181

 Research Article

2020 38(1): 181-196 http://dx.doi.org/10.18820/2519593X/pie.v38i1.13

The values learners 
consider as imporTanT 
in The learning 
of maThemaTics

absTracT

Learners have different values that could affect their learning and 
eventually their performance in mathematics. However, many 
teachers are unaware of these values. Therefore, this paper 
reports on a study that established the values learners consider 
as important in the learning of mathematics. The participants 
were 274 Grade 9 learners, selected purposively from one school 
in Gauteng, South Africa. An exploratory quantitative research 
method was adopted and data were collected with a standardised 
questionnaire developed by Seah (2011b). The results revealed that 
learners value 1) Hard work and effort when doing mathematics; 2) 
Numerous different methods to obtain the answer to a mathematics 
problem; 3) Authentic examples of shapes to understand their 
properties; 4) Demonstration and explanation of mathematics 
concepts and proofs; and 5) Teaching and explaining mathematical 
concepts. This paper highlights the values teachers should 
consider in the teaching and learning of mathematics in order to 
ensure better learner performance in mathematics. Furthermore, 
the paper adds to research on values in Mathematics Education 
within a South African context.

Keywords: learners; values; mathematics; learning

1. inTroducTion
Worldwide there is a concern about the poor performance 
in mathematics at school level (Jerrim, 2015; Spaull, 2013). 
In particular, Simkins (2013), Spaull (2013) and Taylor (2011) 
claim that the performance in mathematics of the average 
South African Grade 9 mathematics learner is two years 
behind that of the average Grade 8 learner from other 
comparable middle-income countries, such as Botswana 
and Honduras. From 2012 to 2014 the average mathematics 
marks of Grade 9 learners have fluctuated between 11% 
and 13%, which besides being low, implies that schools 
are not producing the expected results (Department of 
Basic Education, 2014). Some of the reasons for poor 
performance include learners’ poor work ethic, lack of 
motivation from teachers and non-completion of the 
syllabus within specified timeframes (Makgato & Mji, 2006; 
Schollar, 2015). Peng and Nyroos (2012) add that another 

auThors:
Mrs Tendai Madosi1 

Dr Erica Dorethea  
Spangenberg1 

Dr Viren Ramdhany1 

affiliaTion: 
1University of Johannesburg

DOI: http://dx.doi.
org/10.18820/2519593X/pie.
v38i1.13

e-ISSN 2519-593X

Perspectives in Education 

2020 38(1): 181-196

published:
11 June 2020

Published by the UFS
http://journals.ufs.ac.za/index.php/pie

© Creative Commons  

With Attribution (CC-BY)

http://dx.doi.org/10.18820/2519593X/pie.v38i1.13
https://orcid.org/0000-0003-3073-9239
https://orcid.org/0000-0003-0828-1196
http://dx.doi.org/10.18820/2519593X/pie.v38i1.13
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factor that may potentially impact on the performance in mathematics is many teachers’ 
unawareness of learners’ values in mathematics. Seah, Andersson, Bishop and Clarkson 
(2016) consider values in mathematics as fundamental in facilitating effective learning and, as 
such, teachers should know what values are important for their students.

According to Seah et al. (2016:14), if learners’ values are developed by “whatever sorts 
of beliefs, attitudes and interests they possess, [teachers] should be able to better facilitate 
a more positive and productive view of mathematics learning, and also a more empowering 
and relevant approach to curriculum reform”. However, learners have different values that 
require different teaching methods to be used to cater for these different values (Peng & 
Nyroos, 2012). The idea of using the same teaching method for all learners of the same 
group should be reconsidered since the use of different teaching methods might improve the 
learners’ understanding of mathematics concepts (Peng & Nyroos, 2012).

