By Professor Waleed Deeb

The age-old question remains: To teach math or not to teach math? To answer this, we must explore who truly needs mathematics and how it serves individuals and society.

The Debate: Is Mathematics Necessary?

Questions like, why do we learn math? How can we apply this to our day-to-day life, and other variations of those questions, are usually used to minimize the importance of learning mathematics.  

In a New York Times article titled "Is Algebra Necessary?".

Professor Andrew Hacker argues that the math taught in classrooms may lack relevance to real-world quantitative reasoning. Hacker provocatively states that mastering abstract equations, such as

(x2+y2)=(x2−y2)2+(xy)2x2+y2=(x2−y2)2+(xy)2

does not inherently lead to better political insight or social analysis. Instead, he concludes that mandatory mathematics might stifle young talent by prioritizing rigor over innovation.

This skepticism is counterbalanced by scholars like Professor Peter Braun, who asserts that "Without mathematics, our civilization would collapse."

Mathematics as a Universal Requirement

Regardless of their field of study—whether in science, medicine, sociology, or business—students are required to demonstrate mathematical proficiency through standardized tests like the GMAT, MCAT, LSAT, or GRE. These tests include significant math sections, underscoring the discipline's perceived importance in developing critical thinking and problem-solving skills.

However, this raises a valid concern: do all students need this level of math? Or more importantly, do they need the type of math currently being taught?

The Challenges of Math Education

Mathematics is often cited as one of the most challenging subjects for students. It significantly impacts academic retention and success rates. This brings us to a pivotal question: Is the issue inherent to mathematics, or does it lie in how the subject is taught?

Global Insights: Learning from Singapore

Many countries are adopting new mathematics curricula that prioritize critical thinking, problem-solving, and other essential skills for the modern world. Singapore's groundbreaking initiative in 1997, led by then-Prime Minister Goh Chok Tong, emphasized moving away from rote memorization to fostering thinking skills under the philosophy that "schools that think lead a nation that learns." This model has inspired reforms globally.

The United States adopted the Common Core State Standards, focusing on understanding concepts and applying mathematical reasoning. This initiative seeks to help students analyze problems and understand principles, emphasizing the importance of reasoning in various contexts: “The standards ensure students learn to apply math, not just memorize formulas”

In the United Kingdom, curriculum enhancements are integrating computational tools like programming and spreadsheets, aiming to foster "general quantitative literacy." The Royal Society has highlighted the need for these changes, noting, “Students must be prepared for a world driven by data and technology”  

Estonia, now a global leader in education, has introduced a balanced curriculum emphasizing problem-solving, entrepreneurship, and digital competence. This reform has made Estonia one of the top-performing countries in Europe. As one observer remarked, “Estonia’s curriculum proves how much education systems can achieve with the right focus”.

These initiatives highlight a global shift toward mathematics education that prepares students not just to compute but to think critically and solve real-world problems, taking inspiration from the successes of pioneers like Singapore.

Contrasting this, critiques of traditional teaching methods highlight the pitfalls of a "drill-and-kill" pedagogy. Harold Fawcett's work from 1938 proposed transforming classrooms into environments that promote critical thinking, a concept still relevant today.

The Role of Critical Thinking in Math Education

Historically, mathematics has been a cornerstone of critical thinking. Philosophers like Plato and Aristotle were also mathematicians because math sharpened their reasoning skills. Today, the emphasis should not be solely on solving complex equations but on fostering the thought processes that mathematics demands. A lawyer, for instance, may never need to calculate the diagonals of a 25-sided polygon but will benefit immensely from the analytical skills math develop.

How to Teach Math Effectively

To make math education meaningful, we must shift our focus from memorization to critical thinking. Here are ten principles for teaching math to encourage critical thinking:

1. Encourage Discovery: Let students derive formulas rather than memorizing them.

2. Foster Multiple Solutions: Allow and compare different problem-solving methods.

3. Embrace Critique: Welcome criticism of solutions, including your own.

4. Promote Creativity: Encourage students to create their own problems and solutions.

5. Apply to Real Life: Relate math concepts to practical, real-world scenarios.

6. Evaluate Thought Processes: Focus on how students arrive at answers, not just the answers themselves.

7. Analyze Complexity: Break down complex problems for deeper understanding.

8. Visualize Problems: Use diagrams and shapes to clarify concepts.

9. Be Innovative: Continuously seek and implement new teaching ideas.

10. Model Critical Thinking: Demonstrate critical thinking in your teaching methods.

How NOT to Teach Math

Equally important is identifying ineffective practices that hinder critical thinking. Here are ten ways NOT to teach math:

1. Encourage Memorization: Simply give students formulas to memorize without understanding their origins or applications.

2. Promote Rigid Thinking: Insist there is only one way to solve a problem.

3. Discourage Patience: Rush students for answers without allowing them time to think.

4. Focus Solely on Computation: Emphasize mechanical computation over reasoning and conceptual understanding.

5. Prioritize Answers Over Methods: Value correct answers more than the thought process behind them.

6. Avoid Challenging Questions: Use straightforward questions that don’t require deeper analysis.

7. Repeat Classroom Problems on Tests: Limit assessment to questions already solved in class, reducing the need for independent thinking.

8. Provide a Fixed Question Bank: Give students a set number of questions, implying the test will only draw from these examples.

9. Reject Challenges: Dismiss students' alternative solutions or critiques of your methods.

10. Propagate Negativity: Tell students that math is inherently disliked but mandatory to learn.

Conclusion

Mathematics is not merely a subject to be learned but a skill to be cultivated. By avoiding ineffective teaching practices and prioritizing critical thinking, we can ensure students not only succeed in math but also carry essential problem-solving skills into their future endeavors. If we, as educators, fail to model and nurture critical thinking, how can we expect our students to develop it?

Mathematics matters—not just for its content, but for the intellectual habits it fosters. Let’s ensure we teach it in a way that truly prepares students for the complexities of the modern world.

References:

After 30 years of reforms to improve math instruction, reasons for hope and dismay. Center for Education Policy Research at Harvard University. (2021, February 4). https://cepr.harvard.edu/news/after-30-years-reforms-improve-math-instruction-reasons-hope-and-dismay  

Pickard, J., & Jack, A. (2024, September 2). Maths education in UK schools needs to be revamped, says Royal Society. Subscribe to read. https://www.ft.com/content/07450024-a2b2-476c-8f7a-e336a7747827?utm_source=chatgpt.com

‍

Sylvester, R. (2024, November 22). Estonia’s curriculum is one of the best - what can it teach us? The Times & The Sunday Times. https://www.thetimes.com/uk/education/article/estonias-curriculum-is-one-of-the-best-what-can-it-teach-us-l56hmdxq0?utm_source=chatgpt.com&region=global  

‍