DEPORTES DE EQUIPO A) REGLAS TÉCNICAS COMUNES

Pedagogical content knowledge affects how a teacher thinks about their subject and their knowledge, as well their understanding of the subject. According to Shulman (1986), there are several key elements of pedagogic content knowledge. The first element is knowledge of representation, which refers to content knowledge. The second is understanding learner impressions of the subject and implications for the subject. The third is general pedagogic knowledge, that is, different teaching methodologies and strategies. The fourth is curriculum knowledge. The fifth key element is knowledge of educational contexts and the last element is knowledge of the purposes of education (Solis, 2009).

Subject-expert teachers are crucial in this regard. For them to perform these acts effectively and subsequently, teach knowledge sufficiently and excellently to their learners (as is the case in countries that seem to have succeeded in doing so), subject knowledge expertise is important. The expertise of the teachers in these countries is discussed below to highlight aspects that are crucial to their professional education. In Finland, teachers’ professional development (as it is referred to in Finland) and in- service programmes vary. Teacher education programmes focus and prioritise subject content knowledge, pedagogical content knowledge and pedagogical knowledge (Mogari, 2014, p. 16). Teachers are also well educated and continue to be developed professionally well after their studies are complete. All teachers in Finland hold at least a Master’s degree as there is no option of being a teacher without it (Sahlberg, 2010). During a student’s studies, emphasis is placed on pedagogical thinking skills to enable the teachers to manage the teaching process and balance theory and practice effectively (Sahlberg, 2014).

Specifically, for Mathematics, during the teacher preparation, the teachers develop a balance between personal and professional competency and are taught not only the discipline of Mathematics but the Mathematics didactics. Both emphasise pedagogical content knowledge (Mogari, 2014). In other words, teachers in Finland are taught the language of Mathematics, how to do Mathematics and why mathematical concepts are the way they are. In addition, each school and municipality have the responsibility to train and take care of new teachers. In this way municipalities are responsible for

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teacher education and are required to provide it as per individual needs (Sahlberg, 2010). Teachers spend up to seven days per year in teacher training courses.

Municipalities also provide a budget for schools - the use of which is solely for resources such as textbooks, worksheets, abacus’ and counting blocks, to name just a few (Finnish National Board of Education, 2014). The result is that teachers are able to choose their resources and usually decide on these collectively, especially as subject teachers (Finnish National Board of Education, 2014). Teachers in Finland are, therefore, more autonomous and are able to supply learners with a vast number of different resources to aid them in understanding Mathematics.

In Singapore too, teachers are required to be highly trained and cannot teach a subject that they last interacted with in high school. Prospective teachers wishing to teach a certain subject must have done that subject at university as well (Tinlam, 2017). In every pre- and post-training session, teachers are exposed to better ways of instruction, content knowledge and pedagogical knowledge (Dindyal, 2006). With regards to Mathematics, student teachers are required to have at least one module in calculus and algebra in their undergraduate studies before they can be considered for a Mathematics teaching post (Tinlam, 2017). This ensures that the teachers are confident in their understanding of the Mathematics content. It also enhances their pedagogical knowledge. Singaporean teachers of Mathematics, Science and Literacy specifically, are also required to complete at least one-hundred hours of training per annum in order to improve their knowledge and skills consistently (Dindyal, 2006). In the past, teachers were allowed to only use textbooks developed by the Ministry of Education. However, in 2001 this changed (Fong, 2004). Schools are now allowed to purchase textbooks from different publishers, but the Ministry screens them to ensure authenticity (Fong, 2004). Permitting this choice of textbooks promotes more diversity and ensures that schools have enough textbooks for all learners and multiple resources (Fong, 2004).

Australia focuses more on what teachers should be able to do before they can graduate. The competencies are broken up into standards, expanded and further developed as they progress through their careers. It is only when each standard is met that students graduate and are considered competent in their subject. There are seven requirements of graduate teachers: know the students and how they learn; know the

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content and how to teach it; plan and implement effective teaching and learning; create and maintain safe learning environments; assess, provide feedback and report on learning; engage in professional learning; and engage professionally with colleagues, parents and community (Australian Institute for Teaching and School Leadership, 2011). Through the use of these standards, teachers become more aware of their specialisation subjects’ requirements and how to teach them effectively.

Further professional development occurs through either half day or full day workshops which teachers are required to attend for a certain number of hours per year - roughly nine days of training (Ling & Mackenzie, 2015). In Australia the circumstances are, at times, the same to those of South Africa, with disadvantaged schools having a greater need for resources (Thomson, 2017), therefore, the majority of the teachers who attend further professional development sessions are Mathematics, Literacy and special needs teachers (Ling & Mackenzie, 2015).

In South Africa, the new teacher education policy (Department of Basic Education, 2011b) was formulated to bring about change in the classroom practices of teachers, as well as in their attitudes and beliefs (Mokhele & Jita, 2010). However, to become qualified, students only need to have completed a Bachelor’s Degree in Education (four years). This is interesting as, out of the three countries discussed above, South Africa seems to require the least professional education for future teachers. It is thus not surprising that teachers, specifically in public schools, are deemed to lack basic teaching skills and are unable to complete some of the mathematical content that they are expected to teach (Spaull, 2013). In order to teach effectively, they need to understand their intellectual field and the codes that function within it. Teachers have to understand these codes and their significance to the pedagogic device they have to use in order to communicate and develop the acquisition of knowledge when teaching.