Seah (2016) argues that learners who value achievement in mathematics overcome most 
barriers to success and seem to better understand and remember the mathematics concepts 
they value. The values that learners subscribe to, relate to their conceptual understanding of 
mathematics (Seah, 2013), but also provide learners with the motivation and determination 
to work diligently in mathematics classrooms (Seah et al., 2016). Values, such as working 
hard and putting in effort when doing mathematics, may cognitively affect learners’ levels of 
reasoning and intellectual capacity, while values, such as appreciation for the usefulness of 
mathematics in real-life, may effectively contribute to learners’ emotional experiences and/or 
motivation in learning mathematics. Seah et al. (2016) include that if learners are supported 
in appreciating what they value, it will encourage more positive and profitable learning of 
mathematics and might enable a significant approach to educational curriculum change. 
Therefore, what learners value as important in the learning of mathematics could impact 
directly on their learning of the subject.

This paper reports on a study aimed to establish the values that Grade 9 learners from a 
public school in Gauteng, South Africa consider as important in the learning of mathematics. 
A better understanding of learners’ values could assist teachers to infuse values in their 
pedagogies to teach mathematics, which may lead to a better performance in mathematics.

Studies on values in the learning of mathematics are mostly limited to countries external 
to the African continent, such as Australia, Asia and Turkey (Seah, 2011a). Australian learners 
value memorising mathematical facts and shortcuts to solving a mathematical problem. 
Learners in Hong Kong and Malaysia value achievement, which motivates them to work hard 
to achieve their intended goals. Learners from Turkey are expected “to grow as citizens who 
embrace, protect and improve the Turkish nation’s national, ethical, humanitarian, spiritual 
and cultural values” (Dede, 2011:605). Despite much research on the reasons underlying 
poor performance in mathematics (De Matthews, 2016; Makgato & Mji, 2006; Masekoameng, 
2014), the researcher could not find any pertinent studies on learners’ values associated with 
mathematics learning that has been conducted in South Africa. The authors of this study 
argue that if teachers could identify what values learners view as important in their learning 
of mathematics, they will be able to align these values according to mathematics education 
aspects, which, in turn, could lead to better performance in mathematics. Therefore, this 
paper could add to the body of literature on learners’ values, with specific reference to the 
South African context. Thus, the research question arising is: What values do Grade 9 

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mathematics learners from a public school in Gauteng, South Africa consider as important in 
the learning of mathematics? 

In the following sections, values in the learning of mathematics will be defined and 
motivated, followed by a discussion on the main theoretical underpinnings on values-based 
studies. Thereafter, the research methodology utilising a quantitative research approach will 
be outlined, followed by a discussion on findings from the data analysis process. 

2. values in maThemaTics
Values refer to choices about what one regards as important, such as freedom to choose, 
having alternatives to choose from, as well as choosing after keen thought of the results of 
each option, prizing and appreciating (Raths, Harmin & Simon, 1987). Chin and Lin (2001) 
agree that values are preferences of individuals related to their personal standards of thoughts 
and actions that are important and worthwhile to themselves. In particular, mathematics 
educational values are connected to the teaching and learning of mathematics and refer to 
the degree to which standards and procedures that can be associated with teaching and 
learning of mathematics are viewed as important (Sam & Ernest, 1997). Bishop (1996) adds 
that mathematics education values are deep affective qualities that education aims to put into 
effect through engagement in mathematics. These values are reflected in the views that an 
individual has believed as being important and worthwhile for their learning of mathematics 
(Seah & Andersson, 2015). Therefore, for this paper values are defined as something 
important to a learner and worth doing. 

The importance of values in the learning of mathematics is foregrounded in this paper 
since values influence the way learners choose to engage with mathematics tasks (Peng & 
Nyroos, 2012). Askew, Hodgen, Hossain and Bretscher (2010) found that good performance 
may be much more closely connected to learners’ values than to particular arithmetic 
instructing practices. Valuing provides an individual with the will and determination to work 
in mathematics, as learners tend to engage in mathematics tasks they value (Seah, 2013). 
Values improve learners’ conceptual understanding, thus maximising learners’ learning 
(Seah, 2013). Values are dynamic and they do not have the same meaning for everyone as 
learners’ values differ (Peng & Nyroos, 2012). When values are incorporated into the learning 
of mathematics, different approaches to teaching have to be employed depending on what 
the learners value (Dede, 2009). Therefore, different teaching methods must be employed to 
cater for learners with different values.

