Allgemeinbildung, Mathematical Literacy, and Competence Orientation

Abstract

The first part of this chapter has been written by Rolf Biehler on the basis of his presentation at ICME 13. Mogens Niss was invited to react to this presentation at ICME 13 and elaborated his reaction as the second part of this chapter. Although the authors are only responsible for their respective sections, they both belong together and are therefore published here as a joint chapter. The first part gives a sketch of the discussion on 'Allgemeinbildung' (general education for all) and mathematical literacy in Germany from the late 1960s to today. In the 1970s, educational goals for Allgemeinbildung were condensed in different visions, for example, a 'scientifically educated human being', a 'reflected citizen', an 'emancipated individual being able to critique society', and a person 'well educated for the needs of the economic system'. In the early 1990s, a book by H. W. Heymann on Allgemeinbildung and mathematics education initiated a controversial discussion, which will be critically examined and related to other conceptions. Due to bad results in TIMSS (Third International Mathematics and Science Study) and PISA (Programme for International Student Assessment) starting in the late 1990s, a new discussion on educational goals in mathematics arose and made PISA's conception of mathematical literacy popular in Germany. However, the idea of mathematical literacy was modified and extended by the German debate, some traits of which can be traced back to Humboldt and the 19th century. In his reaction "Allgemeinbildung, mathematical competencies and mathematical literacy: Conflict or compatibility?" Mogens Niss relates the German discussions to the international development on competence orientation, featuring the KOM project (Competencies and Mathematical Learning), including the various conceptualisations in the PISA frameworks. Keywords Bildung • Allgemeinbildung • General education • Mathematical literacy • Mathematical competencies • Mathematical literacy R. Biehler with a reaction by Mogens Niss (B)

Tales from three countries: reflections during COVID-19 for mathematical education in the future

“…German goals for school mathematics are deeply influenced by the idea of "Allgemeinbildung." 6 This idea became historically relevant in the German tradition of mathematics education (see Biehler, 2019;Jahnke, 2019 for the historical development and background, Biehler, 2019 for the relation to mathematical literacy) and therefore became a cornerstone in all three documents of the Bildungsstandards after primary education 7 (KMK, 2003(KMK, , 2004(KMK, , 2012. While there is no suitable English counterpart to the concept of Allgemeinbildung (see Niss in Biehler ( 2019)), it is defined by Winter as "knowledge, competencies, and skills that are essential to every human being as an individual and as a member of societies independent of their gender, religion, and profession, etc."…”

When teachers construct tests for assessing students’ competencies: a taxonomy

“…For quite some time, various notions of mathematical competence and competencies, as well as the corresponding notions of skills, abilities, capabilities, and proficiencies, have been given increasing importance in the formulation of learning goals and standards in mathematics (Biehler, 2019;Niss & Højgaard, 2019;Niss et al, 2017;Pettersen & Braeken, 2019), and in the mathematics education literature worldwide (Department of Education, 2013;Kilpatrick et al, 2001;Niss, 1993;Niss & Højgaard, 2002;Swedish National Agency for Education, 2000). And they cover results of mental processes connected to doing mathematics by several competency frameworks (Kilpatrick, 2020).…”

Middle school students’ beliefs about mathematics as a discipline

“…Moreover, a democracy entails critical questioning of experts and lawmakers, partly to prevent abuse of power. Therefore, citizens in a democracy must obtain a mathematical competence that enables them to exercise these rights and obligations, making mathematics an important part of what in German is called an individual's Allgemeinbildung, which-in lack of an appropriate English term-is used to describe a person's life skills, or general education (Biehler, 2019;Winter, 1995).…”