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Critical Mathematical Thinking: A Guide for Parents and Teachers

In today’s rapidly changing world, mathematics plays a crucial role in our daily lives.

Using maths critically allows us to consider complex personal and socio-political issues, such as health, the economy and the environment, says Professor Kim Beswick, Director of the Gonski Institute and Head of the School of Education at UNSW. It helps us make informed decisions about various aspects such as food, time, costs, and more. However, these decisions often go beyond simple mathematical calculations and have broader societal implications. As parents and teachers, it’s essential to understand the significance of critical mathematical thinking in education and how it can empower our students to become more engaged citizens.

Prof. Beswick is partnering with a team of national and international experts on an Australia Research Council (ARC) project DP220101015, ‘Enabling students’ critical mathematical thinking’which will generate new insights into teaching practices that can promote or inhibit students’ development of critical mathematical thinking.

Introducing children to new mathematical concepts through more complicated problems – “the good stuff” – without so many broken down steps, rather than starting with easier problems and getting progressively more complex, is one possible approach, she says.

“Focusing only on the maths, separate from its applications, results in students thinking maths is irrelevant and, for too many, not something they want to pursue.”

Mathematics Beyond Calculations

Mathematics education isn’t just about solving equations and performing calculations. It goes far beyond that. Developing children’s critical mathematical thinking skills is the key to sound decision-making and problem-solving. Critical mathematical thinking involves using mathematical techniques and reasoning across different contexts, finding patterns, forecasting outcomes, and solving complex national and international challenges.

Teachers’ beliefs around student capability also affects their approach to teaching, including their likelihood to teach in a way that fosters critical maths thinking, says Professor Beswick

Seeing the Bigger Picture

Critical mathematical thinking encourages students to consider the consequences of proposed solutions, both socially and ethically. It teaches them to think beyond mathematical formulas and explore various factors that influence decisions. For instance, students can learn to analyze whether residents of flood-affected areas should accept the government’s offer to buy back their properties. They realize that while the mathematical aspect might suggest it’s a good deal, there are other considerations like finding a new home, social networks, and schooling options to think about.

Questioning Information and Assumptions

One of the core elements of critical mathematical thinking is encouraging students to question how information is presented or framed. In real life, situations are often messier than math problems. Critical mathematical thinking prompts kids to consider the assumptions made and recognize their limitations. It inspires them to ask the right questions: “Do I have all the information I need? What don’t I know? What should I ask? How can I find additional information?” This type of thinking also encourages students to consider the motivations and vested interests behind the information they encounter in the media.

Empowering Young Minds

Critical mathematical thinking goes beyond preparing students for STEM (Science, Technology, Engineering, and Mathematics) careers. It empowers them to be active, informed citizens who can make better arguments and understand medical treatment, financial advice, and government policies. It equips them to engage in society and ask meaningful questions, fostering an inquisitive and well-rounded approach to decision-making.

Challenges in Math Education

Many students struggle with mathematical reasoning. Traditional teaching methods tend to focus on routine algorithmic procedures, which can lead to a lack of depth in understanding. Additionally, teacher shortages exacerbate this issue, as students often learn from educators who may not specialize in mathematics.

Promoting Critical Mathematical Thinking

As parents and teachers, we can promote critical mathematical thinking by introducing students to more complex problems and emphasizing conceptual understanding. Instead of starting with simpler problems and gradually moving to more complex ones, we can present students with challenging problems from the beginning. This approach encourages students to explore mathematical concepts in depth and see the real-world relevance of mathematics.

Beliefs about Student Capability

Our beliefs as parents and teachers significantly influence our students’ mathematical education. High expectations and providing the necessary support are essential. Rather than closing doors for struggling students, we should aim to help them catch up and understand mathematical concepts from different perspectives.

Inspiring the Next Generation

Our role as parents and teachers is not just to teach mathematics but to inspire a lifelong passion for the subject. We can show students how mathematics can be used to make informed decisions on both personal and societal levels. By demonstrating the relevance of mathematics in the real world, we can inspire more students to study the subject. By promoting critical mathematical thinking, we can equip our students with the tools they need to become informed and engaged citizens, making a positive impact in the world. It’s not just about numbers; it’s about shaping the future.