Gratitude

With Thanksgiving being today I feel a need to muse on gratitude. There is plenty of stuff online about the benefits of gratitude but I would just like run a stream of consciousness about why I'm grateful. There will probably be some acknowledgements of thanks, but I just want to pants this. Free form writing can bring out things that structured prose doesn't always allow. Sometimes this is a good thing - sometimes not.

In any event, I see gratitude as an acknowledgement of that which we appreciate, often obtained through the help of others or as a gift, i.e. through means beyond our choice and control. We may ask for things but the gratitude comes form the receiving of our request be the free will of another. Most often expressed using the phrase, "Thank you."

There are a number of things that I get from being gracious. Humility is probably at the top of the list. By being grateful to others I acknowledge my own limitations. In addition, because acts deserving gratitude are given by another's free will I can be humbled by others' trust or dedication to me. This is the reason I am very grateful for my wife - because she voluntarily sticks around and hasn't killed me yet. I am grateful for my children and the way that they act and think. I've tried to teach them, even to condition them, but the choice is ultimately theirs. The fact that my children want me to give them hugs and kisses at bed time and tell me that they love me really drives me to humility as I am a very imperfect person and yet, somehow, my children feel that I am deserving of their love.

Gratitude also gives me closer relationships with friends and family. This is imply an extension of common politeness. Being around someone who is not gracious can be draining and not pleasant, particularly when you're working on something together. Ungrateful people tend to be a little more self-centered or egotistical. Sometimes people just don't feel that people need to thank them, and so following the golden rule they don't thank others. Often these people are already close friends or I've arrived at an understand with them for working purposes. However, I've found that when I'm more free with my thanks it increases the strength of my relationship with others. A sincere "thank you" can help strengthen those bonds that you consider the most important. I cannot stress what it has done to strengthen the relationship with my wife.

When I express my gratitude I find that I am generally a much happier person. My day appears a little more bright and my experiences tend to be more positive. For whatever reason this is, I enjoy the fact that with a simple and relatively small act I can increase my general well being. Also, by being active with my gratitude I see more opportunities to express it. It's amazing what you can find yourself thankful for even when you're going to difficulty.

I also feel fortunate that as a man of faith I can always thank my Heavenly Father that is God for those things that I have that have come to me by chance, circumstance, or even my own efforts. I believe that anyone can achieve great achievements through diligent work and focus and I believe that those opportunities are given to us by God. It was He that brought us to live upon this earth and established our history and abilities. I believe that He has given us the agency to choose our paths and that he is a fair and just God who loves us like I love my own children. Just as I provide opportunities for my children to attend school, play, and learn it is up to them to actually do so and to make the most of their experience. I am proud of every achievement my children accomplish and if they don't thank me for providing the opportunity because they are too busy making the most of it, I can understand that. Still it's very nice when they let me know how much they appreciate the opportunity. I feel that our gratitude to God is the same. There may be things that we receive directly from him - my son surviving being born 27 weeks early with minimal difficulty was a miracle of both medical and divine power. I thank God for my son every time I see him. I also thank God for the opportunity to meet my wife and have children. I still had to do the looking, the courting, and the wedding, but I am still thankful to God that the opportunity was there.

I am very thankful for my life which was initiated by a loving God, influenced by family and friends, and enhanced by the wonderful opportunities that I've had. I am able to tell how grateful I should be by how happy I am. And I am very happy.

Dreams

I had a dream this week where I underwent a number of adventures in a spooky and sinister town. It seemed quite real with time progressing. Like the movie Stalker I remember the dream being tense, but nothing actually happened. The weirdest part of the dream was the end. The dream ended with me getting into bed at the end of my dream day and ended as my alarm went off, waking me up to reality. My first thought on waking was, "My heavens! I just lay down. Did I get any sleep?" It was then that I remembered / realized that I had experienced a rather life-like dream. That got me thinking about dreams, what causes them and how they effect us.

Most people know that we sleep in cycles, moving through different kinds of sleep and that dreams occur in the final stage, Rapid Eye Movement (REM) sleep. While REM sleep doesn't last very long (18 to 23 minutes on average of a 90 min sleep cycle) the images and sounds we experience seem very real. Our bodies are actually paralyzed (by our mind) to prevent us from acting out our dreams. As we shift between sleep cycles, just like shifting gears in a car, we occasionally slip and not make the full transition. This can cause us to act out our dreams, to wake partially but still be paralyzed, to have our dreams superimposed on our awake vision, and various other things. While there is a whole host of sleeping disorders, dissociations in sleep, and parasomnia, but that's not what I am looking at here. I just want to look at dreams.

