From Professing to Doing: Mathematical Values Practices of Mathematics Teachers

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From Professing to Doing: Mathematical Values Practices of Mathematics Teachers

https://doi.org/10.21203/rs.3.rs-4893772/v1

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There is a widespread belief that mathematics is the most value-free of all school subjects among stakeholders in mathematics education, especially teachers. However, some mathematics educators and researchers are convinced that mathematics is culture-embedded and, therefore, value-driven. This present study aimed at exploring senior high school (SHS) mathematics teachers’ teaching practices of mathematical values in a municipality in Ghana. In the quest to achieve the purpose of this study, we employed explanatory sequential mixed methods. In the quantitative study, a census was employed to include all 53 SHS mathematics teachers within the Tano South Municipality. For the qualitative phase, purposive sampling was used to select six SHS mathematics teachers recruited to complete the questionnaires in the quantitative phase to participate in interviews. The quantitative data were analyzed using both descriptive statistics (percentage, frequency, mean, and standard deviations) and inferential statistics (one-way between-groups analysis of variance [ANOVA]). The qualitative data also was analyzed using a thematic analysis. From the study’s findings, it was concluded that SHS mathematics teachers often practiced the mathematical values of objectism, control, progress, and openness. In contrast, other mathematical values, such as rationalism and mystery, were sometimes practiced. The mathematical values teaching practice among SHS mathematics teachers who teach at Basic 10, 11, and 12 were statistically significantly different. It is, therefore, recommended, among others, that teacher education institutions review their mathematics programs to promote values and valuing in mathematics education among pre-service mathematics teachers.

mathematical values

values in mathematics education

values teaching

mathematics teachers

sequential explanatory mixed methods

The Ghanaian SHS students' mathematics performance in the West Africa Examination Council (WAEC) has persistently been below expectations. The Education Sector Performance report in 2018 showed a decrease in the percentage of pupils who obtained grades A1-C6 in core mathematics in the West African Secondary School Certificate Examination (WASSCE) between 2013 and 2015 (36.6–25%). Notwithstanding, there was an increase in proportion between 2016 and 2017, moving from 32.8–42.2%, respectively (Ministry of Education [MoE], 2018). Zeroing on regional performance, Brong Ahafo region recorded the “highest percentage of WASSCE students obtaining between grades A1 to C6 in core subjects with over 60% of students obtaining A1 to C6 in WASSCE” (MoE, 2018, p. 33). However, there was a decrease in students’ performance in the year 2018 to 38% (MoE, 2019). These indicate that students in SHSs in Ghana are not performing well in mathematics as expected.

The implications are that over the past years, many SHS graduates could not satisfy the minimum criteria for proficiency in mathematics to gain admission into tertiary education. This adversely affects Ghana's human development and economic fortunes as a nation. In light of this, researchers, government, and other mathematics education stakeholders have tried first to understand the problem, and possibly proffer solutions. In response to poor performance, the Ministry of Education has implemented programs and policies to enhance students' performance and support mathematics teachers in effective instructional delivery. The government, for instance, has introduced a free SHS policy for students and the license and comprehensive professional development programs for teachers to enhance the caliber of teachers and enhance students' academic achievements. Notwithstanding all these endeavors, students' proficiency in mathematics has not met the anticipated standards (WAEC, 2020, 2021, 2022).

Bishop (1988) asserted that the emphasis on knowledge acquisition at the detriment of values in mathematics teaching and learning constitutes the core issue we encounter as an education system in mathematics education. This assertion truly reflects the Ghanaian situation in mathematics education today. According to Davis and Abass (2023), much of the focus as a country has been on research on the effectiveness of pedagogies and professional development programs, with little attention on values in teaching and learning of mathematics. The reason could be that many mathematics teachers and educators do not appreciate the significance of values in mathematics teaching and learning (Bishop & Clarkson, 1998).

