Teachers’ Achievement Goals and their Relationship to Math Anxiety and Self-Efficacy

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Pre-service elementary teachers’ achievement goals and their relationship to math anxiety and self-efficacy

Abstract

Math anxiety remains a critical issue affecting student performance and confidence across grade levels, including pre-service elementary teacher education.  Given the potential impact teachers’ math anxiety might have on their learning as well as that of their future students, one unique purpose of this research is to investigate how achievement goals relate to math anxiety among 182 pre-service teachers enrolled in undergraduate elementary education math methods courses. While low self-efficacy is a significant predictor of math anxiety, our results indicate that taking into account pre-service teachers’ achievement goals increases our ability to predict math anxiety over that afforded by their level of self-efficacy alone.  In particular, students adopting either mastery-avoidance or performance-avoidance goals while learning mathematics, may be particularly susceptible to math anxiety.  Further, self-efficacy does not moderate the relationship between achievement goals and math anxiety, so the relationship between achievement goals and math anxiety is consistent across levels of self-efficacy.  Finally, both approach goals were positive predictors of pre-service teachers’ self-efficacy for learning mathematics.

Keywords: Math Anxiety, Achievement Goals, Motivation, Pre-service teachers

 

 

 

Negative attitudes toward mathematics and math anxiety are serious obstacles for students in all levels of schooling today (Geist, 2010).  Yet only limited attention has been devoted to the antecedents of math anxiety, which may include social factors like exposure to teachers who themselves suffered with math anxiety (Maloney & Beilock, 2012).  In particular, math anxiety of early elementary school teachers, who are predominantly female, can impact their female students’ math achievement by influencing girls’ gender-related belief about who is good at math (Beilock, et al., 2010). Therefore, of particular interest to this investigation is examining the predictors of pre-service elementary teachers’ math anxiety given the potential impact it may have on not only their own learning, but also that of their future K12 students’ mathematical learning.  Specifically, this study investigates how achievement goals relate to math anxiety among students enrolled in an undergraduate elementary education math methods class.  Because achievement emotions shape students’ learning behaviors, knowledge of their origins would be of benefit to classroom practices, and achievement goals are a potentially relevant antecedent of these emotions (Goetz, Sticca, Pekrun, Murayama, & Elliot, 2016).  Our review of the literature  did not locate any research looking at the specific dynamics we have outlined in our investigation examining the relationships between four achievement goals and math anxiety (as well as between the goals and more adaptive motivational behaviors) among pre-service elementary teachers.

Math Anxiety

Math anxiety has been defined as a negative emotional response that arises when confronted with a mathematical task (Beilock, et al., 2010).  Anxiety is the most widely researched emotion in learning and achievement situations, and it has been found that the study of mathematics elicits anxiety in particular (Frenzel, Pekrun, & Goetz, 2007).  It can result in a feeling of panic, helplessness, paralysis, and mental disorganization (Núñez-Peña, Suárez-Pellicioni, & Bono, 2013).  Test anxiety by far is the most extensively investigated emotion (Boehme, Goetz, & Preckel, 2017).  When considering older high school and college age populations, math test anxiety is identified as a major component of math anxiety, potentially because of failure experiences in past coursework (Alexander & Martray, 1989).

An individual’s lack of success with math may be a cause of math anxiety and be heightened by any one of several factors including poor math instruction, an insufficient number of math courses in high school, or unintelligible textbooks.  To compound the problem, people may attribute their failures with mathematics to their lack of a mathematical mind or the idea that men are better than women at math (Zhang, Schmader, & Hall, 2013).  Many studies have found self-efficacy to be negatively correlated with anxiety in math (Bong, 2009; Kesici & Erdogan, 2009; Pajares & Kranzler, 1995; Skaalvik, 1997; Wolters & Pintrich, 1998). In fact, individuals’ beliefs about their competence may be one of the strongest significant predictors of math anxiety (Ahmed et al., 2012; Meece et al., 1990).  The more they lack self-confidence in their mathematical ability, whether because of experiencing past failure or receiving negative persuasory feedback from significant others concerning math tasks, the more likely they would be to experience anxiety for executing mathematical tasks.

