Contextualization

The current world is loaded with data and information. It is an era known as the 'information age', where the ability to collect, process, and understand data has become an increasingly valued skill in various areas of life. This is no different in mathematics, where the study of data and statistics is a crucial part of the curriculum. In this project, we will explore the concept of research and its importance in data collection and interpretation.

Research is an effective way to gather information on a specific topic. It can be used to collect data on a wide variety of subjects, from political opinions to consumer habits, and is a common tool in many disciplines, including marketing, social sciences, politics, and, of course, mathematics.

Introduction

Mathematics is a discipline that goes far beyond the equations and formulas that often come to mind when we think about the subject. It is the language of logic and reason, and is used to describe and understand the world around us. One of the most fundamental concepts in mathematics is the principle of counting and measurement, which is the basis of many other topics, including statistics and probability.

Statistics is the discipline that deals with the collection, analysis, interpretation, presentation, and organization of data. It is used in a wide variety of academic and professional fields and is an essential skill for anyone who wants to understand numbers and use them to make informed decisions.

Probability, in turn, is a mathematical concept that measures the likelihood of an event occurring. It is used in a multitude of contexts, from calculating risks in business and finance to predicting the weather.

Practical Activity

Activity Title: The Mathematics of Social Research

Project Objective

The objective of this project is to apply the concepts of statistics and probability in practice, conducting a social research within the school and collecting, analyzing, and interpreting the data obtained.

Detailed Project Description

In groups of 3 to 5, students will choose a relevant social practice within the school. Examples of topics could be: 'percentage of students who practice sports', 'school subject preference', among others.

After choosing the topic, students will define a series of questions for the research, which should be answered by the participants. They will then develop a data collection plan, deciding who they will interview, how many people, and how they will approach the interviewees.

Once the data is collected, students will be responsible for organizing and interpreting it using spreadsheets. This step involves the preparation of tables and graphs, the performance of statistical calculations, and the analysis of the results obtained.

In their analysis, students should be able to identify patterns, trends, and correlations in the data, as well as calculate probability measures associated with the events investigated by the research.

Required Materials

• Paper and pen for notes and planning.
• Internet access for research and use of spreadsheets.
• Calculator, if necessary for calculations.

Detailed Step-by-Step for Activity Completion

1. Choose the research topic and define the questions that will be asked to the participants.
2. Develop a data collection plan.
3. Carry out data collection, according to the established plan.
4. Enter the collected data into an electronic spreadsheet.
5. Organize the data into tables and graphs.
6. Perform statistical analysis of the data.
7. Interpret the results, identifying patterns, trends, and correlations.
8. Calculate the probabilities associated with the investigated events.
9. Write a report detailing the entire process and the results obtained.

Project Deliverables

Students must deliver, at the end:

1. The questionnaire used in the research;
2. The spreadsheet with the collected data and the analyses performed;
3. A written report that should contain:

3.1 Introduction: Contextualizing the relevance of the chosen topic and the mathematical concepts used in data analysis.

3.2 Development: The research step-by-step should be described, from the choice of the topic to the data collection, analysis, and interpretation. The methodology used to calculate probabilities and analyze the results should be explained. In addition, the obtained results should be discussed in light of the theoretical concepts covered.

3.3 Conclusions: The main points of the work should be summarized, highlighting the learnings obtained and the conclusions drawn about the project. Possible improvements or future directions for related research should also be suggested.

3.4 Bibliography: Indication of the sources they relied on to work on the project such as books, web pages, videos, etc.

It is expected that by the end of the project, students will be able to understand the relevance of statistics and probability concepts in the real world, as well as have improved skills such as time management, communication, problem-solving, creative thinking, and proactivity.