The relationship between different kinds of students' errors and the knowledge required to solve mathematics word problems

Abstract

The main objective of this research is to examine the relationship between different kinds of errors and the knowledge required to solve word problems in Arithmetic, Algebra and Geometry. Kinfong's and Holtan's framework supports the analysis of the errors, and Mayer's theory was implemented to understand the necessary knowledge for solving math word problems. The research methodology follows a semi-experimental method. Research tools comprise both a descriptive math test and a directed interview. The research findings revealed that students' errors when solving arithmetic word problems result from the lack of linguistic, semantic, structural and communicational knowledge; when solving the geometric word problems, the lack of semantic, intuition and structural knowledge were the cause of the students' errors. Regarding algebra word problems, miscalculation was the reason for the higher error rate. HAGHVERDI, M.; SEMNANI, A. S.; SEIFI, M. deficiency is mainly related to the lack of semantic, structural and communicational knowledge.Keywords: Word Problems. Arithmetic. Algebra. Geometry. Necessary Knowledge. Students' Errors. ResumoO principal objetivo desta pesquisa é examinar a relação entre diferentes tipos de erros cometidos por estudantes e os conhecimentos necessários para resolver situações-problema em Álgebra, Aritmética e Geometria. Para a análise de erros seguimos as considerações de Kinfong e Holtan e para investigar o conhecimento necessário para ultrapassar os erros mobilizamos a teoria de Mayer. A metodologia de pesquisa é semiexperimental, envolvendo um teste de matemática com seis questões e entrevistas dirigidas. Os resultados da pesquisa revelaram que os erros na solução dos problemaspalavra aritméticos resultaram da falta de conhecimentos linguísticos, semânticos, estruturais e comunicativos; no que diz respeito aos problemas-palavra, os erros vinculamse à lacunas no conhecimento semântico, estrutural e intuitivo. Em relação aos problemaspalavra algébricos os erros devem-se a lacunas quanto às operações matemáticas. Em síntese, os resultados mostram que a maior deficiência dos alunos relaciona-se a lacunas relativas ao conhecimento semântico, estrutural e comunicativo.

Analisis kesalahan siswa dalam menyelesaikan soal cerita matematika berdasarkan kriteria Watson

“…Selain itu, siswa juga akan mengalami kesulitan dalam menyelesaikan jenis soal tersebut, khususnya ketika mengubah soal tersebut ke dalam bentuk atau kalimat matematika, ketika soal tersebut melibatkan operasi pada variabel-variabel (Nursuprianah & Nisa, 2013). Dengan demikian, menyelesaikan soal cerita matematika merupakan suatu hal yang tidak mudah bagi siswa dan bahkan mereka menghadapi berbagai kesulitan ketika menyelesaikan soal tersebut (Haghverdi et al, 2012). Kesulitan yang dialami siswa dalam memecahkan masalah matematika berpotensi menyebabkan mereka melakukan kesalahan (Hadi et al, 2018;Rafi & Retnawati, 2018).…”

“…Salah satu pertimbangan yang mungkin dapat digunakan adalah jenis-jenis kesalahan yang siswa lakukan ketika menyelesaikan soal cerita matematika. Ini sesuai dengan yang dikemukakan oleh Haghverdi et al (2012) bahwa salah satu pendekatan yang dapat digunakan oleh guru untuk memfasilitasi siswanya dalam proses menyelesaikan soal cerita matematika adalah melalui identifikasi terhadap kesalahan-kesalahan yang dilakukan oleh siswa dalam menyelesaikan soal tersebut. Sejalan dengan yang dikemukakan oleh Haghverdi et al (2012) tersebut, Pradini (2019) menyebutkan bahwa identifikasi dan analisis terhadap kesalahan yang dilakukan oleh siswa merupakan langkah awal untuk menentukan strategi yang tepat untuk mengatasi kesulitan siswa dalam menyelesaikan masalah matematika.…”

Word problems: a review of linguistic and numerical factors contributing to their difficulty

“…Such parity effects have received little attention in WP research so far. Furthermore, it seems that most WPs, especially for children, contain single-digit numbers ; e.g., each answer was in the range of 1–9, e.g., in Lean et al (1990) , or Powell and Fuchs (2014) , only few use multi-digit numbers ( Haghverdi et al, 2012 ). In Nesher (1976) the range of numbers is smaller than 100, contained division two-digit numbers into one-digit number.…”

“…In the study of van der Schoot et al (2009) the final answers were between 14 and 40, included no fraction, no negative number, no numerical value twice, and none of the possible answers resulted in another. However, different types of numbers were presented in WPs in some more studies: (i) fraction ( Raduan, 2010 ), (ii) whole number, (iii) decimal number ( Haghverdi et al, 2012 ); and their effect has been rarely investigated. Koedinger and Nathan (2004) found an effect for decimal numbers: “however we also observed a smaller situation facilitation effect whereby story performance was better than word equation performance under certain conditions: namely dealing with decimal numbers.”…”

Secondary School Students’ Representations for Solving Geometric Word Problems in Different Clinical Interviews

“…From this point of view, researchers conducted studies especially on arithmetic and algebraic word problems with students at various grade levels in order to understand students' difficulties and to overcome them. The results of these studies reveal that students had difficulties due to various reasons as (i) inadequate reading comprehension abilities (Björn et al, 2014;Erdem, 2016), (ii) the semantic and syntactic structure of statements in the problems (Bernardo, 1999;Çelik & Taşkın, 2015;Mellone et al, 2014), (iii) types of numbers used in the problem (Haghverdi, Semnani, Seifi, 2012;Raduan, 2010), (iv) types of required operation (De Corte & Verschaffel, 1987;Varol & Kubanç, 2015;Vicente, Orrantia, & Verschaffel, 2007), (v) presence of relevant and irrelevant statements of problems (Gürsoy et al, 2015;Wang et al, 2016), and (vi) types of representations given in the problem situation (Boonen et al, 2014;Canköy & Özder, 2011;Deliyianni et al, 2016;Göbel, Moeller, Pixner, Kaufmann, & Nuerk, 2014). In conclusion, these studies showed that there are many factors influencing students' word problem solving.…”