The construct validity of mathematical reasoning and proof test instrument integrated with GeoGebra: Second-order confirmatory factor analysis

Abstract

[English]: Mathematical reasoning and proof instruments assess students' reasoning in solving proof problems. The importance of reasoning and proof in mathematics is documented in skills that students need to be developed in several curricula. However, there are some issues in the assessment of mathematical reasoning and proof in Indonesia. One of them is no instruments that meet construct validity. The existing instruments only confirm the teacher's interpretation by focusing on mathematical problems that measure students’ knowledge. Therefore, there is a need to determine the construct validity of items in assessing mathematical reasoning and proof. For this need, this research aims to develop and evaluate the construct validity of the developed instrument. There are four aspects of a mathematical reasoning and proof instrument integrated with GeoGebra, namely CMR (Creative Mathematical Reasoning), IR (Imitative Reasoning), FP (Formal Proof), and EP (Empirical Proof). The data was obtained by conducting tests on 300 high school students in East Java, Indonesia. Second-order confirmatory factor analysis (CFA) was used to analyze the data using Lisrel 8.80 software. The results showed that the developed eight items are valid or unidimensional, with a t-value > 1.96 and a loading factor value > 0.5. This reveals that the parameter of the item is unidimensional; hence, it can measure students’ mathematical reasoning and proof. [Bahasa]: Instrumen penalaran dan pembuktian matematika merupakan alat untuk menilai kemampuan penalaran siswa dalam memecahkan masalah pembuktian. Pentingnya penalaran dan pembuktian dalam matematika didokumentasikan dalam keterampilan yang harus dikuasai siswa dalam beberapa kurikulum. Akan tetapi, terdapat kesenjangan penilaian penalaran dan pembuktian matematis di Indonesia, yaitu belum adanya intrumen yang memenuhi validitas konstruk sehingga instrumen yang dikembangkan hanya menegaskan interpretasi guru dengan menitikberatkan pada masalah matematika yang mengukur pengetahuan siswa. Oleh karena itu, ada kebutuhan untuk menunjukkan validitas konstruk item dalam penilaian penalaran dan pembuktian matematika. Untuk memenuhi kebutuhan tersebut, penelitian ini bertujuan mengembangkan dan menentukan validitas kontruk instrumen yang dikembangkan. Terdapat empat aspek instrumen penalaran dan pembuktian matematika terintegrasi GeoGebra, yaitu CMR (Creative Mathematical Reasoning), IR (Imitative Reasoning), FP (Formal Proof), dan EP (Empirical Proof). Data diperoleh dengan melakukan pengujian tes terhadap 300 siswa SMA di Jawa Timur, Indonesia. Data dianalisis menggunakan analisis faktor konfirmatori orde kedua (CFA) berbantuan perangkat lunak Lisrel 8.80. Hasil penelitian menunjukkan bahwa, dari semua item, sebanyak 8 item valid atau unidimensional, dengan nilai t > 1,96 dan nilai faktor loading > 0.5. Hal ini menunjukkan bahwa parameter butir soal tersebut unidimensi sehingga dapat mengukur komposisi penalaran dan pembuktian matematis.

Factors influencing Chinese EFL students’ online learning anxiety in the post-COVID-19 era

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Evaluating graphing quadratic worksheet on visual thinking classification: A confirmatory analysis

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