Values are thought to control the alignment of a teacher's emotional and cognitive attitudes toward the teaching aspects of mathematics. Seah (2018) states that values provide students and instructors with the determination and perseverance to sustain a mindset of "I want to" throughout the process of studying and teaching mathematics. Bishop (2008a) categorizes values into three types: General educational, mathematics educational, mathematical values. The general educational values are linked to the standards of a specific society and educational establishment (Bishop, 2008a). These values are not directly correlated with the understanding and teaching of mathematics. The mathematics educational values refer to the values integrated into the curriculum, textbooks, and classroom practices. These values are also influenced by other values (Bishop, 2008a). The principles encompassed in mathematics courses are typically instilled and reinforced by teachers, textbooks, homework assignments, and problem-solving activities. Mathematical values are values that have evolved alongside the advancement of mathematical knowledge in Western societies (Bishop, 2008a). The development of mathematical values is derived from the cultural context in which mathematicians and mathematics educators shape the discipline of mathematics. When a teacher presents and examines a mathematical problem, such as "describe and compare two distinct proofs of the sum of interior angles of a regular polygon," they communicate the mathematical principles of rationalism and openness.

Over the past few decades, researchers in mathematics education have begun to appreciate that what teachers and students value in mathematics teaching and learning influences the quality of instructional delivery and mathematics achievement by students (Kyeremeh & Dorwu, 2023). The current advancements in mathematics and culture have intensified the attention on the question of values in mathematics education (Kyeremeh & Dorwu, 2023). Values are integral to culture, defining who we are as people. Thus, peoples’ culture reflects something of their values either consciously or unconsciously. Mathematics is a discipline influenced by human culture and subject to personal opinions, ideas, and values. Individuals' experiences with mathematics education often shape these personal perspectives during their school years. Understanding the mathematical values that SHS mathematics teachers advocate, and how these are explicitly engaged in the classroom is considered to be very vital for more conscious values development through mathematics education. This is because we convey values as teachers to the next generations through the learning and teaching process consciously or unconsciously (FitzSimons et al., 2001).

Despite this growing interest, values are rarely discussed when it comes to teaching of mathematics. There appears to be little research (e.g., Aktas et al., 2019; Bishop, 2008a; David & Abass, 2023; Kyeremeh & Dorwu, 2023) about mathematics teachers’ awareness of their own values, the values they teach, and how these values are enacted in the classroom. From the literature, there is a dearth of empirical research (David & Abass, 2023; Kyeremeh & Dorwu, 2023) in the Ghanaian context investigating values espoused by mathematics teachers. Also, these few mentioned studies do not investigate how teachers engage the values they advocate in the classroom. To fill this gap, this study examines high school teachers’ mathematical values, and how these are engaged in teaching in the classroom.

In the face of the dearth of research in this field, this study brings to light the mathematical values that SHS mathematics teachers espouse, how these values are engaged in the classroom, and whether these values are in line with those enshrined in the high school mathematics curriculum. The knowledge of mathematical values SHS mathematics teachers espouse and enact in the classroom would help identify those values that could be detrimental to mathematics teaching as suggested by the curriculum. We believe that the quality of mathematics teaching at the SHS level could be enhanced by acquiring a deeper understanding of this phenomenon. This study highlights the key values mathematics teachers at the SHS in Ghana prioritize in mathematics education and how these values are engaged in teaching. It also encourages discussions among mathematics education stakeholders on how to assist teachers in meeting the value needs of their students through instructional decisions. Moreover, it is important to acknowledge that not all values that are always transferred in learning environments are positive. In this context, there is a great need for studies such as this to shed light on the nature of mathematical values SHS mathematics teachers advocate and enact in the classrooms. Given this, this current study sought to answer the following research questions:

To what extent do senior high school mathematics teachers engage mathematical values in teaching mathematics in the classroom in Tano South Municipality?

Does statistically significant disparity exist in the mathematical values teaching practices among SHS mathematics teachers across grade levels?

Teachers’ Practices of Values in Mathematics Education

Values demonstrated by instructors in mathematics classrooms are connected to their pedagogical identities (Chin et al., 2001). Seah and Bishop (2001) define teachers' values as their understanding and perception of emotional factors, such as beliefs and attitudes, and the subsequent integration of these values into their personal emotional and cognitive systems. Values play a critical role in the affective contexts of mathematics classrooms, significantly impacting students' decisions to either participate or abstain from engaging with mathematics and science. The impact and course of this impact will be determined by the teachers' understanding of the values associated with the specific subject, the values conveyed through their choice of teaching methods, and their awareness of whether they are imposing their own personal values (Bishop, 2008a). Bishop (2002) observed that any instruction on values that occurs during mathematics classes is implicit rather than explicit.

