Markov Chain and Classification of Difficulty Levels Enhances the Learning Path in One Digit Multiplication

In this work we focus on a specific application named “1x1 trainer” that has been designed to assist children in primary school to learn one digit multiplications. We investigate the database of learners’ answers to the asked questions by applying Markov chain and classification algorithms. The analysis identifies different clusters of one digit multiplication problems in respect to their difficulty for the learners. Next we present and discuss the outcomes of our analysis considering Markov chain of different orders for each question. The results of the analysis influence the learning path for every pupil and offer a personalized recommendation proposal that optimizes the way questions are asked to each pupil individually.

[1]  Martin Ebner,et al.  Web analytics of user path tracing and a novel algorithm for generating recommendations in Open Journal Systems , 2013, Online Inf. Rev..

[2]  Nasser M. Nasrabadi,et al.  Pattern Recognition and Machine Learning , 2006, Technometrics.

[3]  Frank Linton,et al.  Recommender Systems for Learning: Building User and Expert Models through Long-Term Observation of Application Use , 2000, User Modeling and User-Adapted Interaction.

[4]  Joseph N. Payne.  Mathematics for the Young Child , 1990 .

[5]  D. Geary,et al.  Cognitive addition and multiplication: Evidence for a single memory network , 1986, Memory & cognition.

[6]  George Karypis,et al.  Selective Markov models for predicting Web page accesses , 2004, TOIT.

[7]  Martin Ebner,et al.  It's just about learning the multiplication table , 2012, LAK.

[8]  Sergey Brin,et al.  The Anatomy of a Large-Scale Hypertextual Web Search Engine , 1998, Comput. Networks.

[9]  Wim Fias,et al.  Neighbourhood effects in mental arithmetic , 2005 .

[10]  Diane J. Briars,et al.  USING A BASE-TEN BLOCKS LEARNING/ TEACHING APPROACH FOR FIRST- AND SECOND-GRADE PLACE-VALUE AND MULTIDIGIT ADDITION AND SUBTRACTION , 1990 .

[11]  E. Duval.  Attention please!: learning analytics for visualization and recommendation , 2011, LAK.

[12]  Katherine Garnett,et al.  Developing Fluency with Basic Number Facts: Intervention for Students with Learning Disabilities. , 1992 .

[13]  Martin Ebner,et al.  On using markov chain to evidence the learning structures and difficulty levels of one digit multiplication , 2014, LAK '14.

[14]  Shlomo Moran,et al.  The stochastic approach for link-structure analysis (SALSA) and the TKC effect , 2000, Comput. Networks.

[15]  Mark H. Ashcraft,et al.  A network approach to mental multiplication. , 1982 .

[16]  Donald L. Chambers.  Direct modeling and invented procedures: building on students' informal strategies , 1996 .

[17]  Martin Ebner,et al.  Teachers Little Helper: Multi-Math-Coach. , 2013 .

[18]  Mark Levene,et al.  Evaluating Variable-Length Markov Chain Models for Analysis of User Web Navigation Sessions , 2007, IEEE Transactions on Knowledge and Data Engineering.

[19]  George Siemens,et al.  Learning analytics and educational data mining: towards communication and collaboration , 2012, LAK.

[20]  Martin Ebner,et al.  Learning Analytics in basic math education – first results from the field , 2014 .

[21]  S. Bunk.  Teaching science graduates to think business. , 2002, Nature.