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APOS-ACE (Action, Process, Object, and Schema-Activities, Classroom discussion, and Exercises) is applied in this article to explore the teaching and learning of derivative by giving emphasis on its graphical understanding. For this purpose, a Genetic Decomposition is developed based on the outcomes of previous studies and on our personal teaching experiences. An ACE cycle is designed with the help of the Maple software and implemented on a group of freshmen Iranian students (experimental group). The outcomes of this implementation are evaluated by comparing the performance of the experimental group to the performance of another equivalent student group (control group), to which the same subject was taught in the traditional, lecture-based way. Our findings demonstrated students' who were in the experimental group shown a better understanding of the derivate compared to the control group. Therefore, such ACE cycle with Maple could be used more frequently for teaching calculus, especially derivative.

Towards the end of 2019, a novel coronavirus, known as COVID-19, was detected and quickly spread worldwide. The resulting pandemic led many countries to lockdown and teaching and learning switched to fully online provision. This study explores how Norwegian higher education lecturers and students of mathematics experienced online provision following this switch in March 2020 when the national lockdown was imposed. Data are generated and analysed using an exploratory sequential mixed methods approach that first entailed interviews with ten mathematics lecturers and six undergraduate students as the foundation for developing a survey instrument. The instrument was designed to explore further how a larger sample of mathematics lecturers and students perceived their experiences following the switch to online teaching and learning. One hundred and twenty-seven university students from four universities and eighteen mathematics lecturers from seven universities responded to the survey. The data generated indicate that advanced technology and the internet were not entirely successful in supporting many students and lecturers to adjust to the lockdown environment. Additionally, it appears that some mathematics lecturers were not aware of several challenges that students experienced following the switch. This paper aims to increase the awareness of the mathematics education community at the tertiary level about the challenges mathematics lecturers and students experience through online education. Further, it is hoped to prompt collaboration within the community to address these challenges in order to be better equipped for any use of online teaching and learning of mathematics in higher education.

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