Abdullah and Leung (2019) conducted a case study in Brunei Darussalam to examine the values and valuing of instructors in mathematics teaching. During their debate on instructional tactics, the teachers agreed to utilize tangible resources, as well as visual aids such as images or diagrams, to communicate the lesson. The agreed-upon concrete materials were colored folding sheets used as bar models and pizza models. The decision of teachers to utilize actual materials or visual aids such as images and diagrams indicates their appreciation for objectism in the instruction of fractions. Teachers implemented their desired ideals in teaching by setting class goals and requesting pupils to recite them prior to the lesson’s commencement. These educators consistently review the learning objective and engage in conversations about the criteria for achieving success. The teachers' actions demonstrate their appreciation for transparency, as they openly communicate the lesson's objective to the pupils at the beginning of the course. This study examined the value indicators of teachers, shedding light on the factors that influence their preferences. For example, certain teachers experienced a conflict between prioritizing rationalism and prioritizing objectism in order to encourage their students to express their mathematical reasoning.

Aktas et al. (2019) examined the fundamental principles impacting teachers' ability to observe and make decisions during critical moments of a class. The underlying principles of noticing that the instructor values were categorized into three groups: advanced mathematical process, democracy, and achievement. These values are shaped by the educational and assessment system in Turkey and mirror the norms and values of the classroom and school environment. Teachers' problem-solving strategies encompass using precise and consistent methods to solve problems and faithfully following the lesson plan they have established. This also involves effectively managing and supervising the classroom. Here is an example of a dialogue that illustrates the concept of control in a different dimension. Mathematical reasoning is essential for humans to communicate and connect ideas in learning mathematics and applying it in everyday situations. The lesson plans created by teachers to enhance students' abilities to reason, articulate and defend their beliefs, analyze experiential facts and make predictions all contribute to the development of reasoning skills. The conditions indicated, classified as rationalism by Bishop (2008b), have been identified as mathematical reasoning in the outcomes of this study.

Aktas (2023) conducted a case study to examine and compare the ways to align values that two primary mathematics teachers choose in face-to-face and remote education settings. The data gathered from video recordings of two basic mathematics teachers were subjected to content analysis. The analysis revealed that the participants employed various methods to align their values. These tactics included focusing, reprioritizing, equilibrium, redefining, signaling, and ignoring. Traditional in-person teaching frequently uses a pedagogical approach considering students' principles, such as the equilibrium strategy. Nevertheless, within the realm of distant education, certain ways have surfaced in which the teacher's ideals hold sway, one of which is known as the beacon strategy. Skilled educators employ a range of choices to direct fruitful classroom activities. These activities encompass but are not restricted to commencing or concluding talks, constructing discussions, acknowledging the contributions of quiet students, engaging all participants in discussions, inspiring students to contribute fresh topics into debates, and fostering diverse perspectives (Giberti et al., 2022). These teacher judgments can be classified as markers of mathematical values in mathematics instruction.

Clarkson et al. (2000) examined the specific values that mathematics teachers teach in the mathematics classroom. They engaged in a process with mathematics teachers that included a preliminary interview, a classroom observation, and a post-observation debriefing interview, all of which took place on the same day. The teaching practices of mathematics teachers encompass contemplation, strategic thinking, openness, precision, clarity, proofs, reasoning, and justification. It is crucial to acknowledge that while teachers may meticulously arrange for the values they will officially teach, there are more values that they impart indirectly. Given this literature review on mathematics teachers’ values practices in mathematics education, it is obvious that there is limited literature in this area of values research. What is even more limited in terms of research is the studies on mathematical values practices among mathematics teachers. This study, therefore, fills this gap in the literature.

Theoretical Framework

In this study, we used Bishop's (1988) six-values cluster model of mathematical values, which was established through a review of texts on the actions of mathematicians in Western history and culture. This model organizes six value clusters into three pairs complementary to each other and associated with the three aspects of ideology, sentiment/attitude, and sociology. Bishop has described them as complementary pairs, where rationalism and objectism are the twin ideologies of mathematics. These ideological values highlight the epistemology of the knowledge of mathematics. Rationalism emphasizes argument, reasoning, logical analysis, and explanations, arguably the most relevant value in mathematics education whereas objectism emphasizes objectifying, concretizing, symbolizing, and applying the ideas of mathematics (Bishop, 2008a).

