The initial search got 414 articles in total. After applying exclusion criteria, 186 articles were left. Among 186 articles, only 13 clearly stated the definition of math attitudes, while the rest articles did not define the term at all. Three types of definition were commonly used in those researches which explicitly defined the term: simple unidimensional definition, bi-dimensional definition and multidimensional definition.

## Unidimensional Definition

Unidimensional definition refers to a simple affect either positively or negatively associate with mathematics (Aiken & Dreger, 1961). Aiken defined it as “a learned predisposition or tendency on the part of an individual to respond positively or negatively to some object, situation, concept, or another person” (p. 551, 1970). Similarly, Haladyna, Shaughnessy & Shaughnessy proposed that attitude toward mathematics is “a general emotional disposition toward the school subject of mathematics” (1983). In McLeod’s work, attitudes were also simply defined as positive or negative feeling which is between unstable emotions and stable beliefs (1992).

This simple definition has several limitations. First of all, this definition treats attitudes as somewhat unstable affective feelings, such as ‘liking’ or ‘disliking’. However, the unstable present attitudes can be influenced easily by many other factors, but deeper factors that form a stable opinion towards the subject need to be explored. More importantly, the unidimensional definition focused solely on affective aspects but largely ignored the cognitive aspects (Martino & Zan, 2001). Though a lot of researches follow this definition in their studies, they still adopt items regarding to beliefs to measure students’ attitudes (Martino & Zan, 2001). For example, one of the most generally used item is “I think mathematics is useful”. Putting beliefs in the measurements implicitly suggested that affective emotions were not enough to represent students’ attitudes towards mathematics. Last but not least, the simple definition also ignored the behavioural aspects, which made it inadequate to predict students’ behaviour in mathematics learning (Martino & Zan, 2009).

## Bi-dimensional Definition

Bi-dimensional definition acknowledges the importance of cognitive aspect and suggests that mathematics attitudes is the combination of emotions and beliefs towards the subject (Daskalogianni & Simpson, 2000).

Though this definition represents the main components that mathematics attitudes reflect, one disadvantage would be neglecting the behavioural aspects. A lot of researches emphasized the behavioural aspects of attitudes and used the items such as “I try to avoid mathematics situation”, which cannot be represented by bi-dimensional definition. Furthermore, like one-dimensional definition, bi-dimensional definition was not supported by any theoretical framework.

## Multidimensional Definition

Multidimensional definition treats mathematics attitudes as three parts: cognitive, affective and behavioural dimensions (Martino & Zan, 2003). Neale (1969) thinks attitude is “a liking or disliking of mathematics, a tendency to engage in or avoid mathematical activities, a belief that one is good or bad at mathematics, and a belief that mathematics is useful or useless (p. 632)”. Similarly, Heart thinks mathematics attitudes are composed of one’s emotions, beliefs towards mathematics and how he/she act towards the subject (1989).

Multidimensional definition has few advantages. Unlike the other two definitions which were not supported by any theoretical framework, this multidimensional definition is lined up with tripartite model (Martino & Zan, 2003). Tripartite model regards attitudes as a complex term with cognitive (the knowledge of the object, ideas and beliefs towards the object), affective (feelings associate with the object) and behavioural (actions towards the object) components and it was commonly used in the field of social phycology (Eagly & Chaiken, 1998). Later the tripartite model was adopted in mathematics education and be referred by mathematics educators (Leder, 1992; Ruffell et al., 1998). Moreover, with the support of tripartite model, multidimensional definition helps clarify the confusing instruments of mathematics attitudes in the field as McLeod indicated that the unclear instruments is caused by lacking appropriate theoretical framework (1992).

Finally, Kulm (1980), and Ruffell suggested that mathematics attitudes is ‘observer’s construct’ and the definition serves as a mean to answer research questions (1988). In this way, the multi-dimensional definition contains all aspects used in research and theory, which lines up with the goal of this systematic review (to clarify the construct of mathematics attitudes from existing literature in order to provide a holistic view in mathematics education). In sum, because of the advantages over other two definitions, this paper adopts the multidimensional definition of mathematics attitudes.