I wish people of all ethnicities would learn the meaning of ALL and SOME. All white cops aren’t racist pigs, and all black people are not thugs. In mathematics we use lots of symbols as a shorthand way of writing statements.

One of the symbols, ∀, means “for every,” “for each,” “for all.”

Another symbol, ∃, means “there exist(s),” or “there is at least one,” or “there are some.”

The symbol, ≠, means “is not equal to.”

Another symbol is ~, which means “it is not the case that” or “it is not true that.”

Another symbol, ∋, means “such that.”

For instance, if I say let x represent “a white police officer” and let y represent “racist.” Then I could make the statement: ∀x, x = y. (That reads, for EVERY white police officer, that police officer is racist.) That statement is FALSE, and we know it. But if I say:
∃x ∋ x=y (which reads there exist, or there are some white police officers such that those officers are racist.) That is a TRUE statement. I could write: ∃x ∋ x= ~y OR ∃x ∋ x≠y. (There exist white police officers such that those white police officers are not racist.) that is a TRUE statement.

Then I could say change it up and let x represent “black people” and let y represent “thugs.” I could use the same symbols to make the same three statements and they would still be false, true, and true…in that order.

I wish people of all ethnicities would learn the meaning of ∀ and ∃.

Life doesn’t grade on a curve. Your progress is not predicated on the progress of others. You either learn the lesson, or you repeat the lesson. It’s that simple. It doesn’t happen in life; and it doesn’t happen in my classroom. I refuse to perpetuate a culture of competition among students in a subject area that they ALL should MASTER. Be your own competitor! Let that last failed test be your competitor! Don’t look at what tests other people are passing. We can’t all get the best grades in the class; but we can all be the best we can be. Your test is for your path. Their test is for their path. Do you!

I’m not the only one who feels this way. Take a look at this article. Take it and apply it outside of the classroom. Peace!

A relative and I watched a show on television in which a woman said she did not think she could live without her husband. My relative’s response to the woman’s statement absolutely floored me. She said, “I don’t understand these people who say they can’t live without a person…how you can’t live without him when you had to meet him at some point?” Let that marinate for a few minutes….because I know you didn’t get it.

YOU had to meet him at some point!!!!

You had to MEET him at some point!!!!

You had to meet HIM at some point!!!!

You had to meet him at SOME point!!!!

You had to meet him at some POINT!!!!!

In case your brain is navigating in slow motion, let me break it down. If you met him (or her) at some point, then that means there was a time in your life that you did not even know him…and YET you lived! There was life before him or her. And just like you had to be introduced to him, there are some things that you do that you didn’t always do. You had to be introduced to these things. And there are some beliefs you hold that you didn’t always believe. You had to be introduced to those concepts. One of the things we have to do as mature people is assess the people, habits, and beliefs that we have embraced to determine whether our life…no not just our life, our LIVING…has been made better or worse because of them.

I have heard that there are three types of people in the world: 1) those that can help you, 2) those that can hurt you, and 3) those that can’t do anything for you. Remember, however, that this works both ways; so you have to decide in which of the three ways you want to affect the people around you. Do you add to the people in your life? Do you subtract from them (financially, emotionally, spiritually)? Or are you a non-factor in their lives?

Our goal should be to help as many people as we can and to be helped by as many people as we can. It is inevitable, though, that we will hurt people and we, ourselves will experience hurt. If you’re smart, some good can come out of experiencing hurt….that is, the lesson you learn from it. But remember, if they’re smart, the people you hurt are learning a lesson, too! The one kind of person we should avoid at all costs and avoid being is the kind that is a non-factor! The non-factor can’t help anyone and they can’t even teach a lesson through hurt. They’re just floating through life, letting life happen to them. They’re not affecting anything or anyone, and they’re not being affected by anything or anyone.

Now is a good time to assess your relationships, habits, and beliefs. If your life was better (happier, healthier, more financially stable) before you were introduced to him/her/it, then you need to remember that you did not always know him/her/it…and yet you lived!!!

Focus, foundation, follow-through, finish, and face!

