significant marks even if he/she makes a small calculation mistake towards the end of a solution when the focus is on the development of the reasoning process and its understanding.
However, if an assessment asks for an explanation, then an answer with no supporting work will be rewarded to a lesser degree than an answer that is correct and supported with work.
Demonstrating Conceptual Understanding
In recent years, some of the questions on math tests have been about communicating mathematical ideas in students’ own language. Students will not necessarily be asked to solve an equation; they might be asked to explain why a given method is suitable or to compare two or more methods for solving a problem.
These activities will help to determine if students have understood mathematical concepts or simply performed a rote-learned process.
Benefits for Students
Encouraging Deeper Learning
Instructing students that they will be graded on their explanations will make them more likely to concentrate on understanding concepts, instead of memorising formulas. This helps to build stronger foundations, which enable support for future learning.
Students start to ask, ‘Why does this method work?’, rather than ‘What do I get when I use it?’. That attitude towards learning ensures long-term learning gains.
Minor errors can be a major burden in a project
Explanation-based assessments may be a more justifiable representation of student ability. It’s okay to make a minor mistake in arithmetic, but it will not discount evidence of good reasoning and problem-solving skills.
If the student grasps the content, then meaningful credit can be given even if the numerical answer is not correct, as it is not the numerical answer that is of interest, but rather the process of thinking.
Developing problem-solving approaches in the real world
In real life, outside of the classroom, people are not usually evaluated on the results. Engineers, analysts, scientists and financial experts need to clearly communicate their reasoning and provide explanations for their decisions and justifications for their recommendations.
Planning to take Explanation Based Math Exams
It’s important that students get used to studying for the new online assessments. The ability to do calculations is still significant, but shouldn’t be the only thing that is practised (OECD, 2023).
Rather, they should explain their solutions orally, write the steps in the solution process, and revisit the concepts of formulas in their solutions. Solving a complex problem and keeping track of the reasoning by writing it down can help to understand the problem and do better on an exam.
Conclusion
The landscape of mathematics assessment is changing towards greater sophistication in measurement, beyond the notion of right and wrong answers, to the online medium. Emphasis on explanations, reasoning and processes of problem solving allows teachers to get a more accurate picture of student understanding. This will encourage students to think critically, learn more deeply in the discipline of mathematics and possess analytical skills that will help him/her in other areas of life. The need for students to be able to clearly articulate their mathematical thinking will continue to be critical to their success in digital education.