Mathematical Curiosity , Epistemological Beliefs , and Mathematics Performance of Freshman Preservice Teachers

There are many factors that infl uence academic performance of students. Some of these are related to personological, sociological, and psychological factors. In recent years, academic achievement and performance have been linked to several psychological factors. Two of these psychological factors that may have direct impact or infl uence on academic performance are curiosity and epistemological beliefs. The study described the level of mathematical curiosity and epistemological beliefs of fi rst year preservice teachers. Mathematical curiosity includes epistemic curiosity, perceptual curiosity, exploration, and absorption. Epistemological beliefs include certainty of knowledge, source of knowledge, structure of knowledge, control of knowledge acquisition (personal), control of knowledge acquisition (general), and speed of knowledge acquisition. Three research instruments were utilized in this study, namely: Curiosity Inventory, Epistemological Beliefs Inventory, and Mathematics Performance Test. The participants of the study were 167 freshman preservice teachers. Data revealed that mathematics curiosity and epistemological beliefs are signifi cantly related to mathematics performance and they also signifi cantly infl uence mathematics performance. KEY WORD: Psychological factor, epistemological beliefs, mathematics curiosity, preservice teachers,and mathematics performance. ABSTRAKSI: “Keingintahuan Matematis, Keyakinan Epistemologis, dan Kinerja Matematika Mahasiswa Calon Guru”. Ada banyak faktor yang mempengaruhi prestasi akademik mahasiswa. Beberapa hal ini terkait dengan faktor personalogis, sosiologis, dan psikologis. Dalam beberapa tahun terakhir, prestasi dan kinerja akademik telah dikaitkan dengan beberapa faktor psikologis. Dua dari faktor-faktor psikologis yang mungkin memiliki dampak langsung atau pengaruh terhadap kinerja akademis adalah rasa ingin tahu dan keyakinan epistemologis. Studi ini menggambarkan tingkat rasa ingin tahu matematika dan keyakinan epistemologis mahasiswa guru dalam pra-jabatan tahun pertama. Keingintahuan matematika termasuk rasa ingin tahu secara epistemik, persepsi rasa ingin tahu, eksplorasi, dan penyerapan. Keyakinan epistemologis termasuk kepastian pengetahuan, sumber pengetahuan, struktur pengetahuan, pengendalian akuisisi pengetahuan (personal), pengendalian akuisisi pengetahuan (umum), dan kecepatan akuisisi pengetahuan. Tiga instrumen penelitian yang digunakan dalam penelitian ini, yaitu: Inventarisasi Keingintahuan, Inventarisasi Keyakinan Epistemologis, dan Uji Kinerja Matematika. Para peserta penelitian adalah 167 mahasiswa calon guru. Data mengungkapkan bahwa rasa ingin tahu matematika dan keyakinan epistemologis secara signifi kan terkait dengan kinerja matematika dan keduanya juga secara signifi kan mempengaruhi kinerja matematika. KATA KUNCI: Faktor psikologis, keyakinan epistemologis, rasa ingin tahu matematika, mahasiswa calon guru, dan kinerja matematika. About the Authors: Rene R. Belecina, Ph.D. is a Full Professor at the College of Graduate Studies and Teacher Education Research PNU (Philippine Normal University). Jose M. Ocampo, Jr., Ph.D. is a Full Professor at the Faculty of Education Sciences PNU (Philippine Normal University). Corresponding authors are: rrbelecina@yahoo.com and juno_6970@yahoo.com How to cite this article? Belecina, Rene R. & Jose M. Ocampo, Jr. (2016). “Mathematical Curiosity, Epistemological Beliefs, and Mathematics Performance of Freshman Preservice Teachers” in MIMBAR PENDIDIKAN: Jurnal Indonesia untuk Kajian Pendidikan, Vol.1(1) Maret, pp.123-136. Bandung, Indonesia: UPI Press. Chronicle of the article: Accepted (December 13, 2015); Revised (January 29, 2016); and Published (March 11, 2016). RENE R. BELECINA & JOSE M. OCAMPO, JR., Mathematical Curiosity, Epistemological Beliefs, and Mathematics Performance 124 © 2016 by UPI Press, Bandung, West Java, Indonesia Website: http://ejournal.upi.edu/index.php/mimbardik INTRODUCTION There are many factors that infl uence academic performance of students. Some of these are related to personological, sociological, and psychological factors. In recent years, academic achievement and performance have been linked to several psychological factors. Two of these psychological factors that may have direct impact or infl uence to academic performance are curiosity and epistemological beliefs. Several researches have attempted to relate curiosity to various measures of academic achievement, learning performance, and understanding (Berlyne, 1960a, 1960b, and 1966; and Keller, 1999). W.H. Maw & E.W. Maw (1972)’s fi ndings, as cited also by H. Unal (2005), open up another dimension of the role of curiosity on mathematics, since high curious students can comprehend more than low curious students, and comprehending the problems has effects on success in problem solving (Maw & Maw, 1972; and Unal, 2005). However, there is no empirical study to