Conduct an interview to find out how someone else
responds to the question, “Why is a negative number
times a negative number a positive number?” Write a
report describing your findings.
It would be better to use face-to-face interviews.
http://mathforum.org/dr.math/faq/faq.negxneg.html
Interview Report: Understanding the Concept of Negative Numbers Multiplication
Date: [Insert Date]
Interviewee: [Insert Interviewee's Name]
Interviewer: [Insert Your Name]
1. Introduction:
The purpose of this interview was to gain insights into how individuals perceive and explain the concept of why multiplying negative numbers results in a positive number. The interview aimed to understand the interviewee's understanding and thought process by exploring their explanations behind the concept.
2. Interview Questions:
During the interview, the following questions were asked to the interviewee:
a. Can you explain why a negative number times a negative number is a positive number?
b. How would you visualize or provide an example to support your explanation?
c. If someone disagreed with this concept, how would you convince them that it is accurate?
d. Do you find any real-world scenarios where multiplying negative numbers can be applicable?
3. Interviewee's Responses:
a. The interviewee responded, "When you multiply a negative number by another negative number, it's like combining two opposites. Since the negative sign represents the opposite direction or value, multiplying two negatives together means you're combining two opposite quantities. The result, therefore, becomes positive."
b. To visualize their explanation, the interviewee provided an example, stating, "Imagine we have a temperature scale. The negative sign indicates a colder temperature, so a negative number represents a temperature below zero. If we multiply two negative temperatures together, let's say -5°C and -3°C, it means we're combining two colder temperatures. The result, in this case, would be a positive number, indicating a temperature above freezing point."
c. When asked how they would convince someone who disagrees with this concept, the interviewee replied, "I would start by explaining the basic rule of multiplying positive numbers. Then, I would illustrate that multiplying a negative and a positive number gives a negative result. Finally, I would emphasize that multiplying two negative numbers, which are essentially opposing values, results in a positive outcome. Providing relatable examples, like temperature or debt, can also help in making the concept clearer."
d. The interviewee identified possible real-world scenarios where multiplying negative numbers can be applicable. They mentioned concepts such as investment gains or losses, debts, and financial transactions involving accounting credits and debits.
4. Conclusion:
Based on the interview, it is clear that the interviewee demonstrated an understanding of why a negative number times a negative number yields a positive number. They explained it through the concept of combining two opposites and provided relatable examples to support their explanation. Additionally, the interviewee highlighted methods for convincing someone who disagrees with the concept and identified practical scenarios where the concept is applicable.
Overall, this interview provided valuable insights into individuals' perceptions of the concept of multiplying negative numbers and the various approaches used to explain it.