However, math anxiety is likely the result of both pre-existing difficulties in mathematical cognition as well as other factors like exposure to teachers who themselves experienced math anxiety (Maloney & Beilock, 2012).  Unfortunately, teachers suffering from math anxiety may in turn affect their students’ mathematical success (Gündüz, 2015).  Teachers who are afraid of math may pass on math anxiety to the next generation by modeling behaviors of their own discomfort with the subject (Furner & Gonzalez-DeHass, 2011; Geist, 2010; Kutner, 1992; Reys et al., 2015).   Reviewing research examining this influence, Johnson and vanderSandt (2011) explain how teachers might pass on this anxiety to their own students, or negatively impact their own students’ math achievement, as a result of teachers’ discomfort with the subject, decreased time spent in math lesson preparation, or ineffective use of math instructional time.  Math anxiety is also more common among women than men (Beilock, Gunderson, Ramirez, & Levine, 2010).  In particular, math anxiety of early elementary school teachers, who are predominantly female, can impact their female students’ math achievement by influencing girls’ gender-related belief about who is good at math (Beilock, et al., 2010; Maloney & Beilock, 2012). Their female students are more vulnerable to falling victim to the stereotype that only ‘boys are good at math’.

A teacher’s math anxiety may have carried over from their teacher preparation years.  Students of all educational levels can experience math anxiety, and this includes pre-service teachers (Finlayson, 2014).  Some studies have found that as high as 93% of pre-service teachers express some anxiety, with anxiety beginning as early as elementary-school (Bekdemir, 2010; Dunkle, 2010; McAnallen, 2010; Brown, Westenskow, & Moyer-Packenham, 2012). Among various college majors, pre-service elementary teachers have some of the highest rates of math anxiety while coupled with below average math proficiency (Novak & Tassell, 2017).  Many elementary education majors report having poor experiences with math courses in K-12 (Bekdemir, 2010; McAnallen, 2010), and many enroll in lower level or remedial level mathematics courses in college (McAnallen, 2010).  Given the impact a teacher’s math anxiety may have on their own students’ learning, studies addressing the roots of math anxiety in pre-service elementary teachers is important before teachers graduate and enter classroom teaching.  Achievement goals are a potentially relevant antecedent of achievement emotions like anxiety (Goetz, Sticca, Pekrun, Murayama, & Elliot, 2016).  Therefore, investigation into how achievement goals relate to math anxiety may prove an important avenue for understanding predictors of pre-service teachers’ math anxiety.

Achievement Goals

The study of achievement emotions has been linked with achievement goal theory (Huang, 2011). Achievement goal research examines how the types of achievement goals students adopt relate to important academic outcomes (Ames & Archer, 1988; Dweck & Leggett, 1988; Elliot, 2005; Elliot & McGregor, 2001).  The most prevalent achievement goal model identifies four achievement goals (Elliot & McGregor, 2001): where individuals adopting mastery goals are motivated to master a task and advance their learning (mastery-approach) or are focused on avoiding misunderstandings and leaving tasks un-mastered (mastery-avoidance), and those adopting performance goals may be motivated to outperform others (performance-approach) or to avoid performing worse than others (performance-avoidance).  Individuals adopting different goals will be engaged for different reasons.  A student with a mastery-approach goal will seek out challenge and pursue opportunities to extend their learning whereas a student with a mastery-avoidance goal is more concerned with not being able to master the assigned task.  A student with a performance-approach goal will strive to do better in comparison to others in front of the class on a given task, while the student with a performance-avoidance goal just wants to avoid being judged unfavorably by classmates.

Of particular relevance to the current study, Elliot & McGregor (2001) found both avoidance goals were related to test anxiety and undergraduate psychology students worrying about making mistakes.  In contrast, research across diverse student ages and academic subjects has shown mastery-approach goals linked to positive emotions like enjoyment and predicted lower anxiety, while performance-avoidance goals have predicted more negative emotions including anxiety and shame (Goetz, et al., 2016; Huang, 2011; Ranellucci, Hall, & Goetz, 2015).    Performance-approach goals have also predicted students’ pride (Goetz, et al., 2016).  Unfortunately, most studies examining the relationships between the goals and math anxiety have not included the mastery-avoidance goal in analyses.  However, Huang’s (2011) meta-analytic review of research did suggest that mastery-avoidance goals tended to correlate more highly with negative achievement emotions, but conclusions were only suggestive and required further investigation.

Achievement Goals Related to Math Anxiety

Published studies have not yet investigated the relationships between achievement goals and math anxiety among pre-service elementary education students.  However, research has begun to investigate the relationship between the goals students adopt for their learning and their math anxiety in other student populations.  These studies predominantly utilize self-report surveys of students’ adopted achievement goals.  Results with college students enrolled in a statistics course revealed that while both avoidance goals were significant predictors of negative affectivity and anxiety, mastery-avoidance goals were a more salient predictor of anxiety and negative affect than any other goal type (Sideris, 2008).   In contrast, mastery-approach goals significantly predicted lower negative affect.  Luo et al., (2014) investigated achievement motivation among secondary students in Singapore and also found both of the avoidance goals to be predictive of math anxiety (particularly mastery-avoidant goals), while mastery-approach goals were a predictor of lower anxiety.  However, Korean elementary and middle- school students who reported having performance-approach, mastery-avoidance and performance-avoidance goals showed evidence of more math anxiety (Bong, 2009).   This research also showed that mastery-approach goals appear to be particularly favorable, providing a stronger ‘psychological armor’ or protective shield, in warding off harmful thoughts and combating adolescents’ test anxiety in math classes.

