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Articles 1 - 29 of 29
Full-Text Articles in Education
Education In The Era Of Google, Wikipedia, And Deep Learning: Are We Humans Still Needed And If Yes For What?, Miroslav Svitek, Olga Kosheleva, Vladik Kreinovich
Education In The Era Of Google, Wikipedia, And Deep Learning: Are We Humans Still Needed And If Yes For What?, Miroslav Svitek, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
One of the main purposes of education is to teach skills needed in future life and future jobs. What is important and what is useful changes with time. Before the industrial revolution, routine mechanical work was an important part of human activity – now machines can do it (and do it better). Before printing, copying was an important activity – now copy machines do it. Before computers, humans were needed for computing – now computer do it better. With Wikipedia and Google, there is not much need for scholars being erudite. Even extracting dependencies from data – one of the …
When Is Deep Learning Better And When Is Shallow Learning Better: Qualitative Analysis, Salvador Robles Herrera, Martine Ceberio, Vladik Kreinovich
When Is Deep Learning Better And When Is Shallow Learning Better: Qualitative Analysis, Salvador Robles Herrera, Martine Ceberio, Vladik Kreinovich
Departmental Technical Reports (CS)
In many practical situations, deep neural networks work better than the traditional "shallow" ones, however, in some cases, the shallow neural networks lead to better results. At present, deciding which type of neural networks will work better is mostly done by trial and error. It is therefore desirable to come up with some criterion of when deep learning is better and when shallow is better. In this paper, we argue that this depends on whether the corresponding situation has natural symmetries: if it does, we expect deep learning to work better, otherwise we expect shallow learning to be more effective. …
Motivations Do Not Decrease Procrastination, So What Can We Do?, Olga Kosheleva, Vladik Kreinovich, Christian Servin
Motivations Do Not Decrease Procrastination, So What Can We Do?, Olga Kosheleva, Vladik Kreinovich, Christian Servin
Departmental Technical Reports (CS)
Students often start working on their assignments late and, as a result, turn them in late. This procrastination makes grading more difficult. It also delays posting correct solutions that could help students understand their mistakes – and this hinders the students’ progress in studying following topics. At first glance, motivation seems to be a solution to all pedagogical problems: a motivated student eagerly collaborates with the instructor to learn more. Motivation indeed increases students’ knowledge, but, unfortunately, it does not decrease procrastination. So what can we do? We can institute heavy penalties for late submissions, but this would unfairly punish …
A Natural Causality-Motivated Description Of Learning, Olga Kosheleva, Vladik Kreinovich
A Natural Causality-Motivated Description Of Learning, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Teaching is not easy. One of the main reasons why it is not easy is that the existing descriptions of the teaching process are not very precise -- and thus, we cannot use the usual optimization techniques, techniques which require a precise model of the corresponding phenomenon. It is therefore desirable to come up with a precise description of the learning process. To come up with such a description, we notice that on the set of all possible states of learning, there is a natural order s ≤ s' meaning that we can bring the student from the state s …
Video Or Text? Bullets Or No Bullets? Why Not Both?, Olga Kosheleva, Vladik Kreinovich, Christian Servin
Video Or Text? Bullets Or No Bullets? Why Not Both?, Olga Kosheleva, Vladik Kreinovich, Christian Servin
Departmental Technical Reports (CS)
Some students – which are, in terms of pop-psychology – more left-brain – prefer linear exposition, others – more right-brain ones – prefer 2-D images and texts with visual emphasis (e.g., with bullets). At present, instructors try to find a middle grounds between these two audiences, but why not prepare each material in two ways, aimed at both audiences?
