Identifying effective e-teaching and general mathematical teaching profiles to predict student mathematical cognition and affect by latent profile analysis

Abstract

The aim of this study was to identify the profiles of approaches to e-teaching and general teaching (g-teaching) and to explore the differences between the profiles in terms of student mathematical cognition and affect. Latent profile analysis (LPA) was applied to evaluate 3,978 Taiwanese 15-year-old students’ perceived e-teaching and g-teaching behaviors (formative assessment, student orientation, and teacher direction) in mathematics classrooms. LPA identified four e/g-teaching profiles: parsimony, conservation, moderation, and liberal. Multivariate analysis of variance (MANOVA) and post hoc tests were used to examine profile differences in each element of cognition and affect; structural equation modeling (SEM) was used in latent constructs of cognition and affect. The combined MANOVA and SEM results indicated that moderation e/g-teaching benefits both cognition and affect, parsimony benefits cognition at the expense of affect, and both conservation and liberal benefit affect.

本研究旨在辨識E化和一般數學教學法的組合類型，並探討所辨識出的教學組合類型在學生數學認知和情意上的差異情形。以潛在剖面分析（LPA）方法分析3,978名臺灣15歲學生在數學教室中的E化數學教學和三項一般性的數學教學法（形成性評量、學生導向和教師指導）。LPA的結果辨識出四種E化與一般數學教學法組合：節約、保守、協調和自由使用E化與一般數學教學法的組合。接著，使用多變量變異數分析（MANOVA）和事後檢驗，來考驗四種教學法組合在學生各數學認知和情意細項內容上的差 異，並且使用結構方程模式（SEM）考驗四種教學法組合在認知和情意二潛在構念上的差異。MANOVA和SEM的分析結果顯示：協調的E化與一般數學教學法組合同時有益於學生認知和情意，節約的E化與一般數學教學組合有利認知但犧牲情意，保守和自由的E化與一般數學教學組合有利於情意。