Notes, summaries, assignments, exams, and problems for Mathematics

Teaching and Learning Concepts

Concrete Bases (Teaching)

Convert mathematics into something concrete. Create recognizable contexts to which children can assign their own meanings.

Construction (Learning)

Learning is a constructive activity, contrary to the idea that children simply absorb knowledge presented to them.

Models (Teaching)

To achieve progress, students must have tools at their disposal that enable them to establish a link between informal and formal mathematics. Models and materials are important.

Raising the Level (Learning)

The learning process occurs at different levels of formality. Changes can be sudden and create discontinuity in the learning process.

Time for Reflection (Teaching)

The teacher has to find time to include reflection... Continue reading "Principles of Math Teaching and Learning" »

Secondary Data Analysis: Sources and Elaboration

Secondary data analysis considers both qualitative and quantitative perspectives. It uses references like coding sheets in quantitative designs and identifies interviews or focus groups for qualitative data. Official statistics and public sources are used to verify field data.

Desrosieres argues that statistical indicators from official sources reflect social reality in institutions. These indicators are presented without analysis, as tables of results. This means the original data has been elaborated, which is typical of secondary sources. Secondary sources have developed, summarized, and synthesized the data. The degree of elaboration is the key difference between secondary data analysis and... Continue reading "Secondary Data Analysis: Sources, Types, and Elaboration" »

Hurwicz Criterion: Coefficient of Optimism

In this approach, a decision-maker may have an intermediate attitude. Since no probabilities are associated with each state of nature, this author suggests using a coefficient of optimism, simultaneously called C, and a coefficient of pessimism, (1 - C), where 0 ≤ C ≤ 1.

The coefficient C indicates the decision-maker's stance toward risk. When it is closer to 1, the decision-maker will be more optimistic, while closer to 0, the decision-maker is more pessimistic.

This criterion focuses only on the extreme scores of each alternative, weighing the result of maximum optimism with the coefficient C and the result of minimal value with the coefficient of pessimism (1 - C). The sum of these two products... Continue reading "Decision-Making Under Uncertainty: Criteria and Tables" »

Fortran 90: Implicit None and Vector Management

Implicit None

In Fortran 90, undeclared variables starting with I, J, K, L, or M are treated as integers, while others are treated as real numbers. However, it's best practice to avoid implicit declarations. Use IMPLICIT NONE right after the program instructions to disable implicit typing. This forces you to explicitly declare all variables, preventing potential errors due to character misuse.

Vector Management Forms

Ordering one-dimensional arrays (vectors) is a common operation. Here are three simple methods: selection, insertion, and bubble sort.

In all cases, we'll assume a one-dimensional array of N elements.

Selection Sort

1. Find the smallest element in the vector.
2. Swap it with the element in the

Joint Cost Allocation Methods

Joint costs are costs of a production process that yields multiple products (co-products). Here's a breakdown of common allocation methods:

Criterion: Market Value

This method allocates joint costs based on the relative sales value of each co-product. Here's how it works:

1. Calculate Total Sales Value:
   • List each co-product (e.g., A, B, C).
   • Determine the sales value per unit (e.g., per kg).
   • Determine the quantity of each co-product produced (e.g., in kg).
   • Multiply the sales value per unit by the quantity to find the total sales value for each co-product.
2. Distribute Total Joint Costs:
   • Calculate the total sales value of all co-products.
   • For each co-product, divide its total sales value by the total sales value of all co-products.

Fundamentals of Statistical Analysis

Frequency Distribution

Ungrouped Data

Ungrouped data are lists of observed values when the pooled data represent a mass of observed data.

Pooled Data

When data are grouped in a frequency distribution.

• Collect data and make a tally sheet

Determination of Range

The range is the difference between the highest observed value and the lowest value observed.

Determining the Range of Classes

The range of classes is the enactment between the midpoint of classes.

Determine the Midpoints of the Class

The midpoint of the class must include the minimum data value in that class.

Determine the Class Boundaries

The class limits are the extreme values or limits of a class and are called the upper limit and lower limit.

Identify the Frequency

Grounded Theory: Strategies and Methods

Grounded theory has two main strategies:

Theoretical Sampling

Involves adding to the sample of subjects or situations encountered, additional comments, or further interviews. It seeks to find different cases.

Constant Comparative Method

It is a method to analyze the data at different times in which the researcher interacts with:

1. Classified portions of data:
   • Words
   • Phrases
   • Paragraphs

Categories arise, either intuited or implicit (they are marked, but without a name).

Constant Comparative Method

As the process of selecting pieces of data advances, categories appear with more explicit rules.

The task is to identify:

1. Emerging categories = Issues
   • Categories = Properties
2. Central category = Recurring Themes

Links between categories... Continue reading "Grounded Theory: Strategies, Methods, and Analysis" »

**Purchase Operations**

Shopping is any transaction by which a person receives the domain of property for valuable consideration. The purchase consists of two stages or operations:

**Request for Purchase or Requisition of Goods**

This is a formal request made by a department or warehouse operations, being directed to the purchasing department.

**Order Form**

The purchasing department receives the application and analyzes the real need, according to the financial situation and market conditions, as the article refers.

**Reception Guide**

This is a document issued by the warehouse when it acquires the goods from suppliers. Prior to the receipt, the warehouse manager must take care to verify if the merchandise received matches the packing list issued... Continue reading "Purchase and Sales Operations: Essential Documents" »

Key Warehouse Functions

Departure

• Monitor the consumption of items by various departments.
• Suitably distribute articles.

Entry

• Reject material that does not meet the requirements of the order.
• Monitor and handle the exchange of expired material.

Storage

• Protect and oversee all the products stored.
• Register and control the movements of stock.
• Avoid losses in the stored materials.
• Ensure items are consumed before the expiry date.
• Design documents necessary for good control of the warehouse.
• Request resupply when stocks are minimal.

When to Start Product Replacement

Replacement of a product should start before falling below the minimum stock.

High Maximum Stock: Advantages and Disadvantages

Maximum stock refers to the maximum amount of a particular item above... Continue reading "Warehouse Functions and Inventory Management in Healthcare" »