HISTORY OF TEACHING MATHEMATICS (By Shambhu Prasad Nirala, H.O.D Mathematics)

  

HISTORY OF TEACHING MATHEMATICS

                                                           

                                                                             

✍️ By Shambhu Prasad Nirala

                                                                          (H.O.D Mathematics)

 

 

From Antiquity to Enlightenment

For mathematics, number was at the beginning (Boyer, 2011). Even today, many mathematicians believe that number is not only the historical beginning of mathematics, but–more broadly and fundamentally–its deepest foundation. Thus, its first  beginnings are seen in counting, in the emergence of the concept of “abstract natural number”, in the formation of names and symbols for numbers, and later in the first steps towards elementary computation with such introduced numbers (Boyer, 2011).

Skills in calculation were taught even in the earliest times before our era. This is confirmed by ancient documents found in the temple of the god Baal in Nippur, which bear symbols of numbers and arithmetic operations (Friberg, 2000). These documents date back to several millennia before our era. Instructions for arithmetic operations are also found on ancient Egyptian monuments and papyri (Peet, 1931b). The Egyptians used a counting board called an abacus, which had movable stones, for calculations.

The Romans also used a similar abacus and introduced it for practical use throughout their empire (Sugden, 1981). The Egyptians also had a highly developed geometry due to practical needs in measuring fields along the Nile and in construction (Peet, 1931a). Based on what we know today about ancient Egyptian mathematics, it seems they considered it an empirical science.

Mathematics only became a deductive science in ancient Greece (Logan & Pruska-Oldenhof, 2022). In the Middle Ages, all arithmetic instruction took place on abacuses (Evans, 1977). Without their assistance, solving calculations with “large” numbers was very difficult, as positional numeral systems were not yet known (Pisano & Bussotti, 2015). The positional numeral system, or the Indian-Arabic numeral notation in decimal composition, had a significant impact on the development of mathematics and culture in general. However, despite its advancement, mathematics was not introduced into schools as a compulsory subject for a long time. In the Middle Ages, “arithmetic masters” emerged in cities who taught computational skills (Ulivi, 2016).

The most famous medieval arithmetic master was the Frenchman A. Riese (1492-1559). Arithmetic in the Middle Ages was taught solely for practical needs in crafts and trad

 

From Enlightenment to 20th Century

The first breakthrough of the direction that demanded arithmetic instruction to fulfill educational tasks was established in pedagogical practice only with the educator and psychologist J. H. Pestalozzi (1746-1827) (Mesquida et al., 2017). For him, arithmetic instruction was truly education and the development of young people, not just rote learning. Although Pestalozzi exaggerated with arithmetic exercises in special tables and delved into excessive arithmetic formalism (Hartung, 1962), we must recognize the merits he has for the development of arithmetic instruction. His works inspired numerous educators (e.g., Tillich, Harnisch, Diesterweg, and Grube) of the 19th century to begin studying and developing arithmetic instruction, thus continually improving it (cf. Bullynck, 2008). The principles of arithmetic instruction of 19th century educators were largely considered by the pedagogue E. Hientschel at the beginning of the 20th century. His arithmetic calculations served as a model for arithmetic instruction for many years. He introduced a concentric arrangement of teaching content and thus made a significant contribution to the meaningful construction of the curriculum, especially for arithmetic.

 

 From Past to Present

A significant milestone in the teaching of mathematics at the beginning of the 20th century was the conference in Merano in 1905 (Hamley, 1934). The gathered scientists attempted to adapt arithmetic to children’s psychophysical abilities, considering the results of youth psychology and experimental pedagogy. Above all, they wanted arithmetic and geometry instruction to develop functional thinking, concrete perception of spatial relationships, and to discover mathematical relationships in nature, society, and life (Jahnke et al., 2022). The scientists who significantly influenced the development of mathematics in the first half of the 20th century were V. Prihoda, J. Kühnel, and J. Wittmann (Beyer & Walter, 2014). Despite their efforts to improve mathematics instruction, we can conclude that mathematical instruction until the middle of 20th century was limited to the necessity of providing students with indispensable tools for practical activities; that is, acquiring the necessary techniques for the four basic arithmetic operations. Thus, students learned only “practical” arithmetic. Geometry was less important; its instruction was narrowed down to planning shapes, making models of solids, calculating the perimeter and area of shapes, as well as the surface area and volume of solids.

 

Present

The year 1950 marks the beginning of significant changes in the teaching of mathematics worldwide. In that year, scientists, including psychologist J. Piaget, mathematician G. Choquet, and educator C. Gattegno, formed the CIEAEM commission: Comission Internationale pour l’Etude et l’Amelioration de l’Enseignement des Mathematiques [International Commission for the Study and Improvement of Mathematics Teaching] (De Bock, 2023). They extensively discussed modern mathematics and developmental psychology, giving rise to the idea of a radical reform of mathematics instruction at all levels of schooling. After 1960, renewal processes began in most countries (the renewal had an international character), involving mathematicians, psychologists, educators, and teachers (Furinghetti et al., 2012). Various tendencies emerged during the reform of mathematics education, often conflicting and divergent.

This renewal took place in three phases (Furinghetti & Giacardi, 2023):

1. changes in content,

2. changes in teaching and learning approaches, and

3. realization that not only content and approaches matter, but above all,  

    the child for whom content and approaches are intended

                                                                                                   

References:

International electronic journal of mathematics education