Mathematics and Economics

Applied mathematics in economics can be an effective tool for raising the curiosity of children and the desire to study individually. The economic environment and economy in general, with its essential components, production, performance of works, provision of services, identification / utilization / exploitation of financial resources, are a good source of problems whose economic content is easily understood and whose solution involves the use of a mathematical apparatus that is studied in gymnasium.

First of all, we should mention that in any field of activity people are confronted with problems, some of them being solved easily, others requiring great efforts to search for the solution and some of them remain unsolved. At school, to the educational objects, the students encounter different problems, similar to those that they will later encounter in everyday life, and therefore, they must be taught even from the school’s desks to distinguish the problematic situations, to put and formulate problems, to heuristically seek solutions to them, to solve them.

The study of some situations in the economy as a source of applications for mathematics has a double positive effect: on the one hand, it helps us convince students that mathematics is not only an abstract science (and therefore arid), it can also be used to formalize real life situations and solve real life problems; on the other hand, it familiarizes students with some economic notions that enable them to better understand what is happening in society, the possibility of forming and early development of entrepreneurial spirit, thus being an expected effect of this optional course.

General Competences

  • Knowing the use of some economic terms: production, commerce, finance, interest, etc.
  • Identifying mathematical relationships and their correlation according to various economic contexts.
  • Processing of quantitative, qualitative, structural and contextual data contained in mathematical statements referring to economic situations.
  • Using algorithms of mathematical concepts for the global characterization of economic situations.
  • Expressing quantitative or qualitative mathematical characteristics of economic situations and the algorithms for their processing.
  • Mathematical modeling of problematic contexts of economic nature by integrating basic knowledge about economics.

Values and Attitudes

  • Enterprising spirit
  • Efficiency and rationality in the use of resources
  • Freedom of thought in decision-making
  • Active, responsible behaviour
  • Creating the habit of resorting to mathematical concepts and methods in dealing with practical situations
  • Establishing the motivation to study mathematics as a relevant field of social life.

I) Specific Competences
_  Recognition, listing of production factors
_ Making calculations specific to the different phases of the production process
_ Analysis of the efficient use of resources
_ Identifying solutions to rationalize resource use
_ Making calculations of incomes related to the production process
_ Making calculations regarding the profit and its distribution

Learning Activities
– Examples and brief description of the production process;
– Highlighting the essential components of the products;
– Making calculations regarding the costs for raw materials, staff, utilities, storage and marketing of products.
– Practical examples regarding unit costs for the same product type, from different economic agents;
– Highlighting the limited nature of resources;
– Making alternative calculations regarding:
– the opportunity of a product;
– different technological processes;
– Studying the significance of exceptional financial operating income;
– Making calculations regarding the profit and its distribution

1. Production
• Factors of production
• Productivity
• Cost of production
• Profit – gross profit, net profit, profit rate

II)Specific Competences
_ Identify solutions for rational choice of acquisitions sources
_ Recognition of the essential components of the selling price
_ Making calculations regarding the commercial addition, VAT, the selling price
_ Formalizing situations specific to marketing process and establishing the working algorithms used
_ Making calculations regarding commercial discounts

Learning Activities
– Drafting comparative tables regarding the acquisition options with consideration of some criteria: price, quality, volume, design etc.
– Collecting, presenting information regarding the components of the selling price and making calculations of the selling price of some products;
– Calculation of collected / refunded VAT for different products;
– Putting problems in equations and solving them;
– Assimilation of the specific terminology regarding the trade discounts and calculation of the purchase / sale price, in the conditions of receiving / the discount agreement.

2. Trade
• Purchase price
• Commercial addition
• Selling price
• Increases and reductions in prices

III) Specific Competences
_ Identifying the interest as income / financial expense
_ Making calculations specific to simple and compound interest
_ Identifying financing solutions based on the projection of income / expenses generated by the collection / payment of interest

Learning Activities
–  Assimilating the definitions regarding the simple interest and compound interest;
– Solving problems related to receiving / granting a loan;
– Examples of funding resources and calculations leading to optimal variants

3. Interest
• What is interest?
• The interest rate
• Simple interest
• Compound interest

IV) Specific Competences
_ Use of economic tools necessary to solve problems belonging to the private environment
_ Identifying financial tools  usable in a market economy
_ Identifying the opportunities and difficulties of acquiring, managing and alienating financial tools
_ Making specific calculations to determine the yield of financial tools

Learning Activities
– Examples of new businesses
– being successful
– being a failure
– Studying the policy, cheque, promissory note and simulation of their use;
– Studying some examples of stock price evolutions / their obligation;
– Solving problems regarding the placements, placement decisions, yields.

4. Financial Tools
• Policy
• Cheque
• Promissory note
• Share
• Bonds

Nowadays, on all the levels of education, a special attention is paid to the study of economy, due to the fact that it contributes to a great extent to the development of the students’ psychic attributes and at the same time it enlightens them with a series of knowledge and useful skills or habits for life.

Moreover, in order to acquire a thorough knowledge of economy, a significant place also deals with the problem solving.

The active-participative teaching and learning methods aim stimulating the students to study mathematics and economics, developing creativity and their investigative capacity, opening up individual learning and learning paths.
It is  to combine the usual ordinary resolutions with those that focus on solving clustered issues or problems around a property with a central role in solving, problem-building on a given idea, using the heuristic methods and procedures in order to find the revealing idea; and these, being based on the use of active-participatory methods that put the student in the center of the training process, with his questions and perplexity or bewilderment, with his real possibilities. The new approaches in didactics, the use of child’s psychology acquisitions, as well as the experimental approach of the specific problems did noway mean abandoning or discrediting what had been validated as effective for education and training.

I put the student on the first plan and his participation in the lesson, putting him in the learning situation in order to develop thinking, the observation spirit, imagination, flexibility in thinking, creativity.

prof. Alina-Gabriela Țepeș

Școala Gimnazială Nr. 13 Ștefan cel Mare, Galați (Galaţi) , România
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