The problems that practitioners consider crucial and worth researching as well as the appropriate solutions they seek are vary by community. As a result, the types of knowledge produced by communities also differ. This paper aims to explain three types of knowledge, namely jutsu (術), hō (法), and Hyō (表), in the context of Wasan by identifying and discussing their meanings and functions and comparing them. Jutsu is considered a procedural and mechanical algorithm and can also be seen as a procedure by which operations and computations are applied to the values in mathematics problems step by step to result in an answer. Jutsu is an instrument for obtaining numerical solutions and the types of solution preferred by Wasan mathematicians. Sometimes, Jutsu connotes a formula or theorem and reveals an abstract relationship between values or magnitudes. Hō is a procedural mathematical operation or method through which Wasan mathematicians can calculate values, and it is often a subprogram or a subprocedure of the primary algorithm in the procedure of Jutsu. Hyō records and condenses mathematical knowledge and reveals the structures of and relationships between mathematical concepts and mathematical objects, and it is treated as an instrument for problem solving and is used in the processes of exploring and justifying knowledge. When Wasan mathematicians propose mathematics problems, two aspects of knowledge activities related to mathematics research and practice are considered: They construct Jutsu using the hō or the hyō or mathematical knowledge relevant to problems, and they operate and calculate step by step on paper or another surface used for calculating to obtain the numerical solutions according to the steps of Jutsu through the use of calculators.
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The meanings and characteristics of mathematic knowledge in Wasan - Jutsu, hō and Hyō
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