One thing I don’t like to hear students say to me is, “I’m not like you; I hate math. You can’t expect me to understand it like you understand it.” To that I say something like, “Don’t use my success as a reason for your failure. Be patient and don’t give up.”

The two hardest lessons that I’ve learned as a teacher is that 1) you can’t help them all, and 2)  you have to remember that you (the teacher) know and (hopefully) like your subject matter, and although you may be teaching it for the thousandth time, this is probably the very FIRST time your students are hearing it. I have to remind myself daily that what seems so obvious to me can utterly obfuscate a person who’s never heard what I’m talking about. Now I know that many of my students have HEARD it before from another teacher, but they were not LISTENING, so it’s just like new material to them.

So it is with our own children…many times they have to repeat a lesson because they fall short with whatever instructions we have given them. And so it is with us…many of us have to retake life tests (I’m speaking figuratively) because we, ourselves, are slow learners sometimes! But we can’t give up! We can’t say, “Well so and so has good credit, and I have bad credit, so I’ll never be able to buy a house.” Bad credit is something that can be fixed. We can’t say, “Well so and so can afford a trainer, but I can’t afford a trainer, so I’ll never lose weight.” Being overweight is something that can be fixed. We can’t say, “I live in the hood, so I can’t buy fruits and vegetables.” We find a way to get everything else we want…find a way to make good food choices. We can’t say, “Well you’re good in math, and I’m bad in math, so I’ll never pass this class.” Math-phobia is something that can be overcome.

When I hear, “I’m not good in math,” I tell them…1) focus on the problem at hand, 2) use what you DO know to frame up a foundation for the solution, 3) follow through with logical steps, so you can 4) finish the challenge in order to 5) face the next challenge. We would all be wise to do this when we feel defeated. I know it helps me. What say you?

I saw a sign today that said, “Don’t judge a book by its movie.”  I was immediately struck because it reminded me of something I often think about.

In conversations, I often hear people say, “So and so has a strong personality.” What does that really mean? Does it mean “aggressive,” or “gregarious,” or “audacious”? That can’t be it. I know it can’t, because I have known many people, both male and female, who rarely spoke above a whisper and who tended to avoid the spotlight, but whose humility and quietness was NEVER mistaken for weakness. In fact, most times it takes more strength to be quiet and submissive than to be boisterous and combative. (Ask me how I know!) No…personality is neither strong nor weak…it just is what it is. It’s the complex outer wrapping that each of us clothes our “person” in. It’s the thing that we notice first about other “persons.” It’s the thing that makes us like or dislike what we think we know about other “persons” within hours, or even minutes of meeting them. I believe you can describe personality, but, I mean, really how can personality be quantified in degrees of strength? I don’t believe that it can.

Strength of character…now that’s another thing all together! The character of a person is not a function of his personality. How often have we chosen friends and mates based on their personalities, and then questioned our very ability to make intelligent choices when things got thick and we learned the real character of the person? I’ll answer it for you…hundreds of times! The problem is that character is not presented in the things we do, or even in how we do them. Character is present in the why we do the things we do. It has more to do with intention than pretension. In other words, personality is the movie, but character is the book!

Check out an interesting article on this topic and let me hear from you.

Peace!

My son is reading a series of books for which a series of movies has also been made. The deal he and I made months ago was that after he finished a book, then and only then could he watch the movie associated with that book. I told him that reading at least two chapters a day would allow him to finish by the date he wanted to finish. Well today he told me that he only has 10 more chapters to read and that the book is so good that he wishes he could read more than 2 chapters a day so he could watch the movie sooner. I realized that he had been reading “at most” two chapters, when I’d told him to read “at least” two chapters. I was reminded that many times we do as little as we can and then get frustrated when situations in our lives don’t change as quickly as we’d like. In this case, my son really thought I was enforcing a limit on him that I had never intended! Needless to say, he read five more chapters before he went to bed! I’m sure he will be watching the movie tomorrow! He learned that going above and beyond that which is expected is the way to achieve dreams and desires. I learned that instructions and expectations must be clearly stated and understood, no matter how small the task.