Why Online Teaching Amplifies The Differences Between Instructors' Success, Olga Kosheleva, Vladik Kreinovich, Christian Servin
Why Online Teaching Amplifies The Differences Between Instructors' Success, Olga Kosheleva, Vladik Kreinovich, Christian Servin
Departmental Technical Reports (CS)
Empirical studies show that online teaching amplifies the differences between instructors: more successful instructors become even more successful, while the results of the instructors who were not very successful becomes even worse. There is a simple explanation for why the performance of not-perfect instructors decreases: in online teaching, there is less feedback, so these instructors get an indication that their teaching strategies do not work well even later than usual and thus, have fewer time to correct their teaching. However, the fact that the efficiency of good instructors rises is a mystery. In this paper, we provide a possible explanation …
Shall We Ignore All Intermediate Grades?, Christian Servin, Olga Kosheleva, Vladik Kreinovich
Shall We Ignore All Intermediate Grades?, Christian Servin, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In most European universities, the overall student's grade for a course is determined exclusively by this student's performance on the final exam. All intermediate grades -- on homework, quizzes, and previous texts -- are, in effect, ignored. This arrangement helps gauge the student's performance by the knowledge that the student shows at the end of the course. The main drawback of this approach is that some students do not start studying until later, thinking that they can catch up and even get an excellent grade -- and this hurts their performance. To motivate students to study hard throughout the semester, …
How To Teach Advanced Highly Motivated Students: Teaching Strategy Of Iosif Yakovlevich Verebeichik, Olga Kosheleva, Vladik Kreinovich
How To Teach Advanced Highly Motivated Students: Teaching Strategy Of Iosif Yakovlevich Verebeichik, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
The paper describes and explains the teaching strategy of Iosif Yakovlevich Verebeichik, a successful mathematics teacher at special mathematical high schools -- schools for students interested in and skilled in mathematics. The resulting strategy seems counterintuitive and contrary to all the pedagogical advice. Our explanation is not complete: it worked well for this teacher, but others who tried to follow seemingly the same strategy did not succeed. How he made it work, how can others make it work -- this is still not clear. In the words of Verebeichik himself, while mathematics itself is a science, teaching mathematics is an …
How To Best Write Research Papers: Basic English? Sophisticated English?, Martine Ceberio, Christian Servin, Olga Kosheleva, Vladik Kreinovich
How To Best Write Research Papers: Basic English? Sophisticated English?, Martine Ceberio, Christian Servin, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Instructors from English department praise our students when they use the most sophisticated grammatical constructions and the most appropriate (often rarely used) words -- as long as this helps better convey all the subtleties of the meaning. On the other hand, we usually teach the students to use the most primitive Basic English when writing our papers -- this way, the resulting paper will be most accessible to the international audience. Who is right? In this paper, we analyze this question by using a natural model -- inspired by Zipf's law -- and we conclude that to achieve the largest …
Building Postsecondary Pathways For Latinx Students In Computing: Lessons From Hispanic-Serving Institutions, Anne-Marie Núñez, David S. Knight, Sanga Kim
Building Postsecondary Pathways For Latinx Students In Computing: Lessons From Hispanic-Serving Institutions, Anne-Marie Núñez, David S. Knight, Sanga Kim
Departmental Technical Reports (CS)
While the COVID-19 pandemic has transformed the use of technology in education and the workforce, a shortage of computer scientists continues, and computing remains one of the least diverse STEM disciplines. Efforts to diversify the computing industry often focus on the most selective postsecondary institutions, which are predominantly White. We highlight the role of Hispanic-Serving Institutions (HSI) in gradating large numbers of STEM graduates of color, particularly Latinx students. HSIs are uniquely positioned to leverage asset-based approaches that value students’ cultural background. We describe the practices educators use in the Computing Alliance for Hispanic-Serving Institutions, a network of 40 HSIs …
Rosenzweig, Equality, And Assignment, Olga Kosheleva, Vladik Kreinovich
Rosenzweig, Equality, And Assignment, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In his seminal book "The Star of Redemption", the renowned philosopher Franz Rosenzweig illustrated his ideas by the intuitive difference between mathematical statements A=B and B=A. Of course, from the purely mathematical viewpoint, these two statements are always equivalent, so to a person trained in mathematics -- even in simple school mathematics -- this illustration is puzzling. What we show is that from the viewpoint of common folks, there is indeed a subtle difference between how people understand these two equalities. To us, the understanding of this difference helped us better understand Rosenzweig's ideas. But we believe that this difference …