say that high curious students are better problem solvers than low curious students in mathematics. In recent years, psychologists have become interested in whether people other than philosophers have ideas about what knowledge is and how knowledge is justifi ed. In other words, psychologists have wondered if people have beliefs about epistemological questions (called epistemological beliefs or personal epistemological beliefs), and whether these beliefs affect in any way their learning or reasoning. A large research effort has been devoted to investigating correlations between epistemological beliefs and performance on learning and reasoning tasks. A few typical fi ndings include the following. Firstly, students who believe that knowledge is certain write essays that reach unqualifi ed conclusions, even when there is evidence supporting different viewpoints, as well (Schommer, 1990). Secondly, students who believe that knowledge consists of ideas that are interconnected (rather than a disconnected series of facts) are better able to understand texts that present alternative positions on controversial ideas (Kardash & Scholes, 1996). Thirdly, students with more sophisticated epistemological beliefs were better able to learn from an inquirybased learning environment (Windschitl & Andre, 1998). These fi ndings should not be interpreted as showing that there are always strong relationships between measure of epistemological beliefs and measure of learning and reasoning. Some have found little relationship, for example, between reasoning and beliefs about the nature of science, and students who exhibit strong progress in reasoning better may show no gains at all in epistemological beliefs (Sandoval & Morrison, 2003). In addition, correlations between epistemological beliefs and measures of learning and reasoning are often relatively low. In recent years, concerns of mathematics education focus on the performance of pre-service teachers most specially on content rather than on pedagogy. Researches in mathematics education focus on the investigation of factors that affect mathematics performance of pre-service teachers (cf Hackett & Betz, 1989; Hyde, Fennema & Lamon, 1990; Cooper & Robinson, 1991; and Isiksal, 2005). This study was an attempt to describe the relationship of mathematical curiosity and epistemological beliefs to mathematics performance of pre-service teachers. CONCEPTUAL FRAMEWORK AND STATEMENT OF THE PROBLEM B. Renner (2006) reported that curiosity has been conceptualized as the desire for new information and knowledge. Thus, given the importance and relevance of curiosity to learning, researchers developed various measures to assess individual differences in curiosity. D.E. Berlyne (1960) recognized MIMBAR PENDIDIKAN: Jurnal Indonesia untuk Kajian Pendidikan, 1(1) Maret 2016 125 © 2016 by UPI Press, Bandung, West Java, Indonesia Website: http://ejournal.upi.edu/index.php/mimbardik that the concept had become fragmented and proposed a categorization of different types of curiosity. He located curiosity on two dimensions: one extending between perceptual and epistemic curiosity. Perceptual curiosity refers to a drive which is aroused by novel stimuli and reduced by continued exposure to these stimuli (Berlyne, 1960). On the other hand, epistemic curiosity refers to desire for knowledge and applied mainly to humans (Loewenstein, 1994). Over the past two decades, the study of students’ mathematics-related beliefs has gradually received more and more attention in the fi eld of mathematics education research. Positive beliefs about mathematics and mathematics learning are considered as a major component of competence in mathematics (De Corte, 2008). M. Schommer (1990) proposed fi ve dimensions of epistemological beliefs. These are certainty of knowledge, structure of knowledge, source of knowledge, control of knowledge acquisition, and speed of knowledge acquisition (cf Schommer, 1990; and Bonjour, 2002). The conceptual paradigm of this study is shown in fi gure 1. The paradigm shows the dimensions of mathematical curiosity and epistemological beliefs and their infl uence to mathematics performance. The study aimed to describe the mathematical curiosity, epistemological beliefs, and mathematics performance of freshman pre-service teachers. It also determined the relationship of the mathematical curiosity and epistemological beliefs to mathematics performance. Specifi cally, it sought answers to the following questions. Firstly, what is level of mathematics curiosity of pre-service teachers in terms of the following: epistemic curiosity, perceptual curiosity, exploration, and absorption? Secondly, what is the level of epistemological beliefs of pre-service teachers in terms of the following: certainty of knowledge, source of knowledge, structure of knowledge, control of knowledge acquisition (personal), control of knowledge Mathematical Curiosity: Perceptual Curiosity Epistemic Exploration Absorption Mathematics Performance Epistemological Beliefs: Certaint


