Cognitive dimensions in students’ mental models of linear light polarization

Learners often struggle to develop expandable mental models of polarization due to its abstract nature and the multitude of models used to describe it. A closer examination of the structure of mental models for linear polarization is therefore worthwhile in order to gain insight into mental abstraction processes. Existing research has largely documented misconceptions, leaving the underlying cognitive structures of mental models insufficiently explored. To address this gap, we employed the Fidelities Model of Conceptual Development (FMCD) to investigate learners’ cognitions of linear polarization. The framework, distinguishes two dimensions of students’ mental models: Gestalt, which refers to visual and structural representations, and Functionality, which captures how well a model explains underlying processes. The degrees to which these dimensions align with reality allow for a typification of learners’ reasoning patterns. We developed a test instrument based on established students’ mental models and validated it through expert review and think-aloud studies. In a cross-sectional survey with <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>N</a:mi> <a:mo>=</a:mo> <a:mn>178</a:mn> </a:math> German secondary school and university students, confirmatory factor analysis confirmed a robust two-factor structure ( <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>CFI</c:mi> <c:mo>=</c:mo> <c:mn>0.96</c:mn> </c:math> , <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>RMSEA</e:mi> <e:mo>=</e:mo> <e:mn>0.03</e:mn> </e:math> , <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mi>SRMR</g:mi> <g:mo>=</g:mo> <g:mn>0.07</g:mn> </g:math> ) with solid factor-reliability ( <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:msub> <i:mi>ω</i:mi> <i:mtext>FF</i:mtext> </i:msub> <i:mo>=</i:mo> <i:mn>0.71</i:mn> </i:math> , <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:msub> <k:mi>ω</k:mi> <k:mtext>FG</k:mtext> </k:msub> <k:mo>=</k:mo> <k:mn>0.81</k:mn> </k:math> ). Descriptive results showed developmental trends: while secondary students often exhibited “dual” models combining both FG and FF, university students increasingly relied on functionally oriented reasoning. The findings validate the FMCD in the domain of polarization and provide a diagnostic tool that informs instructional design for supporting students’ conceptual development in optics.