Aims of the study: 

• Investigate the factorial structure of the goals items in the Australian Reframing Mathematical Futures II (RMFII) Project survey
• Investigate the existence of statistically significant differences between the derived factors (dependent variables) and the independent variable Year Level.

Within the field of mathematics education, it has been widely acknowledged that affective variables, such as attitudes, beliefs, and motivations, play a significant role in the teaching and learning process. However, despite the large amount of work exploring these variables in educational psychology, the construct of motivation within the mathematics domain has not been as extensively explored (Middleton & Spanias, 1999). 

Motivation is defined as the “reasons individuals have for behaving in a given manner in a given situation” (Middleton & Spanias, 1999, p. 66). Some individuals are motivated to obtain rewards or avoid punishments (extrinsic motivation), and others are motivated by their desire or drive to learn (intrinsic motivation). However, one of the most prominent theories around motivation in educational research has been the Achievement Goal theory (Senko, Hulleman, & Harackiewicz, 2011). Goal theorists focus more on achievement behaviour and early research in this field aimed to describe how “different goals elicit qualitatively different motivational patterns” (Ames, 1992, p. 261). As a result, two main types of goal orientations arose in the 1980s: mastery goals, which focus on personal improvement, and performance goals, which focus on demonstrating ability (Ames, 1992; Patrick, Ryan, & Kaplan, 2007).

Of the two types of goal orientations, the mastery goal orientation has tended to provide the most favourable results in educational research (Senko et al., 2011). Patrick et al. (2007) noted that the development of a mastery-oriented classroom could encourage students to have a greater desire for self-improvement:  

Conveying support and promoting respect among students will contribute to an environment in which students can focus on understanding content rather than diverting attention to how they are being perceived by others or contributing to anxiety about ridicule if they experience difficulty or uncertainty. (p. 85)

On the other hand, research on performance goal orientations has been mixed and inconsistent. Although there have been studies that demonstrate positive outcomes (see review by Midgley, Kaplan, & Middleton, 2001), other studies have linked the performance goal orientation with negative outcomes (Senko et al, 2011). These inconsistencies in research led to the development of an additional dimension to mastery and performance goals. Mastery goals were divided into mastery-approach and mastery-avoidance goals (avoid a lack of mastery) and performance goals were divided into performance-approach and performance-avoidance goals (avoid appearing incompetent) (Senko et al., 2011). The addition of an “avoidance” dimension helped to address the inconsistencies evident in early performance goal research as many of the negative outcomes linked with performance goals appeared to be confined to the performance-avoidance orientation (Senko et al., 2011).

In this paper we will present the outcomes of the data analysis of a survey instrument based on this theory, to investigate students’ goal orientations and how they differ across different contexts. The aims of this study were to explore the factorial structure of the goal orientations items from the survey instrument, used as part of the Australian Reframing Mathematical Futures II (RMFII) research project (2014-8), and to examine whether statistically significant differences were evident between the derived factors and the variable Year Level. 

An online survey was undertaken as part of the Reframing Mathematics Futures II (RMFII) Research Project (2014-8) conducted in Australia, which aimed to find ways to improve the teaching and learning of mathematics students in Year 7 to 10 and to develop learning progressions (trajectories) in mathematics education. The purpose of the survey was to examine students’ motivations, goals, preferences and attitudes regarding their learning experiences in mathematics. The participants came from Australian State and Catholic schools involved in the RMFII project across various Australian States and Territories. A total of 606 Year 7 to 9 students from nine schools across the New South Wales (NSW), Queensland and South Australia States and the Northern Territory responded to the survey. The survey consists of 95 items and was designed by adapting items from instruments developed in prior studies (Dweck, Chiu, & Hong, 1995; Frenzel, Goetz, Pekrun, & Watt, 2010; Midgley et al. 2000; PISA, 2006; Watt 2004; 2010; Wyn, Turnbull, & Grimshaw, 2014; You, Ritchey, Furlong, Shochet, & Boman, 2011). The items in the survey were designed to examine the following constructs: Mathematics Learning Climate, Friends Perceptions of Mathematics, Perceptions of the Australian National Assessment Program - Literacy and Numeracy (NAPLAN), Homework, Mathematics Motivations and Perceptions, Gender Perceptions of Mathematics, Personal Goals in Mathematics, Mathematics Mindset, Perceptions of School, Perceptions of Mathematics Teaching, and Mathematics Career. For the purposes of this paper only the 2016 Personal Goals in Mathematics item responses have been analysed. There are 14 Personal Goals in Mathematics items in the survey, which have been adapted from the Patterns of Adaptive Learning Scales (PALS) developed by Midgley et al. (2000). A link to the online survey was provided to participating students by their teachers from September 2016 and it was completed either in the students’ own time at home or during class time. The survey was anonymous and students and their respective parents were made aware of the purpose of the survey. In order to investigate the factorial structure of the goals items of the RMFII Project survey an Exploratory Factor Analysis (EFA) was conducted. An Analysis of Variance (ANOVA) was also conducted to examine if statistically significant differences existed between the three identified factors and the independent variable Year Level.

In order to investigate the factorial structure of the goals items of the RMFII Project student survey an Exploratory Factor Analysis (EFA) was conducted. The results from this analysis found that together three factors, explained 75.3% of the variance. The three identified factors were consistent with the study from which the items were adapted from (Midgley et al., 2000) and were labeled as follows: Performance Approach Goal Orientation, Mastery Goal Orientation, and Performance Avoidance Goal Orientation. An Analysis of Variance (ANOVA) was conducted to examine if statistically significant differences existed between the three identified factors and the independent variable Year Level. Results showed that statistically significant differences were evident and that there were interaction effects between Factors 1 and 2 and the independent variable Year Level. Post hoc analysis showed that The Year 8 students’ scores had a mean score higher than both the Year 7 students’ and the Year 9 students’ mean scores and the Year 7 students’ scores had a higher mean than the Year 9 students’ mean scores. In other words, Year 8 students valued mastery orientation, such as extending their understanding, more than the Year 7 and the Year 9 students and the Year 7 students valued a mastery orientation approach more than the Year 9 students did. There is limited research exploring changes in goal orientation over time, however, an earlier longitudinal study conducted by Anderman and Midgley (1997) found that students in the fifth grade (elementary school) were more oriented towards mastery goals than when they moved into the sixth grade (middle school). Further investigation involving different classroom environments in other countries could provide more insights into how student perceptions of their classroom environment can orient them towards particular goals.

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