Proximidad conceptual del Buen Vivir

Empowerment is “the gaining of power in particular domains of activity by individuals or groups and the processes of giving power to them, or processes that foster and facilitate their taking of power” (Ernest, 2002, p. 1). This study seeks to determine the extent to which the subject APM can empower a learner in his/her learning of Mathematics.

Ernest (2002) distinguishes three different but complementary domains of empowerment concerning Mathematics and its uses, i.e. mathematical, social and epistemological empowerment.

(a) Mathematical empowerment

A person is mathematically empowered if he/she has power over the knowledge and skills, as well as over the language and symbols of Mathematics and can confidently apply them in school Mathematics. He/she will be able to demonstrate a wide range of cognitive capabilities such as performing algorithms and procedures or applying mathematical strategies.

80

Mastery over the knowledge and skills of Mathematics is the more traditional psychology perspective, where a successfully empowered learner has certain cognitive mathematical capabilities such as applying and using general facts, skills, concepts and all forms of mathematical knowledge, application of strategies and carrying out plans to solve problems (Ernest, 2002). This also involves meta-cognition, the management of one’s own cognitive processes (Ernest, 2002; Flavell, 1976; McMillan, 2001). Cognitive strategies are used when a Mathematics problem is solved, but metacognitive processes are employed when learners are aware of their thinking about the problem, or when they begin to evaluate their progress in solving the problem. In practice, learners constantly alternate between metacognitive and cognitive processes (Larkin, 2009).

Mastery over the language and symbols of Mathematics is the semiotic perspective where the successfully empowered learner has the ability to “make sense of, write and judge the correctness of mathematical texts concerning mathematical tasks and questions as well as their solutions and answers, including asking the questions themselves” (Ernest, 2002, p. 3).

(b) Social Empowerment

“Social empowerment through Mathematics concerns the ability to use Mathematics to better one’s life chances in study and work and to participate more fully in society through critical mathematical citizenship” (Ernest, 2002, p. 4). Examination and test results or certificates in Mathematics often open doors of opportunities to advanced studies and several rewarding occupations not only in STEM courses, but also in other highly paid occupations, such as the caring professions, financial services and management positions (Ernest, 2002).

Many researchers have noted the role of Mathematics as a ‘critical filter’ controlling entry to higher education and higher paid occupations (Ma & Johnston, 2008; Stinson, 2004). In South Africa, there has been a lot of debate on the ‘gatekeeper’ role of Mathematics. It is argued that Mathematics has disempowered and excluded many previously disadvantaged learners from higher education and its privileges, because it did not provide them with the “key to the gate” (Stinson, 2004, p. 4). Critics argue that

81

the post-democracy goals of transformation and equity have not been achieved in practice (Fleisch, 2008; Jansen & Sayed, 2001; Volmink, 1994). Skovsmose (2000) in his writings raises awareness of the two faces of Mathematics – on the one hand granting inclusion and empowerment, and on the other hand leading to oppression, exclusion and disempowerment.

Social empowerment also concerns critical mathematical citizenship, where students view the world critically, can use their mathematical knowledge and skills to think independently, see the detailed as well as the bigger picture, and make balanced judgments. Hopefully this will “lead to the promotion of social justice and a better world for all” (Ernest, 2002, p. 6).

(c) Epistemological empowerment

Epistemological empowerment concerns the individual’s growth of confidence not only in using mathematics, but also a personal sense of power over the creation and validation of knowledge. For a learner to obtain epistemological empowerment through mathematics, it must over a long term become an integral part of his personal identity (Ernest, 2002).

Ernest’s description of what it means when Mathematics becomes an integral part of a learners identity is critical to the argument in this study. He argues that learners need to:

 be confident in their mathematical knowledge and skills;

 be confident in their ability to apply these capabilities both in routine and non- routine mathematics tasks, and in applied social contexts;

 be confident in their ability to understand mathematical ideas and concepts including new ones;

 have a sense of mathematical self-efficacy, i.e., a confident self-image of themselves as successful in mathematics;

 have a sense of personal ownership of mathematics including a sense that they can be creative in Mathematics (Ernest , 2002, p. 12).

82

To achieve these goals, the most important factor will probably be the quality of student- teacher relationships in the classroom. Other important factors are firstly learners’ success at mathematical tasks over a long time and ownership of this success. Secondly, increasing the cognitive demands in set tasks is vital so that challenge and hence levels of attainment increase. Thirdly, a variety of mathematical tasks and projects should be used to encourage use of initiative and creativity. Fourthly, providing the opportunity for learners to make and express judgements and valued contributions and finally a shift away from individual competitive work towards more group sharing of mathematical ideas are necessary (Ernest, 2002). These suggestions of Ernest to achieve the goals of epistemological empowering are in line with the arguments of Bandura on the courses of improving self-efficacy, as described in section 3.5.1(c). Ernest (2002) claims that epistemological empowerment is the culmination of all the other types of empowerment.

Ernest (2002, p. 13) writes:

It is only when learners are fully empowered mathematically that they will feel they are entitled to be confident in applying mathematical reasoning, judging the correctness of such applications themselves, and critically appreciated by others, across all types of contexts, in school and society.

3.5.4 Ackerman, Kanfer and Beier’s findings on APM as domain knowledge