Proof and proving in school and university mathematics education research: a systematic review

Abstract

This systematic review aims to provide a complementary to existing synopses of the state-of-the-art of mathematics education research on proof and proving in both school and university mathematics. As an organizing framework, we used Cohen et al.’s triadic conceptualization of instruction, which draws attention not only to the main actors of the didactical process (i.e., the Teacher and Students) and the Content around which the actors’ work is organized (herein, content related to proof and proving), but also to the relationships among the actors and the content. Out of the 103 papers we reviewed, almost half fell in the Student-Content category, which is consistent with the existence of a substantial number of frameworks, methods, and research findings related to students’ engagement with proof and proving. About a quarter of the papers fell in the Student–Teacher-Content category, which reflects an emphasis on viewing instructional practice in proof and proving in a holistic, systemic way. Only few papers fell in the categories that did not include Content in them, namely, the categories of Student, Teacher, and Student–Teacher; this suggests mathematics education research on proof and proving has a strong disciplinary identity, which potentially differentiates it from other mathematics education research strands. About a fifth of the papers were oriented towards ‘breaking ground’ through making an explicit theoretical and/or methodological contribution (Student–Teacher-Content and Content were the main categories where such contributions appeared), whilst the majority of the papers were focused on ‘building ground’ through elaborating or employing existing methodological and/or theoretical approaches.

İlköğretim Matematik Öğretmenlerinin Kanıt Şemalarının İncelenmesi

“…Çünkü kanıtlama esnasında bir teoremi açıklama, bu teoremin doğruluğunun ya da yanlışlığının neden olduğunu ifade etme; farklı mantıksal düşünme yöntemlerini ve kanıt çeşitlerini seçme ve kullanma söz konusudur (Baki, 2014). Matematiksel kanıt sayesinde öğrenciler, matematik bilgilerinin aşamalarını inşa ederek keşfedebilir (Stylianides, 2007). Yine matematik bilgileri kanıtlama sayesinde öğrenciler tarafından neden sonuç ilişkileri kurularak öğrenilebilir ve kavranabilir (Hanna, 1990).…”

Formulating a conjecture through an identification of robust invariants with a dynamic geometry system

“…In addition, the conjecturing activity is critically important for students because this activity can support and give meaning to students' engagement with proof (G. J. Stylianides, 2008).…”

Manipulatives in Learning Fraction for Improving First-Year Elementary Students’ Understanding

“…The National Council of Mathematics claims that learning in Grade 3 to Grade 5 should cultivate more than the students' abilities to make sense of mathematics; it should enhance their ability to solve problems (Schoenfeld, 2016;Stylianides, 2007). Memorizing facts without understanding underlying concepts makes it increasingly difficult for students to acquire new mathematical skills.…”