On Using Markov Chain to Evidence the Learning Structures and Difficulty Levels of One Digit Multiplication Behnam Taraghi, Martin Ebner, Anna Saranti, Martin Schön Graz University of Technology Münzgrabenstrasse 35/I, 8010 Graz, Austria {b.taraghi, martin.ebner}@tugraz.at, s0473056@sbox.tugraz.at, mrtnschn@googlemail.com ABSTRACT Understanding the behavior of learners within learning applications and analyzing the factors that may influence the learning process play a key role in designing and optimizing learning applications. In this work we focus on a specific application named “1x1 trainer” that has been designed for primary school children to learn one digit multiplications. We investigate the database of learners’ answers to the asked questions (N > 440000) by applying the Markov chains. We want to understand whether the learners’ answers to the already asked questions can affect the way they will answer the subsequent asked questions and if so, to what extent. Through our analysis we first identify the most difficult and easiest multiplications for the target learners by observing the probabilities of the different answer types. Next we try to identify influential structures in the history of learners’ answers considering the Markov chain of different orders. The results are used to identify pupils who have difficulties with multiplications very soon (after couple of steps) and to optimize the way questions are asked for each pupil individually. Categories and Subject Descriptors H.2.8 [Database Management]: Database Applications – Data mining General Terms Algorithms, Measurement. Keywords Learning Analytics, Markov chain, difficulty level, one digit Multiplication, Math, elearning, primary school 1. INTRODUCTION The goal of Data Mining is to enhance the knowledge by interpreting implicit and gathered data. If the data itself or the context where it is used relates to education, the research approach is called Educational Data Mining [16]. Romero & Ventura stated in 2010 that educational data mining (EDM) is a field that exploits statistical, machine-learning, and data-mining (DM) algorithms over the different types of educational data. Learning Analytics (LA) can be seen as a further development and as a step towards a more human based assistance. Baker et al [1] mentioned that both research fields have an extensive overlap, but also subtle differences. EDM is more or less about using data to understand how learning occurs and how to improve it. LA strives to assist the learning process by giving educators a deeper insight to it based on data analyses. Duval [7] pointed out that we have to think about learners’ traces and their learning efforts. Siemens and Baker [18] defined LA as the measurement, collection, analysis and reporting of data about learners and their contexts, for purposes of understanding and optimizing learning and the environments in which it occurs. So it can be concluded that the educator or the teacher plays an essential role in LA, because she or he is responsible for intervening in a pedagogical manner if the data analyses points out any hint [8]. Graz University of Technology has been developing math trainers since 2010 with the aim to improve the basic math education for primary schools [9]. First of all the so-called 1x1 trainer [17] was implemented, followed by the multi-math-coach [10] as well as the addition / subtraction trainer 1 . In primary schools, learning the one digit multiplication table is one of the major goals in the four-year period of education. Language implications in general [13], the role of math as first non-native language [14] and pure “row learning” [11] are some of the difficulties of this learning problem. Therefore a web-based application was developed which can both assist the learning process of the pupils and the pedagogical intervention of the teachers. According to the needs of the learners, four main parts are provided from the application: (a) the system is able to define a competence level of the learner; (b) the system is able to choose the given exercises according to the competence level of the learner. The implanted algorithm is responsible that the exercise is neither too easy nor too difficult; (c) the system ensures that already well-done exercises are repeated and practiced on a regular basis; (d) the system has to be appropriate for children from the age of 7-10 from the usability point of view. The full 1 http://mathe.tugraz.at (last visit 24.01.2014) Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted,without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from Permissions@acm.org. LAK '14, March 24 - 28 2014, Indianapolis, IN, USA Copyright 2014 ACM 978-1-4503-2664-3/14/03…$15.00. http://dx.doi.org/10.1145/2567574.2567614