The attitudinal values which drive mathematical development involves control and progress. These values portray individuals relate to the knowledge of mathematics. Control emphasizes the power of mathematical knowledge through the mastery of rules, facts, procedures and established criteria, whereas progress emphasizes the ways that mathematical ideas grow and develop, through alternative theories, development of new methods and the questioning of existing ideas (Bishop, 2008a). Sociologically, the values of openness and mystery are “those related to potential ownership of or distance from mathematical knowledge and the relationship between the people who generate that knowledge and others” (Bishop, 1988, p.82). Openness emphasizes the democratization of knowledge, through demonstrations, proofs and individual explanations, whereas mystery emphasizes the wonder, fascination, and mystique of mathematical ideas (Bishop, 2008a).

Research Design

I utilized explanatory sequential mixed approaches to accomplish this study's objective. By employing this design, we could follow up on the quantitative results obtained through close-ended questionnaires and explore the results in more depth through interviews (Creswell & Creswell, 2018).

Selection of Participants

In the quantitative study, a census was employed to include all 53 SHS mathematics teachers within a municipality in the Ahafo Region of Ghana. An effort was made to involve all 53 SHS mathematics teachers in the quantitative study due to the relatively small population of mathematics teachers. Among these SHS mathematics teachers, 48 offered to participate in the quantitative study by responding to the questionnaire. We employed purposive sampling by selecting six SHS mathematics teachers recruited to complete the questionnaires in the quantitative phase to participate in interviews. The decision to use six participants is based on Constantinou et al. (2017) findings that data saturation can be reached with five interviews in a qualitative study.

Instruments

In this current study, we employed questionnaires and interviews to gather the quantitative and qualitative data, respectively. The questionnaire for the quantitative phase, which has 18 four-point Likert-type scale (Never, Sometimes, Often, and Always) items, examined the extent to which mathematics teachers engage mathematical values in teaching mathematics in the classroom. These items were self-constructed based on the literature of Bishop (2008a) and Bishop (2008b). We employed semi-structured interviews in the qualitative phase to explain the key findings on how mathematics teachers engage mathematical values in teaching from the quantitative phase. The semi-structured interview guide was designed based on the findings obtained from the quantitative study questionnaire. The interview protocol consisted of four items.

Ensuring Validity and Reliability

In ensuring quality measures for data-gathering methods in the quantitative phase of the study, validity and reliability were established. In order to determine the face and content validity of the questionnaire, we presented the preliminary version of the questionnaire to one expert in the field of study to provide their expert assessment regarding the correctness and suitability of the instrument and its items and their relevance to the study purpose. Based on experts' comments, some of the items, such as Encourage your students to argue in classes (item 3), and Emphasize the checking of right answers (item 7), were revised as Encourage your students to argue seriously with each other in your classes (item 3), and Emphasize the checking of right answers, and the reasons for other answers not being 'right' (item 7), respectively.

In order to ensure the reliability of the questionnaire, a pilot test was conducted among 20 SHS mathematics teachers from a different municipality in the Ahafo Region of Ghana using the questionnaire. This sample is believed to possess characteristics similar to those of the population regarding available resources, conditions of service, and competencies. In the context of this study, we conducted internal consistency reliability on the data from the pilot test to measure the extent to which the items clustered initially within the questionnaire. The study assessed the internal consistency of the questionnaire by computing the Cronbach Alpha coefficient. This test showed high internal consistency, with a Cronbach’s Alpha reliability coefficient of 0.71, suggesting the instrument's acceptability (Tayakol & Dennick, 2011).

Trustworthiness of the Qualitative Study

In order to establish the credibility of the current study, the data collection process was extended over five months, which enabled us to have casual interactions with the participants. The field notes accurately documented the events and details of the interview. To ensure the dependability and confirmability of the study, we kept audit trail of the process logs and engaged in debriefing with a colleague. To transferability, we presented a comprehensive and detailed account of the findings, allowing readers to independently determine the applicability of the study results to their own research situations.