Yet the relationships between the achievement goals and math anxiety is not always as one would expect.  In a study of secondary students in England (between 11 and 12 years of age), Putwain & Daniels (2010) found weak to moderate positive correlations between the test anxiety subscales of worrisome ‘thoughts’ about a negative outcome for tasks and all four achievement goals.  The same was true for the correlations between the ‘autonomic reaction’ subscale (such as shaky hands when taking tests) and all four goals.  However, these correlations were slightly more pronounced for both avoidance goals.  In particular, when students had low perceived competence in math, they reported more worrisome thoughts when they also held mastery-avoidance goals.

Other studies have also examined the relationship between math anxiety and achievement goals using the earlier trichotomous framework (earlier theoretical frameworks consisted of just three goals with a mastery goal, considered conceptually similar to a mastery-approach goal, and the two performance goals).  Research with Asian and Anglo American undergraduate students in an introductory psychology course investigated relationships between students’ achievement goals and motivational outcomes for mathematical tasks (Zusho, Pintrich, & Cortina, 2005).  Performance-avoidance goals were related to higher levels of anxiety and nervousness surrounding mathematics tasks, while mastery and performance-approach goals had positive outcomes that included higher levels of personal interest and task enjoyment, mathematics achievement, and perceptions of their competence for successfully completing mathematical tasks.  However, in earlier research, the adoption of the either performance goal predicted students’ ‘emotionality’ or how nervous or tense sixth and eighth-grade Norwegian students felt during math lessons (Skaalvik, 1997).  Both performance goals, especially the performance-avoidance goal, were a predictor of test anxiety in math among sixth-grade students in the United States (Middleton & Midgley, 1997).    Therefore, it appears that both avoidance goals may be predictors of math anxiety.  This may be due to the mastery-avoidance fear of being faced with their inability to master math tasks, and the performance-avoidance goal’s concern with avoiding poor evaluations of their performance.  In contrast, an individual with a mastery-approach goal may not be as concerned with negative effects of a failure experience, as they may interpret any initial failure as a springboard for further learning and better understanding.  However, the impact of the performance-approach goal is more inconsistent.  For some, the desire to be seen as outperforming others may not necessarily lead to math anxiety like it might for some students.  It may be that this depend on their level of self-efficacy for mathematical tasks.

Self-Efficacy

Judgments of self-efficacy (defined as a personal set of beliefs about one’s competence in a specific area) affect one’s choice of activities and effort and persistence in those activities (Bandura, 1986; 2006; Usher & Pajares, 2008).   Most importantly, judgments of self-efficacy may affect the emotional reactions to those activities (Bandura, 1986; 2006; Usher & Pajares, 2008), and this includes math anxiety (Ahmed et al., 2012; Meece et al., 1990).  People with low self-efficacy may dwell upon personal deficiencies, and their misgivings can create stress and divert attention from more productive problem-solving (Bandura, 1986).  While self-efficacy is a known predictor of anxiety, it would be of interest to examine if pre-service teachers’ achievement goals serve as another predictor of math anxiety. Some researchers have treated self-efficacy as a moderator between goals and outcomes, where sixth-graders with low self-efficacy who also adopt performance goals may be more likely to display a helpless pattern (Middleton, et al., 2004). Another study also found some support for a moderational hypothesis and concluded that when secondary students in England had low perceived competence in math, they reported more worrisome thoughts when they also held mastery-avoidance goals (Putwain & Daniels, 2010).

It would also be of interest to examine how pre-service teachers’ achievement goals will predict their self-efficacy for math.  Teachers’ self-efficacy with math anxiety are especially crucial as a teacher’s beliefs impact their students’ perceptions of math, and self-efficacy may be one factor to help mediate the effects of math anxiety (Hoffman, 2010). Further, pre-service teachers’ math self-efficacy positively relates to their efficacy for teaching mathematics (Zuya et al., 2016).  Research in the area of mathematical learning has been conducted to examine how self-efficacy is associated with the earlier trichotomous framework of goals (that does not include the mastery-avoidance goal).  Performance-approach goals again show some positive outcomes with regard to self-efficacy, especially when students adopt both mastery and performance-approach goals (Pintrich, 2000).  This latter finding suggests that performance-approach goals may not diminish the adaptive learning outcomes generally associated with mastery goals.  In fact, both mastery goals and performance-approach goals have been shown to be predictive of self-efficacy (Greene et al., 2004) and both have been positively correlated with self-efficacy (Bong, 2009).   Because of the reciprocal relationship between self-efficacy and math anxiety, self-efficacy also would be expected to influence one’s self-efficacy (Ahmed et al., 2012).  This is in line with Bandura’s theoretical model where one’s physiological and affective state is seen as a source of influence on self-efficacy, and judgments of self-efficacy may affect the emotional reactions to those activities (Bandura, 1986; 2006; Usher & Pajares, 2008).

