This paper attempts a look at the knowledge of the subject matter of mathematics of National Teachers’ Institute’s (NTI) graduates who teach mathematics. It resulted from the poor performances of students at general examinations like the West African Examination Council (WAEC) and National Examination Council (NECO) examinations for which teachers receive the blame, especially those teaching at the basic levels (primary and junior secondary schools levels) of which the NTI graduates are the majority, FCT-UBE(2010). Hence they are being used for the study. The population of primary and junior secondary teachers in FCT Abuja was considered and a sample of one hundred and fifty (150) National Teachers’ Institute’s graduates who teach mathematics was used in carrying out the study to reveal their levels of knowledge of the subject matter of mathematics which will eventually guarantee positive learning and improve the performances of the students in the subject-Mathematics. The graduates were given three questions which validity and reliability were ascertained by three West African Examination Council (WAEC) team leaders in mathematics; to divide a whole number by fraction; multiply a three digit number by two digit number; compare the volumes of two cylinders in different ways using the same rectangular sheet of metal. They were to:(i)Provide the solutions to the problems,(ii)Explain giving reasons for the steps taken to reach their answers. Three phases of subject matter knowledge were used in the classification and discussions;(i)Professional tradition,(ii)Practical wisdom and(iii)Deliberate reflection. The data collected was analyzed using quantitative method. It shows that most of the students are still in the tradition phase and that there is no significant difference between the mean score of the male and female students. Among the recommendations is that teachers should endeavor to achieve both practical wisdom and deliberate reflection and inculcate same in their students.
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