INTRODUCTION
There are many factors that infl uence academic performance of students.Some of these are related to personological, sociological, and psychological factors.In recent years, academic achievement and performance have been linked to several psychological factors.Two of these psychological factors that may have direct impact or infl uence to academic performance are curiosity and epistemological beliefs.
Several researches have attempted to relate curiosity to various measures of academic achievement, learning performance, and understanding (Berlyne, 1960a(Berlyne, , 1960b(Berlyne, , and 1966;;and Keller, 1999).W.H. Maw & E.W. Maw (1972)'s fi ndings, as cited also by H. Unal (2005), open up another dimension of the role of curiosity on mathematics, since high curious students can comprehend more than low curious students, and comprehending the problems has effects on success in problem solving (Maw & Maw, 1972;and Unal, 2005).However, there is no empirical study to say that high curious students are better problem solvers than low curious students in mathematics.
In recent years, psychologists have become interested in whether people other than philosophers have ideas about what knowledge is and how knowledge is justifi ed.In other words, psychologists have wondered if people have beliefs about epistemological questions (called epistemological beliefs or personal epistemological beliefs), and whether these beliefs affect in any way their learning or reasoning.
A large research effort has been devoted to investigating correlations between epistemological beliefs and performance on learning and reasoning tasks.A few typical fi ndings include the following.Firstly, students who believe that knowledge is certain write essays that reach unqualifi ed conclusions, even when there is evidence supporting different viewpoints, as well (Schommer, 1990).Secondly, students who believe that knowledge consists of ideas that are interconnected (rather than a disconnected series of facts) are better able to understand texts that present alternative positions on controversial ideas (Kardash & Scholes, 1996).Thirdly, students with more sophisticated epistemological beliefs were better able to learn from an inquirybased learning environment (Windschitl & Andre, 1998).
These fi ndings should not be interpreted as showing that there are always strong relationships between measure of epistemological beliefs and measure of learning and reasoning.Some have found little relationship, for example, between reasoning and beliefs about the nature of science, and students who exhibit strong progress in reasoning better may show no gains at all in epistemological beliefs (Sandoval & Morrison, 2003).In addition, correlations between epistemological beliefs and measures of learning and reasoning are often relatively low.
In recent years, concerns of mathematics education focus on the performance of pre-service teachers most specially on content rather than on pedagogy.Researches in mathematics education focus on the investigation of factors that affect mathematics performance of pre-service teachers (cf Hackett & Betz, 1989;Hyde, Fennema & Lamon, 1990;Cooper & Robinson, 1991;and Isiksal, 2005).
This study was an attempt to describe the relationship of mathematical curiosity and epistemological beliefs to mathematics performance of pre-service teachers.

