What You Can Learn from Thinking Mathematically by J. Mason

A Thinking Mathematically by J. Mason Guide by the University of Dating​

"Thinking Mathematically, 2nd Edition" is a mathematics book written by J. Mason, L. Burton, and K. Stacey, and was published by Pearson in 2010. This book aims to deeply explore mathematical thinking and problem-solving approaches, with a particular focus on the processes involved in mathematical thinking. It emphasizes the "ways of thinking" necessary for learning mathematics and offers guidance on how to solve or approach mathematical problems.

Content Overview​

1. Emphasis on Mathematical Thinking This book focuses not on mathematics as just a tool for calculation or memorizing formulas, but on developing mathematical thinking. Mathematical thinking involves understanding problems and logically deriving solutions. This approach is especially beneficial for students in the early stages of learning or for readers who want to deepen their understanding of mathematics.

2. Strategies for Problem Solving The book introduces various strategies for solving mathematical problems. For instance, methods for breaking down problems, relating them to other problems, and solving them through both intuitive and logical approaches are explained. This broad range of techniques helps readers find their own solutions.

3. Mindset for Learning Mathematics The book also touches on the mindset and attitudes needed for learning mathematics. It proposes approaches to overcome anxieties and fears towards mathematics, encouraging readers to enjoy learning it. For students who often find mathematics abstract and difficult, the book teaches the joy of "thinking" mathematically.

4. Concrete Problems and Practical Examples The book includes numerous concrete mathematical problems and examples, allowing readers to practice problem-solving. This helps them understand how the theories and strategies they have learned are applied in real problem-solving situations.

5. Developing Critical Thinking As suggested by the title "Thinking Mathematically," one of the book's main goals is not just to learn mathematical techniques but to foster critical thinking. It encourages readers to consider multiple perspectives on a problem, enhancing their ability to find the optimal solution.

Features of the Book​

• Holistic Approach: The focus is on "thinking" mathematically, rather than simply obtaining answers, and it emphasizes the process and methods of thinking.
• Progressive Learning: The content is structured in a way that allows gradual learning, starting with basic mathematical thinking and moving towards more advanced problem-solving techniques.
• Practical Exercises: The book provides numerous practical problems and exercises, encouraging hands-on learning.
• Application to Other Areas: Mathematical thinking is shown to be applicable not only to mathematics but also to everyday life and other academic fields, offering broad applicability of the learned concepts.

Chapter Summaries​

Here is an overview of each chapter in "Thinking Mathematically".

1. Everyone can start​

This chapter explains the starting point for approaching mathematics. The key message is that anyone can begin thinking mathematically. Mathematics is not a subject that requires special talent but can be approached by anyone as part of daily problem-solving. The chapter emphasizes that no special preparation or background is needed to learn mathematics, and everyone can start from the same point.

2. Phases of work​

This chapter discusses the various stages in the process of mathematical problem-solving. It explains that problem-solving is not instantaneous but progresses through multiple stages. For instance, understanding the problem, generating ideas, trial and error, and eventually reaching a solution. Skills and approaches necessary at each stage of problem-solving are introduced.

3. Responses to being STUCK​

This chapter addresses how to handle situations when you get "stuck" while solving a mathematical problem. It presents methodologies and attitudes for moving forward when you feel blocked. For example, it suggests stopping for a moment to recheck the problem, looking at it from a different perspective, or seeking advice from others as effective strategies.

4. ATTACK: conjecturing​

The focus of this chapter is on conjecturing—making predictions about the solution to a problem at the initial stages. The chapter emphasizes the importance of hypothesizing and how this can help guide the problem-solving process. Readers learn how to refine their conjectures as they proceed through the problem.

5. ATTACK: justifying and convincing​

This chapter discusses justifying and convincing—explaining why a mathematical approach or solution is valid. It stresses that mathematical reasoning and solutions must be logically justified and convincing, not just presented as opinions. The importance of proofs and logical explanations in mathematics is highlighted.

6. Still STUCK?​

The chapter continues from the previous one, focusing on how to deal with ongoing difficulties in problem-solving. It explores new methods for overcoming blockages and stresses the importance of persistence and creative thinking in resolving mathematical challenges.

7. Developing an internal monitor​

This chapter focuses on the importance of self-monitoring. It teaches the skill of assessing your own thought processes and the progress of your solutions while solving mathematical problems. Constantly questioning whether your answer is correct and evaluating your own approach is encouraged to help improve problem-solving abilities.

8. On becoming your own questioner​

This chapter emphasizes the importance of self-questioning. To deepen mathematical thinking, it is not enough to simply answer others' questions; you must also ask questions yourself to probe the essence of the problem. By constantly questioning your own thinking process, you can gain a deeper understanding and enhance your problem-solving ability.

9. Developing mathematical thinking​

This chapter explores how mathematical thinking is not just about performing calculations, but about understanding abstract concepts and systematically thinking through solutions to problems. It argues that developing mathematical thinking requires more than just memorizing answers; it involves recognizing the structure and principles behind problems.

10. Something to think about​

This chapter provides readers with thought-provoking content, offering an opportunity to consider how mathematical problems and their solutions can be applied to everyday life or related to other disciplines. It invites readers to reflect on how mathematical thinking intersects with other problem-solving skills.

11. Thinking mathematically in curriculum topics​

This chapter discusses how to apply mathematical thinking to various curriculum topics. It explains how mathematical thinking can be fostered and applied within educational contexts. The chapter shows that learning mathematics is not just about learning formulas but also about developing problem-solving and logical thinking skills.

Throughout these chapters, methods and mindsets for deepening mathematical thinking and improving problem-solving skills are clearly outlined.

Conclusion​

"Thinking Mathematically" is a book designed not just to teach mathematics but to help readers understand the mathematical way of thinking and enhance their problem-solving abilities. It is a valuable resource for developing mathematical intuition and logical thinking. Rather than limiting mathematics to the memorization of formulas and theorems, the book offers a learning experience that connects mathematics to real-life applications and other disciplines.

【Important】 For Those Who Want to Enjoy a Life Without Struggling to Find Dating Partners​

There are many people out there who, despite learning Problem Solving, waste their time by studying in a way that fails to connect their knowledge to creating meaningful shared experiences through dating.

We, on the other hand, have dedicated ourselves to learning in ways that truly connect to creating meaningful shared experiences through dating, and as a result, we’ve been able to enjoy a life where we never struggle to find dating partners.

Would you like to join us at the Dating University and focus on learning that directly connects to creating meaningful shared experiences through dating—and enjoy a life where dating partners are never in short supply?

Begin Your Journey Today​

"I want to live a life where finding a date is never a struggle."
If that’s how you feel — yet your daily life still feels stuck or unfulfilled — you’re not alone.
When even a hint of doubt or unease lingers in your heart, that’s the perfect time to reach out.
We invite you to take that first step.
Let us help you explore how the right kind of learning can turn dating into something natural — and transform your everyday life.