![]() Through a quantitative analysis, students’ self-assessment and tutors’ assessment were compared data were cross-checked with students’ answers to a questionnaire. Each problem was assessed by a tutor and self-assessed by students themselves, according to a shared rubric with five indicators: Comprehension of the problematic situation, identification of the solving strategy, development of the solving process, argumentation of the chosen strategy, and appropriate and effective use of the ACE. Participants are grade 11 students (in all 182 participants) in school year 2020/2021 who were asked to solve 8 real-world mathematical problems using an Advanced Computing Environment (ACE). In particular, the investigation focuses on how accurate the students’ self-evaluations are when compared to external ones, and if (and how) the accuracy in self-assessment changed among the various processes involved in the problem-solving activity. The goal of this research is to study the relationship between self-assessment and the development and improvement of problem-solving skills in Mathematics. It is defined as “the evaluation or judgment of ‘the worth’ of one’s performance and the identification of one’s strengths and weaknesses with a view to improving one’s learning outcomes”. Self-assessment, in the education framework, is a methodology that motivates students to play an active role in reviewing their performance. The assumed simulation study could be useful for statistics teachers to motivate their students for lectures in computational statistics and fundamentals of probability. All computer code used in this article is provided on GitHub. For this application we obtained as a solution, an average number of 950 packages needed to complete the album, at an average cost of 3,800 reals (Brazilian currency), assuming that the collector does not exchange any of its repetitions with nobody. The simulation was based on a computational code written in R. In this case, the complete album has N = 670 stickers, which are sold in packages containing n = 5 stickers each. In addition, we propose a simulation algorithm to find the solution to the problem, where we present as a numerical illustration an album of stickers related to the Qatar 2022 Official Football World Cup, which is being sold in Brazilian newsstands. So whether your studies are in algebra, calculus, or physics, Wolfram|Alpha can be your resource for learning about vectors.This paper considers some computational issues related to the problem of the coupon collector behavior. Wolfram|Alpha can even help you add and subtract two vectors using the tip-to-tail method. The radius gives you the magnitude of your vector, while the angles specify its direction. If you want to find both the magnitude and direction, you can represent the vector in polar or spherical coordinates. You can query Wolfram|Alpha for the vector’s length to find its magnitude:Īnd to find the direction, you can ask for the angles between the vector and the coordinate axes: Suppose you know only the point in R^n corresponding to your vector and you want to know its magnitude and direction. Wolfram|Alpha can now plot vectors with this arrow representation in 2D and 3D and return many other properties of the vector. The direction of the arrow matches the direction of the vector, while the length represents the magnitude of the vector. A vector is commonly defined as a quantity with both magnitude and direction and is often represented as an arrow. For example:Īnd in fact, Wolfram|Alpha can give lots of information on vectors. What do you get when you cross a mountain climber with a mosquito? Nothing-you can’t cross a scalar with a vector!īut what do you get when you cross two vectors? Wolfram|Alpha can tell you.
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