Mathematics achievement is an important topic that is being addressed in educational research. It is emphasized in an increasing number of research that mathematics achievement is related to students' attitudes towards motivation (Ma, 2006; Ma & Kishor, 1997; Singh, Granville, & Dika, 2002), emotions (Daher, Anabousy, & Jabarin, 2018), mathematical anxiety (Ashcraft and Krause, 2007; Hembree, 1990; Ma, 1999) and perceptions of mathematics (McGowen & Tall, 2010; Yalçın, 2016).  The results of these research draw attention to the importance of the cognitive dimensions as well as the affective dimensions in the success of the students.

Mathematical resilience, additionally, is another important factor that is found to be related to the mathematical success. Resilience refers to the “behavioral, attributional, or emotional response to an academic or social challenge that is positive or beneficial for development” (Yeager and Dweck, 2012, p. 303). Mathematical resilience have defined by Johnston-Wilder & Lee (2010) as the term used to describe “a learner's stance towards mathematics that enables students to continue learning despite finding setbacks and challenges in their mathematical learning journey”. Considering the relationship with mathematics achievement, mathematical resilience has been examined in a number of studies. The research results demonstrated that mathematical resilience and mathematics achievement were positively correlated (Johnston-Wilder, Brindley, & Dent, 2014; Kooken, Welsh, McCoach, Johnston-Wilder & Lee, 2013; Kooken, Welsh, McCoach, Johnston-Wilder & Lee, 2016).

            In the literature, perceptions have been tried to be measured by various ways (e.g. questionnaires, scales, metaphors). There are studies that investigated perceptions on mathematics through metaphors (Boero, Bazzini & Garuti, 2001; Chiu, 2001; McGowen & Tall, 2010). Results of these studies showed that perceptions of mathematics can be examined through metaphors and it is useful for handling perceptions in terms of broader framework.

When the overall literature were reviewed, relationship between mathematics achievement, students’ mathematical resilience, perceptions on learning mathematics, being successful in mathematics, and mathematics teacher had not been examined together through metaphors so far. In this study, the relationship between mathematical resilience, academic achievement and the perceptions on mathematics teacher, learning mathematics, being successful in mathematics were examined and furthermore cluster analysis was performed to observe the clusters based on these variables. Accordingly, two research questions have been formulated: (a) Is there a significant relationship between mathematics achievement and students’ mathematical resilience, the perceptions on mathematics teacher, learning mathematics, being successful in mathematics? (b) How students are clustered according to their mathematical resilience, the perceptions on mathematics teacher, learning mathematics, being successful in mathematics and mathematics achievement?

As persistence in mathematics coursework is considered as an significant factor developing student success in science, technology, engineering and mathematics (STEM) careers, more research is needed to gain deeper insight into the factors predicting mathematics achievement in an international context (Kooken et al., 2013; Kooken, et al., 2016). It is expected that the results of this research will be beneficial for the mathematics teachers who are practitioners of the mathematics program to organize the educational environments in a mathematics course. The results of this research may provide an insight into how students who are successful in mathematics perceive their mathematics teachers, learning mathematics and being successful in mathematics. 

Participants In order to investigate the relationships between mathematics achievements and related factors (e.g. mathematical resilience, the perceptions towards mathematics teacher, mathematics learning, being successful in mathematics), the data from 500 students from Turkey was collected (261 female). The ages of the students were ranged from 11 to 15 (M=12.83, SD=0.931). The students were attending 5th to 8th grade. Instruments Student mathematics achievement was obtained from mathematics course term grades. Four scales were used to measure the mathematical resilience, the perceptions towards mathematics teacher, mathematics learning, being successful in mathematics scores of the students. The Mathematical Resilience (MR) Scale: The MR Scale (Kooken, Welsh, McCoach, Johnston-Wilder & Lee, 2016) contains three factors: value (eight items), struggle (nine items) and growth (seven items). Metaphors regarding Mathematics Teacher (MTM) Scale: The MTM Scale (Yalçın & Eren, 2016) contains three factors: mathematics teacher as a supportive person (11 items), mathematics teacher as a knowledgeable person (five items) and mathematics teacher as a fear element (three items). Metaphors regarding Learning Mathematics (MLM) Scale: The MLM Scale (Yalçın & Eren2016) contains four factors: a challenging process (five items), a funny process (five items), a process that requires effort (five items), a process (three items). Metaphors regarding being Successful in Mathematics (MSM) Scale: The MSM Scale (Yalçın & Eren, 2016) contains three factors: a difficult process (ten items), a race process (five items), a process of happiness (six items). Data Analysis Firstly, the construct validity of the scales was tested by confirmatory factor analysis with LISREL 8.7. Cronbach’s alpha coefficients of the scales and their subscales were calculated separately. For the first research question, relations between the variables (scores obtained from the scales used in the research and students’ mathematics achievement scores) were calculated by Pearson Moments Product Correlation Coefficient using the bootstrap technique. For the second research question, the hierarchical clustering analysis (using the Ward method) were performed to separate the students into the classes according to their mathematical resilience scores, mathematics achievement and their perceptions of mathematics teacher, mathematics learning, to be successful in mathematics. A discriminant analysis was performed to test the validity of the clusters determined by hierarchical cluster analysis. Whether the individuals in both groups differed significantly in terms of the same variables was determined by MANOVA.

