Guidelines issued by the Centers for Disease Control and Prevention and the World Health Organization state that healthcare workers should wear N95 masks or higher-level protection during all contact with suspected cases of severe acute respiratory syndrome. Before use, the manufacturer recommends performing a user seal check to ensure that the mask is fitted correctly. This study aimed to test the ability of the user seal check to detect poorly fitting masks. This study is a retrospective review of a mask-fitting programme carried out in the intensive care unit of the Prince of Wales Hospital in Hong Kong. In this programme, all staff were tested with two types of N95 mask and one type of N100 mask. The results of the documented user seal check were then compared with the formal fit-test results from a PortaCount. Using a PortaCount reading of 100 as the criterion for a correctly fitted mask, the user seal check wrongly indicated that the mask fitted on 18-31% of occasions, and wrongly indicated that it did not fit on 21-40% of occasions. These data indicate that the user seal check should not be used as a surrogate fit test. Its usefulness as a pre-use test must also be questioned.

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In this chapter, we first provide an overview on our previous investigations, then the methodologies employed are evaluated. A variety of research methodologies such as questionnaires, open-ended questions, interviews, classroom observation, episode writing, and mind maps have been employed at different stages of our intellectual journey. These methods are effective tools and helped us understand students' and teachers' beliefs and values about mathematics, mathematics learning and teaching. However, one's value is hidden and therefore not apparent. It is a deep-down notion in the sense that it is not easily unfolded. Thus, if we want to have a more holistic understanding on teachers' and students' values (in mathematics), we need a sharper methodology in which the participant is forced to make decision under a dilemmatic situation so that their values can be revealed. After providing examples of such situation that we used, we would argue that the use of hypothetical situations can enhance the investigations of values and related issues. What we used include (a) asking whether one is doing mathematics when provided with some hypothetical situations, (b) what a teacher would respond if his/her students asked whether one is doing mathematics in the given hypothetical situations, (c) how one respond to some famous mathematicians' quotes in which some controversial situations are involved, (d) hypothetical classroom situations and (e) hypothetical lesson planning. We believe that our discussions can enrich the study of values in mathematics education.