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Mathematical Thinking and Learning
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Risks of aiming to kill two birds with one stone:
the affect of mathematically gifted and talented
students in the dual realities of special schooling
Kyeong-Hwa Lee , Yeongjun Kim & Woong Lim
To cite this article: Kyeong-Hwa Lee , Yeongjun Kim & Woong Lim (2020): Risks of
aiming to kill two birds with one stone: the affect of mathematically gifted and talented
students in the dual realities of special schooling, Mathematical Thinking and Learning, DOI:
10.1080/10986065.2020.1784696
To link to this article: https://doi.org/10.1080/10986065.2020.1784696
© 2020 The Author(s). Published with
license by Taylor & Francis Group, LLC.
Published online: 02 Jul 2020.
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Risks of aiming to kill two birds with one stone: the aect of
mathematically gifted and talented students in the dual realities of
special schooling
Kyeong-Hwa Lee
a
, Yeongjun Kim
a
, and Woong Lim
b
a
Department of Mathematics Education, Seoul National University, Seoul, Republic of Korea;
b
Graduate School of
Education, Yonsei University, Seoul, Republic of Korea
ABSTRACT
Mathematically gifted and talented students have unique cognitive and
emotional needs. Thus, their schooling should consider their social and
emotional development. This study investigated student aect in a science
high school in Korea to determine how the specialized school’s curriculum
and instruction inuence student aect. Data were collected through inter-
views and a survey. Our ndings show that gifted and talented students
generally demonstrate a positive aect toward mathematics, but high anxi-
ety and low self-concept play a key role in shaping students’ negative
attitudes toward mathematics. In this paper, we argue that two dierent
goals – gifted education and college preparation – could cause such negative
student aect. The dual educational goal manifests itself in fast-paced
instruction and memorized problem solving, which can ultimately cause
students to lose condence and interest in mathematics.
ARTICLE HISTORY
Received 12 December 2018
Revised 16 June 2020
Accepted 16 June 2020
KEYWORDS
Mathematically gifted &
talented; science high
school; mathematics-related
affect; student beliefs; big-
fish-little-pond effect
In the past two decades, there has been increasing interest in providing gifted and talented (G&T)
students with effective educational programs. Research has documented various strategies or models
of G&T education, including accelerated programs, special interest communities, club activities, and
specialized classes/schools (Braggett, 1985; Callahan et al., 2014; Hoge & Renzulli, 1993; Karp, 2016).
In particular, special school-based G&T programs are an efficient model for identifying G&T students
and providing the students with intensive fast-track learning. To date, however, there has been limited
research on the effects of such programs on students’ learning experiences (Karp, 2016).
A few research studies have reported that there are G&T students who develop low academic self-
concepts while enrolled in special schools but that they recover a positive attitude and confidence
when they transfer out of special schools and back into regular schools (Goetz et al., 2008; Huguet
et al., 2001; Marsh et al., 2000). Therefore, these studies suggest that the social context in school, in
addition to academic content and cognitive performance, plays a significant role as an affective factor
(e.g., academic self-concept), which in turn may influence student academic performance and future
career choices (Dai & Rinn, 2008; McCoach & Siegle, 2003). In the field of mathematics education,
Hong and Milgram (2008) argue that talent loss occurs when G&T students lose confidence and
interest in mathematics, which is a negative affect that results in untapped human potential and
achievement (Marsh et al., 2007). Thus, an investigation into the affect of mathematically G&T
students and how it may change over an extended period of time can serve as an important indicator
of the effectiveness of educational experiences and programs for G&T students in special high schools.
It can also provide insight into the design and implementation of G&T policy and programs in
a national and international context.
CONTACT Woong Lim woonglim@yonsei.ac.kr Graduate School of Education, Yonsei University, Seoul 03722, Republic of
Korea
MATHEMATICAL THINKING AND LEARNING
https://doi.org/10.1080/10986065.2020.1784696
© 2020 The Author(s). Published with license by Taylor & Francis Group, LLC.
This is an Open Access article distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives License (http://
creativecommons.org/licenses/by-nc-nd/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the
original work is properly cited, and is not altered, transformed, or built upon in any way.
Literature review
Identication and education of G&T students
Some researchers have argued that the nature of giftedness and talent remains obscure, thus hindering
research on selecting and educating G&T students (e.g., Ambrose et al., 2012; Renzulli, 2011).
Likewise, there is no unifying definition or interpretation of giftedness and talent (E. L. Mann, 2006;
Sriraman, 2005). In the early 2000s, G&T students were selected and educated based on intelligence
quotients. Over time, new and emerging theories of mathematical giftedness and talent (Gavin, 2005)
have led to multiple assessments (Gavin, 2009, p. 440): (a) out-of-level achievement tests in math to
determine what knowledge students have already acquired and whether they are more advanced than
their peers; (b) peer, teacher, or parent checklists of academic and affective behaviors that might be
characteristic of students who are gifted in mathematics; (c) portfolios of math work collected over
time, which include the students’ reflections on their products or performances; (d) observation of
improvements in student math performance over time where the teacher assesses, teaches, and
reassesses; and (e) general reasoning, such as intelligence tests that focus on problem solving.
G&T programs include acceleration, enrichment activities, and a combination of both through
a variety of instructional settings, such as pull-out programs, ability or cluster grouping, differentiated
curricula, and special schools (Peters et al., 2013; Plucker & Callahan, 2014). With the variety of
definitions and attributes regarding mathematical G&T compounded by the large number of pro-
grams of study for the students, it makes more sense to support G&T students with multiple options of
mathematics learning programs rather than aim for a best education program that works for all G&T
students (Rotigel & Fello, 2004). However, as Karp (2016) points out, there still exists limited research
on educational programs for mathematically G&T students, especially on specialized schools with
state or public funding for mathematics. Further, Dimitriadis (2016) argues that the field of gifted
mathematics education needs gifted research and theory that reflects the practice with students gifted
in mathematics and so it remains valid to design and investigate the education of gifted students in
mathematics. In particular, there is little systematic research on how mathematically G&T students
respond to school-based pedagogy depending on instructional material or teaching methods.
Moreover, mathematics continues evolving and expanding, as do the cognitive and affective char-
acteristics of G&T students with social and cultural change. Therefore, further research on how
school-based G&T programs for mathematics meet the cognitive and affective needs of students,
which would thus confirm or refute the literature, is warranted. This study investigates the state of
G&T students’ affect in a specialized school.
Aective characteristics of G&T students in mathematics
Research on mathematics-related affect involves multiple constructs, including mathematics anxiety
(Hembree, 1990), attitudes toward mathematics (Fennema & Sherman, 1976), beliefs (Schoenfeld,
1989), identity (Black et al., 2010), self-efficacy (Pajares & Miller, 1995), self-control (Zimmerman &
Schunk, 2012), interest and enjoyment (Ainley & Hidi, 2014), intimacy and integrity (DeBellis &
Goldin, 1999), emotions (Hannula, 2015), and motivation/anxiety (Wang et al., 2015). Research on
mathematics-related affect has also shifted toward investigating factors affecting individual learners
through the lens of environment, culture, and society. For example, Hannula (2012) indicates that
mathematics-related affect involves not only psychological constructs such as beliefs, attitudes, and
emotions, but also a wide range of emerging constructs, such as embodied approaches to cognition
and the social nature of human emotions.