The Present Study

Given the potential impact teachers’ math anxiety might have on their future students, one unique purpose of this research investigation is to examine how achievement goals relate to the phenomenon of math anxiety for pre-service teachers specifically.  To our knowledge, research has not yet been conducted to examine these relationships among pre-service elementary teachers.  Additional novel features of this investigation will be to include all four goals, because not as many studies to date have examined all four goals when investigating links between achievement goals and math anxiety.

Our first research question examines to what degree does taking into account pre-service teachers’ achievement goals increase the predictive accuracy of math anxiety, in addition to the accuracy afforded by self-efficacy?  If significant, which goals predict a students’ math anxiety?  As previously discussed, judgments of self-efficacy may affect the emotional reactions to those activities (Bandura, 1986; 2006), and this includes math anxiety (Ahmed et al., 2012; Meece et al., 1990).  Given existing research showing how both avoidance goals in particular might predict math anxiety, we would hypothesize that the four scales together would increase the predictive accuracy of math anxiety over that available from self-efficacy (which would also remain an important predictor).  In contrast, we would expect that the mastery-approach goal would predict lower rates of math anxiety.  Patterns for the performance-approach goals are a more inconclusive.  However, we expected that those with performance-approach goals would not evince higher rates of math anxiety given a lack of consistent link in prior literature.

Our second research question examines whether the relationships between pre-service teachers’ achievement goals and anxiety for their mathematical learning is moderated by their level of self-efficacy.  In other words, does the relationship between achievement goals and math anxiety change as a function of self-efficacy?  Some research has supported a moderational hypothesis where students with mastery-avoidance or performance goals may be more likely to suffer anxiety if they also hold low self-efficacy,  Therefore, it may be that the relationships between pre-service teachers’ achievement goals and anxiety for their mathematical learning in undergraduate coursework are moderated by their level of self-efficacy.

Our third research question examines which factors, taking into account the four achievement goals and math anxiety, are predictive of a student’s level of self-efficacy?  Because of the reciprocal relationship between self-efficacy and anxiety (Bandura, 1986), we also chose to include math anxiety as a potential predictor of pre-service teachers’ self-efficacy.  Given the existing research, it is expected that pre-service teachers with mastery-approach goals would evidence higher rates of self-efficacy.  In contrast, those with performance-avoidance or mastery-avoidance goals are predicted to be more likely to show lower rates of self-efficacy.  Patterns for the performance-approach goals are a bit more inconclusive, however, it is tentatively expected that results will be in line with existing research that has shown these goals to be predictive of self-efficacy (Greene et al., 2004; Zusho et al., 2005).

Method

Participants

The study sample consisted of 182 university students enrolled in multiple sections of an undergraduate elementary education math methods course.  All students taking the course were either elementary education majors or elementary special education majors taking the course as a requirement for completing their program as elementary school teachers. Of those choosing to participate, 163 were women and 16 were men.  All participants were 18 years or older.  There were only a few cases of missing data where participants did not report their gender. The researchers used listwise deletion to handle missing values.  Participants had taken two other college level math classes as pre-requisites for this math methods course. The participants took this class in their last two years of upper-division course work and this class is designed to offer a review of mathematics information and skills and methods for teaching in the K-9 setting.  The majority of the participants were junior (n=85), followed by senior (n=68), graduate students (n=18), sophomore and freshman (n=7) and grade missing (n=4). While information about ethnicity was not collected, the university the participants attended is ranked   as 32nd nationally in the number of bachelor’s degrees conferred upon minorities (FAU, 2012).

Instruments

An online survey was distributed and stored electronically through Google.doc. The online survey was composed of four components: The Achievement Goal Questionnaire (AGQ) by Elliot and McGregor (2001), the Motivated Strategies for Learning Questionnaire (MSLQ) by Pintrich, Smith, Garcia and McKeachie (1991), the Abbreviated version of the Mathematics Anxiety Rating Scale (MARS) by Alexander and Martray (1989) and demographic questions on age and gender and grade level.