According to Seah (2013), learners who value achievement, work hard and succeed. 
Therefore, appropriate valuing might arm learners with a powerful force to overcome barriers to 
success. If learners have negative attitudes about mathematics, but they value achievement, 
this valuing will give them the determination to do well in mathematics (Seah, 2013). Learners 
understand and remember the concepts they value more than what has been taught to them 
in class (Bishop, 1999). Seah (2013) advises teachers to incorporate that what learners value 
in the learning of mathematics as it will improve conceptual understanding, thus maximising 
learners’ learning. Incorporation of learners’ values might in turn enhance learners’ performance 
in mathematics.

Most studies incorporating values in the learning of mathematics have been conducted in 
countries such as Malaysia, Japan, Turkey, Asia and Australia (Seah, 2011a). Sam and Ernest 
(1997) conducted a research study in Malaysia to explore the values contained in the Malaysian 

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mathematics curriculum and revealed that values on “effectiveness, responsibility, self-discipline 
and appreciation of the importance and beauty of mathematics” are emphasised (Malaysia 
Curriculum Development Center, 1993:2). In addition to the curriculum analysis, teachers using 
this curriculum added that persistence, patience, punctuality and discipline might make learners 
develop good behaviours, which could lead to better mathematics learning.

According to Stigler and Hiebert (1999), Japan’s mathematics teachers value a flexible 
approach, which allows a learning environment filled with disruptions, discussion and new 
ideas. Ueda, Baba and Matsuura (2014) conducted another study on values in Japanese 
mathematics education and found the use of an open-ended approach that values learners’ 
mathematical thinking. Learners are allowed to work individually in order to build mathematical 
ideas in the lesson (Ueda et al., 2014). 

A research study by Dede (2011:609), with 107 randomly selected pre-service primary 
mathematics teachers enrolled at Cumhuriyet University in Sivas, Turkey, revealed that these 
teachers valued developing learners as citizens who embrace, shield and improve the Turkish 
nation’s national, ethical, humanitarian, religious and cultural values. This value is similar to 
the South African curriculum, where emphasis is placed on access, equity, redress and being 
a critical citizen (Masekoameng, 2014). However, Dede (2011) found that mathematics in 
Turkey is taught without relating the mathematical content to daily life. The textbooks and 
mathematics syllabi are incorrectly presented as value free. The research further revealed 
that mathematics achievement of Turkish learners is at a very low level compared to other 
countries where research on values was carried out. 

Seah and Wong (2012) conducted research in East Asia to harness relevant values in 
mathematics pedagogy and found that learners from the region valued achievement that 
pushed them to work hard to achieve their intended goals. Mullis, Martin and Foy (2008) also 
revealed that although many Asian learners fear and even hate mathematics, they perform 
well in the subject and thus value achievement. Asian learners value achievement much more 
than they hate or dislike the subject. 

Seah and Bishop (2000) conducted a study in Singapore and Australia where they studied 
lower secondary mathematics textbooks. They found that textbooks in both countries value 
teaching mathematics using routine drill questions. As a result, most of the textbooks test 
learners’ knowledge and memorisation. 

Seah and Barkatsas (2014) conducted a research study focusing on what primary school 
learners from Australia value in mathematics learning. The sample consisted of 63 grades 
5–6 learners in a single Catholic school in suburban Melbourne, Australia. They found that 
these learners value memorising of mathematical facts and shortcuts to solve mathematical 
problems. They also value knowing the stages of the solution that are formulated to get the 
answer and knowing the multiplication tables. Furthermore, these learners value the use of 
calculators, understanding the concepts they are learning through examples, and being able 
to analyse if the solutions are correct or wrong. Finally, they found that these learners value 
teachers who pose questions to them while providing individual help and feedback, and allow 
them to complete mathematical tasks individually and to know the importance of examinations 
and tests. 

One of the few studies in Africa, conducted in Ghana, examined what learners intrinsically 
and extrinsically value. The sample consisted of 1 256 learners from 18 primary and secondary 

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state schools across urban and rural settings in the Cape Coast Metropolis of Ghana (Seah, 
Davis & Carr, 2017). Learners in Ghana value “achievement, relevance, fluency, authority, 
resourcefulness, learning environment, strategies, feedback, communication, fun, connections, 
engagement, applications, and accuracy in their mathematics learning” (Seah et al., 2017:1). 
The values appear to be more extrinsic than intrinsic to the mathematics discipline, which 
imply they value things that are not really mathematically related. 

