A course of Elementary Probability Course

2020 ◽  
Author(s):  
Gane Samb LO ◽  
Aladji Babacar Niang ◽  
Lois Chinwendu Okereke
Keyword(s):  
Probability Theory ◽  
Problem Solving ◽  
Secondary School ◽  
Mathematical Statistics ◽  
Mathematical Concepts ◽  
Foundations Of Probability ◽  
Counting Methods ◽  
General Chapter ◽  
Mathematical Foundations ◽  
Present Text

This book introduces to the theory of probabilities from the beginning. Assuming that the reader possesses the normal mathematical level acquired at the end of the secondary school, we aim to equip him with a solid basis in probability theory. The theory is preceded by a general chapter on counting methods. Then, the theory of probabilities is presented in a discrete framework. Two objectives are sought. The first is to give the reader the ability to solve a large number of problems related to probability theory, including application problems in a variety of disciplines. The second is to prepare the reader before he takes course on the mathematical foundations of probability theory. In this later book, the reader will concentrate more on mathematical concepts, while in the present text, experimental frameworks are mostly found. If both objectives are met, the reader will have already acquired a definitive experience in problem-solving ability with the tools of probability theory and at the same time he is ready to move on to a theoretical course on probability theory based on the theory of Measure and Integration. The book ends with a chapter that allows the reader to begin an intermediate course in mathematical statistics.

scholarly journals Different Perspectives on Success in Solving Stand-Alone Problems by 14 to 15-Year-Old Students / Različite prespektive o uspješnosti 14 i 15-godišnjaka u rješavanju izoliranoga problema

2021 ◽  
Vol 23 (1) ◽  
Author(s):  
Nives Baranović ◽  
Branka Antunović-Piton
Keyword(s):  
Elementary Schools ◽  
Problem Solving ◽  
Secondary School ◽  
Mathematical Task ◽  
Mathematical Concepts ◽  
Urban Elementary Schools ◽  
8Th Grade ◽  
Verbal Problem ◽  
Set Up ◽  
Problem Solving Process

The paper defines a special type of problem tasks and considers its didactic potential, as well as the success of students in solving the selected problem. The research instrument used is a geometrical task from the National Secondary School Leaving Exam in Croatia (State Matura). The geometrical task is presented in three versions: as a verbal problem, as a verbal problem with a corresponding image and as a problem in context. The material analysed in the present paper was collected from 182 students in 7th and 8th grade of Croatian urban elementary schools. The didactic potential is considered from the aspect of use of mathematical concepts and connections. The success of students in problem-solving is considered from the aspect of implementation of the problem-solving process and producing correct answers, depending on the manner in which the tasks are set up. The results show that the stand-alone problem, as a special type of problem task, has considerable didactic potential. However, the students’ skills of discovering and connecting mathematical concepts and their properties are underdeveloped. In addition, the manner in which the tasks are set up considerably affects the process of solving the task and consequently the success of that process. Based on the results of the research, proposals are given for application of stand-alone problems in teaching mathematics.Key words: isolated problem; mathematical task; problem solving; problem evaluation.  --- U radu se definira posebna vrsta problemskoga zadatka te se razmatra njegov didaktički potencijal kao i uspješnost učenika u rješavanju odabranoga problema. Instrument istraživanja je geometrijski zadatak s državne mature koji se postavlja u tri inačice: kao tekstualni problem, kao tekstualni problem uz odgovarajuću sliku te kao zadatak u kontekstu. U istraživanju je sudjelovalo 182 učenika 7. i 8. razreda hrvatskih gradskih osnovnih škola. Didaktički potencijal razmatra se s aspekta iskoristivosti matematičkih koncepata i veza, a uspješnost učenika u rješavanju problema razmatra se s aspekta provedbe procesa rješavanja i otkrivanja točnoga rješenja ovisno o načinu postavljanja zadatka. Rezultati pokazuju da promatrani problem kao posebna vrsta problemskoga zadatka ima veliki didaktički potencijal, ali da učenici imaju nedovoljno razvijene vještine otkrivanja i povezivanja matematičkih koncepata i njihovih svojstava. Osim toga, način postavljanja zadatka značajno utječe na proces rješavanja, a posljedično i na uspješnost određivanja rješenja. Na temelju rezultata daju se prijedlozi primjene opisane vrste problema u nastavi Matematike.Ključne riječi: izolirani problem; matematički zadatak; rješavanje problema; vrednovanje problema

scholarly journals Learning of Mathematical Concepts in Relation to Spatial Ability and Problem Solving Skills among Secondary School Pupils

2017 ◽  
Vol 6 (1) ◽  
pp. 106
Author(s):  
J. Shakila
Keyword(s):  
Problem Solving ◽  
Secondary School ◽  
Mathematics Classroom ◽  
Mathematics Learning ◽  
Integrated Approach ◽  
Transmission Model ◽  
Mathematical Concepts ◽  
Problem Solving Skills ◽  
Constructive Process ◽  
Secondary School Pupils

<div><p><em>Mathematics with all its branches plays an important role in everyday life. It is created to investigate the whole range of knowledge. Learning mathematics is basically a constructive process, which means that pupils gather, discover, create mathematical knowledge and skills mainly in the course of some social activity that has purpose consequently mathematics classroom instruction should move away from the information transmission model. Meaningful and authentic context should play a crucial role in mathematics learning and teaching, therefore, we need an integrated approach to mathematics teaching.</em></p><p><em>Problem solving is an integral part of developmental activities and provides opportunities for children to practice what they have learned by applying their learning situations. The amount of practice needed by any learner is reduced if he understands the concepts and skills to be practiced. How can we make our students good problem solvers in mathematics? This is possible only when we make mathematics education more meaningful and interesting. Mathematical abilities like logical thinking, rational reasoning, concentration of mind, orderly presentation, precision and accuracy, analytical and inductive skills, and above all general problem solving abilities. So the present study is intended to learning of mathematical concepts in relation to problem solving skills among secondary school pupils.</em></p></div>

The Interplay Between Mathematical and Computational Thinking in Primary School Students’ Mathematical Problem-Solving Within a Programming Environment

2021 ◽  
pp. 073563312097993
Author(s):  
Zhihao Cui ◽  
Oi-Lam Ng
Keyword(s):  
Problem Solving ◽  
Mathematical Thinking ◽  
Mathematics Learning ◽  
Mathematical Problem ◽  
Computational Thinking ◽  
Programming Environment ◽  
Primary School Students ◽  
School Students ◽  
Mathematical Concepts ◽  
Block Based

In this paper, we explore the challenges experienced by a group of Primary 5 to 6 (age 12–14) students as they engaged in a series of problem-solving tasks through block-based programming. The challenges were analysed according to a taxonomy focusing on the presence of computational thinking (CT) elements in mathematics contexts: preparing problems, programming, create computational abstractions, as well as troubleshooting and debugging. Our results suggested that the challenges experienced by students were compounded by both having to learn the CT-based environment as well as to apply mathematical concepts and problem solving in that environment. Possible explanations for the observed challenges stemming from differences between CT and mathematical thinking are discussed in detail, along with suggestions towards improving the effectiveness of integrating CT into mathematics learning. This study provides evidence-based directions towards enriching mathematics education with computation.

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