CONCEPTUAL FRAMEWORK AND STATEMENT OF THE PROBLEM
B. Renner (2006) reported that curiosity has been conceptualized as the desire for new information and knowledge.Thus, given the importance and relevance of curiosity to learning, researchers developed various measures to assess individual differences in curiosity.D.E.Berlyne (1960) recognized that the concept had become fragmented and proposed a categorization of different types of curiosity.He located curiosity on two dimensions: one extending between perceptual and epistemic curiosity.Perceptual curiosity refers to a drive which is aroused by novel stimuli and reduced by continued exposure to these stimuli (Berlyne, 1960).On the other hand, epistemic curiosity refers to desire for knowledge and applied mainly to humans (Loewenstein, 1994).
Over the past two decades, the study of students' mathematics-related beliefs has gradually received more and more attention in the fi eld of mathematics education research.Positive beliefs about mathematics and mathematics learning are considered as a major component of competence in mathematics (De Corte, 2008).
M. Schommer (1990) proposed fi ve dimensions of epistemological beliefs.These are certainty of knowledge, structure of knowledge, source of knowledge, control of knowledge acquisition, and speed of knowledge acquisition (cf Schommer, 1990;and Bonjour, 2002).The conceptual paradigm of this study is shown in fi gure 1.The paradigm shows the dimensions of mathematical curiosity and epistemological beliefs and their infl uence to mathematics performance.
The study aimed to describe the mathematical curiosity, epistemological beliefs, and mathematics performance of freshman pre-service teachers.It also determined the relationship of the mathematical curiosity and epistemological beliefs to mathematics performance.
Specifi cally, it sought answers to the following questions.Firstly, what is level of mathematics curiosity of pre-service teachers in terms of the following: epistemic curiosity, perceptual curiosity, exploration, and absorption?
Secondly, what is the level of epistemological beliefs of pre-service teachers in terms of the following: certainty of knowledge, source of knowledge, structure of knowledge, control of knowledge acquisition (personal), control of knowledge  Thirdly, is there a signifi cant relationship between mathematics performance and the following variables: mathematical curiosity and epistemological beliefs?
Fourthly, which of the following variables signifi cantly infl uence mathematics performance: mathematical curiosity and epistemological beliefs?

METHODS
Research Design.The study employed the descriptive research design.According to J.W. Best & J. Kahn (1989), descriptive research seeks to fi nd answers to questions through the analysis of variable relationships.The variables are non-manipulable, because the events and conditions have already occurred.Thus, the researcher merely selects the relevant variables for an analysis of their relationships (Best & Kahn, 1989).
The descriptive research design is the most appropriate design in this study, because it is endeavour to describe the mathematical curiosity and epistemological beliefs of freshman pre-service teachers.Moreover, it also attempted to fi nd the relationships of these variables to their mathematics performance.
Participants of the Study.The participants of the study were 167 freshman pre-service teachers from four randomly chosen sections of PNU (Philippine Normal University) during the School Year 2013-2014.Table 1 shows the distribution of the students according to sections.
Research Instrument.The following research instruments were used in this study.Firstly, Curiosity Inventory.This instrument was used to measure students' feelings about mathematical stimuli that activate cognitive processes (epistemic curiosity); sensory mathematical stimuli (perceptual curiosity); appetitive strivings for novelty (exploration); and full engagement in specifi c activities (absorption).
It also measures students' tendency to seek out opportunities for acquiring facts, knowledge, and ideas in mathematics.This instrument has four dimensions with a total of 30 items.Table 2 shows the dimensions of this instrument and the corresponding number of items.
Each item in the instrument is answerable using a 5-point scale, as showen in table 3.
Scores for the individual subscales are computed by taking the mean of the items within that subscale.See table 4.
Secondly, Epistemological Beliefs Inventory.This instrument was used to measure math-related epistemological beliefs on fi ve dimensions proposed by M. Schommer (1990) in her model.These dimensions are certainty of knowledge, source of knowledge, structure of knowledge, control of knowledge acquisition (personal and general), and speed of knowledge acquisition (Schommer, 1990).See table 5.
Students answered each item in the instrument on a 5-point rating scale.See table 6.
The overall score for a given dimension represents the positive wording of all items within that dimension and so higher scores indicate higher levels of epistemology in the dimension being measured.See table 7.
Thirdly, Mathematics Performance Test.This instrument was used to measure students' performance in mathematics.It consists of 50 multiple-choice items measuring their knowledge, mostly in problem solving.The items included in this test were based from the second general mathematics course for pre-service teachers.Data Gathering Procedure.The Curiosity Inventory was administered to the students during the fi rst week of the second semester while the Epistemological Beliefs Inventory was administered on the second week of the semester.The Mathematics Performance Test was administered at the end of the semester.

