This paper extends the T method to the measurement of educational effectiveness in university mathematics education. While the professor’s lesson and the students’ learning occur simultaneously, each student has different ability and learning method. And also, in pedagogy, Cronbach refers to the characteristic “heterogeneity” as aptitude-treatment interaction (ATI), in which the effects of the lecture methods, details, and materials vary according to the learner’s’ aptitude. See Cronbach and Snow(1977), Snow(1989), Snow,Federico and Montague(1980) in detail for aptitude-treatment interaction. In this paper, we analyze the increases of students’ internal knowledge which is the knowledge employed by the students based on their individual ability by using the T method. The T method is one method of MT System which is a new concept for pattern recognition thinking. We apply this method to measure the educational effectiveness of the Mathematics for System Bcourse. The Mathematics for System Engineering B is a course that aims to teach students vector analysis, which is calculus for vector-functions and used for analyzing spatial variations. We modified the gain scale as the objective variable which represents increases of students’ internal knowledge.　See Meltzer(2002) in detail for the gain scale.

Our research questions for analyzing the increases of internal knowledge by using the T method are about “the positioning of the lecture,” “the awareness of lecture content,” “the learning interest,” “the learning strategies,” “the metacognition” and “the learning styles.” For example, concretely, about the positioning of the lecture, our survey items are “How important do you consider learning the content of the course for your future university life and job?,” and “Do you know about the future potential of vector analysis?” About the awareness of lecture content, our survey items are “Are you concerned about your achievements so long as you earn a credit ?” and “ Did you give a greater importance to your interest in this subject or to the easy acquisition of a credit in this subject?” About the learning interest, “Do you feel satisfied after solving a difficult question in the course ?,” “ Was your motivation toward learning and university life enhanced by the course?” and “Is the course an interesting course because it helps you to judge your own improvement ?” About the learning style,” Do you often study by referring to several textbooks (textbook and collection of exercises ) ?,” “Do you choose long-term planned study than short-term concentrated study?,” “Do you often study with your friend while teaching each other?,” “Can you explain the learned unit to others?” and “Do you often pose questions to your mathematics teacher if it is difficult to understand a part of the subject?”

And also, we use scores of the first-stage examination, the mid-term examination and the term-end examination for analysis.

Then we analyze the data and investigate which items are important for the increases of students’ internal knowledge by using the T method in order to measure the relationship between the educational effectiveness and student’s learning methods.

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