Elementary school students? understanding of equality and inequality symbols and the relationship between these understandings

This study was conducted to explore how elementary school students think about equality and inequality symbols, and how it changes over the years. A total of 257 students from the 4th, 5th, 6th, 7th, and 8th grades studying in two primary schools in a province in the Marmara Region between the years 2009 and 2010 participated in the study. After quantitative data collection, qualitative data was collected through interviews with 11 students.Two different tests- the Equality Test and the Inequality Test- formed the data collection tools for the study. The equality test was divided into two parts. In the first part, equality and inequality symbols were provided to the students, who were then asked to write what they understood from these symbols. Equalities in the second part were directly taken from Yaman?s (2004) study. Questions in the Inequality test were prepared in correspondence with the questions in the Equality test by the researchers.The students? answers to the equality and inequality tests were entered into a statistics software package and analyzed as to whether there were significant relations between the total test scores. The total test scores were also compared with respect to the grades. The answers of the students interviewed were analyzed one by one and inferences were made to determine what meanings students assign to the ?equal to? symbol and the inequality symbols.The results of the analysis showed that 33% of the students who participated in the study view equality symbol as an operation symbol which moves from left to right. Students? perception of the inequality symbols showed that 8 out of 11 students could recognize and explain the meaning of ?not equal to? symbol, 6 of whom explained the relational meaning of the symbol, while 2 students focused on the operational meaning of the symbol. Despite the fact that students knew the names of the ?less than? and ?greater than? symbols, it was understood that they confused them in context and in order not to confuse the symbols, they drew a vertical line on the left side of the symbol. It was also understood that students conceptualized ?greater than or equal to? and ?less than or equal to? symbols in a way similar to that of ?less than? and ?greater than? symbols and they tried to prove the inequalities in this way. It was seen that students had an understanding of inequality symbols similar to that of ?equality? symbol and proved the inequality by doing the sum from left to right, ignoring the sum on the right. Few students were detected to conceptualize the relational meaning of the equality and inequality symbols.The findings from the quantitative data showed that students? scores from equality and inequality tests increased with grade, with the exception that the mean score in 5th grade was greater than that of 6th grade. It was also shown that 7th and 8th grade mean scores were very close, because the 8th grade students had just learnt the ?greater than or equal to? and ?less than or equal to? symbols. As a result of the ANOVA test, it was found that the way students perceived the inequality symbols changed significantly with grade. The examination of the relations between the total scores from the equality and inequality tests showed that there is a medium positive correlation between the total scores.