Affective characteristics of G&T students in mathematics are diverse and often complex, and they
can be summarized briefly as follows. First, G&T students in mathematics demonstrate a more positive
affect than regular students, show higher interest and confidence in mathematics, and express a high
degree of satisfaction from studying mathematics (Greenes & Mode, 1999; Heid, 1983). Additionally,
G&T students in mathematics show higher intrinsic motivation, self-efficacy, and self-control (Heid,
2K.-H. LEE ET AL.
1983; Malpass et al., 1999). This type of positive affect is evident in cases where a G&T student shows
greater patience and persistence in complex problem solving than regular students (Budak, 2012; cf.
Krutetskii, 1976 for a comparison on mathematical thinking). G&T students are also more willing to
take intellectual risks and tend to develop a curiosity for knowledge (Hong & Aqui, 2004), as they are
both interested in and exceptional at understanding the problem, often going beyond just finding an
answer to find different methods to solve problems (Gorodetsky & Klavirb, 2003). In contrast, G&T
students may demonstrate a negative affect. This is best illustrated in the account of G&T students in
a peer group (Marsh, 1987, 1991, 2005). The big-fish-little-pond effect (BFLPE) refers to how G&T
students demonstrate contrasting academic self-concepts in classrooms/schools with non-gifted peers
versus in specialized classrooms/schools with gifted peers. This notion is based on social comparative
theory (see Goethals & Darley, 1987) which posits that G&T students tend to define their ability and
shape their learner identity in comparison with superior peers – that is, for some G&T students’
academic self-concept, being a big “gifted” fish in a little pond with his or her “regular” or (not as
gifted) peers is better. Here, we do not mean to reduce the negative affect in gifted mathematics
education down to a gifted student’s feelings in response to his or her superior peers.
Other factors influencing the affect of gifted students include teachers’ attitudes and practices (see
R. L. Mann, 2006, for gifted students with verbal learning difficulties) and perfectionism (Speirs
Neumeister, 2017; Stoeber, 2017) in gifted students. Further, Ziegler and Phillipson (2012) call for
a systemic approach that considers the interactions of elements (e.g., values, relationships, and
practices of the school community) that shape exceptionality in order to better understand it. Later,
Pepin and Roesken-Winter (2015) conceptualized affect in mathematics education as a dynamic
system “situated in various contexts (e.g., relative to particular mathematics topics, within the cultures
of different nationals, among the experiences of collective groups)” (Jansen et al., 2017, p. 106) as a set
of emotions, attitudes, beliefs, values, and motivations. That said, we recognize the importance of
gifted schooling that addresses both cognitive and non-cognitive strengths and challenges of gifted
students, and this study helps foreground the BFLPE as part of (but an important part in the context of
special schooling in Korea) the broad picture of gifted education involving parents, teachers, peers, the
community, and educational practices and policies.
While extensive research has been conducted to develop instruments for investigating student
affect, such efforts have faced some uncertainty regarding the validity of the instruments being used
(e.g., Leder, 1985; Di Martino & Zan, 2011). Overall, research about affect in mathematics education
has gone from the measurement era to the problem-led and to the dynamic model such that the
focus of the research has shifted from researchers’ use of scales to the analysis of participants’
experiences (Hannula et al., 2016). Some researchers have attempted to extend the literature to the
relationship between factors of student affect through the use of survey instruments to clarify
complex interconnections and distinctions between affect and cognition. Eventually, interpretative
approaches such as essays, diaries, and interviews have been used to analyze participants’ narratives
(Di Martino & Zan, 2010; Hannula, 2002). Di Martino and Zan (2011) identified emotional
dispositions toward mathematics, view of mathematics, and perceived competence in mathematics
as three key dimensions in students’ narratives, proposing an analytical model of beliefs, emotions,
and behavior (the three-dimensional model for attitude [TMA] in Di Martino & Zan, 2011; see
Figure 1). This model is useful in gathering students’ views to better investigate student affect. In
particular, the model can be instrumental in revealing a causal relationship between emotions and
behavior, as well as a causal relationship between certain beliefs and emotions. That is, researchers
can analyze student writing (as opposed to rating scales) about their experience in school and use
the TMA model to confirm the mathematically G&T students’ conceived confidence in mathe-
matics, feelings toward mathematics, and behavior in mathematics learning.
This study aims to investigate G&T students’ math-related affective characteristics using both
a survey instrument and in-depth interviews concerning their beliefs and emotions for mathematics in
classrooms as the lens to reflect on the practices of doing mathematics and social factors in a science
high school. The research questions that guided our study include the following:
MATHEMATICAL THINKING AND LEARNING 3
How do students’ grade level, perceived competence, and selection of mathematics as their college
major relate to the students’ mathematics-related affect in a science high school in Korea?
How do students perceive the extent to which their school experiences at a science high school have
an impact on their mathematics-related affect?
Method
Context of the study
A science high school in Korea was selected as the site of this study. Science high schools are special
schools funded by the government, with the intention to identify G&T students in early adolescence
and develop national elite human resources in mathematics and science. For example, the Korean
team won the third place, behind the US and Chinese teams, at the 60th International Mathematical
Olympiad (also known as the world championship in mathematics for high school students) held in
Bath, the United Kingdom, in 2019, and all of the six members of the team were science high school
students. The school has a highly selective admissions process, requiring students to graduate in the
top 2% of their middle school class with recommendation letters from math/science teachers, a board
approval by the G&T education committee of the middle school, and cognitive tests, including
a creativity test, problem-solving test, and observation test on math modeling and problem-solving
tasks, and interviews with additional tasks to assess applicants’ creative and critical thinking skills
(Choi & Hong, 2009; Jeon, 2004; see Pfeiffer, 2008 for similar methods to identify G&T students).
An additional context for this study is the educational culture in Korea. A diploma from elite
universities in contemporary Korea is rewarded by social and financial mobility, as well as high-
ranking government or corporate positions (Kim & Park, 2010; Lee & Brinton, 1996). Thus, elite
universities in Korea are highly competitive and, hence, there is high-stake application pressure in
favor of students with high standardized test scores and high GPAs. In particular, elite universities in
Korea use mathematics as the topic of their problem-based admission interviews or tests for admission
into the university engineering and science divisions. Consequently, the subject of mathematics has
the strongest influence on college admission. Regarding the dominance of mathematics as the bench-
mark for college admission criteria, we note that the science high school offered 6 to 8 credit hours
per semester in mathematics courses. Thus, the course grade in mathematics counts at least twice as
much toward students’ GPA. Second, students in Korea are often expected to study the school
curriculum (especially mathematics and science) through private tutoring before instruction is
provided in schools (Hultberg et al., 2017). Likewise, a typical student at the science high school has
a head start on gifted education. Beginning in elementary school, G&T programs are offered by
universities and research institutes for G&T education (Choi & Hong, 2009; Choi & Jang, 2012).
