How Do Students Prove Their Learning and Teachers Their Teaching? Do Teachers Make a Difference?

Abstract

Problem Statement: Gaining reasoning skills in early years affects the formal proving skills in the following years, thus it is quite significant. The acquiring of this skill is only possible with the approaches that the teachers used in the process. At this point, the problem to be researched in terms of making proofs is seen in how middle school students prove a mathematical expression; what kinds of reasoning and proof types they use in this process; how the teachers of these students prove the same expression; and how they reflect it to their instruction. Purpose of the Study:The purpose of this study is to investigate the middle school students' and their teachers' reasoning types and proof methods while proving a mathematical expression.

Proses Sistematisasi dalam Pembuktian Matematika

“…Pembuktian langsung adalah membuktikan teorema yang berbentuk implikasi (  ), sedangkan pembuktian tidak langsung adalah dengan mencari kebenaran kontraposisi dari suatu implikasi (~~) (Hernadi, 2013). Menurut Herizal, Suhendra, & Nurlaelah, (2019); Nurhidayah, Rosjanuardi, & Nurlaelah, (2019), Siswa masih mengalami kesulitan dalam melakukan pembuktian, kesulitan siswa dalam melakukan pembuktian membuat mereka melakukannya dengan cara mencoba-coba (Tanisli, 2016). Faktor yang mempengaruhi peningkatan keterampilan siswa dalam melakukan pembuktian adalah perilaku mengajar guru (Brunner & Reusser, 2019).…”

“…Faktor yang mempengaruhi peningkatan keterampilan siswa dalam melakukan pembuktian adalah perilaku mengajar guru (Brunner & Reusser, 2019). Akan tetapi banyak guru yang kurang mampu dalam melakukan pembuktian (Noto, Priatna, & Dahlan, 2019;Tanisli, 2016) dan buku teks yang digunakan memuat kurang dari 6% latihan yang berbasis pembuktian (Thompson, Senk, & Johnson, 2012).…”

“…Empat hal yang dapat dilihat dalam pembuktian matematika (Maslahah, 2019) yaitu : verifikasi, penalaran (reasoning), pengkomunikasian, dan sistematisasi. Dalam penelitian ini pembuktian mahasiswa hanya dilihat pada proses sistematisasi, yaitu kemampuan dalam mengaitkan definisi, sifat atau teorema yang relevan dalam membuktikan, karena Minggi, Paduppai, & Assagaf (2016) menyatakan bahwa pemahaman konsep dan prinsip matematika mahasiswa masih rendah dan guru hanya dapat melakukan pembuktian matematika pada tahap verifikasi dan explanation (Tanisli, 2016).…”

Perspetivas dos alunos sobre as suas experiências de aprendizagem

“…Por outro lado, a ideia de que "os professores fazem a diferença" e de que "a formação de professores faz a diferença", que já nos anos de 1970 deu título a algumas publicações (MOOD, 1970;GOOD, BIDDLE, BROPHY, 1975) aponta para o papel fundamental e a influência que os professores têm (ou podem ter) no ensino e também na vida dos alunos. A tese de que os professores fazem a diferença permaneceu até hoje e certamente continuará a ser destacada na pesquisa educacional (HATTIE, 2004;WILKINSON, HAMILTON, 2003;BROUWER, KORTHAGEN, 2005;KORTHAGEN, 2010;TANISLI, 2016).…”

Questioning as a Tool to Instill Reasoning Skills among Seventh Grade Students in Science Subject

“…Likewise, Arslan ( 2007) found in his study that students have lowlevel reasoning skills at the elementary level in school (cited in Tanisli, 2016). Besides, these studies also describe that different methods and techniques can be used to develop reasoning skills but for this, students and teachers must be asking "why?"…”