LBR Resources
Mathematics
Insights
Nature of Mathematics
- Mathematics is the elegant language of the material universe.
SUGGESTED REFLECTION QUESTION
- What is the value and function of mathematics?
- “The laws of nature are written in the language of mathematics.” (Galileo)
- Mathematics is the lens that allows us to see patterns in the world that may otherwise remained undetected. We find math in nature, art, and technology.
- Math is not about fast calculations but deep understanding and sound reasoning.
- Among the four stages of doing mathematics, computation is but one and is not even the most important one. The four stages are: (a) posing a mathematical question based on data, (b) constructing a mathematical model or formulation to answer the question, (c) performing the mathematical calculation, and (d) verifying the findings by going back to the real world.
SUGGESTED REFLECTION QUESTION
- In what ways does a mathematical model illuminate–and in what ways does it distort?
- Not everything that can be counted counts, and not everything that counts can be counted (Attributed to Albert Einstein).
SUGGESTED REFLECTION QUESTION
- What are the limitations of mathematics?
- Even if we often think that “numbers don’t lie,” our decisions about which quantitative data to use and how to interpret and present them can misrepresent reality.
SUGGESTED REFLECTION QUESTION
- How accurate and objective are numbers? What are the limitations of mathematics?
- Mathematical situations can be represented verbally, numerically, in tables, symbolically, or graphically. We need to make thoughtful choices regarding which form can best interpret or communicate information.
SUGGESTED REFLECTION QUESTION
- Which representation is most useful in this situation? Which representation can best tell the story of this relationship, pattern, trend, etc? Is there a representation that can make the significant relationships more obvious?
Problem Solving
- There can be more than one way to solve a mathematical problem and even to arrive at the same solution, with some solutions more efficient than others.
SUGGESTED REFLECTION QUESTION
- Which of the following solutions is best? Why?
- A quantity can be represented numerically in many ways. Which one to use depends on what is the most useful representation for a specific situation.
SUGGESTED REFLECTION QUESTION
- What does this equation “look like”?
Descriptive Statistics
- There are faces and stories behind the numbers.
SUGGESTED REFLECTION QUESTION
- Whose stories are being told by these numbers? Whose stories are not?
- Disaggregates data tell a different story. Aggregated data can hide information.
SUGGESTED REFLECTION QUESTION
- Which stories do these numbers tell? Whose stories do we never hear?
