This study assessed secondary school students’ conceptions of some basic mathematical concepts. There is a general trend of failure in mathematics among students in Nigeria secondary schools as shown by performance in all external examinations. Students might not have been able to learn mathematics effectively as they lack knowledge of the subject matter and clear understanding of the underlying basic mathematics ideas or concepts. In many countries of the world, recent research efforts have been centered on finding out students conceptions in Science and Mathematics. The purposes of such researches are to help develop curriculum materials that will enable students to learn effectively and to develop methods that are in line with the two major pathway of learning the continuous and discontinuous pathways. When the conceptions of a student are identified, efforts are made either to guide the learning of the student continuously with the existing conceptions or to discontinue the pathway if it is in contrast with the existing conceptions. It is therefore important that the Nigerian students conceptions of some mathematical concepts be investigated and documented.
The study employed the survey research design. The survey design consisted of four independent variables: Gender (Male and Female), School Location (Urban and Rural), School Type (Public and Private), and School Mode (Boys, Girls and Mixed Schools). The stratified random sampling technique was used to select 4332 subjects that adequately represented all the specific groups in the population. The instrument for the study was a two-tier diagnostic multiple-choice instrument for assessing Students’ Conceptions of Mathematics Ideas (SCMI). The items in the instrument were specifically designed to identify right conceptions and alternative conceptions in limited and clearly defined content areas in Number and Numeration, Algebra, Measurement, Geometry and Statistics. Experts in Mathematics Education and Measurement and Evaluation validated the SCMI instrument. The reliability of the SCMI was established through the Kuder-Richardson Formular 20 and coefficients of 0.76, 0.70 and 0.85 were obtained for answers, reasons, and right conceptions respectively. Descriptive statistics by use of frequencies and percentages were employed to answer the two research questions. Inferential statistics such as the Pearsons Chi-square (), Pearson correlation coefficients, the t-test statistic, One-way Analysis of Variance (ANOVA) and the Univariate Analysis of Variance