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Abstract

Keywords

Culture mathematics education values values-alignment valuing

Highlights

Values and valuing are seen as enhancing pedagogical actions.

Throughout the papers, the review of the literature is complemented and each research includes specific theoretical constructs.

Regarding research methods, quantitative comparative research projects, which explore students' values related to mathematics, have been influencing other research about values.

A broad and shared theme by the group is the observation of the educational phenomena from a perspective that acknowledges culture and the humanness of the mathematical knowledge. In their research, the collective of authors truly incorporates humaneness in the production and in the teaching and learning of mathematics.

Introduction

It is exciting to share my thoughts on the collection of papers in this Special Issue of the ECNU Review of Education. And it was a great pleasure to receive the invitation to comment upon them.

Each paper shared by the group of authors is specially revealing. Thus, the selection as a whole is better understood by zooming out of the immediate research context that is constituted in each paper. As an overall approach, I consider that a broader view of the research represented in this Special Issue emerges when stepping back from each particular investigation, turning the attention to the collective contribution to an ongoing theoretical network on values and valuing. Reflections as such will inevitably revise the specific demands and contradictions that are inherent to research processes and to any research group.

In my comments, I also seek to understand the internal relations underlying the different research papers, expressing them through convergences, singularities, and controversies in their investigations shared in this Special Issue of the journal.

Beyond viewing the selection of papers in the research field of mathematics education with a focus on recent understandings of the notion of values, convergences of several research subgroups reveal the characteristics of a collective of authors. At the same time, they are organized into research lines. What stands out in the foreground as a broad and shared theme by the group is the observation of the educational phenomenon from a perspective that acknowledges culture and the humanness of mathematical knowledge, where values play a central role both in knowledge production and use and in teaching and learning. From a pedagogical perspective, learners’ effective engagement in mathematical activities is seen as closely related to values. Educational policies around the world have more recently included expectations on values alignment for mathematics education in particular and in educational standards in general, a theme which seems to have been naturally embraced by the authors here.

Theoretical approaches

Convergences in the group also include the theoretical perspectives on values adopted by the authors. The various studies reported in this Special Issue are broadly based on approaches that were first introduced into mathematics education by Alan Bishop in the 1980s.

Bishop (1988) considers values as “the ideals and the principles lying behind the actual language or symbols developed by a culture” (p. 61). Such a conception per se exposes the complexity permeating the notion, as we, human beings, belong to intercultural spaces. Bishop conceives three pairs of opposing but complementary mathematical values—rationalism and objectism, control and progress, openness and mystery. They are not to be taken as a list, and the three pairs may leave out important features to be captured by different cultures.

In 1996, Bishop elaborates the notion of values in mathematics education as “affective qualities which education aim to foster through the school subject of mathematics” (p. 19). He also organizes values in Western mathematics classrooms in three dimensions, namely, related to the mathematical knowledge itself, to mathematical education, and to education in general.

The above frameworks are the theoretical bases for the collection of papers we see here. In a true movement away from universal points of view, the theoretical network crafted in each research indicates the intention to gradually and truly incorporate humaneness and culture both in investigations on mathematics production and on the teaching and learning of mathematics. Values and valuing and values-alignment are two key theoretical notions particularly studied and discussed throughout the papers, foregrounding the research singularities. As pieces of a jigsaw, the various papers offer to readers a theoretical overview of the research area related to these constructs.

For example, Pang and Seah’s (2021) paper briefly retraces the framework on values within the affective domain (Hannula, 2012; Philipp, 2007), reflecting on differences between beliefs and values. They remind readers that other than being regarded as an affective construct, values have also been presented as a volitional variable (Seah & Andersson, 2015), and more recently as a conative variable (Seah, 2019). The authors further explain the notion as mediating cognition, affect, and behavior, defining “valuing” “as an individual’s embracing of convictions in mathematics pedagogy which are of importance and worth personally” (Seah, 2019, p. 107).