The countries mentioned above had similar learner values such as effectiveness, self-
discipline and achievement. Teachers in Japan value learning that promotes higher order thinking 
while teachers in Singapore and Australia promote routine drill questions and memorisation. 
Learners in these countries value working individually and memorisation respectively.

3. TheoreTical underpinnings
The two theoretical underpinnings for the study this paper reports on are the value theory 
in Mathematics Education of Bishop (1996) and Seah’s (2011a) five value dimensions. 
Bishop (1996) classified values taught in mathematics lessons into three kinds, namely 
general educational values, mathematical values and mathematics educational values. First, 
general educational values are not subject-related concepts, but include values such as good 
behaviour, honesty, respect, humanity and humility. Secondly, mathematical values are the 
values that mirror the type of mathematical knowledge and are shaped by mathematicians 
who have grown up in different cultures, such as rules, conjectures or inferences. Lastly, 
mathematics education values connect the pedagogical approaches and norms of teaching. 
For example, some teachers might value showing all working out when answering questions 
and not to rely on a calculator when doing calculations. 

Bishop (1999) classifies mathematical values taught into three categories. Firstly, 
rationalism/objectism refers to the values that learners have about mathematics. “Rationalism 
elaborates on correctness of results and explanations, while objectism value shows objects 
and symbols which is an instrument to concretize mathematics that has an abstract language” 
(Dede, 2011:86). Secondly, control/progress is open to development and can be used in 
other subjects in school lessons. Control involves forming rules or conjectures. Progress 
incorporates generalising. Lastly, openness/mystery is revealed when deliberating and 
analysing mathematical concepts, thoughts, outcomes and influences. Asking learners to 
explain their ideas to the whole class is a good way of developing openness. On the other 
hand, mystery indicates how wonderful and surprising mathematics can be. This paper 
focuses specifically on these mathematics education values.

The second theory underpinning this study is Seah’s (2011a) five value dimensions, namely 
relevance, accessibility, formalistic view, relational view and process (tool or procedure). 
According to Dede (2011), relevance implies values where learners can solve everyday issues 
and make more brilliant ways through which the society develops. Accessibility indicates the 
values focusing on doing and preparing of mathematical activities by everyone or just by 
people with the talent to execute them. The formalist views mathematics learning as including 
consistent thinking and pleasant learning, whereas the extremist sees mathematics learning 
as including natural thinking and discovery learning (Dede, 2011). A relational view refers to 
values associated with learning of rules, procedures and formulae, while process implies the 
use of a tool and a procedural view of mathematics learning (Seah, 2011a). 

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Seah’s (2011a) five value dimensions are related to Bishop’s (1996) five mathematics 
educational values. Relevance view is equated to progress–control dimension; accessibility 
view to openness–mystery dimension; formalistic view to explanation–exploration dimension; 
relational view to recalling–creating dimension whilst process (tool or procedural) view is 
equated to process–product dimension.

These two underpinnings support the view that values provide the individual with the will 
and strength of character to maintain any development chosen in the learning and teaching of 
mathematics. These theoretical underpinnings endorse good behaviour, honesty and respect; 
reflect the nature of mathematical knowledge; and attribute success to effort and excellence 
of the teacher.

4. meThod
An exploratory quantitative research method was used to collect data. The data collection 
instrument was a standardised questionnaire developed by Seah (2011a). The instrument 
comprised ten (10) semantic differential items where participants had to tick one of the blocks 
to indicate if phrase A was more important to them in the learning of mathematics than phrase 
B, or vice versa. If a participant placed a tick in the middle block, this would mean that phrases 
A and B were equally important to the learner. Table 1 represents an example of an item in 
the questionnaire.