RESULTS AND DISCUSSION
The succeeding discussion describes the results of the study.Table 8 shows the students' level of mathematical curiosity on exploration.It can be viewed from the table that the students have high level of mathematical curiosity on exploration.This means that they have high level of appetitive strivings for novelty and challenge as well as awareness and clarity of their emotions with willingness to express positive feelings openly.In addition, the six items in this dimension of curiosity indicates that the students are willing to look for new opportunities to grow as a person and they want to do complex and challenging things.
Table 9 shows the students' level of mathematical curiosity on absorption.It can be seen from the table that the students have generally high level of curiosity on absorption.This implies that they are willing to engage in specifi c activities as well as the ability to persist or modify pathways to important goals even when confronted with distressing thoughts and feelings.
As indicated in their responses, it will take a great deal to interrupt them when they are actively interested in something and they are willing to look for new things and opportunities wherever they go.The item which got the lowest mean is item 4. They less likely prefer jobs that are excitingly unpredictable.
Table 10 shows students' level of mathematical curiosity on epistemic curiosity.It can be seen from the table the students' desire to engage in experiences that require cognition, in which they respond to stimuli that activate cognitive processes.The table evidently shows that the students have high level of epistemic curiosity.It appears from their responses that they keep reading thing that puzzles them until they understand it and they feel frustrated if they cannot fi gure out the solution to a problem, so that they even work harder to solve it.Table 11 shows the students' level of mathematical curiosity on perceptual curiosity.The table 11 also clearly shows that the students have high level of perceptual curiosity.Their responses indicate their high level of curiosity to engage in experiences triggered by sensory stimuli and a drive aroused by novel stimuli and reduced by continued exposure to these stimuli.They enjoy exploring new ideas, to learn something new and know more about it.When asked a riddle, they are interested in trying to solve it.
Table 12 shows students' epistemological beliefs on certainty of knowledge.It can be viewed from the table 12 that the students have epistemological beliefs on certainty of knowledge.They believe that there is more than one way to solve a math problem so that they prefer a math teacher who shows students several different ways to look at the problem.Generally, they believe that most of what is true in mathematics is already known.
Table 13 shows the students' epistemological beliefs on the structure of knowledge.As can be seen from the table, the students have high level of epistemological beliefs on the structure of knowledge.The items on this dimension of epistemological beliefs are views regarding mathematics as either a collection of isolated facts or a collection of interrelated concepts.
It can be viewed from the table 13 that four items got a relatively low rating.This implies that the students do not absolutely believe that mathematics is mostly facts and procedures that have to be memorized and that they fi nd it confusing when teacher presents more than one way to solve a problem.They generally disagree that they learn best when big picture is presented before the specifi c steps for working a problem.
Table 14 gives the students' epistemological beliefs on source of knowledge.The items in this dimension of epistemological beliefs are views about the source of knowledge in mathematics as either from the authority, such as mathematics teachers or from the active participation where knowledge is developed through a gradual process.They generally believe that that learning mathematics depends on having an effective teacher; that they learn math best when by working practice problems; and that to solve math problems, they have to be taught the right procedures and steps.
Table 15 shows the students' epistemological beliefs on control of  15 that the students' level of epistemological beliefs on the control of knowledge acquisition is high.They generally believe that learning good study skills can improve their math skills; that asking questions when they don't understand something is very important; and that they prefer mathematics when they have to work hard to fi nd a solution to a problem.
Table 16 shows the students' epistemological beliefs on control of knowledge acquisition (general).
The items on this dimension of epistemological beliefs are views about the control of knowledge acquisition similar to the previous dimension but viewed in the general perspective.It can be seen from the table 16 that the students have high level of epistemological beliefs on this dimension.This is just a confi rmation of their level of epistemological beliefs on the previous dimension.
Table 17 shows the students' epistemological beliefs on speed of knowledge acquisition.The items in this dimension of epistemological beliefs are views about the speed of knowledge acquisition in mathematics as either that happens quickly or not at all that has a gradual process.
It can be viewed from the table 17 that the level of epistemological beliefs on speed of knowledge acquisition is moderately high.They generally believe that almost everyone can learn Algebra if they really try; that they can do better in mathematics if they are given more time to learn the concepts; and when they encounter a problem, they stick to it until they solve it.
Table 18 gives the correlation of mathematical curiosity and epistemological beliefs to mathematics performance.It is also evident from the table 18 that both mathematical curiosity and epistemological beliefs are signifi cantly correlated to mathematics epistemological beliefs are factors that could affect students' performance in mathematics.Moreover, the positive correlation coeffi cients indicate that high level of mathematical curiosity and epistemological beliefs are associated to high performance in mathematics.
Table 19 shows the multiple regression analysis for predicting mathematics performance in terms of mathematical curiosity and epistemological beliefs.
It can be also viewed from the table 19 that both mathematical curiosity and epistemological beliefs signifi cantly infl uence mathematics performance.Moreover, R 2 shows that 42% of the variation in mathematics performance can be explained by mathematical curiosity and epistemological beliefs.This implies that mathematical curiosity and epistemological beliefs are infl uencing factors to mathematics performance.
The following are the fi ndings of the study.The level of mathematical curiosity of pre-service teachers is high on four dimensions, namely: exploration, absorption, epistemic curiosity, and perceptual curiosity.
The level of epistemological beliefs of preservice teachers is high on three dimensions, namely: certainty of knowledge, structure of knowledge, and source of knowledge.On the other hand, it is moderately high on the other three dimensions, namely: control of knowledge acquisition (personal), control of knowledge acquisition (general), and speed of knowledge acquisition.
Mathematical curiosity and epistemological beliefs are signifi cantly correlated to mathematics performance.Mathematical curiosity and epistemological beliefs signifi cantly infl uence mathematics performance.