As an article I found in Psychology Today starts, Freud was well known for his thoughts on dreams - presenting them as "poems we tell ourselves at night in order to experience our unconscious wishes as real." The article goes on to say that Freud was only partially right and then presents five theories currently held today. A search on Google of "Why we dream" will pull up a variety of different theories. As the article I start this paragraph with includes theories put forth by many other sites and sources, I'll stick with it. The long and the short of it is that we still don't know everything about dreams. the theories (and that is exactly what they are) propose in a nut shell that dreams are the brain processing information from the day. Whether it's to sort it, locate the important stuff, or "defrag our hard drive" dreams are often heavily influenced by the activities, thoughts, and emotions from the day. But just because you have a particular dream doesn't mean that you experienced a specific sequence of stimuli that codified your dream. Dream interpretation is, at best, "metaphor mongering," posing the most plausible symbolic and / or rational reason for the cause of the dream. There are plenty of people that think that dreams have no specific purpose but are simply a natural part of our brain.

Interestingly, we often talk about our deepest desires, fantastic ideals, or things aspire towards as our "dreams." This may be because we often live out our fantasies in our dreams, particularly when we have what are referred to as lucid dreams. A lucid dream is one that we know that it is a dream and knowing that we are dreaming often allows us to take control of the dream and use the broken physics and logic of our imagination to do what we want. My father has told me that his favorite dreams are when he is falling - because he quickly realizes that it's a dream and that lets him fly.

One of my favorite lines in Voyages of the Dawn Treader by C.S. Lewis is when they rescue a man from a sinister isle. He tells them to get away as fast as they can. When questioned why he responds, "It's where dreams come true." When the crew starts exclaiming what a great place it must be, he clarifies, "not those dreams." Nightmares are a classic icon of terror, suspense, and anxiety. But people have given them a more realized image as well. In Piers Anthony's Xanth books (where all things are literal - literally) nightmares are black female horses which bring bad dreams to people. I found it fun that a similar image was used used in the recent Rise of the Guardians movie from Dreamworks. However, upon waking up from a nightmare there is little that is entertaining. Because dreams are often emotionally driven our nightmares don't feel fake.

Dreams may never be understood. There are certainly parts of them that are, but enough that is not to make it still puzzling. Here's hoping for sweet dreams for all who read this.

The Unknown Expectation of College

This is a topic that I used to teach in a full day lecture and have presented a profession conference. I'm a big fan of cognitive theory and the things we can gain from it. While this isn't one of the "student development" theories it is a very real one when it comes to college. It also explains why algebra is required for college degrees. You might have seen it before in regards to note taking, asking questions, but I think that a basic understanding of this concept teaches students what their professors expect from them.

This pyramid was developed by Benjamin Bloom back in the 1950s and is referred to as Bloom's Taxonomy of Learning. The basic idea of the taxonomy is that not all learning is equal. As we learn new things we progress through the different levels of leaning. We cannot move into higher levels of learning without first achieving the levels below them. The levels are broken down as follows:

Knowledge (basic learning) - being able to repeat information as it was given to you. Defining terms, listing components, repeating concepts you have heard.

Understanding (simple comprehension) - the ability to explain in your own words. Taking the information out of context and replaying it to someone else.

Application (initiation of action) - using the information to accomplish a task or other such action. seeing how the information works in the context of the material.

Analysis (Deep understanding) - breaking the information down into its respective components and seeing how the parts interact. Also, seeing how the information fits into the greater context and outside of the initial context. Identifying relationships between the information and itself and other topics and facts.

Synthesis - (deep application, creation) - using the information to create new ideas, conclusions and applications. Using the component pieces to produce new ends and means.

Evaluation (defending your conclusions and actions) - having the ability to defend your conclusions and actions to others using clear and developed arguments and evidences.

The best way to break down the levels is with the use of action verbs - verbs that require action or demonstrate clear objectives. These verbs are often found in the assignments, tests, and research proposals that professors give. Being able to associate the verb with the level helps students understand what kind of depth or quality the professor is looking for. There are many lists of action verbs, but I like this one from Clemson University. It's got a nice layout and a good list of verbs.

Now, the expectation that I explain to college students. In high school the basic standard of teaching and learning is that students are expected to demonstrate that they know and understand the material as it was presented to them. Teachers and students do not progress much beyond the first to layers of the pyramid. However, when student arrive at college, the professors will often times help them achieve those same levels of a topic, but then will expect work on the higher levels. They try to give the tools to help students move from one to the next, but they are not content if students just linger in the levels of knowledge and understanding. This is often why new freshman will complain that their tests are not fair. "The test was about stuff that we didn't cover in class." or "I don't remember seeing this in class." These responses are often the case because the student leaned the material on a minimal level but the professor is testing their higher level learning.