It is well documented in survey studies that G&T students in elementary and middle schools
demonstrate much higher interest, self-efficacy, and intrinsic motivation in mathematics than their
non-G&T peers (Hoogeveen et al., 2009; Ma, 2002; Ma & Cartwright, 2003). Naturally, this pattern of
student affect among G&T students would be expected to persist in these students’ freshmen year of
Figure 1. The TMA model (Di Martino & Zan, 2011, p. 476).
4K.-H. LEE ET AL.
special high schools in mathematics and science. However, whether and how G&T students sustain
and develop positive affect over a long period of time (i.e., 3 years) in special high schools remains
largely unexplored. In light of: (1) the close relationship between social context and cognitive
performance, and (2) the need for more research on factors that may sustain or hinder student affect
in secondary G&T schooling for both college preparation and talent development, it is important to
examine how G&T students at science high schools in Korea develop and sustain positive affect. Thus,
this study investigates the relationship between factors such as students’ grade level, perceived
competence, and selection of mathematics as their college major and G&T students’ mathematics-
related affect in a science high school in Korea. In addition, it examines how the learning experience of
attending a science high school has an impact on student affect.
Participants
This study included 212 of the 249 students from a science high school in a mid-sized city in South
Korea. There were 77 participants out of the 83 students in 10th grade (freshmen class), 83 out of the
85 in 11th grade, and 52 out of the 55
1
in 12th grade (senior class).
Data collection
We administered a survey to participants along with individual interviews in the spring of 2017. The
survey consisted of three sections: student demographic information, student perceptions of mathematics,
and student affect. More specifically, the survey (see Appendix 1) inquired about students’ intended
majors (or areas of study/concentration) in college, perceived competence, interest in mathematics,
perceptions of the value of mathematics in life, the emotions students experienced while studying
mathematics, and beliefs about mathematics. The survey also asked two open-ended questions about
students’ motivations for studying mathematics and the attitude/emotion formations or changes that they
experienced while learning mathematics in the school. We note that the participants in 10th grade were
not asked about their areas of study or changes in attitude because most 10th graders were still undecided
and had had only 3 months of high school at the time of the study. For the section on student affect (see
Appendix 1 with C as scale ID), the study used a survey instrument (C. Lee et al., 2011 with a total of 30
items on six subscales) to measure types of mathematics-related affect. Building from six domains (i.e.,
emotional states, attitudes, beliefs, values, morals, and ethics) of affect proposed by DeBellis and Goldin
(2006), C. Lee et al. (2011, p. 249) proposed mathematics-related affect as having six domains: learning
directivity (5 items), self-control (6 items), anxiety (4 items), interest (5 items), student perceptions of the
value of mathematics (shortened to “value” in this study, 6 items), and confidence (4 items). Learning
directivity (cf. grit or persistence in Duckworth et al., 2007 as a similar construct) refers to the attitude
regarding embracing challenge and persisting in complex and unfamiliar problem-solving situations. Self-
control (cf. metacognition in Schneider & Artelt, 2010 as a similar construct) is learners’ awareness of their
own effective learning strategies and the ability to regulate thinking and behaviors to engage in mathe-
matics. Anxiety describes learners’ worried or anxious psychological state when they deal with mathe-
matics. Confidence means learners’ positive beliefs about their mathematical ability. Interest is about the
learners’ interest or motivation to study mathematics and participate in related activities. Lastly, value is
the learners’ perceptions or decisions related to mathematical use – its value and importance in social,
academic, career, and life contexts. We view these six domains as possibly related in various ways to
disposition, perceived competence, and vision in the TMA model (see Appendix 1).
Next, we interviewed participants individually and collected qualitative data (verbal and written
statements) on factors contributing to and shaping their affective competency in the science high
school. To reduce bias, the study aimed to select a representative sample of participants from each
grade and a band of class ranks for the interview portion of the study. For this purpose, one math
classroom in each grade was randomly selected, and students in the class were grouped by perceived
academic performance (i.e., class rank). For participants in 11th and 12th grades, the survey
MATHEMATICAL THINKING AND LEARNING 5
responses on the causes of experienced changes in attitudes and emotions were used to select a fair
sample of interview participants. In addition, the majors that students intended to pursue in college
were taken into consideration to ensure a greater diversity of interview participants. Consequently, 8
participants in 10th grade (FS1–FS8), 8 participants in 11th grade (SS1–SS8), and 11 participants in
12th grade (TS1–TS11) were selected for semi-structured interviews, each lasting 20 to 30 minutes.
Our probing questions regarding the aspect of affect, which we derived from the TMA model for
explaining the affect of the participants in this study, included opening questions such as “What do
you think about mathematics?” “How are you doing in the math class?” and “What has changed in
your attitudes and emotions toward mathematics since you started studying in the science high
school?” We also included the following follow-up questions such as “What caused these changes?”
“What happened?” “How so?” and “Can you tell me more about . . . ?” These questions were intended
to elicit more details from the students in their responses during interviews regarding their affect
and vision of mathematics, changes of affect, the factors and nature of the changes, and perceived
competence. In addition, their purpose was to actively listen to the students and help them feel
comfortable sharing their ideas and experiences.
Data analysis
To answer the first research question, we conducted a one-way analysis of variance (ANOVA) to
make inferences about the mathematics-related affect of students in the science high school by
grade level and academic performance level, and used the Scheffé test to determine significant
differences of means. Lastly, t-tests were conducted to explore differences in affect between
students intending to major in mathematics and those intending to major in other subject areas.
Regarding the second research question, we analyzed qualitative data from open-ended items
and from transcribed interviews to assess the varying degrees of affect in students relative to
school experience. Following analytic induction (Taylor & Bogdan, 1998), the qualitative data
were analyzed to identify themes and make assertions regarding the focal points that emerged.
Our analysis draws from the research of Di Martino and Zan (2011), focusing on identifying
how one dimension plays into other dimensions. For example, students’ negative affect may
contribute to a negative vision of mathematics or a low self-concept in mathematics, or vice
versa. The thematic codes for the study originated from the TMA model: (a) negative emotional
disposition/vision of mathematics, (2) negative emotional disposition/perceived competence, and
(c) vision of mathematics/perceived competence. For example, descriptive or declarative state-
ments about mathematics were coded as “vision” or “disposition,” while statements about
academic performance were coded as “competence.” Since we were interested in the chronolo-
gical nature of student affect, each code was grouped by grade levels. Student statements on the
curriculum and instruction were coded “school” and “non-school.” Thus, outside tutoring was
coded as “non-school (+ or −, depending on the feeling expressed by the interviewee),” fast-
paced instruction was coded as “school (−),” and a research experience was coded as “school
(+).” The comments that did not fit in with the TMA model were initially tagged with
“descriptors,” but they were revisited with a code when a relevant theme emerged. For example,
“[I] do not plan to study math in college” was initially marked as “vision (−)” and then later
coded as “career (−)” as we began to recognize a link between the affect and students’ interest in
mathematics as a choice of major in college. We note here that the relationship between one
dimension and another evident in student narratives may not be logical but is identified as
largely social, ethical, or psychological (Bruner, 1990) to elucidate the social, ethical, and
psychological causation between learning experiences and student affect, which may be implicit
at best in the quantitative data.
