Contextualization

This math project will address the interesting field of 'Research 3', a key component in data collection and statistical analysis, which allows extracting important information from large data sets. To have a complete understanding of the topic, we will explore concepts and techniques such as sampling, measures of central tendency, range, sample selection, census research, and sample research. Throughout the project, we will also work on topics related to the Portuguese discipline, including report writing and result discussion.

The importance of research in our lives is immeasurable. Whether deciding which candidate is the most popular in an election, analyzing customer satisfaction with a new product, or evaluating the effectiveness of a new medication, research provides critical information that helps make informed decisions. In this sense, research is not just a mathematical skill but a crucial tool for life in the 21st century.

Introduction

Research is rooted in a branch of mathematics known as statistics, which is the study of techniques for collecting, organizing, analyzing, and interpreting data. In statistics, 'sampling' is the practice of selecting a subsection of a population to obtain the necessary information. 'Measures of central tendency' (mean, median, and mode) and 'range' are tools used to analyze the collected data.

On the other hand, 'sample selection' is essential to ensure that the sample is representative of the population under study. There are different ways to select a sample, including simple random sampling, systematic sampling, and stratified sampling. Furthermore, it is crucial to understand the difference between a 'sample survey', which studies a small representative part of the population, and a 'census survey', which examines every member of a population.

Students will have the opportunity to delve deeply into each of these concepts and techniques, applying them in a real research study. This project will develop practical and theoretical skills in statistics, as well as socio-emotional skills such as time management, communication, problem-solving, and creative thinking.

Practical Activity

Activity Title:

'Applying Research and Statistics: A Study of the School Environment'

Project Objective:

Learn and implement concepts of sampling, measures of central tendency, and the difference between census and sample surveys while conducting a real study on a topic relevant to their school life.

Detailed Project Description:

Students, in groups of 3 to 5, will select a topic from the school environment to conduct a research. This topic can range from 'satisfaction with cafeteria food' to 'sports preferences in school', or they can choose a current topic, such as 'the effectiveness of remote versus in-person learning'. The idea is for students to formulate research questions, collect data, analyze this data using measures of central tendency, and finally, provide a substantial discussion of their results in a formal report.

Required Materials:

• Paper and pen/pencil to take notes of their findings
• Materials for data collection (e.g., printed or digital questionnaires, internet access, etc.)
• Data analysis software (can be something as simple as Excel)
• Access to the resources mentioned in the contextualization for consultation and learning.

Detailed Step-by-Step for Activity Execution:

1. Brainstorming to select a research topic and formulate research questions (2 hours)
2. Decide on the type of sample to be used and develop a sampling plan (2 hours)
3. Create and distribute the survey (4 hours)
4. Collect and organize survey data in a usable format (3 hours)
5. Analyze the collected data using measures of central tendency and range (4 hours)
6. Discuss the results and prepare a research report (6 hours)
7. Review and finalize the research report (3 hours)
8. Presentation of results in the classroom (4 hours)

Project Deliverables:

• A detailed research report format containing the following topics:
  1. Introduction: Description of the selected research topic, its relevance, the reason for sample selection, and the research's relevance.
  2. Development: Description of the research planning, how the survey was distributed, how the data was collected, and a detailed explanation of the calculations of the measures of central tendency used.
  3. Results and Discussion: Presentation of data sets in appropriate graphs and discussion of the results obtained based on measures of central tendency and range.
  4. Conclusions: Reflection and interpretation of the results and their implications in the school environment.
  5. Bibliography: Listing of resources used in the project.
• A classroom presentation on the research process and the results obtained.

The written report and the classroom presentation should complement the practical work done. At the same time, the report will allow students to deepen their theoretical knowledge of research and statistics, while the presentation will give them the opportunity to develop their communication and collaboration skills.