Regarding the constructs of valuing and value, Seah et al. (2021) propose focusing on the verb (i.e., “valuing”) rather than the noun (i.e., “value”), emphasizing that what matter are the actions, and not whether the values are subscribed to or not. Hill et al. (2021) contribute with references tracing back the attempts to define values as beliefs (Rokeach, 1973), as beliefs in action (Clarkson et al., 2000; DeBellis & Goldin, 2006) and as centralized convictions (Halstead & Taylor, 2000); as sociocultural norms (Schwartz et al., 2001); as an affective construct (Bishop, 1996; McLeod, 1989; Zan et al., 2006), conative in nature (Emmons, 1986), and as a motivational construct (Hannula, 2012; Wigfield & Eccles, 2000). Such references not only give us an idea of the lively debate that has gone on for decades but also provide us with a chance to deepen our knowledge on the subject, providing pertinent references in the research literature.

In their paper, Kalegeropoulus et al. (2021) revisit the literature on decision making by Bishop and Whitfield (1972) and results in Seah and Andersson (2015) who propose that “educators, and teachers, in particular, use their craft to play a leading role in facilitating values alignment.” There is also a description of the four value-alignment strategies as conceived originally in Kalogeropoulos and Bishop (2017).

Dede et al. (2021) explore participants’ values in different mathematical modeling contexts in different countries. The six cultural dimensions in Hofstede (1980, 2009) are incorporated to explain the differences in values. In the same vein, the research by Tang et al. (2021) as well as by Hunter (2021), focus on variations on values and cultural dependence. Values which form and change during learning stages are the research interest for the former, while the latter is concerned with value dependence on the culture of the learner. Bishop’s point of view (1988, 1996) regarding values in Western mathematics classrooms is the starting point to explore dependencies of their origins, differences in context and cultures, and overlapping values (Seah, 2008, 2016; Zhang, 2019; Zhang et al., 2016).

In synthesis, by the time we finish reading the entire collection of papers we are able to track, in part, the overall debate and the theoretical paths followed by active researchers in their efforts to elaborate the notion of value in mathematics education.

Researching values and valuing

Concerning research methods, it appears that quantitative comparative research projects which explore students’ values related to mathematics, such as the “What I find important?” (WIFI) study reported in two papers in this Special Issue (Pang & Seah, 2021; Tang et al., 2021) have been influencing other values research. Regarding their theoretical views, research questions, and method, this appears to be incorporated in the research developed by Hunter (2021) when investigating the Pāsifika students’ values and by Dede et al. (2021) in their account of different practices in different countries.

Each paper brings nuances that could distinguish them in different research lines, such as in cases where the special interest is on teachers’ or students’ views, or on the complex relationships established between the two in the educational spaces. Besides, other specificities may emerge from an immersion in each research. Conflicting views, if any, are to be understood as an opportunity to revisit and restructure research or clarify ideas and conceptions.

The thought-provoking paper in this Special Issue by Dede et al. (2021) reports a qualitative research using document analysis. It incorporates culture through considering the variations of the values permeating the different contexts of mathematical modeling tasks, set from different perspectives, in different countries. For each modeling task, they examine the mathematical, mathematics education, and educational values (Bishop, 1988, 1996) permeating them. Values are considered in the affective domain (Bishop et al., 2006; Seah & Bishop, 2000; Seah & Wong, 2012). Also, values in general, and “positive” values (Gellert, 2000) in particular, are understood as transferred through the teaching and learning processes (FitzSimons et al., 2001; Gellert, 2000).

The research aim is to investigate variations in mathematical values, mathematics educational values, and educational values (Bishop, 1988). Regarding the mathematical value dimension, the authors consider the three mathematical value pairs that Bishop (1988) proposes to the Western mathematics culture—rationalism–objectism, control–progress, and mystery–openness. Using semantic content analysis, aspects related to the other two dimensions—mathematics education and educational values—emerged and are organized accordingly.

A variation in notion of culture that is effectively used by the authors in the analysis, or in the sample selected to identify societal values, seems to be the source of some conflicting interpretations. In fact, the research rationale evokes Bishop (1988), and in consequence his notion of culture, and the investigation is drawn upon results based on the latter. The controversial results emerging from Dede et al. (2021) document analysis may be due to the fact that Hofstede’s (2009) cultural dimensions supporting the semantic content analysis incorporate another notion of culture and refers to another sample population profile.