Adversarial Teaching Approach To Cybersecurity: A Mathematical Model Explains Why It Works Well, Christian Servin, Olga Kosheleva, Vladik Kreinovich
Adversarial Teaching Approach To Cybersecurity: A Mathematical Model Explains Why It Works Well, Christian Servin, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Teaching cybersecurity means teaching all possible ways how software can be attacked -- and how to fight such attacks. From the usual pedagogical viewpoint, a natural idea seems to be to teach all these ways one by one. Surprisingly, a completely different approach works even better: when the class is divided into sparring mini-teams that try their best to attack each other and defend from each other. In spite of the lack of thoroughness, this approach generates good specialists -- but why? In this paper, by analyzing a simple mathematical model of this situation, we explain why this approach work …
How To Detect Future Einsteins: Towards Systems Approach, Olga Kosheleva, Vladik Kreinovich
How To Detect Future Einsteins: Towards Systems Approach, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Talents are rare. It is therefore important to detect and nurture future talents as early as possible. In many disciplines, this is already being done -- via gifted and talented programs, Olympiads, and other ways to select kids with unusually high achievements. However, the current approach is not perfect: some of the kids are selected simply because they are early bloomers, they do not grow into unusually successful researchers; on the other hand, many of those who later become very successful are not selected since they are late bloomers. To avoid these problems, we propose to use systems approach: to …
A Recent Result About Random Metrics Explains Why All Of Us Have Similar Learning Potential, Christian Servin, Olga Kosheleva, Vladik Kreinovich
A Recent Result About Random Metrics Explains Why All Of Us Have Similar Learning Potential, Christian Servin, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In the same class, after the same lesson, the amount of learned material often differs drastically, by a factor of ten. Does this mean that people have that different learning abilities? Not really: experiments show that among different students, learning abilities differ by no more than a factor of two. This fact have been successfully used in designing innovative teaching techniques, techniques that help students realize their full learning potential. In this paper, we deal with a different question: how to explain the above experimental result. It turns out that this result about learning abilities -- which are, due to …
How To Assign Grades To Tasks So As To Maximize Student Efforts, Laxman Bokati, Vyacheslav Kalashnikov, Nataliya Kalashnykova, Olga Kosheleva, Vladik Kreinovich
How To Assign Grades To Tasks So As To Maximize Student Efforts, Laxman Bokati, Vyacheslav Kalashnikov, Nataliya Kalashnykova, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In some classes, students want to get a desired passing grade (e.g., C or B) by spending the smallest amount of effort. In such situations, it is reasonable for the instructor to assign the grades for different tasks in such a way that the resulting overall student's effort is the largest possible. In this paper, we show that to achieve this goal, we need to assign, to each task, the number of points proportional to the efforts needed for this task.
Egyptian Fractions Re-Revisited, Olga Kosheleva, Vladik Kreinovich, Francisco Zapata
Egyptian Fractions Re-Revisited, Olga Kosheleva, Vladik Kreinovich, Francisco Zapata
Departmental Technical Reports (CS)
Ancient Egyptians represented each fraction as a sum of unit fractions, i.e., fractions of the type 1/n. In our previous papers, we explained that this representation makes perfect sense: e.g., it leads to an efficient way of dividing loaves of bread between people. However, one thing remained unclear: why, when representing fractions of the type 2/(2k+1), Egyptians did not use a natural representation 1/(2k+1) + 1/(2k+1), but used a much more complicated representation instead. In this paper, we show that the need for such a complicated representation can be explained if we take into account that instead of cutting a …
Geometric Reformulation Of Learning Models Can Help Prepare Better Teachers, Vladik Kreinovich, Olga Kosheleva
Geometric Reformulation Of Learning Models Can Help Prepare Better Teachers, Vladik Kreinovich, Olga Kosheleva
Departmental Technical Reports (CS)
Many researchers have been analyzing how to further improve teacher preparation -- and thus, how to improve teaching. Many of their results are based on complex models and/or on complex data analysis. Because of this complexity, future teachers often view the resulting recommendations as black boxes, without understanding the motivations for these recommendations -- and thus, without much willingness to follow these recommendations. One of the natural ways to make these recommendations clearer is to reformulate them in geometric terms, since geometric models are usually easier to understand than algebraic more abstract ones. In this paper, on the example of …
From Gig Economy To Gig Education, Olga Kosheleva, Julian Viera Jr., Vladik Kreinovich
From Gig Economy To Gig Education, Olga Kosheleva, Julian Viera Jr., Vladik Kreinovich
Departmental Technical Reports (CS)
