My Math Autobiography

Stern blocks

“So what’s our total count for dinner?”, Stella shouts from the dining room.

“Ummmm….”. There are five of us here, and seventeen coming from our youth group in PA. In my mind I stand seventeen vertically, stack the five on top, recognize that three from the five bring the seventeen up to twenty and that leaves two more from the five.

“Twenty-two!” I shout back.

Such basic calculations may be automatic for some people but my mind still works just like it was trained to in first grade. We used Stern math blocks in number tracks to learn addition and subtraction, number partners, division and much more. It must have been the right way for me to learn and we must have done a lot of it because to this day, I add numbers larger than ten by mentally stacking them into a number track.

Math, like all of school, was fun and not very challenging until my eighth grade year. In eighth grade I was introduced to algebra. I struggled through it, determined to succeed like I did in every other area of academics. While my math teacher was not the most effective or inspired, I didn’t lack coaching. My dad is a high school math teacher who has taught various kinds of math to a range of ages over many years. His standard response to my requests for help with math even now is, “But it’s easy: it’s math!”.

I mastered Algebra ½ and headed on to my freshman year of high school. After eighth grade, this stuff was easy! I got a 99% on my Algebra final and remember thinking, “there is no way that anyone should get 99% on a high school math final, especially not me!” so by that point I had decided that I was not good at math and one exam was not going to convince me otherwise.

Tenth grade geometry class didn’t seem like math to me. I found it easy and enjoyable because I could see it and understand it visually. But while I cut out paper triangles and used SINE and COSINE, the knowledge of algebraic thinking I had acquired in the previous year was slowly fading into the background.

After the respite of geometry came Algebra II; in my dad’s figuring, about three levels above Algebra I.  Our teacher was new on the job, though she taught other classes in the school. With her help, I kept on top of the materials, finding that if I worked hard both in class and on homework, I could keep my grades up, even though I did not feel that I had fully mastered much of the content. In March of that year, my sister got married. She was the first from our family and we left school and work for a week of celebration.

When I got back to the real world –  meaning Algebra class – I was a whole week behind and hopelessly confused. The Saxon math method is designed to teach one skill, incorporate it into what’s already learned,  then build off that to teach the next one. So missing just one week left a hole in my understanding of the material that I could not afford to work around. I struggled along but never really caught up.  New lessons built on skills I hadn’t learned and my feeling that math was manageable disappeared. As I penciled in the third answer to the last question of my final exam, I decided that I was done with math class forever.

WVU thought otherwise. My SAT math score placed me in Math 126B which is a  “four day college algebra” course. This wasn’t just any college algebra course either. It was taught by a calculus professor to whom math was as easy as breathing, and my particular section of the course was a control for an experiment involving the effect of math homework on final exam results. Whoever was running this experiment could have saved him or herself a lot of time because the results were not surprising. If you take two classes of 300 freshmen and throw difficult math at them and assign one class daily homework to practice concepts and assess understanding, and do nothing for the other class besides lecture and answer some of the questions to some extent, probably one class will do better on the final exam than the other. So our class was not assigned any homework and was not assessed between exams at all, and lectures were so fast and complicated that they didn’t help me much at all.

Math 126B did teach me something though. It taught me that there are letter grades other than A and B. I hit midterm with a solid D, panicked, began getting intensive tutoring from my genius roommate, and ended the semester with a high B.

Now I’m in math methods courses playing with colored tiles, number lines, and maybe even some Stern blocks. I feel like I’ve come a full circle but I’m not going around it again.

My Reading Autobiography

A class assignment, but one I found enjoyable to write and revealing as to my approach to reading now as a teacher candidate.

“Anetta, It’s 6:15!” I get up from the bed without taking me eyes off the page in front of me. “Thundering, they pounded down to the finish line. So close to the Black’s neck that his body was enveloped by the long flowing mane, Alec called upon his horse for the last time. Between his knees he felt the surge of powerful muscles as the Black extended himself…” (Farley, 1945, p. 194). I flip the page and walk toward the door, eyes still skimming over the text.

Five minutes later I’m still standing in my bedroom, just inside the door, book in hand. “Anetta! Get in here now!”  I wrench my mind away from the pounding hooves and desperate jockeys of The Black Stallion Returns, throw the book on my bed, and hurry next door where my dad is waiting, a frown on his face, and my siblings are gathered for our daily family time.

black stallion returns

Books were my friends, my teachers, my motivators, and my distractors from as far back as I can remember. I would open the curtains of my room and read in the long late summer hours of southeast England hours after I had been told to turn out my light. I would get up especially early on Sundays (the only day of the week we were allowed to sleep past 6 am) so that I’d have more time to read.

I read everything I could get my hands on, but my favorites were anything about horses, dogs, or other animals. Even as a child, I did not choose fantasy fiction and during grade school this developed into a deep-seated aversion to anything not realistic or anything I felt was below my reading level. I loved The Black Stallion series, but hated the Pony Pals. The Black Stallion is higher level; filled with danger, competition, knowledge of horses and the horse racing world, and the love and loyalty between the stallion and the boy. The Pony Pals however, documents the daily activities of a group of insipid and sappy middle school girls. A horse gets its foot stuck but within the next pages it will get out and be totally fine. A girl and a pony get lost but there is no suspense because after a few paragraphs of idiotic speculations by the other girls about what might have happened to her, she comes cantering back having found an abandoned farm with a hungry horse that needs rescuing.

