| Presentation Date: 25 / January / 2024 Program: Developed and Advanced Theoretical Methods in learning Numerical Systems and Mathematics Author and IP Owner: ATHANASIOS KOKONTIS Author and Presenter Biography: Video Link: Author and Presenter LinkedIn Account: https://www.linkedin.com/.in/athanasios-kokontis-47a63923/ Website: kokontis.com.au Duration: 15:00 minutes Presentation Topic: Reading Mathematical Equations and Formulas Correctly: Using the KOKONTIS procedures – Part A Website Link for this presentiton: https://kokontis.wordpress.com/reading-mathematical-equations-and-formulas-with-positive-numerals-and-negative-numbers-correctly-using-the-kokontis-procedures-and-learning-methods-part-1-15-minute-tutorial/ Prerequisite: Reading Mathematical Equations and Formulas Correctly: Using the KOKONTIS procedures – Part 1 https://kokontiscourses.wordpress.com/reading-mathematical-equations-and-formulas-correctly-using-the-kokontis-procedures/ (Link to Part 1 also in video description) This presentation is a part of the course developed by Athanasios Kokontis – Developed and Advanced Theoretical Methods in learning Numerical Systems and Mathematics This presentation and the procedures follow ( DO NOT PRECEDE) the Numerical Systems Course Units and Training. Disclaimer: Kokontis does not provide tutoring services or in class teaching – we developed an education system for use by teachers and tutors, registered training organisation (RTOs), academia, practitioners and industry professionals. This presentation is a part of the course developed by Athanasios Kokontis – Developed and Advanced Theoretical Methods in learning Numerical Systems and Mathematics IMPORTANT – This presentation and the procedures follow (DO NOT PRECEDE ) the Numerical Systems Course Units and Training. – This is an introduction and not a comprehensive tutorial INTRODUCTION TO AUTHOR AND PRESENTER Introduction to the Author, Owner and Publisher, Athanasios Kokontis of this presentation can be found in the video link provided above. Summary: Athanasios Kokontis is the Developer and Intellectual Property Owner of the numerical systems and mathematical procedures education system: Developed and Advanced Theoretical Methods in learning Numerical Systems and Mathematics Description of the education system: Independent education research project developed within a Science and Research Framework: An independent research project to develop a prerequisite Numerical System and Procedural Mathematics Learning course for people to achieve proficiency and prerequisite advanced Numerical Systems and Mathematics skills. The current assumption is that there is a 30% percent chance of success rate in an individual achieving prerequisite high level mathematics skills to enter University or College or advanced mathematics dependent careers. Athanasios Kokontis has confirmed – by developing this advanced Numerical System curriculum and applied Learning Procedures an individuals success rate increases to 80% percent – the remainder 20% is the individuals commitment. The Proficiency case for Current Practitioners, Professionals and Academia: The case for the low 30% success rate leads to assumptions about current occupations who require proficiency in Numerical Systems and Advanced Mathematics Based on the assumption that current Arithmetic Theory, Number Systems and Mathematics curriculum is incorrect, Athanasios Kokontis estimates 50 percent of professionals and individuals in a number or mathematics dependent occupation will highly likely have a low score of proficiency in numerical systems and mathematics, and thus must conduct tasks with the use of computation equipment ( excel, software, online mathematics calculators and calculator equipment. This estimate is based on the estimated low success rate of 30% for an individual to achieve proficiency in advanced mathematics and the incorrect curriculum education methodology used today. On this basis, the case can be made for people currently employed in a number and mathematics dependent occupation – will likely have an approximate 50 percent proficiency score in numeracy and mathematics, as a result of this low score the curriculum program will be promoted to this group. Proprietary and IP Property Terms and Content: The term, instruction, is introduced and used by Athanasios Kokontis in the context of explaining Mathematics Signs, Notations and Symbols, Mathematical Methods and Procedures is considered a propriety term introduced by Athanasios Kokontis. Current Arithmetic Theory, Number Systems and Mathematics publications, textbooks and educational curriculum use different terms. |
| PRESENTATION OBJECTIVE 1. To assist Parents and academic staff currently tutoring children with Mathematics subjects, also applicable for all demographics and skilled level people to commence learning the subjects of Numerical Systems and Mathematics with the correct procedures and methods. 2. This is video presentation can be viewed with , with the preceding presentation – Reading Mathematical Equations and Formulas Correctly: Using the KOKONTIS procedures – an introductory presentation. 