Investigation of students' ability of make proof without words in secondary mathematics teaching and their impact on spatial visualization skills

The aim of this study is to determine the processes of secondary school students to make nonverbal proofs regarding nonverbal proof-based mathematics teaching, their views on the use of nonverbal proof in this process, and the contribution of nonverbal proof-based teaching to students' spatial visualization skills. The research was carried out with 12 students at the 10th grade in a public high school located in a district of Istanbul in the 2021-2022 academic year. Qualitative research method was used in the study. At the beginning of the research, a semi-structured clinical interview with 6 questions was applied to determine the spatial visualization skills of the students. Then, 16 worksheets were created that require spatial skills and contain nonverbal proofs suitable for student learning levels. The application of these worksheets lasted for 5 weeks, 2 days a week, with a 60-minute class hour. At the end of the application process, the clinical interview form was re-applied and the effect of nonverbal proofs on spatial visualization skills was examined. Then, student diaries and worksheets were examined and students' views on the nonverbal proof process were determined. Finally, individual interviews were conducted with the students who fully participated in the implementation process and their opinions on the process were taken. It has been determined that non-verbal proof-based teaching of secondary school students has a positive contribution to students' spatial visualization skills. In this context, it is recommended to include nonverbal proofs in the field of learning geometry. Secondary school students can understand and explain nonverbal proof if the visual expression given in the nonverbal proof is plain and understandable. However, students have difficulty in converting nonverbal proof to algebraic expression, they need support when they need to perform induction. In addition, when the visual expression becomes complex, a prejudice and hopelessness occurs in the students. This situation can be corrected when nonverbal proofs are supported by dynamic geometry tools. The opinions of secondary school students about the use of nonverbal proof in teaching mathematics were mostly positive. Therefore, it is recommended that nonverbal proofs be used by teachers in teaching mathematics lessons and included in the mathematics curriculum.