Contextualization

Mathematics is one of the fundamental pillars of education, as it is a universal language that allows us to understand the world around us. Within mathematics, there is a very important and intriguing concept: research. Mathematical research is a peculiar type of investigation that, unlike other disciplines, does not necessarily require a laboratory or specialized equipment. In fact, all we need to carry out a mathematical research project is an interesting question, a curious mind, and a piece of paper to jot down our findings.

Mathematical research allows students to question, explore, discover, reason, and communicate. They have the opportunity to engage in solving real problems, developing critical thinking skills and mathematical reasoning. Conducting research in mathematics also helps students better understand mathematical concepts and see mathematics in a more positive and enjoyable way.

Mathematical research is everywhere. For example, the statistics we read in newspaper articles, the proportions and scales used in construction, compound interest in a savings account or bank loan, and many other practical applications that we can find in our daily lives. Understanding and knowing how to interpret these mathematical research findings is an important skill in today's society, where we are constantly bombarded with information that needs to be analyzed and interpreted.

Research skills are also highly valued in the world of work. Many careers rely on quantitative and/or qualitative research to solve complex problems, from engineering and medicine to finance and marketing. Therefore, learning how to conduct mathematical research effectively is a valuable skill for the future.

Check out the following resources to delve deeper into the subject:

• Book: "The Use of Research in the Classroom: A Resource for Teachers", by Jo Boaler. Available in libraries and bookstores.

• Website: Khan Academy, an online educational platform that offers free math and other subject lessons. Link to the website

• Video: "The Importance of Mathematical Research", available on YouTube. Link to the video

Practical Activity: "Mathematical Research in Action"

Project Objective

The objective of this project is for students to conduct mathematical research on a topic of their interest. In addition to acquiring knowledge in a specific field, students will learn to read, interpret, and conduct basic research, fostering collaboration, critical thinking, and time management.

Project Description

Groups, composed of 3 to 5 students, must choose a research topic. The topics can be diverse, such as the application of mathematics in sports, art, cooking, the environment, etc. Once the topic is chosen, the groups must develop a research project that includes formulating the problem, data collection, analysis, and interpretation of results.

Necessary Materials

• Paper and pencil for notes
• Computer with internet access for research
• Books and other reference materials

Project Step-by-Step

1. Group Meeting and Selection of Research Topic: Students should gather and choose a topic of their interest that involves mathematics. The groups should justify why they chose the topic and how they think mathematics applies to it.

2. Development of the Research Project: The group must develop the research project. They should formulate the research question, define the methods that will be used to collect and analyze data, and create a work schedule.

3. Data Collection: The group must collect data related to their research topic. They can use various sources, such as books, magazines, internet sites, interviews with experts, etc.

4. Data Analysis: Students must analyze the collected data and interpret it using appropriate mathematical tools. They can use graphs, tables, calculations, etc., to represent and understand the data.

5. Writing the Research Report: The group must write a research report that includes the following topics: Introduction, Development, Conclusions, and Bibliography.

   • Introduction: Should contain the research topic, the relevance of the topic, and the research question.
   • Development: Should explain the data collection method, the analysis and interpretation of data, and discuss the results obtained.
   • Conclusions: Should summarize the main points of the research, discuss the learnings obtained, and draw conclusions about the project.
   • Bibliography: Should contain all sources of information used in the research.

Project Deliverables

Each group must deliver:

• The written research report. This document is a fundamental piece that should highlight their discoveries and analyses of the research project.
• At the end of the project, each student must reflect on the experience and write a brief essay (1-2 pages) about what they learned during the process and how it affected their perception of mathematics and research.

Remember, the purpose of this project is not only the final product but also the learning process. Therefore, it is important for students to document not only their results but also their reflections, discoveries, and challenges along the way.