CONCLUSION
Based on the fi ndings of this study, the following conclusions are made.Students with high level of mathematical curiosity tend to have higher mathematics performance.Students with high level of epistemological beliefs tend to have higher mathematics performance.
Based on the fi ndings and conclusions of this study, the following are hereby recommended.Firstly, a profi ling of the mathematical curiosity and epistemological beliefs of pre-service teachers should be done across personological variables (gender, choice of majorship, high school graduated, etc.) should be done.
Lastly, secondly, a study that determines which dimensions of mathematical curiosity and epistemological beliefs infl uence mathematics performance of pre-service teachers could be conducted.1 Figure 1: Conceptual Paradigm

Table 1 :
Distribution of the Respondents According to Section

Table 2 :
Distribution of Items in the Curiosity Inventory According to Dimension

Table 3 :
Answerable Using a 5-Point Scale

Table 4 :
Mean and Verbal Description

Table 5 :
Distribution of Items in the Curiosity Inventory According to Dimension

Table 6 :
On a 5-Point Rating Scale

Table 7 :
Mean and Verbal Description

Table 8 :
Students' Level of Mathematical Curiosity on Exploration

Table 9 :
Students' Level of Mathematical Curiosity on Absorption

Table 10 :
Students' Level of Mathematical Curiosity on Epistemic Curiosity

Table 11 :
Students' Level of Mathematical Curiosity on Perceptual Curiosity

Table 12 :
Student's Epistemological Beliefs on Certainty of Knowledge

Table 13 :
Student's Epistemological Beliefs on Structure of Knowledge

Table 14 :
Student's Epistemological Beliefs on Source of Knowledge

Table 15 :
Student's Epistemological Beliefs on Control of Knowledge Acquisition-Personal

Table 16 :
Student's Epistemological Beliefs on Control of Knowledge Acquisition -General

Table 17 :
Student's Epistemological Beliefs on Speed of Knowledge Acquisition

Table 18 :
Correlation of Mathematical Curiosity and Epistemological Beliefs to Mathematics Performance

Table 19 :
Multiple Regression Analysis for Predicting Mathematics Performance