Modern economy has benefited from gig economy idea, where, instead of hiring permanent employees, a company assigns each task to the person who is the most efficient in performing this task. This way, each task is performed in the best possible way -- by a person who is the most suited for this job. Why not extend this idea to education? Every student deserves the best possible teacher in every topic. So why not have a teacher who is the best in town in explaining quadratic equations teach quadratic equations to all the students from the town? In this paper, …
Should School Feel Like A Family: Lessons From Business Controversy As Interpreted By Decision Making Theory, Olga Kosheleva, Julian Viera Jr., Vladik Kreinovich
Should School Feel Like A Family: Lessons From Business Controversy As Interpreted By Decision Making Theory, Olga Kosheleva, Julian Viera Jr., Vladik Kreinovich
Departmental Technical Reports (CS)
Traditional business theory promoted the ideal of business as a family: everyone should feel good about each other, all employees should feel good working together towards a joint goal. Recently, however, researchers claim that the well-promoted ideal is unattainable, it is a ruse causing everyone to overwork. Instead, these researchers propose a non-emotional collaboration of adults working temporarily on a joint project. In this paper, we show that this new trend is not just based on anecdotal evidence, it actually has a solid foundation in decision theory. So maybe we should apply this new trend to teaching too - and …
Comparing Us And Russian Grading Scales, Olga Kosheleva, Vladik Kreinovich
Comparing Us And Russian Grading Scales, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In the US, grades are usually based on comprehensive written exams: the larger the proportion of topic in which the student shows knowledge, the higher the student's grade. In contrast, in Russia, the grades are based on oral exams, and the bulk of the grade comes from a student answering questions of a few (usually, three) randomly selected topics. A natural question is: what is the relation between the two grading scales? It turns out that "excellent" and "good" grades means the same in both scales, while the US "satisfactory" level is higher than a similar Russian level.
Psychological Behavior Of English Learners Utilizing A Cognitive Tutor In An Online Pre-Calculus, Julian Viera Jr., Olga Kosheleva, Vladik Kreinovich
Psychological Behavior Of English Learners Utilizing A Cognitive Tutor In An Online Pre-Calculus, Julian Viera Jr., Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
The educational landscape is becoming a digital learning environment. Students in today's digital world draw from multiple sources of information; from hypertext, videos, social media, to video games and internet searches. English Learners, individuals learning two languages at once, who use software written in English have a passive relationship with the computer when software is not in their native language. They feel that this educational software belongs to another culture. This paper will present findings from a study with English Learners' engagement in a fully online pre-calculus course. The authors utilized Cultural-Historical Activity Theory to describe how English Learners' created …
In Education, Delayed Feedback Is Often More Efficient Than Immediate Feedback: A Geometric Explanation, Francisco Zapata, Olga Kosheleva, Vladik Kreinovich
In Education, Delayed Feedback Is Often More Efficient Than Immediate Feedback: A Geometric Explanation, Francisco Zapata, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Feedback is important in education. It is commonly believed that immediate feedback is very important. That is why instructors stay often late at night grading students' assignments -- to make sure that the students get their feedback as early as possible. However, surprisingly, experiments show that in many cases, delayed feedback is more efficient that the immediate one. In this paper, we provide a simple geometric explanation of this seemingly counter-intuitive empirical phenomenon.
Maybe The Usual Students' Practice Of Cramming For A Test Makes Sense: A Mathematical Analysis, Francisco Zapata, Olga Kosheleva, Vladik Kreinovich
Maybe The Usual Students' Practice Of Cramming For A Test Makes Sense: A Mathematical Analysis, Francisco Zapata, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
We always teach students that cramming for a test is a bad idea, that they should study at the same speed throughout the semester – but many still cram. We ourselves are not that different: when we prepare papers for a conference, we often “cram” in the last days before the deadline instead of working with a regular speed for the whole time before the conference. The ubiquity of cramming makes us think that maybe it is not necessarily always a bad idea. And indeed, a simple model of a study process shows that an optimal solution often involve some …
How To Teach Implication, Martha Osegueda Escobar, Olga Kosheleva, Vladik Kreinovich
How To Teach Implication, Martha Osegueda Escobar, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Logical implication is a somewhat counter-intuitive notion. For students, it is difficult to understand why a false statement implies everything. In this paper, we present a simple pedagogical way to make logical implication more intuitive.