Table 1: Example of a semantic item

Number Phrase A -2 -1 0 1 2 Phrase B
1 Leaving it to ability when 

doing mathematics
X Putting in effort when doing 

mathematics

Two hundred and seventy-four Grade 9 learners were purposively and conveniently 
selected from a public school in Gauteng, South Africa. It was convenient since the researcher 
is teaching at the same school under study. Participants agreed to participate voluntarily and 
were from a school where many learners experience challenges with mathematics learning. 
All participants’ home language was English, which made it easy for them to understand 
and respond to the items in the questionnaire, which had been developed in English. 
The biographical information was analysed according to age, gender, race, home language 
and learners’ views on their mathematics achievement. 

Data were collected by means of a printed version of the standardised questionnaire. 
Two hundred and fifty-six participants of the 274 Grade 9 learners, grouped in nine Grade 9 
classes, completed the questionnaire within 30 minutes over a period of two weeks during 
school hours. 

Reliability for the data collection instrument used in this study was mainly confirmed by 
previous studies. One of the studies in Africa, conducted in Ghana by Seah et al. (2017), 
obtained a Cronbach alpha value of 0.947, whilst a study done in Japan by Shinno, Kinone 
and Baba (2014:172) “yielded satisfactory Cronbach’s alpha values for each of the five factors, 
ranging from 0.772 to 0.936”. Although the researcher employed a reliability analysis using 
the Cronbach alpha coefficient, the strength of association was poor (Cronbach α = 0.253). 

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Pallant (2007) acknowledges that it is common to get a low degree of internal consistency for 
small samples, especially if constructs consist of less than ten items. Therefore, inter-item 
correlation was performed as an additional test of reliability to determine whether they fitted 
the optimal recommended range between 0.20 and 0.40, as displayed in Table 2.

Table 2:  Inter-item correlation for the ten semantic differential items

Component for inter-item 
correlation

Mean Minimum Maximum Range Number of items

Item means 3.079 1.949 4.191 2.242 10

Content validity was ensured by using a standardised questionnaire, called What I Find 
Important (WIFI) in Mathematics Learning, designed by Seah (2011a). This questionnaire 
was validated by various research teams from different countries, such as Australia, Brazil, 
China, Hong Kong, Malaysia, Japan, Singapore, Sweden, Taiwan, Turkey and the United 
States in 2012 (Seah et al., 2016). To ensure face validity, 36 learners were randomly selected 
to participate in a pilot study prior to the actual study to rectify any vague questions in the 
data collection instrument that learners might not understand. Face validity was also ensured 
by requesting content experts and colleagues to check if the data collection instrument 
represented what it was expected to measure and to identify items that lack clarity or that may 
not be appropriate for the information needed for the study. 

Ethical clearance was obtained from the University of Johannesburg’s Faculty of Education 
Ethical Committee (clearance number 2017-100) and from the Gauteng Department of 
Education before any empirical work was conducted. The principal of the school, parents and 
learners also gave consent and all ethical measures were adhered to. 

5. resulTs
Data pertaining to the responses on the ten (10) semantic differential items were analysed 
with assistance of a software program, namely the Statistical Package for the Social Science 
(SPSS), version 23, using descriptive statistics methods, such as frequency analysis cross 
tabulations. The percentage response for each phrase on what values participants consider 
as important in the learning of mathematics is presented in Table 3. Table 3 also presents the 
mean and standard deviation of each phrase. The negative values -2 and -1 in Table 3 imply 
that participants value the phrases listed on the left side more than those listed on the right-
hand side in the questionnaire, but also the opposite direction applies. The positive values 1 
and 2 imply that participants value the phrases listed on the right-hand side more than those 
on the left-hand side. 

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Table 3: Descriptive statistics pertaining to what values participants consider as important 
in the learning of mathematics

Statements -2 
Phrase 

A 
Strong

-1 
Phrase 

A 
Mild

0 
Neutral

1 
Phrase 

B 
Mild

2 
Phrase 

B 
Strong

Mean Standard 
deviation

How the answer to a 
problem is obtained 
versus what the answer 
to a problem is.

87 38 66 24 18 -0.65 1.285
37.3% 16.3% 28.3% 10.3% 7.7%

Feeling relaxed or 
having fun when 
doing mathematics 
versus hard work is 
needed when doing 
mathematics. 

