Di Paola B, Battaglia OR, Fazio C (2016) Non-Hierarchical Clustering as a method to analyse an
open-ended questionnaire on algebraic thinking. S Afr J Educ 36(1):1–13
Ding L, Beichner R (2009) Approaches to data analysis of multiple-choice questions. Phys Rev ST
Phys Educ Res 5:020103
Everitt BS, Landau S, Leese M, Stahl D (2011) Cluster analysis. John Wiley & Sons, Ltd,
Chichester
Fazio C, Battaglia OR, Di Paola B (2013) Investigating the quality of mental models deployed by
undergraduate engineering students in creating explanations: the case of thermally activated
phenomena. Phys Rev Spec Top Phys Educ Res 9(2)
Fulmer GW (2015) Validating proposed learning progressions on force and motion using the Force
Concept Inventory: finding from Singapore secondary schools. Int J Sci Math Educ 13
(6):1235–1254. https://doi.org/10.1007/s10763-014-9553-x
Gilbert JK, Boulter CJ (1998) Learning science through models and modelling. In: Frazer B, Tobin
K (eds) The international handbook of science education. Kluwer, Dordrecht, pp 53–66
Gower JC (1966) Some distance properties of latent root and vector methods used in multivariate
analysis. Biometrika Trust 53:3–4
Grunspan DZ, Wiggins BL, Goodreau SM (2014) Understanding classrooms through social
network analysis: a primer for social network analysis in education research. Cell Biol Educ
13:167
Hake RR (1998) Interactive engagement versus traditional methods: a six-thousand-student survey
of mechanics test data for introductory physics courses. Am J Phys 66:64
Hestenes D, Halloun I (1995) Interpreting the force concept inventory: a response to March 1995
critique by Huffman and Heller. Phys Teach 33:502–506
Hestenes D, Jackson J (2007) Revised table II for the Force Concept Inventory (Unpublished).
http://modeling.asu.edu/R&E/Research.html
Hestenes D, Wells M, Swackhammer G (1992) Force concept inventory. Phys Teach 30:141–151
Jammer M (1957) Concepts of force. Harvard University Press, Cambridge, MA
MacQueen J (1967) Some methods for classification and analysis of multivariate observations. In:
LeCam LM, Neyman J (eds) Proceedings of the 5th Berkely symposium on mathematical
statistics and probability 1965/66, vol I. University of California Press, Berkeley, CA, pp
281–297
Mantegna RN (1999) Hierarchical structure in financial markets. Eur Phys J B 11:193197
Rouseeuw PJ (1987) Silhouttes: a graphical aid to the interpretation and validation of cluster
analysis. J Comput Appl Math 20:53–65
Savinainen A, Viiri J (2008) The force concept inventory as a measure of students conceptual
coherence. Int J Sci Math Educ 6(4):719–740
Scott TF, Schumayer D (2017) Conceptual coherence of non-Newtonian worldviews in Force
Concept Inventory data. Phys Rev Phys Educ Res 13:010126. https://doi.org/10.1103/
PhysRevPhysEducRes.13.010126
Scott TF, Schumayer D, Gray AR (2012) Exploratory factor analysis of a Force Concept Inventory
data set. Phys Rev ST Phys Educ Res 2012:020105
Semak MR, Dietz RD, Pearson RH, Willis CW (2017) Examining evolving performance on the
Force Concept Inventory using factor analysis. Phys Rev Phys Educ Res 13:019903. https://doi.