Geert Hofstede defines culture as “the collective programming of the mind that distinguishes the members of one group or category of people from others” (Hofstede, 2009). He has been responsible for a wide (and perhaps unique) comparative study on culture in more than 70 countries (Hofstede, 2009). His primary research data were collected in the 1980s. It was used to conceive his six-dimension framework on cultural value levels of society on behalf of International Business Machine Corporation (IBM). At that time, the participants of the research were IBM’s employees and the research interest was on work-related values. Nowadays, we can learn that the six dimensions “are not based on values but on strategic practices, which unlike national values can to some extent be monitored by the organization’s management, with the support of skilful consultants and coaches” (see https://hi.hofstede-insights.com/models, accessed December 2020).

Pang and Seah (2021) are also referring to this framework in their research. In this case, the WIFI questionnaire used was developed considering the 6 mathematical values in Bishop (1988), 10 mathematics educational values in Seah’s (1999) study, and 6 general educational values expressed by Hofstede et al. (2010) in the form of value continua. In their research, respondents were participants of the survey; thus, participants’ profiles matches. It seems fine, apart from the strikingly different conceptions and intentions involved in one and the other research.

Controversies, convergences, and singularities

But this is not the approach in Dede et al. (2021) anyway. According to them, the research in Cooper et al. (2007) transfer aspects related to Hofstede’s framework to classroom teaching practices. Researchers seem to agree on universal claims such as “in society with a high level of power distance, and uncertainty avoidance, teacher-centred instruction is adopted, and questioning teachers’ teaching is considered disrespectful” (p. 7).

No one would deny, I believe, that the value’s structure of the country they live in affects individuals and their educational practice. On the other hand, a claim such as “Brazil reflects a society that believes the hierarchy must be respected and inequalities between people are acceptable” emerging from data collected with a multinational employees is too narrow to be transferred to schools regarding the two profiles involved. In fact, the affirmation above includes two claims. The latter seems reasonable, while the first does not seem to correspond to reality in regard to “values” and “valuing” in Brazilian schools. Besides, one may agree “the hierarchy must be respected” in work relationships at the same time one may not implement such value at school. In respect, Seah et al. (2021) in this Special Issue, make a distinction in their paper between naming what we find important (where “value” is a noun) “… and the act of embracing what we find important (where ‘value' becomes a verb)”. Similarly, reasons for not questioning teachers are far from being explained by “considering it disrespectful,” in the Brazilian case.

The confidence I am expressing myself by heart on the Brazilian case is due to the fact that, eventually, I am a Brazilian teacher. The claims in the paper about the Brazilian school experiences had drawn my attention since my first reading. It stimulated a parallel study to understand the results. And at this point, we all have issues to learn. Firstly, the very document data qualitatively analyzed in the Brazilian case include dialogical snapshots in the interactions at school classroom (Barbosa, 2006) that could raise doubts about the school culture elaborated in the paper. Second, the research intentions and participants should be accounted for and interpreted in depth; especially if we are concerned with values. Finally, none of these comments is to be taken as a depreciation of the research in this article. The research is well developed, original, and demanding to achieve a systemic approach to understanding the phenomena. Rather, these comments are written as an opportunity to reflect on our own methods and conclusions.

As in Dede et al.'s (2021) research, variations on values regarding cultural considerations seem to be also in Hunter’s (2021) research agenda. The focus is on mathematics educational values (Bishop, 1988, 1996) and their reasons, involving Pāsifika students in New Zealand. As in the research conducted by Dede et al. (2021), Hunter (2021) acknowledges the values as being anchored in society, mathematics and mathematics education. Thus, the cultural background of the learner has a bearing on their values (Lee & Seah, 2015; Seah, 2016; Zhang, 2019; Zhang et al., 2016). Unlike Dede et al. (2021), however, Hunter’s (2021) paper draws on Pāsifika students’ perspectives on mathematical educational values and their reasons while rating their importance for them. In her case, the scope of the research allows her to combine qualitative and quantitative approaches to identify what is important in mathematical education for the group of students, and to develop her own research survey rather than using results from existing ones, even taking the latter as the basis for the first. Hunter’s (2021) research decisions are responses to the challenge of achieving equity in education, incorporating Pāsifika students’ values to the existing educational discourses.

