Academic journal article Kuram ve Uygulamada Egitim Bilimleri

Teachers' Diagnostic Competences and Levels Pertaining to Students' Mathematical Thinking: The Case of Three Math Teachers in Turkey *

Academic journal article Kuram ve Uygulamada Egitim Bilimleri

Teachers' Diagnostic Competences and Levels Pertaining to Students' Mathematical Thinking: The Case of Three Math Teachers in Turkey *

Article excerpt

There is a big difference between good teaching and effective teaching. Good teaching is about what a teacher does while teaching, whereas effective teaching relates to what learners can learn from this teaching (Airasian, 2001). This is also true for teaching mathematics; teachers are expected to have more math skills than math knowledge (Cooney, 1999). For example, skills can be mentioned such as using one's understanding of mathematical knowledge when teaching and seeing one's students both as individuals and as math learners (National Council of Teachers of Mathematics [NCTM], 2000; Shulman, 1987).

To effectively teach math, teachers need to be able to analyze their pupils' and own actions towards teaching and consider how these actions can affect student learning (NCTM, 2000). For this necessary consideration, teachers are expected to be able to interpret students' perceptions as well as their learning outcomes (Aufschnaiter et al., 2011; Cooney, 1999; Zembat, 2013). This interpretation requires being able to analyze students' perceptions and error sources (Ball, Hill, & Bass, 2005) and to understand student thinking in the context of valuing pupils' ideas (Dewey, 1902; Duschl, Schweingruber, & Shouse, 2007; Graeber 1999). Teachers' abilities to analyze and understand student thinking have been introduced into the literature through the concept of diagnostic competence.

Diagnostic competence can be associated with skills for accurately evaluating individuals (Brünken, 2009; Helmke, Hosenfeld, & Schrader, 2004), with the analytical skills required for performing this assessment (Edelenbolos & KubanekGerman, 2004; Prediger, 2010), or with both analytical and evaluation skills (e.g. National Science Foundation [NSF], 2007). Prediger (2010) mentioned that this competence is used for teachers' skills in understanding and analyzing pupils' thinking process -without any concern for grading them. Therefore, diagnostic competence is necessary for making assessments in teaching (Edelenbolos & Kubanek-German, 2004) and involves more skills than just judging student achievement (Schwarz, Wissmach, & Kaiser, 2008). Similarly, this study associates diagnostic competence with understanding and analyzing the nature of student thinking (Prediger, 2010), and its theoretical framework is structured around this meaning.

What is Diagnostic Competence?

The first thing that comes to mind with the concept of diagnosis is the health sector (such as doctors' diagnoses); the word diagnosis is even oft seen used in the field of medicine (Edelenbolos & Kubanek-German, 2004; Hoth et al., 2016). Studies carried out in the field of education on this concept have usually been implemented by German scholars. According to Schrader (cited in 2001, Schwarz et al., 2008), who is one of the most frequently mentioned names, diagnostic competence is the ability of an evaluator to analyze the performance of individuals according to predefined categories, terms or concepts, or readiness in this regard. From another aspect, diagnostic competence is both knowledge and skills in understanding and assimilating students' learning processes as well as their current learning difficulties in order to assess (Deutsches PISA Konsortium, 2001, p.132, as cited in Richter, 2010). This competence can be used not only for student assessment or analysis, but also for adapting to student-centered instruction (Helmke et al., 2004). Therefore, the purpose for which and how diagnostic competence is used is important. This issue becomes clear under the following headings.

What is the Role of Diagnostic Competence in Teacher Education?

The role of diagnostic competence in teacher education becomes a greater issue with the idea that it is necessary for successful and effective teaching (Helmke & Schrader, 1987; Klug, 2011). This role can be explained by the fact that diagnostic competence reflects the education and training aspects in terms of diagnosis and the profession aspect in terms of competence. …

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