My Math Tree
I have always been around numbers. Most of my earliest memories revolve around numbers. Over the past couple of weeks, I have been traveling back in time and reminiscing through my mathematical journey. I have had many teachers throughout my journey, some in school buildings and some outside of those walls.
PLANTING THE SEED–LEARNING THROUGH PLAY
Cards with Grandpa
My first Math teacher was my grandfather. He taught me many concepts. Concepts that have remained with me for over forty years. These are also concepts I understood, but could not identify until much later. Grandpa taught me all about integers, both positive and negative, dot arrays, multiplying, adding, and subtracting. To me, we were just playing.
Grandpa Taught me to Add and Multiply
My grandfather was a very intense card player. He played Poker, Gin Rummy, and Euchre. He invented a game for us to play. It was called Pairs. We had to match the cards together. It is while playing Pairs that I learned to add and multiply. The cards with numbers 1-9 were worth 5 points, the 10 and face cards were worth 10, and the aces were worth 15. I learned my fives, tens and some of my fifteens multiplication tables counting up my points. I was taught to start with the biggest point card and add the remaining points together. I not only needed to know the points I had on the “board”, but also the points still in my hand, if he went out.
Grandpa Taught me to Subtract
I also learned to subtract playing our card game. I would have to deduct the points from my hand from the points on the board to determine my actual score for the hand.
Another lesson in subtraction came through learning to make change. Grandpa had a small country store. He manually added up the purchases and determined the change. I would listen to him count the change back to the customer. He would start at the purchase price and continue until he reached the amount paid. It was in the store that I learned about the value of the various monetary denominations. He also taught me to make change. This skill has stayed with me throughout my life and has served me well.
When I was in high school and college, my parents had a home business. We would go to fairs and other trade shows. My ability to make change was a very important skill and came in handy.
Grandpa Taught me Integers and Dot Arrays
I learned to recognize the numbers on the cards, along with their dot arrays. In order to play cards, one must know what cards they hold. By playing cards, I learned to recognize the integers 1-10. Each card has it’s own dot array. I learned to subitize these dot arrays comprised of diamonds, hearts, spades and clubs. I could look at the suit markings on a card and know which card it was, without looking at the number on the card.
In addition to learning to recognize the integers and subitize the dot arrays, I learned about negative and positive numbers. While calculating my points, I would need to determine whether or not I had sufficient points on the board. If I had more points on the board than were remaining in my hand, I earned points. I, therefore, had a positive number and could add to my score. However, if I did not have sufficient points on the board, I had a negative number and had to lower my score. I also learned that you could actually make a number less than zero. If, at the end of the first hand and sometimes second or third hands, as well, I could find myself “in the hole”. Grandpa would write the number of points remaining in my hand that could not be covered, and place it in a circle. I would need to earn the points to get out of the hole and begin to build my score to 500, before he did.
Sick Days with Mom
My mother was an elementary teacher with Columbus, at that time, Public Schools. On the days that I would be home sick, she and I would play “21", otherwise known as
Not only did Mom help me with my adding and subtracting. She also taught me about tally marks. I can remember watching her make tally marks, while counting for my dad. I can’t remember what they were counting, but I remember the marks and her explanation of them. I also remember counting up the tallies with her. Again, practicing skills I would later need. It was much later that I made the connections between counting by 2's, 5's, and 10's to multiplication. I could just do it.
PROPER FERTILIZATION–CLASSROOM INSTRUCTION
Learning above the Curve
Smart, But Not Smart Enough
I can’t remember a time that I could not read or do math. My abilities were always above grade level in both subjects. I remember when students were being “labeled” as Gifted and Talented. For some reason, I was either gifted and not talented or talented and not gifted. I have never been able to figure out which. I read and did the same math work that the kids in GT did, but was not able to join in the other activities they did throughout elementary school. The only time I can remember having any difficulty in elementary school was in the fourth grade.
Fast, But Not Fast Enough
It was in the fourth grade that I had to pass a timed multiplication test. I just couldn’t answer all of the problems on the page within the five minute time limit. I knew all of the answers, but could not complete them in time. I am somewhat OCD. I have to do things the same way all the time. I drive the same route to church, to school, and home, etc. I hardly ever deviate from my normal routes. I have always been this way. If working a puzzle, whether crossword or word search, I always go in order from the first to the last. It is the same with dittos and math problems. I work from left to right, top to bottom. However, for this timed test, my OCD was not quick enough. I can remember spending hours at my kitchen table with my mother trying to beat the clock.
She gave me a strategy that allowed me to pass the test. I would start at the top left answer each on that line and then answer the problems on the second line from right to left. I repeated the alternating directions through the remainder of the test and was able to complete it in the required time frame. There are some things I still alternate first to last then last to first to complete.
The Alphabet Gets Mixed In
As I progressed through elementary school, I continued to score above grade level and was introduced to Algebra. Math is difficult enough for some people without adding letters to it. In the sixth grade, the advanced math students began learning Algebra, rather than arithmetic. I began to make connections with those early lessons with Grandpa. “Being in the hole” was actually a negative number. Problems from elementary school with a “blank” or “empty box” was Algebra, the only difference was changing the box or blank to the letter “x”. I was amazed by the concepts that I had already mastered without actually knowing it.
To Love It or Not To Love It
I vividly remember my Algebra II teacher stating that we would not be taking Algebra II unless we loved Math. My thoughts at the time were “No, I don’t love Math. It was just always easy.” I pondered that statement for the next two years. I began to love Math my senior year of high school. I was one of three students in the most advanced class. It was then I learned about Calculus and the beginnings of Statistics. My math teacher piloted a math book that was being used at Ohio State. We used the same book and were allowed to borrow the very earliest graphing calculators. Math became not only easily mastered for the most part, but in some ways fun.
There were times when some word problems were not especially easy for me to figure out. It was those times, I would sparingly approach my father for help. His mind was so sharp. The only problem was that most of the time he would say, “I know the answer is 6, but I can’t tell you how to do the problem.” My frustrated response would always be, “I don’t need the right answer, only an equation. I can find the answer, myself.” Needless to say, I tried very hard not to ask him for help.
BEARING FRUIT–A LOVE FOR A LIFETIME
Fun Turns to Love
During my freshman year of college, one of the women on my dorm floor stated that any one who planned to obtain a professional post graduate degree should take Calculus I, II and III. At the time, my only plan was to attend law school. I pondered her advice and signed up for Calculus I, II, and III for my sophomore year. In fact, I loved Calculus soooo much, I took every Calculus class available for the next four quarters. Math became a friend, rather than tolerated acquaintance.
My plan began to change. What if I taught high school math to pay for law school. Good Plan, right! Wrong. I took one education class and determined I was not a teacher. I was placed in a history class, rather than math class and did not feel comfortable. While I decided to leave education behind, I was reluctant to leave my math studies, now that I had discovered my LOVE for numbers.
As you may have guessed, I did follow my initial dream. I attended law school and obtained my license. I not only finished law school, once, I returned recently and graduated with a legal masters in taxation. Again, my love for numbers showed its head and sent me down a new path. I spend many hours each tax season volunteering with other members of my church and some close friends providing tax services for lower income families. I could not be happier in this work.
I remember hearing, why should I study Algebra. I will never need math later on. I still laugh when I remember thinking that way. I use math nearly every day, especially when I am quilting. Geometry has become a great friend. I love looking at tile floors and patio pavers. I see so many different ways to make a quilt. I also need arithmetic and some Algebra to figure out fabric requirements for purchase. Mostly, I use these math forms to cut out my quilts, before I put the shapes together.
The future of the tree looks promising. I can’t wait to see where math will take me next.
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