3, An introduction to the numbers (Interchangeable with the term- Values) used in the current numerical system being POSITIVE numbers and Negative numbers , 4. A distinction is made between Language ( Linguistics, Etymology) and Symbols ( Signs or Characters which are in effect instructions of a process or method of computation when applied to mathematics topics and equations. An the interpretation to Language (formal written and verbal communication Linguistic systems) and – an interpretation into the the Symbols ( +, -, x, / ) number system used in the curriculum of Mathematics of numerical symbols and the language used in the subject and science of Mathematics , instructions, operations and mathematical methods introduced in Part 1, this part will apply the complete, Kokontis computation procedures, introduced in Part 1, using the two equations in Part 1 with a comprehensive applied illustration of the mathematical procedures. 4. This presentation is a part of the course developed by Athanasios Kokontis – Developed and Advanced Theoretical Methods in learning Numerical Systems and Mathematics 5. The Importance of this presentation is to construct the correct understanding of the total computation (calculation) and measurement system called Number Systems, Arithmetic, and Mathematics by introducing the correct interpretation of the components of these system, by defining the; Number System Component = Numbers and Quantities Numerical Language Component = Symbols and Notation (which are the Instructions and Operations(( +, -, X, and /) Computation / Calculation Component: Mathematics Procedures using the Operations ( +, -, X, and /) SUGGESTIONS BY AUTHOR AND PRESENTER 1. Print the online readable version of this presentation using this Link: https://kokontiscourses.wordpress.com/reading-mathematical-equations-and-formulas-correctly-using-the-kokontis-procedures-part-2/ 2. Print the Transcript of this video presentation: Available on YouTube feature. This will allow you to review the content of this presentation offline and starting applying the procedures to your current education. 3. Contact the Author and Presenter, Athanasios Kokontis, for further interpretation by email: customer.enquiries@sitnokglobal.com or leave a comment on the Video page IMPROVING YOUR GRADES AND MATHEMATICS SUBJECT RESULTS 4. Parents and Tutors: assisting a third party (primary, secondary and high school student) with their Mathematics subjects and homework. Current students with low grades: who have become disinterested in their Mathematics subject due to the perceived complexity which is a result of the incorrect curriculum programs used in education today. Multiple views of this video tutorial will increase their understanding of Numeracy, Arithmetics and Mathematics subjects. |
| TOPICS Section 1. Terminology Section 2. Overview of Part 1 Section 3. Constructing a Number System for Measurement (a)The Natural Numbers and Quantities (b) Natural Symbols | 1 | and Notation (c) The Lines as quantities and intervals (d) The Number Line (d-1) Quantities (d-2) Distances (d-3) Intervals (d-4) Numerical Symbols and Notation (e) Explanation of the Mathematical Statement ( Equation ) (e-1) Language of Numerals and Linguistic Language of Communication (e-2) Measurement and Computation Objective (e-3) Instructions ( the Symbols / Notations (e-4) Four Natural Operations – Image of Notations and their relationship to Four Natural Operations ( +,-,X and /) Section 4. Using the Number System for Measurement (A) Using the Number System, Number Line and Ruler Tool for measurement (B) Measurement Requirements: (b-1) The four elements of earth (b-2) Quantities (b-3) Distance (b-4) Area (C)Physical Properties (Positive and Negative Values): Scalars: Temperature Time ( Is also a number Line Scale) (c) (b) Brief explanation of a Graph and Using a Graph Section 5. The Kokontis – Procedures applied to two equation examples The numerical and operation components of an equation |
Section 1 Terminology
1. Numbers = Values = Absolute Values = Number System 2. Number System: refers to the set of numbers (values) in use today: (0,1,2,3,4,5,6,7,8,9) 3. Mathematics Symbols and Notation: Symbols ( +, -, X, and / ) are the instructions forming the equation. 3. Operations = to use the operands of Addition (+) , Subtraction (-), Multiplication (x) and Division (/). Is the task of performing the calculation and computation of the operations (Operand) +, -, x, and / 4. Instructions: A proprietary term introduced and used by Athanasios Kokontis – to demonstrate the action of carrying out a calculation or computation using the above Operand 5. Computation = Calculation = Operation 6. Numerical Symbols Used: | 2 | = Absolute Value or Absolute Number | 2 | = Positive Absolute Value or Number |-2| = Negative Absolute or Number It replaces other explanations of the process and procedures in making a calculation ( Computation ) Example: + – / X = Operations and Instructions 7. Graph Terminology = X – Number Line (Horizontal Ruler) = Horizontal Line and Horizontal Axis = 1st Dimension Y- Number Line (Vertical Ruler) = Vertical Line and Vertical Axis = 2nd Dimension 8. Function = Result of Equation = Computation Result = Output = Y 9. Scalar/s – a physical quantity that is completely described by its magnitude. Examples of scalars are volume, density, speed, energy, mass, and time. Other quantities, such as force and velocity, have both magnitude and direction and are called vectors. Proprietary and IP Property Terms and Content: The term, instruction, is introduced and used by Athanasios Kokontis in the context of explaining Mathematics Signs, Notations and Symbols, Mathematical Methods and Procedures is considered a propriety term introduced by Athanasios Kokontis. Current Arithmetic Theory, Number Systems and Mathematics publications, textbooks and educational curriculum use different terms. |