Grading That Takes Into Account The Need To Learn From Mistakes, Francisco Zapata, Olga Kosheleva, Vladik Kreinovich
Grading That Takes Into Account The Need To Learn From Mistakes, Francisco Zapata, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
It is well known that the best way to learn the new material is to try it, to make mistakes, and to learn from these mistakes. However, the current grading scheme, in which the overall grade is a weighted average of the grades for all the assignments, exams, etc., does not encourage mistakes: any mistake decreases the grade on the corresponding assignment and thus, decreases the overall grade for the class. It is therefore desirable to modify the usual grading scheme, so that it will take into account -- and encourage -- learning by mistakes. Such a modification is proposed …
How To Take Into Account A Student's Degree Of Certainty When Evaluating The Test Results, Joe Lorkowski, Olga Kosheleva, Vladik Kreinovich
How To Take Into Account A Student's Degree Of Certainty When Evaluating The Test Results, Joe Lorkowski, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
To more adequately gauge the student's knowledge, it is desirable to take into account not only whether the student's answers on the test are correct or nor, but also how confident the students are in their answers. For example, a situation when a student gives a wrong answer, but understands his/her lack of knowledge on this topic, is not as harmful as the situation when the student is absolutely confident in his/her wrong answer. In this paper, we use the general decision making theory to describe the best way to take into account the student's degree of certainty when evaluating …
How Success In A Task Depends On The Skills Level: Two Uncertainty-Based Justifications Of A Semi-Heuristic Rasch Model, Joe Lorkowski, Olga Kosheleva, Vladik Kreinovich
How Success In A Task Depends On The Skills Level: Two Uncertainty-Based Justifications Of A Semi-Heuristic Rasch Model, Joe Lorkowski, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
The more skills a student acquires, the more successful this student is with the corresponding tasks. Empirical data shows that the success in a task grows as a logistic function of skills; this dependence is known as the Rasch model. In this paper, we provide two uncertainty-based justifications for this model: the first justification provides a simple fuzzy-based intuitive explanation for this model, while the second -- more complex one -- explains the exact quantitative behavior of the corresponding dependence.
Creative Discussions Or Memorization? Maybe Both? (On The Example Of Teaching Computer Science), Vladik Kreinovich, Olga Kosheleva
Creative Discussions Or Memorization? Maybe Both? (On The Example Of Teaching Computer Science), Vladik Kreinovich, Olga Kosheleva
Departmental Technical Reports (CS)
We all strive to be creative in our teaching, but there is often not enough time to make all the topics creative fun. So sometimes, we teach memorization first, understanding later. We do it, but we often do it without seriously analyzing which topics to "sacrifice" to memorization. In this talk, we use simple mathematical models of learning to come up with relevant recommendations: Namely, all the topics form a dependency graph, and if we do not have enough time to allow students to treat all topics with equal creativity, then the most reasonable topics for memorization first are the …
Why Rozenzweig-Style Midrashic Approach Makes Rational Sense: A Logical (Spinoza-Like) Explanation Of A Seemingly Non-Logical Approach, Olga Kosheleva, Vladik Kreinovich
Why Rozenzweig-Style Midrashic Approach Makes Rational Sense: A Logical (Spinoza-Like) Explanation Of A Seemingly Non-Logical Approach, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
A 20 century German Jewish philosopher Franz Rosenzweig promoted a new approach to knowledge, an approach in which in addition to logical reasoning, coming up with stories with imagined additional details is also important. This approach is known as midrashic since it is similar to the use of similar stories -- known as midrashes -- in Judaism. While stories can make the material interesting, traditionally, such stories are not viewed as a serious part of scientific discovery. In this paper, we show that this seemingly non-logical approach can actually be explained in logical terms and thus, makes perfect rational sense.