## It’s A Math, Math World (Communication Skills II)

From various conversations I have had with industry professionals and college professors, I have been told, overwhelmingly, that good, solid communication skills are the most important skills in the mathematical sciences. These include a good grasp of the English language (in most countries) and the ability to clearly explain complex and sometimes abstract topics in concrete terms. Yet, these skills are often lacking in my observations of today’s students in mathematics and statistics.

As stated above, these problems can be categorized into 2 groups:

- Insufficient written/oral communication skills (see blog dated 07/18/10).
- Inability to explain complex and abstract concepts adequately (which we will cover today).

This week, we will look at the inability of some mathematicians/scientists to adequately explain abstract or complex ideas. I think this boils down to some flaws in our education system:

- Math has been”dumbed-down” so that graphing calculators replace logic and work. Students miss the ability to think logically as in the study of geometry. I have tutored math since 1991 and I have had students who can plug in numbers into a calculator and work all the fancy functions, yet can’t explain why a process works or explain their answer in context. They can’t explain their answer and what it means. That is why I love the 2-column proofs in Geometry class that most of my students dread. These problems force you to reason and think logically. There is something to be said for going through a problem manually and writing each step down, including the formulas. It helps one learn faster and organize their work.
- Also, there was, in some schools, an acceptance of what is known as “fuzzy math” for basic math answers. For example, students in some New York City schools were told, as long as they got approximately the correct answer on an arithmetic test, that was sufficient and they would get credit. I believe in partial credit in more advanced classes since anyone can make basic math errors on tough tests, but if the test is concerning ARITHMETIC, the answer is supposed to be CORRECT! You have to master the basics before you can move onto the harder material. I have seen HS students who can’t do 7 x 8 without a calculator. That is pathetic!
- “There is a shortage of math and science teachers”, we are always told. I can go one step further…..there is a shortage of COMPETANT math and science teachers. For example, in some schools, teachers are teaching math and science who are not certified in that topic. This is a huge mistake. We should insist that teachers of advanced topics be certified in that topic! Also, there are just too may teachers that are not passionate about what subject they are teaching and trust me, a student will pick up on this immediately! I could get into a huge dissertation on weaknesses in the education system (i.e. tenure, lack of merit pay, acceptance of mediocrity, etc.), but I will leave this part for your comments.

A couple of observations from my past education in HS math classes:

- I can point to a great teacher I had in HS for geometry. He went to a military school for 4 years as a teenager and was extremely sharp and disciplined. He told us one day 1 of class that he expected us to know all of our definitions and theorems or we would likely fail his class! He drove us to dig deep within ourselves and work hard, yet he was tough but fair. He helped me develop my drive to be a mathematician and statistician and made me disciplined in my approach to learning new concepts. He was one of my favorite teachers of all time.
- Also, when I went to high school, students only required 1 year of Math to graduate, but you were required to have 4 years of Physical Education. A guess a healthy body trumped a sharp mind! If you were going to college, you needed 4 years of math. Math helps you problem solve and think about the world. In my opinion, everyone should study math or math-related science classes for 4 years in high school.

Some questions to ponder:

- In general, do you agree that math has been “dumbed-down” by the schools and by the use of graphing calculators, “fuzzy math”, etc.? Why or why not?
- To reward the most motivated and gifted teachers, should merit pay be instituted? Why or why not?
- To “weed- out” the inefficient teachers, should tenure be abolished? Why or why not?
- Do you agree that everyone should have a strong understanding (3-4 years) of HS math or math-based applications to help their reasoning abilities? Why or why not?

I look forward to your comments and to a lively discussion. Thank you.

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