Data Collection Procedure

In gathering data for the quantitative phase of the study, we applied to the Humanities and Social Sciences Research Ethics Committee of Kwame Nkrumah University of Science and Technology for ethical approval. Once permission was granted by the Ethics Committee, we wrote a letter with the attachment of ethics approval to the Municipal Directorate of Ghana Education Service for permission to conduct the study in the public SHSs within the Municipality. The obtained ethics and the Directorate’s approval letters were used to seek permission from Headmasters of public SHSs in the Municipality to carry out the study. We invited the sampled teachers to familiarize them with the study and discuss any potential apprehension they may have. Each participant who volunteered to participate was given an informed consent form to read and sign. Afterwards, a discussion was initiated, and agreement was reached concerning the date for administering the close-ended questionnaire. One volunteer from each of the three SHSs was engaged to assist in distributing the questionnaire and their retrieval. The questionnaires distributed to participants were collected the same day after their completion. The close-ended questionnaire for the quantitative phase was administered over four weeks.

In the qualitative study phase, data was collected fortnight after the quantitative survey through face-to-face interviews. First, a visit was conducted to obtain the agreement of potential participants and familiarize them with the study through direct interaction. We provided the interviewers with the option to choose the location where they would feel at ease and secure throughout the interview. We documented the data using field notes, brief written notes, and written summaries of interviews. Participant interviews lasted approximately 45 minutes.

Data Analysis

Data from the questionnaire were analyzed using both descriptive statistics (percentage, frequency, mean, and standard deviations) and inferential statistics (one-way between-groups analysis of variance [ANOVA]). These analyses were done using SPSS version 23. In the case of research question 1, percentage, frequency, mean, and standard deviations were performed to provide descriptive statistics of SHS mathematics teachers’ mathematical values teaching practices. The weighted mean was used to determine the extent of mathematical values teaching practices among senior high school mathematics teachers. In this direction, we employed the weighted mean interpretation proposed by Valdez et al. (2020). The authors described the mean range value of 1.0–1.50, 1.51–2.50, 2.51–3.50, and 3.51–4.50 as Never, Sometimes, Often, and Always, respectively. On research question 2, one-way between-groups ANOVA was performed to test whether a statistically significant disparity exists in the mathematical values teaching practices among SHS mathematics teachers across the three grade levels. One-way between-groups ANOVA was considered appropriate as it enabled me to observe whether a difference exists in the continuous dependent variable (mathematical values teaching practices scores) for the categorical independent variable (three grade levels).

The qualitative data collected from the interviews was analyzed using a thematic analysis. We began by reading the transcripts thoroughly to familiarize myself with the data and understand the patterns (Braun & Clarke, 2021). The coding step commenced after my thorough reading and familiarization with the data. We then created a comprehensive profile for every participant and organized them into categories based on their grade levels. The identified codes were compared with the data extracts that exhibited the codes. We initiated the process of examining the data for recurring patterns or topics. The subsequent stage of the analytical process involved establishing and designation the themes, which commenced when we formulated the topics for ultimate enhancement. In order to accomplish this, we reviewed the compiled data for each theme and systematically arranged the themes to ensure internal coherence with the participants' narratives and study goals. The final phase of writing the study report commenced after we formulated thoroughly elaborated themes.

To what extent do senior high school mathematics teachers engage mathematical values in teaching mathematics in the classroom?

In answering this research question, we employed descriptive statistics to calculate the frequencies, percentages, mean, and standard deviation scores for each response obtained from the questionnaire items. Table 1 details the results as follows:

Table 1

Descriptive statistics on the mathematical values teaching practices among senior high school mathematics teachers
Items	N	S	O	A	M	SD
	f (%)	f (%)	f (%)	f (%)
1. Rationalism
2. 1. “Emphasise the role of proving in mathematics”	13 (27)	19 (40)	13 (27)	3 (6)	2.13	.89
3. 2. “Have structured debates in class”	19 (40)	16 (33)	8 (17)	5 (10)	1.98	1.00
4. 3. “Encourage your students to argue seriously with each other in your classes”	24 (50)	15 (31)	6 (13)	3 (6)	1.75	.91
5. Average Mean					1.95
6. Objectism
7. 4. “Use diagrams to illustrate mathematical relationships”	1 (2)	8 (17)	25 (52)	14(29)	3.08	.74
8. 5. “Encourage your students to invent their own symbols and terminology before showing them the 'official' ones”	18 (38)	23 (48)	3 (6)	4 (8)	1.85	.88
9. 6. “Use concrete materials (e.g. physical models) to demonstrate mathematical relationships”	5 (10)	13 (27)	22 (46)	8 (17)	2.69	.88
10. Average Mean					2.54
11. Control
12. 7. “Emphasise the checking of right answers, and the reasons for other answers not being 'right'”	9 (19)	13 (27)	10 (21)	16(33)	2.69	1.13
13. 8. “Encourage the analysis and understanding of why routine calculations and algorithms 'work'”	6 (13)	18 (38)	16 (33)	8 (17)	2.54	.92
14. 9. “Show examples of how the mathematical ideas you are teaching are used in the real world”	3 (6)	13 (27)	18 (38)	14(29)	2.90	.91
15. Average Mean					2.71
Progress
10. “Encourage alternative, and non-routine, solution strategies together with their reasons”	7 (15)	14 (29)	17 (35)	10(21)	2.63	.98
11. “Encourage students to extend and generalise ideas from particular examples”	2 (4)	14 (29)	18 (38)	14(29)	2.92	.87
16. 12. “Give the students stories and examples of recent mathematical developments”	7 (15)	8 (17)	24 (50)	9 (19)	2.73	.94
17. Average Mean					2.76
Openness
13. “Encourage your students to defend and justify their answers and methods publicly to the class”	3 (6)	16 (33)	12 (25)	17(35)	2.90	.97
18. 14. “Students create posters to display their ideas to the others”	16 (33)	21 (44)	8 (17)	3 (6)	1.96	.87
19. 15. “Demonstrate how mathematical ideas can be shown to be true”	6 (13)	14 (29)	15 (31)	13(27)	2.73	1.01
20. Average Mean					2.53
21. Mystery
22. 16. “Stimulate your students’ mathematical imagination with pictures, artworks, etc.”	6 (13)	21 (44)	11 (23)	10(21)	2.52	.97
23. 17. "Use mathematical puzzles in class”	14 (29)	19 (40)	11 (23)	4 (8)	2.10	.93
24. 18. “Tell students stories about mathematical discoveries”	12 (25)	12 (25)	17 (34)	7 (15)	2.40	1.03
25. Average Mean					2.34
Source: Field data (2023)Key: f–Frequency, N–Never, S–Sometimes, O–Often, A–Always, M–Mean, SD–Standard Deviation

From Table 1, the six mathematical values, Rationalism, Objectism, Control, Progress, Openness, and Mystery, yielded average mean values of 1.95, 2.54, 2.71, 2.76, 2.53, and 2.34, respectively. This suggests that SHS mathematics teachers, to some extent, engage in mathematical values teaching in the classroom in Tano South Municipality. Among the mathematical values practiced in the classroom by SHS mathematics teachers, the values of Objectism, Control, Progress, and Openness were often practiced. Thus, the SHS mathematics teachers moderately practiced these mathematical values. The two remaining mathematical values, Rationalism and Mystery, were sometimes practiced in the classroom by SHS mathematics teachers. This suggests that SHS mathematics teachers slightly practiced the value of Rationalism and Mystery in the classroom.

Does statistically significant disparity exist in the mathematical values teaching practices among SHS mathematics teachers across grade levels?

Before employing a one-way between-groups ANOVA for the data analysis, the initial assessment of the assumptions of normality, outliers, and homogeneity of variance was conducted, and no major violations were detected. In testing the homogeneity of variance, for example, Levene’s test was significant, as shown in Table 2.

Table 2

Test of homogeneity of variances of teachers' mathematical value practices
Levene Statistic	df1	df2	Sig.
.565	2	45	.572

From Table 2, the p-value (.57) of Levene’s test was far greater than the value of .05. This suggests that I have not violated the homogeneity of variance assumption.

A one-way between-groups ANOVA was conducted to investigate whether a statistically significant difference exists in the mathematical values teaching practices among SHS mathematics teachers across class levels. Participants were divided into three groups according to the class level they teach (Group 1: Basic 10; Group 2: Basic 11; Group 3: Basic 12). Table 3 presents the results.

Table 3

ANOVA of Teachers' mathematical value practices
	Sum of Squares	Df	Mean Square	F	Sig.
Between Groups	571.515	2	285.757	7.175	.002
Within Groups	1792.152	45	39.826
Total	2363.667	47

As evident in Table 3, there was a statistically significant difference at the p < .05 level in the mathematical values teaching practices scores for the three groups: F (2, 45) = 7.2, p = .00. The actual difference in mean scores between the groups was found to be large. The effect size, calculated using eta squared, was .24 (Cohen, 1988).

