Heatmap and Hierarchical Clustering Analysis to Highlight Changes in Young Children’s Developmental Progressions Using Virtual Manipulative Mathematics Apps

  • Christina W. Lommatsch
  • Stephen I. Tucker
  • Patricia S. Moyer-PackenhamEmail author
  • Jürgen Symanzik
Part of the Mathematics Education in the Digital Era book series


The purpose of this study was to examine what patterns were revealed using heatmaps with hierarchical clustering to examine preschooler’s performance, speed, and developmental progressions in counting and seriation. The chapter describes a study conducted with 35 preschoolers who used six touchscreen virtual manipulative mathematics apps in two different learning sequences: counting and seriation. The analysis employed heatmaps coupled with hierarchical clustering to highlight changes in children’s performance, speed, and developmental progressions, between a pre- and post- assessment app after using two learning apps. This method allowed for analysis of individual and whole group data examining several tasks within each app and also several apps within each learning sequence. The analysis revealed different clusters of children grouped according to their developmental progressions which were related to incremental changes in performance and speed from the Pre to Post App use.


Virtual manipulative Touchscreen app Developmental progression Performance Speed Heatmap Hierarchical clustering Preschool Mathematics app Seriation Counting 


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Christina W. Lommatsch
    • 1
  • Stephen I. Tucker
    • 2
  • Patricia S. Moyer-Packenham
    • 1
    Email author
  • Jürgen Symanzik
    • 1
  1. 1.The Virtual Manipulatives Research GroupUtah State UniversityLoganUSA
  2. 2.University of LouisvilleLouisvilleUSA

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