Section 2. Overview of Part 1
Section 1. Terminology Section 2. Overview of Part 1 The Term Mathematics explained: Greek Term: Mαθηματικά = Mathematics Greek Linguistic interpretation: Mαθημα-τικά Mαθημα– = To Learn = Knowledge ( γνώση ) τικά – Ancient Greek term (Tέχνη) for Technical Trade Thus: To Learn a technical skill or technical occupation (Technician) And: it is confirmed Mathematics is a Technical System DISTINCTION BETWEEN A NUMERICAL SYSTEM AND MATHEMATICS NUMERICAL SYSTEM = Is a group of numbers forming a system of measurement. MATHEMATICS = Is the use of the system of numbers Online Readable Version to Part 1: See link above Video Link to Part 1 : See link above |
Section 3. Constructing a Number System for Measurement
Section 3. Constructing a Number System for Measurement (a)The Natural Numbers and Quantities (b) Natural Symbols | 1 | and Notation (c) The Lines as quantities and intervals (d) The Number Line (d-1) Quantities (d-2) Distances ( quantities of interval lengths) 1m + 1+m Scale of distances is your choice 1m 1km 100km 1cm (ruler) (d-3) Intervals (d-4) Numerical Symbols and Notation (e) Explanation of the Mathematical Statement ( Equation ) (e-1) Language of Numerals and Linguistic Language of Communication Linguistics is the scientific study of language. It entails the comprehensive, systematic, objective, and precise analysis of all aspects of language — cognitive, social, environmental, biological as well as structural. Linguistics is considered to be an applied science as well as an academic field of general study within the humanities and social sciences. (e-2) Measurement and Computation Objective (e-3) Instructions ( the Symbols / Notations (e-4) Four Natural Operations – Image of Notations and their relationship to Four Natural Operations ( +,-,X and /) (a) Constructing a Number System (b)The Natural Numbers and Quantities (c) The Lines as quantities and intervals (d) Numerical Symbols and Notation (e) Natural Symbols | 1 | (f) The Number Line (g) Quantities (h) Distances (I) Graph explained Absolute Positive Numbers and Absolute Negative Numbers Measuring Positive Direction and Negative Direction Scalars are described by real numbers that are usually but not necessarily positive. The work done on a particle by a force, for example, is a negative number when the particle moves in a direction opposite to that in which the force acts, such as when the frictional force slows down a moving body. Scalars can be manipulated by the ordinary laws of algebra. – Image of Notations and their relationship to Four Natural Operations ( +,-,X and /) 1.. Explanation of the Mathematical Statement ( Equation ) 2. Procedures applied to two equation examples |
Section 4. Using the Number System for Measurement
| Section 4. Using the Number System for Measurement (a) Using the Number System, Number Line and Ruler Tool for measurement (b) Measurement Requirements: Absolute Positive Numbers and Absolute Negative Numbers (b-1) The four elements of earth scalar, a physical quantity that is completely described by its magnitude. Examples of scalars are volume, density, speed, energy, mass, and time. Other quantities, such as force and velocity, have both magnitude and direction and are called vectors. Scalars are described by real numbers that are usually but not necessarily positive. The work done on a particle by a force, for example, is a negative number when the particle moves in a direction opposite to that in which the force acts, such as when the frictional force slows down a moving body. Scalars can be manipulated by the ordinary laws of algebra. (b-2) Quantities (b-3) Distance (b-4) Area Physical Properties (Positive and Negative Values): Temperature Time ( Is also a number Line Scale) (c) (b) Brief explanation of a Graph and Using a Graph |
Section 5. Kokontis -Procedures applied to two equation examples
KOKONTIS – PROCEURES FOR FOR READING AND COMPUTING MATHEMATICS EQUATIONS
The following are the developed procedures
Each procedure and step should be followed in order to achieve the correct skills in mathematics
| The Mathematics Equation (Example) 3-2(3 x 4) and 3-(-2)(3×4) | Correct Method |
| STEP 1 Identify the Values (Numbers) 3-4(3 x 4) | Absolute Values (numbers with lines on each side | x | |3| – |2| (x) |3| x |4| |
| 3-(-2)(3×5) | |3| – |-2| (x) |2| x |5| |
| STEP 2 Identify the instructions (Operation to be processed) Value: |3| Operation: – Subtract Value: |2| Operation: x Multiply Value: |3| Operation: x Multiply Value: |5| | |3| – |-2| (x) |3| x |5| |
| Step 3 Perform Computation (Calculation) using mathematical method (1st Part of Equation) |3| – |2| = |1| (x) (2nd Part of Equation) |3| x |4| = |12| _______ |3| – |-2| = |5| (x) |3| x |5| = |15| | Answer |1| x |12| = |12| Answer |5| x |15| = |75| |
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- Author and Owner: Athanasios Kokontis 2019 – 2023
- Year of publication (2023)
- Title: Developed and Advanced Theoretical Methods in Learning Numerical Systems and Mathematics
- Reference Topic: Reading Mathematical Equations and Formulas Correctly: Using the KOKONTIS procedures (A 15 minute tutorial)
- Place published; Sydney, NSW Australia
- Publisher: Athanasios Kokontis
- Series and volume number (General Tutorial)
- Published on website: kokontis.com.au
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