6K.-H. LEE ET AL.
Results
Quantitative results
Student affect by grade level
The differences in affective characteristics by grade level were tested with one-way ANOVA and the
Scheffé test (see Table 1). The results indicated no statistically significant difference in affect by grade
level in learning directivity, anxiety, or confidence. However, students in each grade level demon-
strated statistically different degrees of self-control, interest, and value (p < .05).
More specifically, students in the 10th grade showed the most positive affect, while students in both
11th and 12th grades demonstrated negative affect. One area of affect that was clearly different in each
grade level was interest, for which the Scheffé test indicated that the mean score for 10th graders was
meaningfully higher than that of 11th graders (15.68 vs. 14.30, respectively). The same holds for self-
control, with the mean score for 10th graders being statistically higher than that of 11th graders (15.27
vs. 14.10, respectively). Students in each grade level demonstrated a similar pattern of learning
directivity, but the difference was not statistically significant. What was notable is that the mean affect
scores of value decreased with the grade level – 10th graders’ mean score was 20.14, and 12th graders’
was 18.76 – and the difference was indeed statistically significant, as confirmed by the Scheffé test.
Furthermore, anxiety scores increased and confidence scores decreased at higher grade levels, but
these differences were not statistically significant.
Student affect by perceived competence
The statistical analysis for this comparison is provided in Table 2. The study survey asked the
participants to rate their academic performance in mathematics as high, middle, or low; academic
performance refers to the students’ self-reported class rank or perceived competence. In response, 44
students rated their rank as high, 94 as middle, and 74 as low. Results indicate that students grouped by
academic performance demonstrated differences in all areas of affect except value (p < .001). The
F-score further confirms that the difference by performance level was greater than the difference by
grade level.
Table 1. Affective characteristics by grade level.
Affect
10th grade
(N = 77)
11th grade
(N = 83)
12th grade
(N = 52) F
Post hoc
(Scheffé)
M SD M SD M SD
Learning directivity (max. 20 points) 15.27 3.10 14.10 3.42 14.44 3.09 2.724
Self-control (max. 24 points) 17.39 2.72 16.11 3.37 16.47 2.47 3.941* 2 < 1
Anxiety (max. 16 points) 9.00 2.45 9.59 2.73 9.75 2.28 1.694
Interest (max. 20 points) 15.68 2.76 14.30 2.90 14.57 2.29 5.587*** 2 < 1
Value (max. 24 points) 20.14 2.77 19.83 2.85 18.76 2.88 3.902* 3 < 1
Confidence (max. 16 points) 9.90 2.27 9.40 2.44 9.01 1.76 2.542
*p < 0.05, **p < 0.01, ***p < 0.005
Table 2. Affective characteristics by academic performance.
Affect
High achievers (H) (N = 44) Middle (M) (N= 94)
Low (L)
(N = 74) F
Post hoc
(Scheffé)
M SD M SD M SD
Learning directivity (max. 20 points) 17.05 2.92 14.63 2.76 13.14 3.17 24.382*** L < M < H
Self-control (max. 24 points) 18.67 3.06 16.45 2.69 15.74 2.75 15.669*** L = M < H
Anxiety (max. 16 points) 7.82 2.16 9.60 2.42 10.14 2.51 13.337*** H < M = L
Interest (max. 20 points) 16.16 2.13 14.88 2.58 14.07 3.05 8.429*** L = M < H
Value (max. 24 points) 20.36 2.35 19.74 2.59 19.20 3.38 2.328
Confidence (max. 16 points) 11.48 2.31 9.40 1.88 8.41 1.84 33.799*** L < M < H
***p < 0.001
MATHEMATICAL THINKING AND LEARNING 7
High-ranked students demonstrated the most positive affect in all affect domains except value,
followed by average students and low-ranked students. One-way ANOVA indicated that confidence
was the most influential contributing factor, as demonstrated by the analysis of the mean scores for
confidence in high, middle, and low achievers (11.48, 9.40, and 8.41, respectively), which was also
confirmed by the post hoc test. Similarly, the level of learning directivity varied based on students’
academic performance. While differences in self-control, anxiety, interest, and value were not statis-
tically significant between the middle and low achievers, the means of high achievers remained far
from both groups in these areas of affect.
Differences in affect between those intending to major in math versus non-math
Previously, we examined whether there was a statistically significant difference in the areas of affect by
the type of schooling, grade level, or class rank. This section presents an analysis of the difference by
area of study (i.e., math major, non-math major). The results are presented in Table 3. Among the 135
students in either 11th or 12th grade, the number of students planning to major in mathematics in
college was 10. We first conducted an F-test to confirm the equality of the two variances of the math
major group and the non-math major group, and then conducted t-tests with the assumption of
homogeneity of variance. The results showed a statistically significant difference between the two
groups in all areas of affect except for value, as was the case with the analysis of difference by academic
performance (p < .05).
Overall, we found that the group intending to major in math demonstrated a more positive affect
than the group not intending to major in math. The most notable area of difference was found in the
affect related to self-control: The math major group had a much higher mean score compared with the
non-math major group (19.10 vs. 16.02, respectively). The other areas of affect in which the two groups
differed significantly included confidence, interest, learning directivity, anxiety, and value, with
severity in the same order.
Qualitative results
There remain three specific areas in our quantitative data warranting investigation on student affect
relative to school experience. First, regarding student affect in each grade level, the 10th graders had
more positive affect than the 11th and 12th graders. With the affect of 10th graders as baseline student
affect, student interview data may be expected to shed light on the factors contributing to the more
negative affect of the older students. Second, high-performing students showed positive affect, except
in the area of value. Third, those intending to major in mathematics in college had more positive affect
than those interested in other disciplines. However, the students who selected mathematics as their
major were not found to have more confidence or interest than their peers, although they had more
self-control. This may imply that the students wishing to major in mathematics in college may exercise
high self-control, while they manage their learning to sustain a positive affect. We can use qualitative
analysis to confirm this implication. In the following sections, a detailed description of each theme in
Table 3. Comparison of affect in math vs. non-math students.
Affect
Math major
(N = 10)
Non-math major
(N = 125)
tM SD M SD
Learning directivity (max. 20 points) 16.70 2.83 14.04 3.25 2.515*
Self-control (max. 24 points) 19.10 3.25 16.02 2.93 3.176***
Anxiety (max. 16 points) 7.90 2.23 9.79 2.54 −2.283*
Interest (max. 20 points) 16.70 1.83 14.22 2.65 2.904***
Value (max. 24 points) 20.50 2.46 19.33 2.92 1.229
Confidence (max. 16 points) 11.20 2.82 9.10 2.09 2.985***
*p < 0.05, **p < 0.01, ***p < 0.005
8K.-H. LEE ET AL.
the TMA model (negative emotional disposition/vision of mathematics, negative emotional disposi-
tion/perceived competence, and vision of mathematics/perceived competence) and representative
supporting comments and statements from students are presented. We take the first two themes in
the TMA model in reverse order, because the second theme provides some context for the first theme.