AGQ. The AGQwas developed by Elliot and McGregor (2001) and included twelve Likert-type items designed to measure participants’ reported achievement goals along each of the four goal dimensions: mastery-approach, mastery-avoidance, performance-approach, and performance-avoidance. Participants had to indicate if they thought the statement was very true (7) or not at all true (1) of them. Each of the goal subscales has three items; a sample item in the mastery-approach scale is: “I desire to completely master the material presented in the class.”  A sample item in the mastery-avoidance scale “I worry that I may not learn all that I possibly could in this class”. A sample item in the performance-approach scale is “It is important for me to do better than other students.” A sample item in the performance-avoidance scale is “My goal in this class is to avoid performing poorly”.  Internal reliability for the scales in the present study yielded coefficient alphas as follows: performance approach (α = .86), mastery avoidance (α =.86), mastery approach (α =.88), performance avoidance (α =.64).  These values were very similar to the ones reported in instrument’s original validation study as well as in Vasquez-Colina, Gonzalez-DeHass and Furner (2014).

MSLQ. The MSLQ was developed by Pintrich, Smith, Garcia and McKeachie (1991) to measure college students’ motivational orientations and their use of different learning strategies. Information on predictive validity and internal reliability coefficients was available for this questionnaire. While the original full MSLQ has two main sections (a motivation section and a learning strategies section, totaling 81 items), only one subsection was chosen based on the purpose of study. Thus, the summarized MSLQ version in the current study included self-efficacy for learning and performance (from the motivation section) with eight items. All questions were Likert-type items and the items ranged from 7(very true of me) to 1(not at all true of me). Sample questions from the self-efficacy scale would be, “I’m confident I can understand the basic concepts taught in this course”, and “I’m confident I can do an excellent job on the assignments and tests in this course”.  Internal reliability for the scale in the present study yielded coefficient alphas as follows: self-efficacy (α =.93),  This value is very similar to the ones reported in instrument’s original validation study as well as in Vasquez-Colina, Gonzalez-DeHass and Furner (2014).

MARS. Originally developed by Alexander and Martray (1989), the Abbreviated Version of the Mathematics Anxiety Rating Scale (MARS) provides a measure of college students’ anxiety associated with math testing and numerical operations, and of math courses. The creators of the Abbreviated Version of the MARS used items from the actual full-scale MARS and from the Fennema-Sherman Mathematics Attitude Scales (Fennema, 1976) to develop the Abbreviated Version of the MARS using an undergraduate student population.  The primary purpose being to create an abbreviated version of the lengthier, 98-item MARS.  Authors stated, because math test anxiety has been identified consistently as the major component of math anxiety in other studies that the 25-item abbreviated MARS would seem to be more appropriate for college students because of its efficiency, economy, and administrative ease in measuring math anxiety.  The MARS scale used had 25 items measuring the level of anxiety an individual experiences, related to a series of contexts: test anxiety, numerical tasks, and math courses.  All items ranged from 5 (very much) to 1 (not at all). Sample questions from the test anxiety subscale would be, “Taking a math section of an exam”, and “Taking an exam (quiz) in a math course”.  The numbers anxiety subscale contained sample questions like “Being given a set of subtraction problems to solve”, and “Being given a set of division problems to solve”. Sample items from the math course anxiety subscale include: “Signing up for a math course” and “Walking into math class”.  Internal reliability for the math-anxiety scale in the present study yielded a coefficient alpha of α =.97.  This value was similar to the one reported in instrument’s original validation study as well as in Vasquez-Colina, Gonzalez-DeHass and Furner (2014).

Procedures

Upon securing institutional review board approval (IRB) for research involving humans subjects, recruitment information was sent to course instructors to distribute in their classes. Participants were invited to participate in an online survey made up of three existing instruments: AGQ, MLSQ sections and Abbreviated MARS.  Instructors were asked to send two reminders via their Blackboard site and email.  Participants were assured that there was no penalty for not participating, that completion of the survey had no relation to their course grade, and that they could withdraw at any time. The survey did not show any student identifiers other than gender, and data were reported in the aggregate. The participants were directed by their instructor to a link that took them to the online survey.

Results

Correlations among pre-service teachers’ achievement goals, math anxiety, and self-efficacy are reported in Table 1.  The researchers used listwise deletion to handle missing data in this section.  There were significant correlations between math anxiety and both avoidance goals, and math anxiety was negatively correlated with self-efficacy.  Self-efficacy moderately correlated with mastery-approach and performance-approach goals and negatively with mastery-avoidance goals.