org/10.1103/PhysRevPhysEducRes.13.010103
Springuel RP, Wittmann MC, Thompson JR (2007) Applying clustering to statistical analysis of
student reasoning about two-dimensional kinematics. Phys Rev ST Phys Educ Res 3:2
Stewart J, Miller M, Audo C, Stewart G (2012) Using cluster analysis to identify patterns in
students’ responses to contextually different conceptual problems. Phys Rev Spec Top Phys
Educ Res 8(2)
200
O. R. Battaglia and C. Fazio
open-ended questionnaire on algebraic thinking. S Afr J Educ 36(1):1–13
Ding L, Beichner R (2009) Approaches to data analysis of multiple-choice questions. Phys Rev ST
Phys Educ Res 5:020103
Everitt BS, Landau S, Leese M, Stahl D (2011) Cluster analysis. John Wiley & Sons, Ltd,
Chichester
Fazio C, Battaglia OR, Di Paola B (2013) Investigating the quality of mental models deployed by
undergraduate engineering students in creating explanations: the case of thermally activated
phenomena. Phys Rev Spec Top Phys Educ Res 9(2)
Fulmer GW (2015) Validating proposed learning progressions on force and motion using the Force
Concept Inventory: finding from Singapore secondary schools. Int J Sci Math Educ 13
(6):1235–1254. https://doi.org/10.1007/s10763-014-9553-x
Gilbert JK, Boulter CJ (1998) Learning science through models and modelling. In: Frazer B, Tobin
K (eds) The international handbook of science education. Kluwer, Dordrecht, pp 53–66
Gower JC (1966) Some distance properties of latent root and vector methods used in multivariate
analysis. Biometrika Trust 53:3–4
Grunspan DZ, Wiggins BL, Goodreau SM (2014) Understanding classrooms through social
network analysis: a primer for social network analysis in education research. Cell Biol Educ
13:167
Hake RR (1998) Interactive engagement versus traditional methods: a six-thousand-student survey
of mechanics test data for introductory physics courses. Am J Phys 66:64
Hestenes D, Halloun I (1995) Interpreting the force concept inventory: a response to March 1995
critique by Huffman and Heller. Phys Teach 33:502–506
Hestenes D, Jackson J (2007) Revised table II for the Force Concept Inventory (Unpublished).
http://modeling.asu.edu/R&E/Research.html
Hestenes D, Wells M, Swackhammer G (1992) Force concept inventory. Phys Teach 30:141–151
Jammer M (1957) Concepts of force. Harvard University Press, Cambridge, MA
MacQueen J (1967) Some methods for classification and analysis of multivariate observations. In:
LeCam LM, Neyman J (eds) Proceedings of the 5th Berkely symposium on mathematical
statistics and probability 1965/66, vol I. University of California Press, Berkeley, CA, pp
281–297
Mantegna RN (1999) Hierarchical structure in financial markets. Eur Phys J B 11:193197
Rouseeuw PJ (1987) Silhouttes: a graphical aid to the interpretation and validation of cluster
analysis. J Comput Appl Math 20:53–65
Savinainen A, Viiri J (2008) The force concept inventory as a measure of students conceptual
coherence. Int J Sci Math Educ 6(4):719–740
Scott TF, Schumayer D (2017) Conceptual coherence of non-Newtonian worldviews in Force
Concept Inventory data. Phys Rev Phys Educ Res 13:010126. https://doi.org/10.1103/
PhysRevPhysEducRes.13.010126
Scott TF, Schumayer D, Gray AR (2012) Exploratory factor analysis of a Force Concept Inventory
data set. Phys Rev ST Phys Educ Res 2012:020105
Semak MR, Dietz RD, Pearson RH, Willis CW (2017) Examining evolving performance on the
Force Concept Inventory using factor analysis. Phys Rev Phys Educ Res 13:019903. https://doi.
org/10.1103/PhysRevPhysEducRes.13.010103
Springuel RP, Wittmann MC, Thompson JR (2007) Applying clustering to statistical analysis of
student reasoning about two-dimensional kinematics. Phys Rev ST Phys Educ Res 3:2
Stewart J, Miller M, Audo C, Stewart G (2012) Using cluster analysis to identify patterns in
students’ responses to contextually different conceptual problems. Phys Rev Spec Top Phys
Educ Res 8(2)
200
O. R. Battaglia and C. Fazio