Is the process of subsidizing the same as counting?

When speaking to my fiancé about teaching math in her Kindergarten classroom, she introduced me to the term ‘subsidizing’ which is the brain’s natural ability to instantly recognize quantities.  In her classroom, she uses dot plates, dice and dominoes to teach this concept of subsidizing. She flashes the card and the students automatically know what number they are seeing without having to count the dots.  I really never considered this as a natural built in skill, but rather something we learn as we get older and have had experience with counting quantities or using dice.

It is very interesting to think about some young students who might not have mastered counting in correct order, but are still able to subsidize and recognize a quantity instantly. This really says a lot about our brain’s innate abilities related to mathematics. Our brains learning to subsidize naturally is a skill that can be quite useful in everyday activities. If an individual is able to easily subsidize quantities, then counting large amounts of items will be made easier by viewing items in small groups such as 5’s rather than 1’s.

I relayed this to math class with Professor Antozs; when using the 1000 units of block ten blocks though the young students are unable to count to 1000, they are able to express the number. Even everyday activities such as looking for a table at a restaurant that will hold all the members of your family can be made easier by subsidizing. Rather than having to count each chair at the tables, your brain helps you by instantly recognizing how many chairs are at each table. I would have to say that subsidizing is a phenomenal asset that we possess, it is inherently math based, which in my opinion is extremely cool! When I have students in math who say they hate math, or can't do it. I will give them an example of their inherent subsidizing skill. Then tell them that they are built in Mathematicians, they can do math!!

Division

I learned division a long long long time ago. So long ago, that I do not recall the exact manner or manners in which I was taught to divide. Whenever I need to divide something now, and do not have the use of a calculator I divide the same way as the example on the right. Seeing as I will be in a classroom in the near future. I will be the one teaching students to divide. In class, Professor Antozs demonstrated a different approach to long division, one that I was unfamiliar with. Instead of doing it the way we see here on the right, it involved taking out large groups of 1000's, 100's, 10's and singles. The division is an entirely new idea. I had difficulty at first rapping my head around it. I will illustrate an example.



As we can see in the example on the left, we are taking out large sums of numbers. Once we have taken out all of the numbers, we add them up to give us our final answer. Observing this at first, I was confused due to the increased number of steps, as well as the fact that there are now two columns. Once I looked at this process a little longer, and tried a few more examples, it became clear that this process works. It works very well!

Looking back, example number 2 does look more complex. However, when looking at step by step, it tends to be easier to follow. What I mean by this is you can see the steps and where the numbers are all coming from. In example 1, the numbers get pushed down without any real reasoning behind why?  Though we arrive at the proper answer, visually the second example leads us in each sequence without any crazy `just because` steps.

In conclusion, both systems work. They both serve well in coming up with the correct answers. The second example tends to be easier to understand. Yet if the children in your classroom can grasp example 1, there is no harm in learning that way too! As a result, I believe that opening up different learning avenues with regards to division is essential in the development of learning. I learned a new technique today. Had I been shown this process as a child there is a possibility that I may have done better in mathematics. All children differ in the way they learn. The 2nd example gives us as teachers some variety when trying to educate our students.

Sports - Statistics

I am an avid sports fan! I play sports nearly as much as I study sports! I am in multiple fantasy pools, all statistics oriented. The more and more in depth I get into these fantasy leagues, the more incentive I have to win these leagues. Not only for the enjoyment of the sport but also for the money $$$$. For example, when I am watching the Detroit Tigers play baseball I am not only routing for my favourite team to win, I am routing for the players on my fantasy team to put great statistics, while routing against certain players to put up poor statistics. When I see Victor Martinez hit a three run homerun, I am not only seeing the Tigers take a 3-0 lead. I am seeing a bunch on statistical numbers. For the week I am plus 1 in homeruns, plus 1 in runs scored, plus 3 in runs batted in, and plus a certain percentage % in both on base percentage and batting average.

The exact same scenario goes for my pitchers. When Justin Verlander tosses a complete game victory, I see more than just a 1 in the win column for the Tigers. 9 innings pitched, 1 win, 1 complete game, 15 strikeouts, 1.50 earned run average, and a 0.75 walk/hits per inning pitched.

Though the game is strictly counted in the win and loss column, there are many more numbers at play. I began to consider the money the individual players make, then the money each team collectively pays their players. I was able to find a graph that compares the average salary of the American League teams and National league teams to the New York Yankees. Over the course of the past few years the difference is astounding. The Yankees pay their players considerably more. So do these numbers pay off?



Upon further review, the salary of the New York Yankees does tend to pay off. Since the year 2000, the Yankees have won 2 World Series titles, 4 American League Pennants, 9 East Division titles and earned 2 wild card berths into the post season. The Statistics tend to point in the direction, that the more money, $$$ or numbers that you are willing to spend. The more playoff game and championships you are likely to win. Therefore, to me it seems as though mathematical numbers are equal to wins, losses, championships, dollar signs, good players, bad players, exceeding and impeding expectations.