In this article, we dive into a fascinating exercise involving number sequences. This activity is designed to show us why it’s important to question our assumptions and look for information that challenges what we think we know.
The exercise starts with a simple challenge: figure out a rule based on a sequence of three numbers. The first sequence given is 2, 4, 8. Participants are asked to suggest their own sets of three numbers. The facilitator then says “yes” or “no” to indicate if the numbers follow the hidden rule.
Participants quickly start suggesting different sequences. For example, sequences like 16, 32, 64 and 3, 6, 12 get a “yes,” meaning they fit the rule. However, when someone suggests 10, 20, 40, they are told it fits the rule but isn’t the rule the facilitator is thinking of.
As the game goes on, participants keep guessing sequences, often using a pattern of multiplying by two. Even though they get “yes” answers, they struggle to find the actual rule. The facilitator encourages them to think carefully and look for clues that might lead them to the right answer.
After many guesses, a breakthrough happens when someone suggests 10, 9, 8, which doesn’t follow the rule. This leads to a discussion about whether the numbers need to be in ascending order. The facilitator confirms this, revealing that the rule is simply that the numbers must be in increasing order.
This exercise is like a metaphor for how we learn and understand things in life. The facilitator takes inspiration from Nassim Taleb’s book, The Black Swan, which talks about how unpredictable events can be and how our theories can have limits.
One important lesson from the exercise is the value of looking for “no” answers instead of just “yes” ones. This idea is similar to the scientific method, where the goal is to test and possibly disprove theories. By actively searching for evidence that goes against our beliefs, we can get a clearer and more accurate understanding of reality.
In conclusion, the number sequence challenge shows us why it’s crucial to question our assumptions and be open to information that might contradict our initial beliefs. By adopting a mindset that values disproving theories, we can improve our critical thinking skills and gain a deeper understanding of the world around us.
Try creating your own sequences of three numbers and test them against the rule. Start with sequences like 5, 10, 15 or 7, 14, 28. See if you can figure out the rule by getting “yes” or “no” responses. Remember, the goal is to find sequences that both fit and don’t fit the rule to understand it better.
Work in pairs to come up with a hidden rule for number sequences. One student creates a rule, and the other guesses sequences to uncover it. Discuss the strategies used to identify the rule and how considering different possibilities helped in the discovery process.
Simulate a scientific experiment by forming a hypothesis about the rule and then testing it with different sequences. Document your findings and analyze which sequences support or contradict your hypothesis. Reflect on how this process is similar to scientific investigations.
Engage in a class discussion about the importance of questioning assumptions. Share examples from the number sequence activity where initial beliefs were challenged. Discuss how this approach can be applied to real-world situations and the benefits of seeking disconfirming evidence.
Create your own number sequence rule and challenge your classmates to discover it. Use creative rules such as sequences where the sum of the numbers is a prime number or where each number is a Fibonacci number. This activity will help you appreciate the diversity of possible rules and the importance of clear communication.
Numbers – Symbols or words used to represent quantities or values in mathematics. – In the equation $3 + 5 = 8$, the numbers 3, 5, and 8 are used to show a mathematical relationship.
Sequences – An ordered list of numbers that often follow a specific pattern or rule. – The sequence $2, 4, 6, 8, ldots$ follows the rule of adding 2 to the previous number.
Rule – A prescribed guide for conduct or action, often used to describe a consistent pattern in mathematics. – The rule for the sequence $1, 4, 9, 16, ldots$ is to square each consecutive integer.
Critical – Involving careful judgment or evaluation, especially in problem-solving or analysis. – Critical thinking is essential when solving complex algebraic equations to ensure all steps are correct.
Thinking – The process of considering or reasoning about something, often used in solving mathematical problems. – Logical thinking helps in determining the most efficient method to solve a system of equations.
Patterns – Repeated or recurring sequences or designs, often found in numbers or shapes. – Recognizing patterns in a set of numbers can help predict the next number in the sequence.
Ascending – Arranged in increasing order, often used to describe numbers or sequences. – The numbers $3, 7, 12, 18$ are in ascending order.
Theories – Systematic ideas or principles that explain phenomena, often used in mathematics to describe concepts. – The Pythagorean theorem is a fundamental theory in geometry that relates the sides of a right triangle.
Evidence – Information or data that supports a conclusion or theory, often used in mathematical proofs. – The evidence for the solution to the equation $x^2 = 16$ is that $x = 4$ or $x = -4$.
Assumptions – Statements accepted as true without proof, often used as a starting point in mathematical reasoning. – In solving the equation $2x + 3 = 11$, we make the assumption that $x$ is a real number.