29 25 65 44 79 0.49 1.355
12.0% 10.3% 26.9% 18.2% 32.6%

Leaving it to ability when 
doing mathematics 
versus putting in effort 
when doing maths.

3 20 23 63 134 1.26 1.013
1.2% 8.2% 9.5% 25.9% 55.1%

Applying mathematics 
concepts to solve a 
problem versus using 
a rule or formula to find 
the answer.

27 19 89 25 82 0.48 1.327
11.2% 7.9% 36.8% 10.3% 33.9%

Truths and facts, which 
were discovered versus 
mathematical ideas and 
practices used in life.

26 37 69 64 43 0.26 1.232
10.9% 15.5% 28.9% 26.8% 18.0%

Someone teaching and 
explaining mathematics 
to me versus exploring 
mathematics by myself 
or with friends.

135 42 41 9 17 -1.10 1.221
55.3% 17.2% 16.8% 3.7% 7.0%

Remembering 
mathematics ideas, 
concepts, rules or 
formulae versus 
creating mathematics 
ideas, concepts, rules 
or formulae.

99 59 49 20 18 -0.82 1.251
40.4% 24.1% 20.0% 8.2% 7.3%

Telling me what a 
triangle is versus letting 
me see examples of 
triangles to understand 
their properties.

12 10 31 59 133 1.19 1.115
4.9% 4.1% 12.7% 24.1% 54.3%

Demonstrating and 
explaining mathematics 
concepts and proofs 
versus keeping 
mathematics magical.

103 66 46 14 15 -0.93 1.115
42.2% 27.0% 18.9% 5.7% 6.1%

Using mathematics 
to predict or explain 
events, for example, 
staying in control versus 
using mathematics 
for development 
and progress

12 19 88 47 76 0.64 1.148
5.0% 7.9% 36.4% 19.4% 31.4%

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The values, as stated by the semantic differential items, were aligned with those values 
identified by Bishop (1999) and Seah (2011a) and illustrated according to their mean values 
as indicated in Figure 1. Furthermore, the values were categorised either as intellectual (Items 
1, 3, 7 and 10) or emotional (Items 2, 5, 6, 8 and 9). Items 1, 2 and 4 were negatively worded 
and the order was reversed.

6. discussion and inTerpreTaTion of resulTs
The discussion of the results should be interpreted with caution as the results are trends 
emerging from the particular context of this study and not pertinent findings that can be 
generalised. From Figure 1 it can be deduced that the intellectual values of participants 
tend to focus more on the application and process of mathematics, than on theoretical and 
procedural knowledge. However, memorisation of mathematics concepts and rules are also 
valued. This finding is aligned with Seah et al. (2016) noting that practising mathematics may 
affect learners’ cognitive capabilities.

Slightly more than half of all participants (n = 125; 53.6%) valued how the answer to a 
problem is obtained (M = 0.65, SD = 1.285) over what the answer to a problem is (n = 42; 18%). 
According to 63 Grades 5–6 learners in a Catholic school in suburban Melbourne, Australia, 
achievement is possible if one knows the steps of the solution (Seah & Barkatsas, 2014). 
Knowing the steps to a solution might lead to the understanding of the concepts learners 
are learning, and their ability to analyse mathematics problems if the solutions are correct or 
incorrect. These steps of getting a solution may be achieved if one values mathematical ideas 
and practices used in life. 

Many participants (n = 158; 64.5%) valued remembering mathematics ideas, concepts, 
rules or formulae (M = -0.82, SD = 1.251) over creating mathematics ideas, concepts, rules or 
formulae (n = 38; 15.5%). Alike to this finding, Seah and Bishop (2000) found that textbooks 
in Singapore and Malaysia value teaching mathematics using routine drill questions. As a 
result, most learners tend to resort to memorisation in order to remember the formula instead 
of generating mathematics understanding. This finding could have transpired because of 
learners not being critical thinkers who could solve problem solving questions on their own, 
but who require the provision of step-by-step calculations.