Negative emotional disposition/perceived competence
Our findings revealed that a few high-performing students were satisfied with their learning at the
science high school. In the example that follows, a student explains how he or she benefited from his or
her school experiences:
Some math concepts are provided in the textbook. But I had to figure out some concepts myself, and the process
of doing it myself was rewarding. Working on a problem, I stumble upon a solution. When the solution actually
works, it is interesting and enjoyable. I learned so much mathematics thanks to my education in the science high
school. That would not have been possible had I attended a regular high school. They do not learn the concepts
like eccentricity in regular high schools. (TS4, individual interview, May 24, 2017)
This student cites the school’s ability to provide an environment where he was able to learn the
concepts deeply and the teacher’s provision of challenges as contributing factors to his or her
increasing confidence and interest in mathematics. However, all the high-performing students besides
student TS4 looked to other factors when describing their success. One student mentioned “working
unreasonably hard” (TS2, individual interview, May 23, 2017), while another student explained the
work as “the extra prep just to get ahead for college admission” (TS9, individual interview, May 28,
2017). These data may indicate that, although it is true these students demonstrate positive mathe-
matics-related affect, such affect was rooted in successful academic performance.
What was also shown is students have little confidence in the school’s assessment systems to level
the playing field in education. During the interview, some students mentioned that their peers at the
science high schools had private tutoring as they prepared for admission and continued to get help
from private tutors during the school year. One student wrote that some math teachers assumed
students knew the materials from private tutoring and provided instruction at a much faster speed,
leaving some students frustrated. Students expressed a negative view of the mathematics instruction
and assessment practices of the school. Their negative sentiments are illustrated in the following
excerpt:
I like mathematics, but I have lost confidence. I have poor grades. I need more practice in problem solving to get
better grades. I need to work harder. Unlike other schools, math is so much more important than other subjects at
science high school. That puts a lot of pressure on students. I wish the school would stop pushing us. (FS7,
individual interview, May 22, 2017)
One student with an excellent academic record added his or her view of the teaching and assessment
practices of the school:
I want to do mathematics creatively . . .. But all I am doing now is regurgitating answers on a test in time. All
exams are timed tests. I need extra time – time to think. I hate mathematics now. I still want to major in
mathematics though . . . . Most students have no trouble understanding the concepts. But the math exams in
school are truly about solving problems quickly – this involves using tricks and techniques. I wish they [the
school] allowed us to solve problems with more time, and it is not always about the right answers. Some of us
want to do real mathematics, but there is no space for thinking deeply and creatively and no opportunity for such
experiences. (SS4, individual interview, May 28, 2017)
These statements indicate that mathematics learning in the context of competitive G&T schooling may
play a larger role for students than just being an academic subject for which they have a gift. This
awareness and a sense of fear (thus resulting in a negative affect) were also found in students with low
perceived competence. One student describes his or her struggle:
[Mathematics] is interesting because it has multiple uses in life. But it has just too many topics to master so it is
not interesting anymore. I loved math when I was in middle school. I always had the right answers. Now math is
frightening. Classes move too fast, and I don’t get much of it. It is completely different from middle school math
MATHEMATICAL THINKING AND LEARNING 9
and I am lost. I never imagined math would become so difficult . . . . I wanted to know more how math is applied
to our lives, but what they teach is too formal. I understand this is important, but it is disappointing that all we do
is formal problem solving, and my teacher briefly explains concepts and ends the lesson. (TS6, individual
interview, May 24, 2017)
Negative emotional disposition/vision of mathematics
The mathematics-related affect of the G&T students in our study became negative and was exacer-
bated over time. This negative affect was well captured in the following statements provided by
students describing themselves when they felt they underachieved despite a great deal of effort on
their part: “trapped by a boulder” (TS3, individual interview, May 23, 2017), “frightened and scared”
(SS6, individual interview, May 22, 2017), and “frustrated, unpopular, pathetic, loser, stupid” (SS3,
individual interview, May 23, 2017). This kind of negative academic self-concept (i.e., a low perception
of one’s academic aptitude for a subject; see Marsh, 1991, 2005) serves as the undercurrent of
a negative vision of mathematics: “math is difficult” (TS10, individual interview, May 23, 2017),
“unsure of the benefit of mathematics” (SS5, individual interview, May 26, 2017), “math is annoying
because it doesn’t matter how much time you study” (TS5, individual interview, May 24, 2017), and
“math is never my best friend no matter how hard I try” (TS7, individual interview, May 24, 2017).
An analysis of student statements and comments showed that few 10th graders provided specifics
when describing their vision of mathematics. All 10th graders explained their vision of mathematics as
solving problems correctly and memorizing problem-solving methods. Representative student com-
ments and statements included “mathematics is trying [to solve] problems on your own after teachers
teach us the methods” (FS3, individual interview, May 28, 2017) and “teaching materials at science
high schools are basically about solving problems, though this may not be real mathematics” (FS7,
individual interview, May 22, 2017). Some students perceived mathematics as the foundation of the
sciences (FS1, FS5, individual interview, May 23, 2017) with one student saying, “I am great at
mathematics. Math is the most interesting subject, and it is the foundation for other subjects” (FS1,
individual interview, May 23, 2017).
In contrast, students in 11th and 12th grades did mention specific content topics and the nature of
mathematics as part of their statements regarding positive affect in mathematics, as illustrated in the
following representative student quotes:
It was great to learn vector outer products in linear algebra. This topic is not taught in regular schools. (TS2,
individual interview, May 23, 2017)
I studied how to use a Taylor series to solve differential equations for my senior thesis and felt I accomplished
something great. (SS7, individual interview, May 18, 2017)
[The class] has made me recognize the importance of making proofs mathematically rigorous and accurate. (SS1,
individual interview, May 23, 2017)
Despite the small number of participants, none of the participants who cited a specific math topic had
a negative feeling toward mathematics. As with 10th graders, most students in the 11th and 12th
grades explained their vision of mathematics as solving complex problems through routines and not
promoting their creativity. Representative narratives included “most problems are labor intensive for
drill and practice” (TS1, individual interview, May 24, 2017) and “I want to learn creative mathematics,
but what I do in the classroom is memorize methods and solve complicated problems on tests” (SS4,
individual interview, May 26, 2017). Most students in the 11th and 12th grades indicated that their
vision of mathematics was negative and that their belief was that mathematics was a body of facts and
pieces of knowledge that had little connection to each other.
Vision of mathematics/perceived competence versus positive school experience
Students at the science high school are required to decide on a college major in the 11th grade. Based on
the major selected, students may have different courses of study, including mathematics, and may be
10 K.-H. LEE ET AL.
taught how to strategize for university admission. Those seeking to major in mathematics may have
recognized the value of mathematics and will continue to study mathematics with the goal of exploring the
content and developing a deep interest in the discipline (see the case of SS2). However, those not planning
to do so may relate to mathematics as a service subject and invest their time studying mathematics as part
of their effort to build a strong academic record for university admission (see the case of TS8).
