DEVELOPMENT AND STANDARDIZATION OF ACHIEVEMENT TEST IN SS MATHEMATICS USING ITEM RESPONSE THEORY
ABSTRACT
This study investigated the development and standardization of achievement test in SS mathematics using item response theory (IRT) framework. The instrument captioned Multiple Choice Test in Algebraic Processes (MCTAPIM) was based on SS mathematics curriculum. One theme under algebraic processes became sufficient for the study because the IRT model used in the study demanded a uni-dimensional construct. Eleven research questions and two null hypotheses guided the study. A total of 31129 SS 3 students in Cross river state public and private secondary schools for the 2010/2011 session constituted the population. A sample of 1557 students selected through proportionate stratified random sampling technique was used for the study. An initial pool of eighty seven (87) items was constructed, validated contently and trial testing, fifty (50) items survived the item analysis and were used for final administration employing the assistance of mathematics classroom teachers of each sampled schools. Both trial testing and the final administration were carried out with SS 3 students randomly drawn from secondary schools in Cross River state. One hundred (100) students (50) each from both public and private schools) were used for the trial testing while one thousand five hundred rand fifty seven students were used for the final administration. The research questions were answered using descriptive statistics, while the hypotheses were tested at 5% level of significance using the lord’s Chi-Square and Students – t – test statistics. All these statistics were generated by the IRT soft ware WINSTEPS 3.72 version by Linacre (2011). The results from the study show 47 items from the 50 items of MCTAPIM made up the standardized version of MCTAPIM. Three items were dropped because their outfit mean square values were higher than 1.5 logit units. The instrument was suitable for IRT because IRT assumptions of unidimensionality and local independence of items were satisfied by the MCTAPIM data. Item difficulty parameters fall within – 0.55 and 3.13 logit units. The items separated the students into 15.84 strata according to item difficulty parameter. Student ability parameters fall within – 0.79 and 4.37 logit units. The between 0.00 and 0.31 logit units. Students’ responses were valid out of 50 items fit the model. Seven of the items were significantly biased against school types, while one of the nine topics (variations) was significantly biased against school ownership types scale for standardization was also computed and constructed re recommended that researchers/Students should be encouraged to develop and standardize achievement test using IRT as alternative to Classical test Theory (CTT).