Insert Table 1about Here

Our first research objective was to examine to what degree does taking into account achievement goals (performance-approach, mastery-avoidance, mastery-approach and performance-avoidance) increase the predictive accuracy of math anxiety, in addition to the accuracy afforded by self-efficacy. The total model indicated that the four scales together incremented the predictive accuracy of math anxiety over that available from self-efficacy, F (4,140) = 5.86, p < .001.  The model also indicated that the unique contribution of self-efficacy was significant F (1,140) = 38.30, p < .001 demonstrating low self-efficacy was a significant predictor of math anxiety. Since only two of the achievement goals had a significant bivariate correlation with math anxiety, we calculated mastery-avoidance and performance-avoidance goals’ individual contributions to predicting math anxiety above that afforded by self-efficacy.  Mastery-avoidance contributes significantly to self-efficacy in the prediction of math anxiety, F (1,143) = 15.08, p < .001, increasing the R2 by .07.  Performance-avoidance contributes significantly to self-efficacy in the prediction of math anxiety, F (1,143) = 8.34, p < .001, increasing the R2 by .04.

Our second research question investigated whether the relationship between achievement goals and math anxiety was moderated by self-efficacy. There were non-significant effects for each of the goals. The product terms were for mastery approach goals, F (1,144) = .35, p >.001, for mastery avoidance, F (1,144) = 1.72, p> .001, for mastery approach, F (1,144) = .1.33, p > .001, for performance avoidance, F (1,144), p > .001. Thus, it is concluded that self-efficacy does not moderate the relationship between achievement goals and math anxiety; that is, the relationship between any achievement goal and math anxiety is consistent across levels of self-efficacy.

Our third research objective was to examine whether self-efficacy could be predicted from math anxiety and any of the achievement goal subscales (performance-approach, mastery-avoidance, mastery-approach and performance-avoidance). Regression results predicting self-efficacy are included in Table 2.  The total model predicted a significant amount (42%) of the variation in self-efficacy, F (5,140) = 20.19, p <.001.  Math anxiety and the performance-approach and mastery-approach goals contributed significantly (p<.05) to the model having all other variables present, whereas mastery and performance-avoidance goals were redundant in respect to the same criterion.  (Only math anxiety was a significant negative predictor.)

Insert Table 2 about Here

Discussion

The current study has a number of unique contributions to the literature examining achievement goals and math anxiety.  First, the current study has included the mastery-avoidance goal when studying the relationships between goals and math anxiety, and only a limited number of studies have included all four achievement goals – especially in the college-age population.  Most importantly, this study looks closely at pre-service teachers’ math anxiety, achievement goals, and self-efficacy to learn mathematics in order to better understand their motivational outlook and confidence in tasks that call for mathematical thinking.  Our review of the literature failed to yield any research looking at the specific dynamics we have outlined in our investigation (investigation of all four goals, math anxiety, and self-efficacy) among pre-service teachers.  Therefore, our results extend the literature in math anxiety and achievement goals in a number of ways.

Math Anxiety

Our first research question examined whether taking into account achievement goals increase the predictive accuracy of math anxiety when also including self-efficacy?  If significant, which goal increments more predictive accuracy? As hypothesized, findings indicate that taking into account pre-service teachers’ achievement goals, affords more insight into the level of math anxiety they may experience, above that afforded by their self-efficacy alone.  According to the results for this predominantly female sample, individuals adopting either mastery-avoidance or performance-avoidance goals while learning mathematics may be particularly susceptible to math anxiety.  Research with other student populations addressing all four achievement goals for learning mathematics has also found both avoidance goals to show the strongest relationship with math anxiety (Luo et al., 2014).

These findings suggest that the thought of under-performing in the eyes of others, or the fear of being faced with their own inability to master and understand material, makes pre-service teachers enrolled in teacher preparation math coursework particularly at-risk for math anxiety.  Adopting a mastery-avoidance goal might inhibit them from tackling more demanding academic tasks and seeking out resources that could further their learning, and adopting a performance-avoidance goal may inhibit them from asking for help during challenging learning moments in their desire to avoid being seen as incapable or not measuring up against their peers.  It may be that because the adoption of these goals curtail pre-service teachers’ opportunities for substantive mathematical learning and supportive assistance, they limit their ability to cope with the learning obstacles they encounter and add to any feelings of panic and helplessness that arise when they are confronted with a mathematical task.  Other results with this pre-service teacher population included the finding that the mastery-approach and performance-approach goals were not a significant predictor of math anxiety.  It was unexpected that mastery-approach goals were not related to math anxiety given other research showed evidence of these goals predicting lower negative affect and anxiety (Luo et al., 2014; Sideris, 2008).  Performance-approach goals have a somewhat uncertain outcome in the literature with some finding them to be linked with math anxiety and nervousness experienced during math lessons (Bong, 2009; Skaalvik, 1997) and others not finding a link with math anxiety (Zusho et al., 2005).  It is important for future research to continue to investigate the nature of the approach goals affect on pre-service teachers’ math anxiety.

