The pandemic of coronavirus disease 2019 (COVID-19) has led to sudden and unexpected circumstances in education for all the involved people (pupils, teachers, education policymakers, parents). International organizations have paid attention to their responses in crises by using alternative modes of teaching. The typical teaching methods had to be replaced by e-learning processes and all the participants needed to adjust themselves and adapt innovative methods. Most studies concentrated on teachers' and students' difficulties, barriers and new challenges. However, a different role was given to parents as well, especially in the case of primary and the first grades of secondary education, as they were asked to facilitate their children to use the e-learning processes and support them during the learning process. The present study examined the change of parental involvement during the pandemic in comparison to the previous situation in the case of mathematical subject. A questionnaire was constructed and administered to parents from Cyprus at the first days of the school year 2019-2020 in order to examine their beliefs and self-efficacy beliefs about their parental role and involvement during homework at their children's mathematical understanding and the development of their children's perseverance strategies during mathematical problem solving. The same questionnaire was administered to them at the end of the e-learning teaching processes in May 2020, after they had alternative experiences in order to identify any differences at their respective beliefs. Only the sample of parents who took part at both phases of the study was used for the comparative analyses. Results indicated that parents, especially in primary education, had the willingness to support their children's learning under the different teaching and learning processes; however they needed training in order to develop appropriate knowledge, relevant experiences, positive beliefs and self-efficacy beliefs.