### EKSPLORASI KONSTRUKSI PENGETAHUAN MATEMATIKA SISWA KELAS VIII SMP NEGERI 1 SURAKARTA MENGGUNAKAN TEORI ACTION, PROCESS, OBJECT, SCHEME (APOS) PADA MATERI POKOK FAKTORISASI BENTUK ALJABAR

#### Abstract

**Abstract:** The objective of the this qualitative research was to describe and analyze the mathematical construction process of eighth graders of SMPN 1 Surakarta in the algebraic factoring topic based on the APOS Theory. The subjects of the research were the eighth graders of SMPN 1 Surakarta and have been selected by using purposive sampling with the following criteria: (1) the students have learning algebraic factoring before; (2) the students were able to communicate his thoughts orally and written; and (3) each students were in high, medium, and low ability group. Data retrieved with the think aloud method and taken by the researcher himself, assisted by two auxiliary instruments; algebraic factoring test and interview guides. The main data sources were the words and actions of students when they were being interview. Data was validated by using data triangulation, where data collection was conducted at two different times. Based on the findings and discussions, it can be concluded as follows. (1) In *action* stage, the students presented their knowledge orally, by using pictures, and in writing form. The students then subtracted the simple algebraic form by classifying the algebraic terms which have the same variables. In *process* stage, the students multiplied the binomial with FOIL method and classified the algebraic terms that have same variables mentally and in the written form. In *object* stage, the students factorized the trinomial procedurally. In *schema* stage, the subject explained that the factor when multiplied by another factor will produce the factored trinomial and linked the *action*, *process**,* and *object* stage to formed a complete concept of algebraic factoring. (2) In *process* stage, there was a student who made mistakes that could be classified as ‘invalid or incompatible distribution’. In *object* stage, there was a student who did factorization in non-procedural way.

**Keywords****:**** **construction of mathematical knowledge, APOS theory, algebraic factoring

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