Thinking Process of Pseudo Construction in Mathematics Concepts

Abstract

This article aims at studying pseudo construction of student thinking in mathematical concepts, integer number operation, algebraic forms, area concepts, and triangle concepts. 391 junior high school students from four districts of East Java Province Indonesia were taken as the subjects. Data were collected by means of distributing the main instrument and tracer instrument to the subjects respectively. Both instruments were deployed for the purpose of digging up the construction process. The construction was clustered on the basis of the pseudo contruction cases and followed with in-depth interviews to three subjects of each case. The findings show that pseudo construction was identified in four cases. The first case was associated with integer operations, operations of algebraic form, the concept of area, and the concept of triangle. They used analogy of "in debt" to construct concepts of negative number operation. In the second case, they used objects (book, pencil, and thing) to describe variables in the algebraic form operation. For the third case, students deciphered unit area (m 2 ) as multiplication m x m. In the fourth case, students did not pay attention to the requirements of the triangle. Although they gave a right answer to their work, their construction concept was completely false.

Penggunaan Model RASCH untuk Menganalisis Miskonsepsi bagi Topik Nombor Integer

“…Semakin meningkat umur seseorang, semakin kompleks susunan sel sarafnya dan semakin meningkat keupayaannya (Kamarudin Husin & Siti Hajar, 2004). Menurut beliau, dalam proses belajar apabila seseorang menghadapi rangsangan baru (perkara baru), terdapat dua proses yang digunakan oleh individu untuk cuba adaptasinya, iaitu asimilasi dan akomodasi (Subanji & Toto Nusantara, 2016).…”

Construction of the mathematical concept of pseudo thinking students

“…This is due to pseudo thinking is a unreal thinking, so the correct answer may not necessarily result from the right thinking process and incorrect answers are not necessarily generated from the wrong thinking process [4]. Pseudo thinking is a thinking process that generates answers to problems or constructs of "incorrect" concepts [8]. The construction of concept does not represent the actual thought.…”

Error Analysis in Solving Geometry Problem on Pseudo-Thinking's Students

“…S1 assumes that ̅̅̅̅ = 4,36 without consider ̅̅̅̅ as the radius of the circle (r). This first error affect the second error, that is, when applying a trigonometric comparison with the sine rule in step 7 . Furthermore, in the last step, that is 16 , S1 unable to justify why to determine measure of ∠ can be obtained by multiplying twice measure of ∠ .…”

“…First, the S2 is asked to look again at the relationship of the radius of the circle and the triangles formed. Second, recalculate the results of the application of Pythagorean theorem in step 6 and trigonometric ratio with the sine rules in step 7 . Third, recall concept of triangle congruence to determine that ∠ = ∠ .…”

“…The pseudothinking process is thinking process that produces "incorrect" answers in problem solving or concept construction [7]. Pseudo-correct in problem solving occurs when learners answer correctly but process of thinking learners is incorrect.…”