Methodological Issues in the Investigation of Values in Mathematics

Abstract

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.

Excellent Mathematical Performance Despite “Negative” Affect of Students in Korea: The Values Perspective

“…This research, part of the wider WIFI study, investigates what students find important in their respective mathematics learning experiences. Even though there are research limitations (e.g., assessing only espoused values rather than enacted values) of identifying students’ values through the survey methods such as the questionnaire (Chan & Wong, 2019; Seah et al, 2017), the intention of the Korean participation has been to shed light on the paradox of how Korean students perform excellently in international mathematics assessment exercises such as PISA, when they are known to be experiencing negative affect with regard to mathematics learning.…”

“…Since the multivariate effect for student confidence is significant (p < .05), we have to interpret the univariate between-subjects effects by adjusting for family-wise or experiment-wise error using a Bonferroni-type adjustment, and we derive the adjusted a level .01 (i.e., .05/5). Using this a level, we have significant univariate main effects for the following two variables: the survey methods such as the questionnaire (Chan & Wong, 2019;Seah et al, 2017), the intention of the Korean participation has been to shed light on the paradox of how Korean students perform excellently in international mathematics assessment exercises such as PISA, when they are known to be experiencing negative affect with regard to mathematics learning.…”

Characters and values in mathematics teaching and learning: A review of research in Indonesia

“…In this part, we will discuss the three points to shed light on the findings and future research regarding the topics. In the discussion, we try attaching relevant theories or prior works such as Bloom taxonomy (Krathwohl, Bloom, & Masia, 1964) which regard the notion of characterization, character education (e.g., Card, 2017;NASEM, 2017;Nucci, 2017;Lickona, 1999), values education (Halstead & Taylor, 2000a;2000b), values in mathematics teaching (Bishop et al, 2003;Chan & Wong, 2019), and affects in mathematics education (McLeod, 1992;Hannula, 2011).…”

“…We mean the measurement aspect as the methods used to measure the values which are taught by the teachers and inculcated in students. Methodological issues were addressed only concerning the investigation of values in research (Clarkson et al, 2000;Chin, Leu, & Lin, 2001;Chan & Wong, 2019). For example, Clarkson et al (2000) utilized classroom observation and interview to reveal what values the mathematics teachers nominated and taught in the classroom.…”

“…Cai and Garber (2012) explicated three inter-related issues concerning the teaching of values, i.e., understanding of values, assessment, and individual and collective nature of values. Some possible reasons why the assessment of values remains the issue are: the position of values are not clear relating to affective or cognitive aspect of learning goals (Cai & Garber, 2012), the nature of values which is hidden and not easily unfolded (Chan & Wong, 2019), and values as learning process or leaning purposes.…”