Out of the 19 interviewed participants in the 11th and 12th grades, 4 (SS2, TS2, TS8, and TS11) were
math majors. These students were high performers in their math classes and demonstrated positive
affect. One student stated, “The world is made of mathematics, and I study mathematics to commu-
nicate with the world” (SS2, individual interview, May 23, 2017). This quote indicates that the student
interprets the world through mathematics, and that mathematics is certainly more than a mere
indicator of academic excellence for university admission. Another student spoke positively about
his or her school experience and mentioned an enrichment activity called research and education
(R&E) as being the best learning experience:
I love mathematics, though I also have doubts. Do I like mathematics because I do better [in math] than [in] other
subjects? I enjoy solving complex problems, and it is exciting to find new methods to solve the problems . . . .
People tell me high school math is [too easy] compared to college mathematics. So, I am worried about whether
I will be able do well in the university and whether I will get to do my own research in math . . . . During the R&E
activity, I experienced what mathematics research is all about. Overall, my education at the science high school
was very satisfactory. (TS8, individual interview, May 24, 2017)
Another student’s vision of mathematics was that “mathematics serves as the instrument of logic for
the sciences, and it is a valuable discipline to learn because nature can be expressed through mathe-
matics” (TS2, individual interview, May 23, 2017). This student also stated that his or her R&E
experience was positive and made him look forward to taking math courses in college. We also had
student comments such as “I liked when I learned ideas behind math formulas that students in regular
high schools would be told to memorize” (TS11, individual interview, May 23, 2017). This quote
suggests that some teachers do teach concepts and mathematical ideas as a part of instruction. The
student continued, “Science high school is great when you get used to it and can overcome challenges,
but it is a nightmare when you’re lost and give up.”
Discussion
Survey results
One of the major findings of the study was that science high school students demonstrated high
learning directivity, self-control, interest, and value. However, of noticeable interest was the fact that
anxiety was prevalent among students. This differs from the low anxiety among mathematically G&T
students in regular academic settings reported by Pajares (1996) and calls for recognizing student
affect in specialized schools.
Regarding the affective characteristics of the students at the science high school, we found that self-
control, interest, and value differed at each grade level. Students developed negative affect in the areas
of self-control, interest, and value across time. Considering that the 12th graders who participated in
the study were not necessarily in the top quartile of the class, we anticipated that this group would have
the most negative affect. However, it was the 11th graders who demonstrated the lowest self-control
and interest. This indicates that the transition time during the first year at the science high school may
have played a critical role in negatively shaping student affect (i.e., self-control and interest) and that
appropriate counseling and other academic support activities are needed to help the students make
a smoother transition. Perhaps there is a honeymoon effect on the first-year students’ affect (see
Goleman et al., 2002 who describe a jump start on new skills in the training program that lasts a short
time) in the beginning and “light at the end of the tunnel” effect (e.g., Ji et al., 2017 about using positive
prospective imagery to increase optimism in mental health interventions) toward the end. However,
there is limited research on affect in educational contexts in reference to the two effects.
MATHEMATICAL THINKING AND LEARNING 11
In addition to examining differences in affect by grade level, the difference was analyzed in terms of
students’ perceived competence. A major finding was that high-performing students showed more
positive affect than their peers, which confirms the extant affect literature that academic performance
in math classes is positively correlated with student affect. On the other hand, we found that the value
differed only slightly by academic performance. We interpret this as a strong indication that students
in this science high school, regardless of their current academic performance, accept mathematics as
a highly valuable subject, either as a tool for science or as a highly weighted subject for GPAs. Because
we suspect this could be true in any group of G&T students in a specific discipline (e.g., mathematics,
music, or physics), this calls for support that fosters positive emotions when learning poses intellectual
challenges. Such support could help shape productive social and academic identities instead of
reinforcing the value of certain disciplines.
As with the students’ perceived competence, an intention to major in mathematics in college was
closely related to positive affective characteristics. That is, those intending to major in mathematics
demonstrated a more positive affect than other students, suggesting that those who have a positive
affect in mathematics are also likely to major in mathematics in college. We also found that the affect
related to value was not as closely related to an intention to major in mathematics in college. This
indicates that a sense of mathematics as a valuable discipline may not be the best attractor to
mathematics as a major in college, but that when students do decide to major in the subject, it is
due to a combination of good grades and a positive affect toward mathematics.
What student voices reect
Our narrative of G&T schooling that explains student affect
One significant takeaway from our quantitative data was that the students at the science high school
demonstrated a different level of affect according to their grade level, perceived competence, and
selection to major in mathematics. We posited that grade level, class rank, and college planning could
be surface features under which different types of factors unique to the science high school may exist.
Our narrative of varying factors that influence student affect in the science high school is as follows in
four themes:
●The policy of accelerated school curriculum promoted fast-paced instruction and resulted in
achievement gaps among G&T students.
●Those who fell behind in class and performed poorly in the traditional assessment system had
a feeling of relative intellectual inferiority in math compared to their high-performing peers.
●Students felt that their struggles were caused by accelerated instruction and that the policy was
inequitable because such instruction rewards those who studied the curriculum in advance
through private tutoring.
●Most students, whether high performers or underperformers, despised rote learning and con-
sidered their student research experience through the R&E activity as reflecting meaningful
mathematics.
Themes 1, 2, and 3 indicate that fast-paced instruction and the traditional assessment system were
the primary cause of negative student affect. That is, a low grade in mathematics causes students to
have a lower perception of their competence in mathematics, which ultimately explains much of the
students’ negative emotions toward mathematics and the vision of mathematics as an automated
exercise of complex routines in problem solving, as implied by Di Martino and Zan (2011). Theme 4,
however, indicates that the student research experience was a meaningful school experience that
played a prominent role in shaping a positive student affect. The fact that most of the mathematically
G&T students at the science high school have developed negative mathematics-related affect poign-
antly reveals that the school, aside from the development of student intellect, may have a different (and
12 K.-H. LEE ET AL.
perhaps overriding) purpose that guides the school’s curriculum and instruction. Next, we discuss this
in detail.
Aiming to kill two birds with one stone
The science high school in this study implemented a twofold G&T schooling that attempts to kill two
birds with one stone, that is complete advanced course work in mathematics and successful college
admission. First, the school provides a college preparatory program. That is, they implement a college-
preparatory school curriculum, and their assessment practices of students’ performance in that
curriculum produce class ranks that serve as a key university admission criterion. In this context,
the summative assessments implemented in the science high school were timed and paper-and-pencil
based, and they tested the content in strict alignment with the school mathematics curriculum.
Summative assessment may cause students to memorize problem-solving techniques and strategies
(i.e., “instrumental understanding” in Skemp, 1976), focusing on practice and drill to solve problems
accurately in a short time along with using short-cuts on timed tests rather than applying conceptual
mathematical understanding (i.e., “relational understanding” in Skemp, 1976) with deep analysis.