Our second research question investigated whether the relationship between achievement goals and math anxiety was moderated by self-efficacy. As expected, self-efficacy was a predictor of pre-service teachers’ math anxiety. This corroborates existing self-efficacy research with K12 student populations that has shown when students doubt their mathematical competence they may be more likely to experience math anxiety.  Current research with pre-service teachers has also shown lack of self-confidence in math to be a cause of math anxiety (Finlayson, 2014).  However, it was unexpected that the results of this study indicated that self-efficacy does not moderate the relationship between achievement goals and math anxiety, so the relationship between achievement goals and math anxiety is consistent across levels of self-efficacy.  Therefore, either avoidance goal may be particularly detrimental for pre-service teachers in terms of their experiencing math anxiety, regardless of their level of perceived competence for learning mathematics.

Self-Efficacy for Learning Mathematics

Our third research objective was to examine whether self-efficacy could be predicted from math anxiety and any of the achievement goal subscales. Our results were expected in light of the research literature.  Math anxiety was a significant predictor of low self-efficacy in this sample. This is in line with Bandura’s model of self-efficacy whereby people rely partly on their physiological or emotional states when judging their capabilities, and they “are more inclined to expect success when they are not beset by aversive arousal” (Bandura, 1997, pg. 106).

Both approach goals (particularly the mastery-approach goal) were positive predictors of pre-service teachers’ self-efficacy in this study This is in line with other research both goals have been shown to be predictive of self-efficacy (Greene et al., 2004) and both have been positively correlated with self-efficacy (Bong, 2009).   These findings suggest that that the desire to perform well in front of others may also encourage pre-service teachers’ mathematical confidence.  This seems to be in line with other findings where performance-approach goals have shown to be predictive of self-efficacy (Greene et al., 2004; Zusho et al., 2005), and when coupled with mastery-approach goals can also be adaptive for mathematical learning (Pintrich, 2000).  The possibility has led to a multiple goals perspective where there is not any one adaptive motivational pathway between goal orientations and mathematical learning (Pintrich, 2000; Zusho et al., 2005).

Overall, current findings do extend upon the existing literature and indicate that when considering all four goals, both the mastery-avoidant and performance-avoidant goals may be particularly maladaptive to their reports of math anxiety, and the mastery-approach and performance-approach goals significantly and positively predicted self-efficacy for mathematical learning in this sample of pre-service teachers.

Implications

Findings from this study have important implications for instructors in elementary education courses who are looking to reduce students’ math anxiety.  Instructors can begin to structure classroom environments that minimize potentially maladaptive goal orientations and make adaptive goal orientations more salient.   Although performance-approach goals were not predictive of math anxiety in the present study, mastery-approach goals highlight the importance of pre-service teachers striving towards professional growth as a future teacher.  Further, when looking across achievement goal research reviewed for this present study, the mastery-approach goals have the most consistent connection to positive academic learning outcomes. Within the achievement goal literature, it is still concluded that learners be encouraged to adopt mastery-approach goals, although because classrooms engender some competition and social comparison we now understand that performance-approach goals may not have the detrimental outcomes for students’ learning once thought (Pintrich, 2000). Therefore, even when some performance cues are present, the overriding classroom goal structure can influence positive motivational patterns when mastery goals are made salient (Ames & Archer, 1988).

Fortunately, we know that classroom practices can influence learners to adopt mastery-approach goals, particularly by looking to the qualities of learning tasks, authority, evaluation, and climate of the classroom (Ames, 1992; Stipek, 1998). Specifically, we may be able to reduce math anxiety by engaging students in math tasks with real-world significance; by involving math students in academic decision-making; by emphasizing evaluation practices that highlight the goals of understanding and improvement; and cultivating an environment that helps students to feel they can take risks, make mistakes, and reveal their lack of understanding (Furner & Gonzalez-DeHass, 2011).  These suggestions in terms of task, authority, and evaluation parallel other recommendations outside of the achievement goal literature that also strive to reduce pre-service teacher anxiety by making math relevant within a constructivist and collaborative learning environment, utilizing diverse types of assessment including self-evaluation, and highlighting that making mistakes are simply an opportunity to improve (Finlayson, 2014).