Tang et al. (2021) present results from a quantitative study on students’ mathematics values in Chinese mainland. The interest is on how the values form and change, with an aim to improve teaching and to promote a competency-based curriculum reform (OECD, 2018; Zhang, 2017). As in the studies of Dede et al. (2021) and Hunter (2021), the focus is on variations of values; in this case, on students’ mathematics learning values across different school level groups. Theoretical references for the research are values in mathematics classrooms introduced by Bishop (1996), as well as values being a conative variable (Seah, 2019). As regards different expressions, such as students’ mathematics values, valuing, students’ mathematics learning values, students’ values and competencies (as mathematics educational values)—which seem overlapping in meaning—they deserve some attention so as to improve our understanding of the research.

The research scope is broader than the one in the study by Hunter (2021) while more restricted than in the case of Dede et al. (2021). The selection of the sample and the methodological procedures are carefully described and justified, and results are important, instigating, opening upon other research possibilities, other than informing teaching. A fascinating result among others refers to aspects of objectism that are valued by Chinese students. As research results, the valuing of objectism is expressed by the use of concrete material, diagrams, other visualizations, examples, and mistakes. According to the authors, this result is aligned with Chinese traditional culture, which gives importance to “draw inferences about other cases from one instance,” “learn through examples,” and to “understand by analogy” (Tang et al., 2021, p. 280). Values as such, resembling aesthetic values, may indicate other epistemologies for mathematical knowledge, or a “Chinese mathematics,” which could have been overshadowed by the Western mathematical culture over the last few decades. More curious about these values is that they are not necessarily being considered in the designing of international comparative assessments, such as the Programme for International Student Asessment (PISA) which in the end can be understood as a modern expression of Western colonialism (see Schubring, forthcoming). It is instructive to remind ourselves that in spite of this, the Chinese students still rank well in these assessments.

For these researchers, there is an agreement that values reflect teachers’ approaches. More than that, sharing their views with Hill et al. (2019), “when values were acknowledged in the mathematics classroom, relationships were strengthened, students’ cultural identities were affirmed, students became more engaged, and, ultimately, mathematics learning was enhanced.” In any case, the transference of values, as considered by Dede et al. (2021), or alternatively the alignment of values, are of importance and interest to be investigated.

Kalogeropoulos et al. (2021) understand values as a conative variable and develop a qualitative research on the interplay between values and decision making at school. In their research, they focus on teacher’s actions taken to align students and teachers’ values in an intervention context. The writing of Kalogeropoulos and Bishop (2017) provides the bases to identify a new alignment strategy in classroom negotiation. The identification of the Beacon strategy contributes as the preliminary evidence to expand contemporary theory regarding values alignment. To this end, the recognition that values alignment support and improve teaching and learning processes indicates the imbricate interdependence between students and teachers.

Issues to be considered in future research would be concerned with alignment strategies from the perspective of students to students or students to teachers. Regarding alignments focusing on students as agents, the anticipated strategies, or perhaps the unconscious tactics playing out in students-to-students and students-to-teacher interactions, may account for the imbalance in power relationships, permeating the entire process. On the other hand, standing from a dialectical view on students and teachers’ relationships, one may idealize that teachers’ values are shaping and are shaped by students’ values (see Seah, 2019), promoting long-term (and perhaps slow) transformations in schools systems.

The quantitative study developed by Hill et al. (2021) has at the core values alignment as shaped by students’ values. The authors urge transformations at school to reduce students' mathematics anxiety and disengagement in mathematics. The investigation involves Australian secondary school students and explores convergences and controversies between students’ well-being and values. They develop a framework of students’ well-being in mathematics education based on current models elaborated by positive psychology scholars. The well-organized and rigorous research report encompasses subtleties and controversies which deserve some comments.

Firstly, the authors propose student–teacher alignments between well-being and values through actions that are to be taken by the teacher. This is a subtlety in the process as a whole, given the shaping alignment direction (from student to teacher) and the agent who is expected to implement the strategy. Thus, if we are concerned with the values alignment strategies available to educators (Kalogeropoulos & Bishop, 2017), it appears we have a case of an intentional and planned-in-advanced refuge strategy style. Second, we may have a conflict between what the agent (the teacher) finds important in mathematics and in the mathematics classroom and the pedagogical norm of well-being alignment. This is not to say we should not consider students’ welfare. On the other hand, I finish my reading wondering if the positive psychology tenet which is to “feel good and function well” (Hill et al., 2021, p. 369) and a sort of conception of “no pain, no gain” upside down are proposed as the same thing. I mean, one might work hard or critically many times when entering into a learning process, and such instances might not be excluded from schools even if they are considered conflicting with students’ notions of “feeling good.”

