## 1 Introduction  
Formative assessment is a crucial component of the learning process, because it measures student's knowledge, maps the path towards learning goals, and tracks progress [1, 2]. This process quickens and makes learning more effective [3]. In addition, recent studies indicate that the use of formative assessment is associated with more feelings of autonomy and competence, and more autonomous motivation in students [4]. In contrast, summative assessment often carries punitive connotations, because students are penalized for their mistakes with a lower grade [5]. Instead of passing judgment on student's knowledge level, the purpose of formative assessment is to provide constructive feedback in order to accelerate learning [6, 7], frame learning goals, and monitor progress towards them [8]. According to [PERSON] [9], this can be accomplished by taking into account three factors that make formative assessment effective. Firstly, formative assessment is most effective when it is used to tailor student's learning paths based on their current level of understanding. Secondly, results of formative assessment should not affect student's evaluation, as they do in the case of summative assessment. This helps students take ownership of their learning process and focus on acquiring new knowledge. Thirdly, formative assessment should be used to provide feedback and guide students towards their learning goals [10]. There is recent evidence that pedagogical benefits of formative assessment are even more pronounced in online, cloud based, and asynchronous environments [11]. According to [PERSON] et al. feedback is the essential pedagogic technique for improving student's performance [12]. Studies indicate that feedback may improve learning outcomes by up to 0.4 standard deviation [13]. However, these results are still being debated [14]. A recent study observed an increase in academic achievement without a noticeable increase in motivation in students, which is often attributed to feedback from formative assessments [15]. One of the factors that contributes to the quality of feedback is how well it addresses the fundamental pedagogic need of closing the gap between current and desired student proficiencies [16]. Another factor is the delay between the measurement of student's knowledge and feedback, which can be days or even weeks in case of manually graded tests. This delay may negatively affect the positive effects of feedback [17]. Finally, feedback in a form of a mark does not provide a path towards increased proficiency [18], and thus does not address one of the main functions of formative assessment and feedback [19].  
Time spent on formative assessment must be taken into account when considering its practical value. Students' knowledge is constantly changing, as consequence students must be repeatedly reassessed [20]. This is time consuming. At the same time, if the student will be forced to demonstrate the knowledge he or she already mastered, the motivation to do the formative assessment might be lost. Therefore, it is necessary to assure the balance between the needed number of tasks and the assessment accuracy (weakest areas of student's knowledge and the best learning path).  
The paper proposes an algorithm capable of reducing formative assessment length while conforming to good formative assessment practices. This computer adaptive testing method may be sufficiently simple to use in a classroom setting with minimal time expenditure. The algorithm does not require pretesting, this could enable educators to host the assessment tool on a cloud and have students partake in formative assessment. While mobile devices may be less convenient than full sized paper and computer tests, greatly reduced by the proposed algorithm quiz length may mitigate this inconvenience.