Abstract:
Recently, studies have been carried out on alternative proof methods due to the change in the perspective of
teaching proof and the difficulties of learners in proof. In this context, proof without words, which are presented
as an alternative to proof teaching, defined by diagrams or visual representations and require the student to
explain how proof is, are discussed in this study. The aim of this study is to examine pre-service mathematics
teachers' explanations of proof without words about the sum of consecutive numbers from 1 to n. The data were
collected by the proof of the sum of consecutive integers. 27 pre-service teachers from a university in the
Middle Anatolia region participated in this study, which was conducted using a basic qualitative research
design. At the end of the study, it was seen that most of the preservice teachers were unable to explain the proof
without words of the sum of integers from 1 to n. One of the reason for this may be related to the spatial
thinking skills of pre-service teachers. However, there are pre-service teachers who can interpret the visual
given in the proof correctly, use the necessary mathematical knowledge, but cannot generalize using the given
visual. The reasons why the pre-service teachers could not express the general situation are considered as the
lack of algebraic thinking
