## 2 Need of New Formative Assessment Algorithms  
Classical test theory (CTT) has a long history of use in test construction and utilization [21], it is based on the assumption that tests measure a sum of a true score and error score. While latent trait theory (LTT), also known as item response theory (IRT) takes a more nuanced approach such as statistical models which take into account different item difficulty and the existence of multidimensional latent trait space [22; 23]. It is based on the idea that the probability of a correct response to an item is a function of the personal latent traits of a student and an item [24; 25]. This approach is often used in computerized adaptive testing [26; 27]. In adaptive testing items presented to a student are chosen based on previously seen items and student's responses. This approach can shorten test times and precision by, for example, maximizing information gain from each item [28; 29]. However, IRT based tests require item pool calibration to determine item parameters used in the calculation of correct answer probability [30; 31]. This increases test creation and iterative improvement complexity. In practical applications, this complexity may inhibit educators in deploying IRT based formative assessment tests. Elo rating based systems can perform similar roles to IRT based solutions. Elo rating was originally developed for matching chess players of similar skills [32]. The same principles can be used to estimate item difficulty, proficiency of students, and matching the two in the educational setting [33; 34; 35]. Both, IRT and Elo rating systems usually utilize the logistic function to determine the probability of correct answer to an item. However, Elo rating based systems determine item parameters dynamically, each answered item's difficulty setting is immediately adjusted during the test. This removes the need for a separate calibration step before the test deployment. As with IRT, multivariate, measuring more than one latent trait, Elo rating systems have been proposed [36; 37]. There are other approaches to model students and knowledge acquisition [38], these include performance factor analysis [39; 40], knowledge tracing [41; 42; 43], and multi-armbandit (MAB) solutions [44; 45; 46]. Multi-armed bandit algorithms are named after a gambler's problem, where they have to choose which slot machine, one armed bandit, to play in order to maximize their reward based on previous pay-off observations [47; 48; 49]. These algorithms offer a way of negotiating exploration and exploitation dilemma, searching for best paying slot machines and exploiting best paying slot machines. This problem arises in many settings, such as education, advertisement placement, website optimization, and packet routing [50; 51; 52]. In this paper, a hybrid testing algorithm based on Elo rating and upper confidence bound (UCB) multi-armed bandit approach is proposed and applied in the educational setting. It combines the advantages of Elo rating systems, such as dynamic calibration of item difficulties, guesses parameters and compatibility with latent trait theory, with an efficient exploration-exploitation trade-off solution. The algorithm is applied in the context of formative assessment, to explore student's knowledge and suggest further learning material in accordance with [PERSON]'s feedback model [16], which is still a dominant model for formative assessment [53]. Firstly, the instructor forms an item pool divided into topics or competencies, \"Where am I going?\" Secondly, students partake in formative assessment where questions are chosen and dynamically calibrated by the proposed algorithm, \"How am doing?\" Thirdly, the algorithm can reveal with weakest areas of knowledge and suggest the easiest items, learning objects, within that area of knowledge to learn, \"Where to next?\" The proposed algorithm can significantly reduce test creation complexity compared to IRT solutions and reduce test length.