Coincidently, a plenary panel debating whether positive affect and students’ performance in mathematics at school are related was presented at the 42nd annual meeting of the International Group for the Psychology of Mathematics Education (see Doreen et al., 2018). It appears that if the educational policy expectation in any national curriculum reform is to guarantee students’ performance while also fostering well-being, the paper that follows presents a case indicating this is not a straightforward relationship.

Pang and Seah’s (2021) conduct of the WIFI Study in Korea explores how a study of students’ values may provide an explanation for Korean students’ outstanding mathematics performance in international assessment exercises, in spite of their less-than-ideal attitude toward mathematics. The investigation draws on the conative construct of valuing (Seah, 2019). Mathematical values are considered as in Bishop (1988), while results from the WIFI study contextualize the mathematical educational values across different regions.

Among the five attributes about mathematics and mathematics pedagogy identified, there are the values of understanding and connections. These results indicate that in the Korean case, students’ relations with mathematical knowledge explain their high performance rather than any positive affect, attitude, or well-being variable, such as those suggested by positive psychology. According to Pang and Seah’s (2021) study, these results are interwoven with the external values associated with mathematics and the societal Confucian cultural traits.

Finally, a paper by Seah et al. (2021) focuses on modes of incorporating humaneness, or “persons” as agents, in the development of mathematics education. A prominent theme in the discussion is related to operationalizing values in the teaching and learning of mathematics. Some would conceive this as transference of values while others might interpret this in terms of values alignment. It might also be regarded more generally as “processes of valuing which teachers and students engage in” (Fan, 2021, p. 392). In fact, taking values as a conative variable—values for students’ engagement and values for teachers’ decision making, speaking about alignment of values seems more appropriate than speaking about transfer of values. The second theme emerging in the debate directs our attention to the role of writers in transmitting or aligning values related to mathematics and mathematics education. To these agents, the authors propose exploring their role as mentors. We may include moviemakers among these mentors. In this manner, both writers and moviemakers are important agents for the popularization of mathematics and science in general. They promote perspectives on the mathematical experience, with values embedded, and which often resonate with students’ out-of-school experiences when valuing in formal institutions.

Concluding remarks

Here, we reach the end of the selection of papers. From the immersion in these research reports, other aspects than those highlighted at the beginning are underlying the reports in this Special Issue. They emerge as convergences, explicit or implicit in the researchers’ discourse. In fact, all authors are interested in improving teaching and learning at schools and share the recognition of the importance of students’ relations with science, technology, and society. Equity and the multiplicity of cultures must be taken into account. Values and valuing are seen as enhancing pedagogical actions. Pioneering this debate in mathematics education, Bishop’s perspectives on mathematical culture and values emerge as natural to be adopted. The review of the literature throughout the papers includes, in each research presentation, specific theoretical constructs. Thus, the entire collection of papers contributes with results that move forward the theoretical network in use. As mentioned before, this is done by means of examples where we sense that the collective of authors are effectively foregrounding the human beings as agents of learning and change, in their efforts to incorporate humaneness in the production and in the teaching and learning of mathematics.

Finally, the authors' analyses in each research reported in the papers show the appropriations of the theory as well as consistent ways in which theoretical tools and methodologies are used. I finish reading, eagerly looking forward already for a next Special Issue on the same theme.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

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(2016). What primary students in the Chinese Mainland, Hong Kong and Taiwan value in mathematics learning: A comparative analysis. International Journal of Science and Mathematics Education, 14(5), 907–924.

Values and Valuing Across Cultures and Time Zones

Abstract

Keywords

Highlights

Introduction

Theoretical approaches

Researching values and valuing

Controversies, convergences, and singularities

Concluding remarks

Footnotes

Declaration of conflicting interests

Funding

References