What does this have to do with algebra? If the goal of college is to get people to think on a higher level then algebra is the natural gateway. Example:

Knowledge level - Define addition: calculating the total of two or more amounts (citation)

Understanding level - Explain addition: what you get when you combine two numbers

Application level - 2+2=? answer: 4

Analysis level - 2+?=4 answer: 2

Basic algebra, even in such a simple calculation, elevates a persons thinking - requiring them to analyze, break down, and find the relationships in the equation. When my old math teach said, "This is to make you think" the desire was not just a cognitive process. Bloom shows us that not all thinking is the same. This is to get you to think deeper then you might normally. This is to stretch your brain so that it doesn't return to its original, limited state, but to enlarge your capabilities. Like I said last week "This is to make you think" is the most accurate response to the question "why do I need to study algebra." i also think that it is the most valid and the best. This is why colleges set a standard on the minimum level of mathematics students must complete. So they can be sure that students are going to have an opportunity to think on those levels that can actually empower students to be proactive and not just reactive.

When will I ever use this?

I've commented on Mathematics in the past but some recent discussion are moving me towards it again. Last time I discussed reasons people may despise math. This time, I would like to look at why math is considered a critical skill college - or at least critical enough to be required for general education. The most well known course for the Quantitative Literacy requirement is MATH 1050 - College Algebra, but it may be one of up to five course options. The office I work in has been tasked with enforcing the math completion policy for our university, so I hear plenty of students complete about, berate, and in so many other way despise the policy, math, math teaching, and everything else related. As the messengers of this policy our staff has be metaphorically shot at on a regular basis. This was the catalyst of the previous post, but I would like to provide an answer to those students who may ask, "When will I ever use this?" It is a fair question and deserves an answer.

My high school math teacher, when confronted with this question used to say, "You won't [use this]. This is to make you think." I feel that this is the most accurate answer to the proffered question. There is a lot in mathematics that is either specialized for specific calculations, or they are more abstract concepts that are the foundation for those specific calculations. With that said, that instructor taught my trigonometry class and as well as other classes required for calculus. Algebra, the basis for all other advanced mathematics, is used more often. I would like to split the usage into two areas: unconscious calculations and intentional calculations.

Unconscious calculations are the ones that you do without even thinking about it. Every time you get in a car and drive you brain is processing velocity, acceleration, position, distance, and time equations faster than your reflexes can even respond. The same is true of any physical activity or sport - to catch a ball is an exercise in those same factors so you know where to move your hand. The world you live in can be described in numbers, vectors, shapes, solids, and velocities. Without your brain's ability to do math people would never had killed enough food to evolve past subsistence level of living. All of this is algebra. This is not to say that if you have difficulty in solving algebra problems in your math book that you are a bad driver. The math that our brain does without thinking about it is intuitive. But if we consider those calculations that we do intuitively - then the answer to our questions is, "Every moment of every day."

Intentional calculations are the ones we actively choose to do or the ones that our math classes require us to do. Even thought these are a active choice there are certain calculations we do all the time without thinking about it. Anytime you look at a clock to see how much time you have, you are doing algebra.

current time + (how much time) = target time. 

Any time you use money, particularly cash, you use algebra. This is very true when figuring out a tip, a discount, or other promotions.

available funds - purchase price = new available funds

original price * discount percentage = new price 

Factor that into the original equation:
available funds - (original price * discount percentage) = new available funds

These two examples may be obvious to most people. Those same people may come back and say that use calculations do not require exponents or fractions. That is true, for the most part - some purchases may be very complex. Even if such calculations are not very complex by studying algebra you are practicing skills that you use every day. The more practice you have the better you get at them, the better you get the more consistently accurate you are and the fast you are. Until such equations, no matter how complex may be.

There are other areas where intentional calculations come into play. Many hobbies that people do use math, including: wood workings (or other building hobbies - measuring, scale, etc.), cooking (one of the few places that people intentionally calculate fractions), gambling (probability), and many other games of all kinds (angles in strategy games, keeping and maximizing score, fields of view, the list goes on.) Again, these may not require exponents or logs, etc, but those develop complexity and give practice. You cannot be good at something unless you are stretched.

The last place that I want to mention that people use algebra every day is in problem solving. I don't think it's a coincidence that the individual calculations that we are required to solve in math classes are referred to as math problems and that the process of resolving difficulties as problem solving. I don't know which came first, perhaps it's an example of  the chicken vs. the egg, but regardless math problems and problem solving go hand in hand. Just like we can describe the vast majority of our physical world in terms of mathematics many of our social, emotional, and mental situations can also be labeled in terms of mathematics.

If X happens, then Y will occur. But if I don't want Y to occur, then I must do Z.

Anytime you have a situation with any number of possible outcomes the ability to reason is key. That reasoning is often termed logic and is the basic language of mathematics. The ability that you gain in learning how to arrange, manipulate, and see the relationships in  numbers translates to other kinds of problems as well. So even though you may never use numbers in your future equations, algebra is again proven to be helpful in everyday interactions and situations.

Perhaps next week I'll go into the biggest reason that math is taught in college in what I call the unknown expectation of college. But until then, I think this is sufficient.