Second, the school provides talent development in mathematics and science and offers a fast-track
secondary education in which students are expected to finish the school curriculum in the first 2 years
of schooling and gain early admission to a science university, or continue to prepare for college in their
senior year. Regarding the school’s specialized curriculum in mathematics and science, students stated
that they recognize the importance of mathematics as the foundational tool for studying science,
which influenced their attitude toward it. Most students indicated that they formed a positive affect in
mathematics thanks to experiences of learning advanced mathematics, where they had the opportunity
to practice college-level mathematics. This exposure to college mathematics in high school fostered
a positive affect for some students in their learning directivity, interest, and value.
In particular, the participants who planned to major in subjects other than mathematics in college
also developed a high level of interest in studying mathematics (see Table 3) as they became increas-
ingly aware that mathematics remained highly relevant to understanding and expressing ideas in
science (evident in student comments, such as “I realized that [math is] the language of science”; “[we
can] represent the nature in math”). Aside from the usefulness of mathematics in learning science,
some students mentioned attaining an increased sense of accomplishment from applying mathema-
tical concepts to science in their research activities. On the other hand, participants expressed
frustration over the reality of competing with their peers highly gifted in mathematics. They perceived
that their study hours in mathematics did not reward them, as the hours did not correlate to their
actual performance in math. Low performance on tests resulted in students having a low sense of
achievement in mathematics, thereby generating a negative affect toward mathematics. A lower sense
of self-worth was exacerbated when students with a low class rank compared themselves to classmates
with a high class rank.
Missing both birds
Based on the findings of this study, we consider that this reality of two different purposes of schooling
(i.e., advanced mathematical knowledge and successful college admission) has bred incongruous
pedagogy and contributed to students’ low affect in mathematics (see Moon et al., 2002, for the US
context; K. Lee et al., 2011 for the Korean context). What we mean by incongruous pedagogy is that
students at science high schools are on a track to finish high school mathematics in one-and-a-half
years, while in traditional high schools, it would take 3 years. Once students complete the school
mathematics curriculum, they learn advanced mathematics and Advanced Placement calculus. This
reality is also the root cause of fast-paced instruction.
In describing the learning experience at science high schools, instructional pacing also emerged
as a highly significant element in understanding G&T students’ affect in mathematics. The
participants described in detail the negative effects of the fast-paced teaching of advanced mathe-
matics content, including their perception that teachers are not teaching basic and fundamental
MATHEMATICAL THINKING AND LEARNING 13
concepts, the lack of processing time to develop a clear understanding of difficult math concepts,
and the excessive number of topics to review, with little study time provided to catch up. According
to students, while fast-paced instruction covers many topics, it fails to engage them in deep inquiry;
students felt that this instructional model lacked opportunities to work creatively. The students
who perceived math classes as moving too fast indicated that teachers assume that students have
learned materials beforehand and thus decide to teach at a faster pace, which the students feel is
harmful to their learning. Representative student narratives include, “there is little time for
exploration in problem solving. Most teachers think we know the material already and move too
fast” (FS3, individual interview, May 28, 2017) and “I fared well when I was a freshman because
I studied the material in advance before school started. But I wasn’t able to get a head start on the
material in 11th grade. In the 11th grade and later, there is a large gap between those who studied
the material in advance and those who couldn’t” (SS8, individual interview, May 18, 2017). SS8’s
statement may explain why students in the 11th and 12th grades more intensely disapproved of the
fast-instructional pacing of their math classes. This conflicting reality further explains why students
felt that those who had a head start on the school coursework through private tutoring were better
positioned to advance in the class rankings and that those who did not prepare in advance fell
behind their peers.
The price of valuing test scores over talent development
The central finding of this study is that students’ negative mathematics-related affect is related to the
perception that their peers are more advanced mathematically because they had private tutoring before
taking the fast-paced advanced math classes. Furthermore, they perceived the pace of instruction as
having more to do with the school’s accelerated curricular policy and little to do with the academic
needs or developmental nature of G&T students. At this juncture, we were compelled to examine more
closely how the participants expressed their emotions about their status in the classroom, especially
when their performance was poorer than that of their peers. The participants indicated that their
affective positions were influenced by mathematics being the school subject in which their performance
plays a key role in raising their class rank. The close tie between math performance and class rank
provided students with school stress and pressure, which resulted in a students’ negative affect toward
mathematics. For example, most participants in the study indicated that they had had a great deal of
motivation and interest in mathematics in middle school but had since lost interest in mathematics,
mainly from the self-realization that after they began competing with highly G&T peers, they might not
be as successful (i.e., they had lower test scores) as they had originally perceived. We refer here to Kim
(2003), who argues that G&T students have high academic self-concepts in a mixed ability group, but
struggle with shaping positive self-identity in a homogenous academic group. Kim also described this
phenomenon as the BFLPE (p. 92; see also Marsh & Parker, 1984).
Students, however, did not form negative affect (i.e., BFLPE) when they participated in R&E as
a homogenous group. In fact, students, regardless of their class rank, major, and grade level, clearly stated
that the R&E activity contributed to their positive affect in mathematics. The BFLPE manifested itself
primarily because the students were under pressure to prepare rapidly for college admission, and their
ranking was based on performance in courses that evaluated student performance in relation to the
performance of students who are highly G&T in mathematics. As a result, the students felt inferior to these
high-performing peers and lost confidence in their performance. This undoubtedly led to their negative
affect in mathematics. This finding implies that these students would benefit from a differentiated college
admission system in which students are recognized for their creativity and excellence in mathematics and
science, as opposed to the mastery of an accelerated school curriculum. Such changes in policy are crucial
to efforts that might directly impact our G&T students in mathematics and science.
The source of positive affect
The G&T students in our study strongly believed that math was a useful subject. The utility of school
mathematics is twofold: It has both instrumental usefulness and an intrinsic value. Instrumental
14 K.-H. LEE ET AL.
usefulness includes the value of mathematics in real life, as a foundational basis for sciences,
a communicative medium, and a study in a formal discipline (Ernest, 2016). We found the students
at the science high school had a clear sense of the instrumental usefulness of math.
The literature discusses the value of a rigorous math curriculum in terms of the extent to which
students achieve cognitive understanding. What our findings indicate goes beyond the cognitive value
of advanced curriculum and supports the idea that G&T students have the capacity to engage in
difficult mathematics and develop positive affect in mathematics. This is especially true when the
difficult mathematics serves as a vehicle for understanding challenging concepts in science. One
finding of this study was that students formed low mathematics-related affect when they encountered
fast-paced instruction and timed tests. At first glance, this finding seems to conflict with research that
G&T students thrive in a rigorous mathematics curriculum. However, our study confirms that
students appreciate challenging math concepts but are stressed about their performance on timed
tests in school mathematics (e.g., Lewis, 2013), as this is the singular criterion not only for social status
on campus, but ultimately also for their college admission decisions.