Therefore, specific suggestions can be tailored to impact mathematic instruction within elementary education coursework.  For example, learning tasks can be contextualized within real-world teaching challenges faced by elementary school teachers. Authentic assignments might ask pre-service teachers to analyze case studies of elementary classrooms that highlight practical challenges related to how teachers adequately encourage students’ confidence in approaching advanced level mathematic tasks, especially for their female students.  Other activities might include detailed lesson-planning for how to prepare their students amidst state math standards of increased difficulty.

The achievement goal literature also indicates that the perception of control appears to be an important factor affecting the learner’s engagement in learning (Ames, 1992). Therefore, instructors might allow opportunities for pre-service teachers to establish the methods and pace of their learning, and exercise self-regulatory and self-directed learning strategies during learning assignments.  Instructors can provide one-on-one feedback that helps pre-service teachers assess their progress, provides encouragement, and offers specific ideas for how they might continue to improve in their use of effective pedagogical or mathematic strategies.   Evaluation feedback would ideally highlight the pre-service teacher’s individual progress.  Evaluation activities might even be chosen from alternative forms of assessment, including journal writing reflecting on their teaching observations and portfolios or performance assessments of teaching accomplishments, so that students can experience a range of ways to demonstrate their grasp of effective math instruction.

Conclusions from the achievement goal literature indicate teachers should create a classroom climate that helps students to feel they can take risks, make mistakes, and reveal their lack of understanding (Stipek, 1998).   This practice can also translate to elementary education coursework.  Pre-service teachers should feel comfortable asking questions in their pursuit to understand class material and master important mathematic skills during their math pedagogy courses.  Errors communicate critical information about where learners should revise work, correct misunderstandings, and increase personal mastery of a mathematical task.  Teachers should also engage students in tasks that encourage cooperative learning of mathematical problem-solving so learners can scaffold each other’s learning.  Overall, the elementary education classroom should be perceived as a community of learners where pre-service teachers engage in constructive relationships that help to motivate them towards mastery of important mathematical and pedagogical skills.

Limitations and Future Directions

Our findings suggest that continued investigation to examine these relationships with larger and more diverse samples is worthy of further study.  However, there are a number of limitations that must be mentioned.  First, this study used a sample of convenience which limits generalizations, and studies with larger and more diverse samples are required in order to replicate findings and decrease chance that findings are a one-time occurrence.  Another limitation of this study was that the sample was predominantly female (which is characteristic of student enrollment in the elementary education major).  The fact that there was some missing data limits the extent of our interpretations. However, a larger and more diverse sample will allow for the examination of how the nature of these relationships may vary by gender.

Ongoing research should also explore the nature of these relationships both in early undergraduate populations and among younger students in secondary education.  This is a critical time when students are beginning to think seriously about their career interests and appropriate college majors that will serve as a path to realizing those interests.   It is critical to ensure students are confident and well prepared in mathematics if they are going to compete for such high-tech jobs today and in the future (Boaler, 2008).  There is a real need for creating more young people who have a passion and interest in STEM fields, people who are confident in their abilities and will set goals to pursue careers in the area of mathematics and the sciences (Furner & Gonzalez-DeHass, 2011).  The National Council of Teachers of Mathematics (NCTM) many years ago in their 1989 Standards created societal goals for our young people, one being creating mathematically confident learners.   It is critical today that our teachers are well versed on how to effectively teach mathematics so as to address math anxiety in students, develop student confidence in math, and help encourage our young people into careers in the STEM fields.  Reducing math anxiety is critical to increasing STEM majors and a scientifically literate STEM population.  Unfortunately, math anxiety can impede not only mathematical performance but also interest and career choice (Ahmed, Minnaert, Kuyper, & van der Werf, 2012).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Table 1

Simple Correlations Between the Study’s Variables among Undergraduate Students (N=140)

M SD 1 2 3 4 5 6 7
  1. Self-efficacy
5.94 .97
  1. Self-Regulation
4.79 .85 .35**
  1. Performance Approach
5.20 1.42 .30** .16*
  1. Mastery Avoidance
3.66 1.71 -.33** .03 -.07
  1. Mastery Approach
6.60 .75 .32** .38** .21* .04
  1. Performance Avoidance
5.33 1.43 .01 .28** .16 .18* .31**
  1. Math Anxiety
2.40 .92 -.52** .08 -.08 .41** .01 .17*

*p<.05.    ** p<.01.

Table 2

Predicting Self-efficacy (Model 1) and

Model 1

(N=146)

Variable B SE B β      
Performance approach .13 .05 .19*
Mastery avoidance -.08 .04 -.14
Mastery approach .37 .09 .29*
Performance avoidance -.01 .05 .01
Math anxiety -.45 .07 -.44*
*p<.05

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