Having found a significant difference in the overall ANOVA, post-hoc tests were run to determine where the differences occurred. The result is presented in Table 4.

Table 4

Multiple comparisons of teachers’ mathematical value practices
(I) At what level do you teach?	(J) At what level do you teach?	Mean Difference (I-J)	Std. Error	Sig.	95% Confidence Interval
(I) At what level do you teach?	(J) At what level do you teach?	Mean Difference (I-J)	Std. Error	Sig.	Lower Bound	Upper Bound
Basic 10	Basic 11	− .190	2.134	.996	-5.36	4.98
Basic 10	Basic 12	7.665	2.325	.005	2.03	13.30
Basic 11	Basic 10	.190	2.134	.996	-4.98	5.36
Basic 11	Basic 12	7.855	2.297	.004	2.29	13.42
Basic 12	Basic 10	-7.665	2.325	.005	-13.30	-2.03
Basic 12	Basic 11	-7.855	2.297	.004	-13.42	-2.29
Note: Dependent Variable: Teachers' mathematical value practices

From Table 4, the post-hoc comparisons using the Tukey HSD test indicated that the mean score for Group 1 (M = 46.59, SD = 7.69) was significantly different from Group 3 (M = 38.92, SD = 5.16), p = 00. This means that SHS mathematics teachers who teach at Basic 10 and Basic 12 differed significantly in the mathematical values teaching practice scores. Also, Group 2 (M = 46.78, SD = 5.57) significantly differed from Group 3 Group 3 (M = 38.92, SD = 5.16), p = 00. This indicates that SHS mathematics teachers who teach at Basic 11 and Basic 12 differed significantly in the mathematical values teaching practice scores. Conversely, Group 1 (M = 46.59, SD = 7.69) did not differ significantly from Group 2 (M = 46.78, SD = 5.57), p = .99. This means that SHS mathematics teachers who teach at Basic 10 and Basic 11 did not differ significantly in the mathematical values teaching practice scores.

A follow-up on the extent to which SHS mathematics teachers engage mathematical values in teaching mathematics was conducted through interviews in the qualitative phase of the study. In the interview, I explored SHS mathematics teachers’ views on how they develop these mathematical values in the classroom and how often. The participants' accounts revealed that SHS mathematics teachers sometimes encourage using different strategies/methods in finding solutions to mathematical problems. This is captured in the excerpt, “If I want to prove to students that a problem can be solved in different ways, what I sometimes do in teaching is that, I sometimes use different approaches in solving some problems in class” (MT1–2/11/2023).

Another SHS mathematics teacher remarked, “In my class, for example, when it comes to solving certain [mathematical] problems, I at times show them the various methods in solving that particular problem” (MT3–3/11/2023).

The quotes above reflect the valuing of Progress. This suggests that SHS mathematics teachers sometimes encourage the value of Progress in their mathematics teaching.

The interviews also revealed that SHS mathematics teachers always emphasize the use of rules and formulas in their mathematics teaching. MT5 recounted that:

As for me, in teaching how to use formulas to solve problems, for example, I state the formula on the chalkboard and take them through the steps. After this, I give similar work for them to use the formula to solve. This is done in all my lessons (MT5–12/11/2023).

MT6 added, “…since mathematics is all about the application of rules and formulas, teachers can state the formula and guide students to use the formula to solve problems, and that is exactly what I always do” (MT6–20/11/2023).

The aforementioned quotes reflect the valuing of Control. This suggests that SHS mathematics teachers always encourage mastery in using rules and formulas in their mathematics teaching.

Contrary to the mathematical values teaching practices, SHS mathematics teachers disclosed that they sometimes encourage group work among students. In the interview, MT4 stated, “To develop collaboration among my students, at times I give them group work to do” (MT4–7/11/2023).

Another SHS mathematics teacher also remarked, “If you look at the current curriculum, we are supposed to do group work. So, sometimes, I give students work to do in groups as and when it is necessary” (MT6–20/11/2023).

The two quotes above reflect mathematics educational value practices. This suggests that SHS mathematics teachers sometimes encourage mathematics educational value in their mathematics teaching.

