The curse of mathematical reasoning refers to the tendency for individuals to rely too heavily on logical reasoning and mathematical calculations without considering other relevant factors. While logical reasoning and mathematical calculations are important tools for problem-solving, they are not always sufficient for making informed decisions or understanding complex situations. Mathematical reasoning is based on the principles of logic and uses formulas and equations to find solutions. It relies on abstraction and simplification to break down complex problems into manageable parts. However, this approach can sometimes oversimplify reality and overlook important factors that cannot be easily quantified or measured. By focusing solely on mathematical reasoning, individuals may fail to consider subjective factors, such as emotions, values, cultural differences, and contextual information.
By focusing solely on mathematical reasoning, individuals may fail to consider subjective factors, such as emotions, values, cultural differences, and contextual information. They may also overlook the limitations and assumptions of the mathematical models they are using, leading to flawed results or solutions that are not applicable in real-world situations. The curse of mathematical reasoning can also lead to a narrow perspective or tunnel vision, where individuals become fixated on finding a single "correct" solution without exploring alternative possibilities or considering the potential consequences of their actions.
The Curse of False Expertise
A growing body of research reveals details of the “Curse of Expertise” in which it is shown that as an individual’s level of expertise increases, their ability to communicate their knowledge to a novice declines. The extent to which an expert assumes information to be common knowledge can be so large that they fail to see the gaps which exist in the understanding of a novice. The take-away is that the expert needs to consciously think like a novice and be deliberate in seeking an understanding of where the novice’s knowledge of a subject strikes its limit.
Physicist and author, Richard Feynman could be considered a master at overcoming the curse of expertise. He understood that the best indication of a truly deep understanding of a concept was revealed in one’s capacity to describe it to a child. His advice: "When we speak without jargon, it frees us from hiding behind knowledge we don’t have. Big words and fluffy “business speak” cripples us from getting to the point and passing knowledge to others.” Feynman understood that his expertise would prove to be a barrier to his students learning and that as such he would need to take actions to ensure his knowledge was accessible; something all educators should do.
But what if our expertise is imagined or false. What if what we think is so, just ain't so. This might be more common than we care to admit, and it is worth considering the source of this difficulty and its implications.
Not just what we were taught but also the way that we were taught things in school shapes our beliefs about what matters, and these messages can be hard to undo. Consider the average mathematics class that the typical teacher experienced when they were forming an understanding of what mathematics is all about. The emphasis was almost certainly on accurate calculations and application of prescribed methods which would result in the correct solution. Today that teacher is likely to believe that mathematics demands this sort of knowledge and that an expert mathematician is one who can quickly and accurately perform calculations. The trouble is this is false expertise as revealed by comparing these beliefs with the way that maths is described by a modern syllabus; "Mathematics is a reasoning and creative activity employing abstraction and generalisation to identify, describe and apply patterns and relationships….The study of mathematics provides opportunities for students to appreciate the elegance and power of mathematical reasoning and to apply mathematical understanding creatively and efficiently.” (NESA, 2017) In place of speedy and accurate calculation the syllabus speaks of “enjoyment”, active participation” and “challenging and engaging experiences”.
The same is undoubtedly true of other disciplines. If you spent time in a typical Science classroom you would likely believe that the work of a scientist revolves around correctly filling in a science lab report. The emphasis of the learning is on accurately filling in the template and a knowledgeable scientist would know the template by heart. In History the lessons seemed to revolve around remembering a list of dates, names and places and expertise could be measured by the number of facts which one might recall on demand. Somehow this does not fit with the rationale for the study of History according to the syllabus: "History is a disciplined process of inquiry into the past that helps to explain how people, events and forces from the past have shaped our world.” And if Geography is a “rich and complex discipline" that “build(s) a holistic understanding” and "is the study of places and the relationships between people and their environments”, how does it get reduced to knowing where you find Muscat on a map. False Expertise.
The implication of this unquestioned false expertise is that it becomes self-repeating. We believe that our knowledge base and underlying beliefs about the disciplines we teach are sound. Our teaching methods are founded upon this knowledge and these beliefs and so we present our students with a view of learning within these disciplines which is aligned with them. We perpetuate false expertise.
We must unlearn and relearn what we know and in doing so question the beliefs upon which our expertise is constructed. We need to examine closely the rationales for what we teach and understand deeply the concepts our students are needing to learn. We need to ask always, What will students actually do with the skills and knowledge they are acquiring and what underpins my belief that this learning will matter in the lives they are likely to live.
The implication of this unquestioned false expertise is that it becomes self-repeating. We believe that our knowledge base and underlying beliefs about the disciplines we teach are sound. Our teaching methods are founded upon this knowledge and these beliefs and so we present our students with a view of learning within these disciplines which is aligned with them. We perpetuate false expertise.
This can hinder creativity, innovation, and critical thinking. To avoid falling into the curse of mathematical reasoning, it is important to recognize the limitations of mathematical models and logical reasoning alone. Decision-making and problem-solving should involve a balance of quantitative analysis and qualitative considerations. This may include gathering and integrating data from various sources, engaging in discussions and consultations with others, considering multiple perspectives, and taking into account the values and context of the situation. By embracing a more holistic approach to problem-solving, individuals can overcome the curse of mathematical reasoning and develop a deeper understanding of complex issues. They can also make more informed decisions that consider a broader range of factors, leading to more effective and sustainable outcomes..
Reviews for "The Curse of Mathematical Reasoning: Embracing Ambiguity in Problem-Solving"
1. John - 2 stars - I was really disappointed with "The Curse of Mathematical Reasoning". I had high hopes for an engaging and thrilling read, but instead, found the plot to be confusing and convoluted. The author seemed more interested in showcasing their mathematical knowledge rather than crafting a cohesive and compelling story. Additionally, the characters lacked depth and I had a hard time connecting with any of them. Overall, I would not recommend this book to others.
2. Sarah - 1 star - "The Curse of Mathematical Reasoning" was a complete letdown. The writing style was dry and monotone, making it difficult to stay engaged with the story. The author's attempt to intertwine math concepts and mystery fell flat, as it came across as forced and unnatural. The pacing was also incredibly slow, and it felt like nothing significant happened until the last few chapters. I struggled to finish this book and would not recommend it to anyone looking for an exciting and well-written mystery novel.
3. David - 2 stars - As someone who enjoys both math and mystery, I was excited to read "The Curse of Mathematical Reasoning". Unfortunately, the execution left much to be desired. The story felt disjointed, with random mathematical explanations thrown in without any relevance to the plot. The characters were poorly developed, and their actions often didn't make sense. I felt like the author was trying too hard to impress readers with their mathematical knowledge, ignoring the need for a cohesive and engaging story. Overall, I was disappointed by this book and wouldn't recommend it to others.
4. Emily - 1 star - "The Curse of Mathematical Reasoning" was a confusing and tedious read. The author's attempts to blend math and mystery led to a convoluted plot that was hard to follow. The constant mathematical explanations disrupted the flow of the story and made it difficult to stay engaged. Additionally, the characters were one-dimensional and lacked depth, leaving me uninvested in their outcomes. I had high hopes for this book, but unfortunately, it fell short in almost every aspect. I cannot recommend it to others.