Most of the participants (n = 197; 81%) valued putting in effort when doing mathematics 
(M = 1.26, SD = 1.013) compared to leaving it to ability when doing mathematics (n = 23; 
9.4%). According to Schollar (2015), good work ethic will result in learners putting in effort 
when learning mathematics. Therefore, it could be derived 

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that it is not only a person’s ability that predicts good mathematics results, but it is about 
putting in effort when doing mathematics.

Slightly less than half of the participants (n = 107; 44.2%) valued using a rule or formula to 
find the answer (M = 0.48, SD = 1.327) rather than applying mathematics concepts to solve 
a problem (n= 46; 19%). According to Seah and Barkatsas (2014), 63 Grades 5–6 learners 
in a Catholic school in suburban Melbourne, Australia believed achievement was possible if 
one knows which formulae to use to arrive at the solution and know the multiplication tables. 
This finding could be a result of learners’ inability to use the correct formula that leads to wrong 
calculations and a possibility of misunderstanding the concepts.

Almost half of the participants (50.8%, n = 123) valued using mathematics for development 
and progress (M = 0.64, SD = 1.148) compared to using mathematics to predict or explain 
events, for example staying in control (n = 31; 12.9%). Mathematics concepts enable learners 
to develop the ability to deal with mathematical challenges of daily life and to progress with 
their study of mathematics in high school and beyond (Kilpatrick, Swafford, & Findell, 2001). 
This study is similar to the findings from Ueda et al. (2014) who revealed that learners value 
mathematical thinking when they have been allowed to work individually to build mathematical 
ideas in the lesson. This skill to think critically and to work independently might allow learners 
to be able to deal with any mathematical challenges in real life.

Evident from Figure 1, participants for this study tend to have a mix of emotional values 
regarding the appreciation of the nature of mathematics and motivation to do mathematics. 
Although they are likely to enjoy doing mathematics, the participants lean towards teachers 
to explain the mathematics to them by means of practical examples. This finding aligns with 
Seah et al. (2016) claiming that valuing the usefulness of mathematics in real-life may add to 
learners’ emotional feelings and motivation in doing mathematics.

About half of the participants (n = 123; 50. 8%) valued that hard work is needed when 
doing mathematics (M = 0.49, SD = 1.355) over feeling relaxed or having fun when doing 
mathematics. This finding is similar to Seah and Wong (2012) who found that some learners 
from two Asian countries, namely Hong Kong and Malaysia, valued achievement that push 
them to work hard to achieve their intended goals. This finding was made after Seah and Wong 
(2012) had identified and had discussed the values espoused by learners and their teachers 
when mathematics had been learnt particularly effectively (from the learners’ perspectives) in 
Hong Kong classrooms. This finding can be interpreted that for one to succeed in mathematics 
one has to work hard. 

More than half of the participants (n = 169; 69.2%) valued demonstrating and explaining 
mathematics concepts and proofs (M = -0.93, SD = 1.115) than viewing mathematics as 
magical (like a dream or supernatural subject) (n = 29; 11.8%). If teachers are mathematically 
proficient, they are able to explain mathematical concepts to learners, carry out procedures 
flexibly, accurately and guiding learners to see mathematics as sensible (Kilpatrick, Swafford, 
& Findell, 2001). This finding is similar to a study by Stigler and Hiebert (1999), who 
revealed that Japan’s mathematics teachers value a flexible approach that allows a learning 
environment filled with disruptions, discussion and new ideas. This finding could be interpreted 
as follows: If teachers demonstrate and explain mathematics concepts well, learners might 
see mathematics as sensible and worth doing, as this might result in a clear understanding of 
what is being taught.

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In addition, less than half of the participants (n = 107; 44.8%) valued using mathematical 
ideas and practices used in life (M = 0.26, SD = 1.232) compared to participants valuing 
truths and facts that they discovered (n= 67; 26.4%). Similar to this finding, Ueda, Baba and 
Matsuura (2014) found that learners from Japan value constructing mathematical ideas in the 
lesson, which implies learning mathematics does not rely only on discovered facts, but facts 
used in a real-life context. This finding could be derived from learners tending to understand 
and remember concepts they see in real life.

