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

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 affect in a science high school in Korea to determine how the specialized school’s curriculum and instruction influence student affect. Data were collected through interviews and a survey. Our findings show that gifted and talented students generally demonstrate a positive affect toward mathematics, but high anxiety and low self-concept play a key role in shaping students’ negative attitudes toward mathematics. In this paper, we argue that two different goals – gifted education and college preparation – could cause such negative student affect. The dual educational goal manifests itself in fast-paced instruction and memorized problem solving, which can ultimately cause students to lose confidence and interest in mathematics.

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.

Literature review

Identification 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 programs 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 characteristics 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.

Affective 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, 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 mathematics, feelings toward mathematics, and behavior in mathematics learning.

Figure 1. The TMA model (Di Martino & Zan, 2011, p. 476)

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:

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 benchmark 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 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 55¹ 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 mathematics. Anxiety describes learners’ worried or anxious psychological state when they deal with mathematics. 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 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 statements about mathematics were coded as “vision” or “disposition,” while statements about academic performance were coded as “competence.” Since we were interested in the chronological 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.

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 demonstrated statistically different degrees of self-control, interest, and value (p < .05).

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

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 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

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 statistically 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).

Table 3. Comparison of affect in math vs. non-math students

Affect	Math major (N = 10)		Non-math major (N = 125)		t
	M	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

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 the TMA model (negative emotional disposition/vision of mathematics, negative emotional disposition/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 mathematics-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 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 exacerbated 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 comments 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 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 communicate 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 mathematics” (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.

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 reflect

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 considered 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 poignantly reveals that the school, aside from the development of student intellect, may have a different (and 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 increasingly 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 mathematical 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 mathematics content, including their perception that teachers are not teaching basic and fundamental 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 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 mathematics 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 mathematics and science should document their students' experiences as part of the international comparative literature on mathematically gifted students.

Additional information

Notes on contributors

Kyeong-Hwa Lee

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

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

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.

Notes

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.

Appendix 1

Alignment between survey items and (1) C. Lee et al.’s (2011) instrument, (2) the TMA model, and (3) the research questions

Table

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 ⑪ 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
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