See also the
Dr. Math FAQ:
why study math?
3D and higher
Browse Middle School About Math
Stars indicate particularly interesting answers or
good places to begin browsing.
Selected answers to common questions:
Art and mathematics.
Law and mathematics.
Medicine and mathematics.
Music and mathematics.
Poetry and mathematics.
What is mathematics?
Was math invented or discovered?
- About Basic Geometry [10/14/1998]
Who developed basic geometry? What is it used for? Who uses it?
- Art and Mathematics [2/8/1996]
Do you know ways that art can be linked to mathematics?
- Definition of Opposite Sides [01/18/2001]
What is the formal definition of 'opposite sides' of a polygon? Does a
regular pentagon have opposite sides? Does a concave polygon have
opposite sides? How can we define it consistent with our intuition?
- Difference Between Math and Arithmetic [11/06/2001]
My students haven't heard the word arithmetic. No one seems to be able to
tell the difference, if there is one, between arithmetic and mathematics.
Is there a difference, and what is it?
- How Can Math Be Made More Interesting? [08/30/2001]
What can I do to help me be more interested in math?
- Mathematics in the Applied Sciences [02/24/1997]
How do civil engineers and others use math in their work?
- More Methodical Than Guessing [06/12/2017]
A young adult who prefers clear procedures struggles with guessing to calculate square roots and factor polynomials. Distinguishing between operations and algorithms, Doctor Peterson surveys a range of methods for finding roots and factoring — some of which require no guessing, others of which involve approximating — before emphasizing the intuition that develops with perseverance.
- The Number e [6/3/1996]
Is "e" a number like Pi? How does "e" relate to continued fractions?
- Numbers: Cardinal, Ordinal, Nominal? [10/25/1999]
Which group of numbers - cardinal, ordinal or nominal - does "time" fit
into? Are there other types of numbers as well?
- Purpose of Algebra [10/15/1996]
What is the purpose of algebra and who came up with the idea?
- Ten Commandments of Math [07/05/1997]
What are the Ten Commandments of Math?
- The Third Millennium [01/23/2000]
When does the Third Millennium begin? Are there any inherent predictions
or unverifiable assumptions within math?
- What is Calculus? [05/06/1997]
What is calculus and how does it work?
- Why Does Math Need Proofs? [03/24/2000]
Why does math need to have proofs?
- Why Is Math Important? [01/02/2002]
Some of it we don't need to know in the real world, so why do they teach
us things we won't need to know?
- Why Study Practical Geometry? [04/26/1997]
What can I do to help my students to see just how important Geometry and
all Math is?
- Why There are 12 Tones in a Scale [12/28/2000]
Why are there 12 tones in an octave? Can you explain the significance or
the equation r^n = 2^m? Also, what's so special about a fifth? Why should
the scale be based on the fraction 3/2?
- Wording Division Problems [08/10/1998]
How would you clarify the wording of division problems like "divide into"
or "divide by"?
- Year 2000 (Y2K) Problem [07/26/1998]
Can you explain the Year 2000 problem in layman's terms? Why is it so
hard to fix?
- 1, 2, 3, ... as Varied as Arabic, Roman, ... Yoruban? [10/08/2011]
A researcher familiar with an African language's words for its counting numbers wants
to know what symbols its native speakers use to write them. Through analogies to Latin and French -- and English etymologies -- which show the distinction between speech and writing, Doctor Peterson explains why a numbering system unique to the Yoruban language likely does not exist.
- Are Calculators Smart? [06/02/2001]
How come calculators are so smart?
- Are Math Symbols Universal? [05/22/2004]
Do Russian math students use the same math symbols that Americans do?
For example, do they use '+' for addition?
- Are Subtraction and Division Commutative and Associative Operations? [05/15/2008]
I don't agree that subtraction and division are not commutative
operations. If we define a - b as a + (-b), then it commutes correctly
into (-b) + a. So why does everyone say subtraction is not commutative?
- As Big As vs. Bigger Than [09/05/2015]
Fifth graders misinterpret the wording of magnitude comparison questions —
or do they? Doctor Peterson discusses the ambiguity before proposing a way forward.
- Avoiding Careless Mistakes [01/30/2002]
How can I avoid careless mistakes?
- Careless Mistakes [02/04/2002]
When it asked me for the range, domain, and inverse of ordered pairs, I
just put the inverse because I misread the question...
- Checking Your Work [9/9/1996]
I've had problems keeping myself from making little mistakes like not
putting commas in, putting the decimal point in the wrong place, and
writing down the wrong number... How can I stop doing this?
- Chefs and Algebra [02/05/2002]
I hope to become a chef someday, and I would like to know how algebra
(specifically polynomials, the quadratic formula, factoring, etc.) could
possibly relate to my future career and my life beyond high school.
- Congruence Considerations [05/30/2015]
When we think and talk about congruence, which properties actually matter? Does
congruency even apply to things in the real world? Doctor Peterson answers with
examples — and an emphasis on abstraction.
- Connecting Algebra and Geometry [07/11/2002]
What are the mathematical connections between algebra and geometry?
- Decimals Versus Fractions: Pluses and Minuses [08/19/2011]
We already have fraction notation, so what's the point of decimals? A new teacher
relaying this question from her middle schoolers wonders if, like other formal
representations in math, decimals just amount to another "shorthand." Comparing
notational systems to tools, Doctor Ian responds with the various computational
advantages and disadvantages of fractions and decimals, before concluding that
different tools suit jobs differently.
- The Difference between Science and Mathematics [09/18/2006]
Is there any difference between a science project and a math project?
We have a science fair coming up and I wanted to do some math, but my
friend says that the scientific process is very different from math.
- Doctors and Math [10/27/1998]
How do doctors use math?
- Don't Use Calculators [12/18/2000]
When children should not use calculators to do math.
- Do We Really Need to Learn Math? [11/19/2002]
Why do we need to know math if we can have a calculator do it?
- Estimation in 3rd Grade [12/16/1996]
How do you learn to estimate? What is its importance?
- Etymology of the Word Mathematics [12/10/2001]
Why do you call maths maths?
- The Fairness of Democracy [09/16/1998]
What are some ideas to think about with regard to the fairness of
- Forgetting and Remembering, Re-inventing and Explaining [02/19/2011]
A student has a knack for learning math easily -- and then forgetting it just as quickly.
To improve her recall, Doctor Ian offers two analogies to skills from his own life, then
two strategies for deepening understanding, and in the process reveals why many
other math doctors volunteer with Ask Dr. Math.
- Help in Studying for Math [08/17/1999]
I was wondering if you had any suggestions or comments that might help me
out a little bit.