The Forgotten Dimension: Personal Support Predicts Shifts in Math Motivation Profiles

We explored how personal support and relational climate shape adolescent students'motivation toward mathematics. Using weighted Principal Component Analysis andKMeans clustering (N = 183), we identified four stable profiles: Discouraged Learners,Math-Engaged Achievers, Positive-but-Detached, and Struggling-with-Gaps. Weightingrelational factors (personal support, atmosphere) reduced the size of the discouragedgroup and enlarged engaged clusters. This study introduces a PCA anchoring methodusing geometrical intuition and visual metaphors ("fish anatomy"), showing how emo-tional tone in the classroom influences long-term academic aspiration. Code, plots, andtransition matrices are provided to support reproducibility and interpretation.