Almost three quarters of the participants (n = 177; 72.5%) valued someone teaching 
and explaining mathematics to them (M = -0.10, SD = 1.221) over exploring mathematics 
by themselves or with friends (n = 26; 10.7%). This finding is comparable to Seah and 
Barkatsas (2014), who found that learners from Australia value teachers who pose questions 
to them whilst providing individual explanation, help and feedback. In line with this finding, we 
have seen as practitioners that there are learners who understand better when mathematics 
concepts are explained to them than when they have to learn these concepts by themselves. 

A considerable number of participants (n = 192; 78.4%) valued seeing examples of 
shapes to understand their properties (M = 1.19, SD = 1.115) over the teacher telling them 
what a shape is (n = 22; 9%). This is similar to the findings from Ueda, Baba and Matsuura 
(2014) who found that learners from Japan value constructing mathematical ideas in the 
lesson, which implies learning mathematics does not rely only on discovered facts, but facts 
used in a real-life context. Seeing real-life models of shapes provide relevance to learners’ 
learning, while giving them an opportunity to connect their world to classroom mathematics 
(Riley, 2012). Some learners might even understand mathematics better, simply because of 
seeing authentic examples of the concept being taught at that moment (Vanada, 2011).

In summary, almost half of all participants valued how the answer to a problem is obtained 
over what the answer to a problem is. The same applies to participants valuing hard work 
when doing mathematics over feeling relaxed or having fun when doing mathematics. The last 
finding shows that learners realise that in order to succeed in mathematics learning, one has 
to work hard through practise, ask questions, do homework and concentrate in class. 

According to the findings, it could be derived that if learners value working hard, they 
will put in effort when doing mathematics instead of only relying on their ability when doing 
mathematics. Most participants value using mathematical ideas and applications in real life, 
rather than valuing truths and facts, which they have discovered. Almost three quarters of the 
participants valued someone teaching and explaining mathematics to them over exploring 
mathematics by themselves or with friends. From the findings, it can be derived that learners 
rather value remembering mathematics ideas, concepts, rules or formulae than creating 
mathematics ideas, concepts, rules or formulae. However, as 21st century mathematics 
teachers, we should enforce skills such as creativity, critical thinking, collaboration, 
communication and problem solving. 

7. conclusion
Poor performance in mathematics at school level is a concern in many countries. A possible 
reason for poor performance could be that teachers are ignorant about what values learners 
consider as important in the learning of mathematics. The identification of values that learners 
view as important in their learning of mathematics could assist in categorising these values 
according to mathematics education aspects, which, in turn, could lead to better performance 

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in mathematics. Therefore, this paper reported on a study that established these values that 
Grade 9 learners from a public school in Gauteng, South Africa consider as important in their 
learning of mathematics.

This study revealed that learners have various values that they associate with mathematics 
learning. Most participants value how the answer to a problem is obtained and hard work and 
effort when doing mathematics. Some participants valued someone teaching and explaining 
mathematics to them, and the remembering of mathematics ideas, concepts, rules or formulae. 
Lastly, learners tend to value the learning of mathematics when teachers let them see real-
life examples of shapes to understand the properties and when teachers demonstrate and 
explain mathematics concepts and proofs to them. 

One limitation of the study reported in this paper was that the researcher only used ten 
semantic questions to determine what values learners consider as important in mathematics. 
Unfortunately, the extent to which these values relate to learners’ performance in mathematics 
was not determined. The localised nature of the study applicable to one single school in 
Gauteng, South Africa, also prevents the generalisation of the results to other contexts. 
Therefore, it is recommended to expand this study to more types of schools, to various grades 
and to different contexts. Further studies could also include the values that teachers find 
important in the teaching of mathematics.

Values influence the way learners choose to engage with mathematical tasks, and 
eventually how they will perform in the subject. Therefore, mindfulness by teachers about 
what values learners consider as important in their learning of mathematics, afford teachers 
the opportunity to use pedagogical approaches that will include these values. The findings 
of the study reported in this paper add to the international body of research on values in 
mathematics and specifically in the context of South Africa. 

8. acKnowledgemenTs
Many thanks to the employers for giving permission to carry out this research, as well as the 
learners who participated in this study.

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https://doi.org/10.5937/inovacije1403069U
https://doi.org/10.5937/inovacije1403069U

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