For the first research question, correlations between mathematics achievement and mathematical resilience, the perceptions of mathematics teacher, learning mathematics, and being successful in mathematics were examined. According to results, there was a significant negative relationship between mathematics achievement and both perception of learning mathematics as a difficult process (r=-0.38) and being successful in mathematics as an extremely difficult process (r=-0.38). There was also a significant negative relationship between perception of mathematics teacher as an element of fear and mathematics achievement (r=-0.27). Relations between mathematics achievement and perception of mathematics teacher as a supportive person (r=0.17) and perception of learning mathematics as a funny process were significantly positive (r=0.23). These findings were supported by the cluster analysis results. As a result of the cluster analysis to answer the second research question, results showed that students were separated into two clusters according to perceptions of mathematics teacher, learning mathematics, being successful in mathematics, mathematical resilience and mathematics achievement. The first group was more successful in mathematics than the second group. The first group regarded the mathematics teacher as a supportive person and a knowledgeable person, whereas the second group regarded him or her as a fear factor. Students in the first group perceived mathematics learning as a process that gives happiness and requires effort, while the second group considered it as a challenging process. While the first group perceived mathematical achievement as a process giving happiness as a result of effort, the second group perceived it as an extremely difficult process. While the first group valued mathematics more, the second group believed that mathematics could not be achieved by everyone.

Ashcraft, M.H. & Krause, J.A. (2007). Working memory, mathematics performance and math anxiety. Psychonomic Bulletin & Review, 14(2), 243–248. Boero, P., Bazzini, L. & Garuti, R. (2001) Metaphors in teaching and learning mathematics: A case study concerning inequalities. Proceeding of PME-XXV (Vol. 2, pp. 185-192). Utrecht: the Netherlands. Chui, M. M. (2001). Using metaphors to understand and solve arithmetic problems: novices and experts working with negative numbers. Mathematical Thinking and Learning, 3(2-3), 93–124. Daher, W., Anabousy, A. & Jabarin, R. (2018). Metacognition, positioning and emotions in mathematical activities. International Journal of Research in Education and Science, 4(1), 292-303. Hembree, R. (1990). The nature, effects and relief of mathematics anxiety. Journal for Research in Mathematics Education. 21, 33–46. Johnston-Wilder, S., Brindley, J. & Dent, P. (2014). A survey of mathematics anxiety and mathematical resilience among existing apprentices. London: Gatsby Charitable Foundation. Kooken, J., Welsh, M., Mccoach, B., Johnston-Wilder, S. & Lee, C. (2013). Measuring mathematical resilience: an application of the construct of resilience to the study of mathematics. In: AERA 2013, San Francisco, California, 27 April-1 May 2013. Kooken, J., Welsh, M., Mccoach, B., Johnston-Wilder, S. & Lee, C. (2016). Development and validation of the mathematical resilience scale. Measurement and Evaluation in Counseling and Development, 49(3) 217 –242. Ma, X. (1999). A meta-analysis of the relationship between anxiety toward mathematics and achievement in mathematics. Journal for Research in Mathematics Education, 30(5), 520–540. Ma, X., & Kishor, N. (1997). Assessing the relationship between attitude toward mathematics and achievement in mathematics: A meta-analysis. Journal for the Research in Mathematics Education, 28, 26–47. McGowen, M.A. & Tall, D.O. (2010). Metaphor or met-before? The effects of previous experience on practice and theory of learning mathematics. Journal of Mathematical Behavior, 29,169–179. Singh, K. Granville, M. & Dika, S. (2002) Mathematics and science achievement: effects of motivation, interest, and academic engagement. The Journal of Educational Research, 95(6), 323-332. Yalçın, M. O. & Eren, A. (2016). Matematik dersi ve mecazlar. Ankara: Gece Kitaplığı. Yeager, D., & Dweck, C. (2012). Mindsets that promote resilience: When students believe that personal characteristics can be developed. Educational Psychologist, 47, 302–314.