In this study, the researchers would like to explore how personal learning style could have effect on the mathematic learning achievements.  There were two aspects of learning styles, one refers to how one prefer to learn something, and the other refers to how prefers to process the learning information.  Some researchers categorized the former as learning style and the later as cognitive style (Peterson, Rayner, & Armstrong, 2009).  In this study, the researchers would like to explore how one’s cognitive styles related their mathematics achievements.

        The were several major models of cognitive styles, including the field-independent vs. field-dependent model (Witkin & Goodenough, 1981), the Myers-Briggs Type Indicator (MBTI), Kolb's Learning Style Model, Felder-Silverman Learning Style Model and Herrmann Brain Dominance (Felder, 1996).  The later four models had been used in the field of engineering education (Felder, 1996). In this study, the researchers will identified the participants’ learning style based on Herrmann Brain Dominance Model (Herrmann, 1981).

        According to Herrmann (1981), learning could be classified as four types based on their brain dominances-Quadrant A(left brain), logical, analytical, quantitative, factual, critical; Quadrant B (left brain), sequential, organized, planned, detailed, structured; Quadrant C (right brain), emotional, interpersonal, sensory, kinesthetic, symbolic; Quadrant D (right brain), visual, holistic, innovative. Graf, Lin, & Kinshuk (2008) analyzed the results of studies applied different models, and concluded that learning styles were related to cognitive trait, high or low working memory.  In their analysis, the researchers content that students who were field-independent had higher working memory capacity, and those learners could also be scored higher on the reflective, intuitive, verbal, sequential dimension in Felder-Silverman Learning Style Model. According to Feldman (1996), engineering instruction tends to biased to fit the reflective, intuitive, verbal, and sequential learners.  Lumsdaine & Lumsdaine (1995) used the Herrmann Brain Dominance Instrument and found that most engineering instructors scored relatively highest on the Quadrant A.  It seems like that the Quadrant A learning style is more approached to the reflective, intuitive, verbal, and sequential polar in Feldman’s dimension, and should scored higher in working memory tasks as Graf et al (2008) content.  As a result, those students should performed better in most academic tasks, especially in mathematics.

        Although learning style per se could have effects on one’s mathematics achievement, the fit between one’s learning styles and the instruction could be more important (Fan & Zhang, 2009).  In Taiwan, most teachers teach mathematics in sequential, organized, planned, detailed, and structured ways, therefore, those who score higher in Quadrant B in HBDI could feel more efficacy and performed better in mathematics classrooms.

        In this study, the researchers would like to explore how learning styles and self-efficacy in mathematics could have effects on mathematics achievements.

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