This present study aimed at exploring senior high school (SHS) mathematics teachers’ teaching practices of mathematical values in a municipality in Ghana. From the study’s findings, it was revealed that SHS mathematics teachers often practiced the mathematical values of objectism, control, progress, and openness. In contrast, other mathematical values, such as rationalism and mystery, were sometimes practiced. These study’s findings corroborate previous studies (Abdullah & Leung, 2019). In Abdullah and Leung’s (2019) study, for example, teachers utilized concrete materials, as well as visual aids such as images or diagrams, to communicate the lesson. The decision of teachers to utilize actual materials or visual aids such as images and diagrams indicates their appreciation for objectism in the instruction of fractions. They reported that certain teachers experienced a conflict between prioritizing rationalism and prioritizing objectism in order to encourage their students to express their mathematical reasoning.

The study found a statistically significant difference in the mathematical values teaching practice scores for SHS mathematics teachers who teach at Basic 10, 11, and 12. Generally, this suggests that SHS mathematics teachers' mathematical value practices in mathematics teaching change as they move across class levels. Among the groups, SHS mathematics teachers teaching at Basic 10 and Basic 12 differed significantly in the teaching practices of mathematical values and among those teaching at Basic 11 and 12. These findings are not quite surprising. In their value practice of Control, SHS mathematics teachers reported that they always encouraged mastery in using rules and formulas in their mathematics teaching. The difference in SHS mathematics teachers’ mathematical values teaching practices as they teach from one class level to another could be attributed to the demands of examination at each particular class level. Students’ academic journey at SHS requires preparing themselves for the summative assessment (WASSCE) organized by WAEC to propel them for admission into tertiary programs. Teachers at this time may want to shift their value focus to emphasizing the power of mathematical knowledge through the mastery of rules, facts, and procedures, which reflects valuing control.

These values are considered to be the fundamental principles driving the advancement of mathematics. As such, they are the essential values that support the growth of mathematical reasoning in the classroom. To effectively address the educational challenges in mathematics, it is crucial for us, as stakeholders in mathematics education, to prioritize research efforts towards exploring strategies for cultivating these values in our teachers. By doing so, we can empower them to instill these values in their students, leading to significant progress in our educational system. The classroom serves as the appropriate setting for the advancements of values and valuing, as within this environment, the community of practice substantially impacts shaping the ideals associated with Mathematical thinking. Policy developments should be formulated to establish new practices rather than to regulate and define them. This values research indicates that introducing new theoretical concepts can assist in shaping teachers' thoughts and actions and provide them with a means to articulate their methods but does not exert direct control over them.

From the study’s findings, it can be concluded that SHS mathematics teachers often practiced the mathematical values of objectism, control, progress, and openness. In contrast, other mathematical values, such as rationalism and mystery, were sometimes practiced. In the value practice of control, SHS mathematics teachers always encouraged mastery in using rules and formulas in their mathematics teaching. The mathematical values teaching practice among SHS mathematics teachers who teach at Basic 10, 11, and 12 was statistically significantly different. Generally, this means that SHS mathematics teachers' mathematical value practices in mathematics teaching change as they move across class levels. For example, among the groups, SHS mathematics teachers teaching at Basic 10 and Basic 12 differed significantly in the teaching practices of mathematical values and among those teaching at Basic 11 and 12.

Although this study was conducted among SHS mathematics teachers in one municipality in Ghana, it could broadly impact mathematics education in terms of teaching mathematical values across the country and beyond. Apart from this study contributing to knowledge in the sociocultural discourse in mathematics education, it also generated useful information that could be used to develop professional development programs for improving mathematics education through mathematical values teaching. The study is about the mathematical values teaching experiences of SHS mathematics teachers, so the implications have been gleaned from these experiences.

Ethical Statement

This study received approval from the Humanities and Social Sciences Research Ethics Committee for using human subjects with approval number: HuSSREC/AP/105/VOL.1.

Conflict of Interest Statement

On behalf of all authors, the corresponding author states that there is no conflict of interest.

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The authors declare no competing interests.

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From Professing to Doing: Mathematical Values Practices of Mathematics Teachers

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Abstract

Introduction

Teachers’ Practices of Values in Mathematics Education

Theoretical Framework

Methodology

Research Design

Selection of Participants

Instruments

Ensuring Validity and Reliability

Trustworthiness of the Qualitative Study

Data Collection Procedure

Data Analysis

Results/Findings

Discussion

Conclusions

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Ethical Statement

Conflict of Interest Statement

References

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