Furthermore, we found that G&T students were able to distinguish between a fast-track curriculum
designed to promote exploration and creativity, and a fast-track curriculum rewarding only those with
prior knowledge of the material from private tutoring. Students’ negative feelings toward the kind of G&T
schooling that promotes academic performance over developing talent and exploring advanced mathe-
matics remained stronger among students in 11th and 12th grades than in 10th grade. It was noticeable
that the students in our study reported enjoying the R&E activity because R&E involves not only the
advanced content, but also independent exploration and research, as well as writing academic papers.
Implications
The field of G&T education in mathematics has focused on defining and identifying mathematically
gifted students and designing and implementing a G&T program. However, G&T programs have not
been successful in resolving the BFLPE, resulting in negative student affect. This study contributes to the
literature by examining the ways in which students develop negative affect in special schools. The study
provides a narrative of student perceptions at a science high school, describing the way the three
dimensions in Di Martino and Zan (2011) study play into the student affect of mathematics in school-
based G&T programs. However, this study found the link between the negative emotional disposition
and vision of mathematics to be not very strong. When students recognize their potential in mathematics
through research activities, they are more likely to have positive feelings and visions in mathematics.
What lies implicit yet resounding in this finding is the way G&T students in mathematics in Korea
demonstrated negative affect due to the BFLPE, but a positive affect emerged when students realized their
potential in mathematics through mathematically rich and meaningful activities, which challenge and
inspire them as opposed to getting compared with and competing with their peers . The thematic factors
of student affect reported in this study are highly relevant to the culture of one country in the Asia-Pacific
region. Therefore, future studies from other countries on G&T students in special schools for mathe-
matics and science should document their students' experiences as part of the international comparative
literature on mathematically gifted students.
Note
1. The reason for the decrease in the number of participants in the senior year is that 29 students with a qualifying
GPA at the time of their first semester in 11th grade either graduated early or received an early admission decision
from universities. The study included 55 senior students who could not graduate early or received no early
decision. We took this into consideration in our data analysis.
MATHEMATICAL THINKING AND LEARNING 15
Notes on contributors
Kyeong-Hwa Lee is a full professor in the department of mathematics education at Seoul National University, Korea. Her
research and teaching interests span creativity education, gender issues, curriculum development, probability and
statistics education, and pre- and in-service mathematics teacher education.
Yeongjun Kim is an undergraduate in the department of mathematics education at Seoul National University, Korea. He
has been engaged in programs for the gifted and talented in mathematics and science as a student and researcher. He is
interested in using modelling approaches to improve student understanding in mathematics
Woong Lim is an associate professor at Yonsei University, Korea. His scholarly agendas include interrelations between
language and mathematics, transition to college mathematics, classroom interactions, and the role of digital technology
in mathematics education.
ORCID
Woong Lim http://orcid.org/0000-0002-4329-952X
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Appendix 1
Alignment between survey items and (1) C. Lee et al.’s (2011) instrument, (2) the TMA model, and (3) the research
questions
Scale
ID Item wording (translated from Korean)
C. Lee et al.
(2011) TMA model
Research
question
B3 What is your current academic achievement level in mathematics? ①
Upper ② Middle ③ Lower
Perceived-
competence
1
B4 How much do you like math? ①like very much ② Like ③ So-so ④
Dislike ⑤ Dislike very much.
Interest Disposition 1
B5 How important do you think math will be in your post-college life? ①
very important ② somewhat important ③ It doesn’t seem to matter.
④ Not important at all
Value Vision 1
B6 Mark any feelings you often feel when studying math or solving math
problems.
① Curiosity ② Comfort ③ Pleasure ④ Confidence ⑤ Achievement
⑥ Upset ⑦ Anxiety ⑧ Confused ⑨ Frustrated ⑩ Withdrawn
Other ( )
Interest,Anxiety,
Learning
directivity
Disposition,
Perceived-
competence
1
B7 Here are several descriptions of mathematics. Please choose the one
you most agree with.
(1) Mathematics is not a final product but a process of inquiry and
accumulation of knowledge.
(2) Mathematics is a single, unchanging system of knowledge, not
created, but discovered.
(3) Mathematics is a tool, a collection of practical rules and facts for
pursuing external ends.
Value Vision 1
C1 I enjoy solving complex and difficult math problems. Learning
directivity
Disposition 1
C2 I often feel nervous about doing poorly before I take a test. Anxiety Disposition 1
C3 I like to solve difficult math problems even though I don’t solve them
correctly.
Learning
directivity
Disposition 1
C4 I am worried and lose sleep over exams. Anxiety Disposition 1
C5 I can focus on studying even when I learn math topics that I don’t enjoy
very much.
Self-control Perceived-
competence,
Disposition
1
C6 I know how to study mathematics effectively. Self-control Perceived-
competence
1
C7 I don’t procrastinate when I need to study mathematics. Self-control Disposition 1
C8 If one is good at mathematics, one can be more successful in one’s
career.
Value Vision 1
C9 I am nervous about making mistakes when I present in the math class. Anxiety Disposition 1
C10 I prefer to solve one challenging than many easy problems. Learning
directivity
Disposition 1
(Continued)
MATHEMATICAL THINKING AND LEARNING 19
Scale
ID
Item wording (translated from Korean) C. Lee et al.
(2011)
TMA model Research
question
C11 I always enjoy solving unfamiliar math problems. Learning
directivity
Disposition 1
C12 I like to solve a math problem that may take a lot of time but makes me
think harder.
Learning
directivity
Disposition,
Perceived-
competence
1
C13 Math is a fun subject. Interest Disposition 1
C14 I don’t lose control and focus until I complete any math test. Self-control Perceived-
competence,
Disposition
1
C15 I don’t like studying mathematics. Interest Disposition 1
C16 If one is good at math, one can go to a good college. Value Vision 1
C17 Math is boring. Interest Disposition 1
C18 If I work harder, I can get better at math. Confidence Perceived-
competence
1
C19 I am worried about making a mistake when I solve a math problem
before class.
Anxiety Disposition 1
C20 Math is very useful in everyday life. Value Vision 1
C21 Time seems to go faster when I study math. Interest Disposition 1
C22 Math helps people think logically. Value Vision 1
C23 I think mathematics is easy. Confidence Perceived-
competence,
Disposition
1
C24 I am good at math. Confidence Perceived-
competence,
Disposition
1
C25 I study math on my own and need nobody to force me to study it. Self-control Perceived-
competence,
Disposition
1
C26 I do not do well in mathematics. Confidence Perceived
competence
1
C27 Math is an important school subject. Value Vision 1
C28 Once I start studying mathematics, I don’t get distracted much. Self-control Perceived-
competence,
Disposition
1
C29 Math will be useful in many jobs in the future. Value Vision 1
C30 I enjoy studying mathematics. Interest Disposition 1
D1 Please explain why you are studying math. Vision,
Disposition,
Perceived-
competence
1
D2 (For Grades 11 and 12) If you have had changes in your attitudes,
beliefs, or feelings about mathematics during your high school
career, please describe them and explain why.
Vision,
Disposition,
Perceived-
competence
2
20 K.-H. LEE ET AL.
