# A PSYCHOLOGICAL ANATOMY OF MATHEMATICS LEARNING

This qualitative study attempts to understand the psychological anatomy of mathematics learners through their thoughts, emotions and behaviours in the context of Singapore education system and society. The main data came from the thought processes, emotional experiences and behaviours that are captured in the reported retrospective memories of 21 polytechnic students with regards to their mathematics learning journey (from young till now) through face-to-face interviews. Six mathematics teachers were also interviewed. The study showed that a student’s internal belief system (consisting of his attitude, motivation and goal) of mathematics learning is influenced by the external expectancy system (expectations of mathematics education set by society, schools, teachers, parents and peers). In explaining the psychological anatomy of mathematics learning, a key stimulus event related to his/her mathematics learning (such as failing mathematics examinations) usually triggers off the student’s appraisal system. Through the process of appraisal as affected by the student’s internal belief system, four types of cognitive thoughts may arise – encouraging, resigned, defiant and accommodating. Encouraging thoughts of mathematics learning enhance the student's future learning while resistant thoughts bring a student to blame external factors for his/her demise. As for a student with resigned thoughts of mathematics learning, he/she is resigned to the fact that he/she will never do well in learning and blames himself/herself for his/her predicament. A student with accommodating thoughts believes that he/she can still achieve an acceptable and average competence in mathematics learning. The students’ self efficacy and perceived competence in mathematics learning and his/her self esteem are affected accordingly too. Depending on the categories of cognitive thoughts the student has formed, he/she may experience four categories of emotions – learning enhancing (such as delight, satisfaction, excitement, confidence, pleasure, pride, interest etc.), self directed (such as worry, concern, nervousness, guilt, apprehension, shame fearfulness, uneasiness, restlessness, fretfulness, impatience, tense, distress, stress etc.), external directed (such as hatred, bitterness, disgust, anger, resentment, betrayal, indifference victimized etc.) and harmonizing emotions (such as acceptance, peace, calmness, optimism, self control, empathy, comfort etc.) respectively. As influenced by his/her cognitive thoughts and emotional state, the student may engage in different types of mathematics behaviours respectively – control, avoidant, resistant and pragmatic strategies. Control strategies are self regulating and effective in learning, while avoidant strategies aim to evade learning. Pragmatic strategies are strategic and focused on passing mathematics examination. As for resistant strategies, they aim to disrupt mathematics learning. These four emotional states are dynamic and students may move from one state to another depending on the emergence of possible new stimulus events.