My abhorrence of The Hardy Boys series was very similar. In incident after incident, the two boys, sons of an animal collector for zoos, get themselves into some stupid and completely unrealistic situation where their lives are supposed to be in grave danger. The drama and suspense is lost after the first three pages though because by then the reader knows that they will undoubtedly escape via some impossible occurrence and live on to create the next series of fantastic escapades.

Even time-tested classics did not pass my realism test. A teacher enthusiastically suggested that I read Black Beauty – how can you go wrong giving an avid reader and horse lover a book about horses? Two pages into the book I complained to my mother that “horses don’t think like people”, “this is not real because a horse did not write this book” and finished the book deeply skeptical and only minimally engaged.

I had plenty of access to books. I come from a family of teachers and readers so when my book supply ran out, I would borrow from my younger brother (art books, bonsai books, or Redwall) or from my older brother (model airplane construction, bird books, or Isaac Asimov). My mother, an elementary and secondary teacher, made a point of knowing what I was reading and making sure I was reading books within my grade level. That is, until I had read every book in that category in my school library and it was only the third month of the school year. She then let me read from the next grades up and I found more and more books that I enjoyed: The Incredible Journey, An Album of Horses, Misty of Chincoteague, For the Love of a Horse, etc.

mistyOfChincoteague

I am convinced that the sheer volume of books I read is the main reason that I was ahead of my peers in reading comprehension, vocabulary knowledge, and writing skills. Through reading I could learn about anything from different kinds of saddles, to life in the Amazon jungle and add words like irascible and usurped to my repertoire and all this during a pleasant and relaxing hobby. In my mind, reading and learning went hand in hand and this may be why I still have little use for fantasy fiction or science fiction.

As child, I could not understand my peers who said they didn’t like to read. The idea that reading was somehow difficult or took work was lost on me. In my family, it was the preferred way to spend a winter evening after dishes were done. My mom and dad and siblings would each grab whatever book they were reading at the time and find a comfortable place in the sitting room and there we would stay, not a word spoken, each person involved in his or her own world created by nothing more than some marks on a page.

I still love to read but rarely have time for pleasure reading. Any time I do have for reading is filled with required readings for any of my seven courses. This is a different kind of reading though. For the most part it involves taking notes just to understand the main points for future reference or looking up things in other texts to check my understanding. Occasionally however, I will have the pleasant experience of coming across a textbook or article that reads like a novel. This is because of its structure and style but also largely because of my interest in the topic.

My favorite authors that have stayed with me from my childhood are James Herriot, A.A. Milne, and Bill Pete. These three in particular have something to offer both children and adults which I love because reading can be an intergenerational past time. As a first or second grade student, each student in my class was paired with an elderly person in the community and we would read together once a week. This formed connections that lasted many years after the reading program was done and made reading a pleasant experience for both students and senior citizens. My parents would also read to my family every evening covering books as diverse as Journey to the River Sea, The Secret Garden, The Lord of the Rings, The Children’s Bible in 365 Stories, Winnie the Pooh, and Sam Levinson. These gathered family experiences around a good book are a pillar of my childhood and I will definitely make this part of my family in the future.

I firmly believe that helping a child learn to love reading and acquire the skills to read well is one of the best gifts a teacher or parent can give their child. If reading becomes a matter of course rather than a struggle; math, history, language, literature, science, and the arts will all benefit. On the other hand, a student who struggles to read will face difficulties in all areas of study as reading is part of every subject. A quotation that my first grade teacher sent me recently says something similar:

Reading is a foundation of life. If a child is going to grow up into an adult who thinks, considers other points of view has an open mind, and possesses the ability to discuss great ideas with other people – then the love of reading is essential. (Esquith, 2007).

My parents and teachers helped me find that love of reading and I am determined to instill this in every student that enters my classroom.

Inquiry of Self: Kindergarten

I can hear it now, her thin strong voice calling us in from the playground. This was one of the few times she would raise her voice. Otherwise, her voice was soft, demanding complete attention and silence while she spoke. “It’s time to go into the classroom. Let’s see if we can sneak in so quietly that Mrs. Meier (the school secretary) doesn’t even notice us!” There was not a sound as we filed past the office toward our classroom. Ms. Withers walked in front, her back ramrod straight, never looking back, her whole body communicating full trust that all of us were doing exactly what she had asked.  She didn’t look back, for the same reason she didn’t raise her voice: she didn’t have to.

Ms. Withers had the biggest “teacher presence” I have ever seen. Something about her personality, her experience, and her confidence created an identity that towered over her slight frame and flashed out of her grey-blue eyes. The biggest eighth grade students in the school would stop at one word from her.

I learned from Ms. Withers to have clear expectations for my students and adhere to these consistently so that students are never left guessing what is being asked of them. It is not a matter of being strict, although I don’t think Ms. Withers would have disagreed that she was strict. It was more the knowledge for us students, that when Ms. Withers said something was going to happen it was going to happen. End of Story. Having a clear understanding between her and and her students saved Ms. Withers from a lot of nagging, administering consequences, and solving arguments. She showed me not to be scared of being firm and clear because once these boundaries are in place, you can accomplish much more with group of students. I know I won’t step into teaching with the skills that Ms. Withers had after thirty years of experience, but I will take from her the challenge to be open with my students, let them know what I expect and don’t fail to see it through. As I learned in Kindergarten, once the little battles of classroom management, respect, and routine are sorted out, there is so much more time and energy for creativity, fun, and learning. 

 

 

Teachers to take on The System

In Savage Inequalities of Public Education in New York (1991), Jonathon Kozol describes schools over-crowded with largely minority student populations, plaster falling from the ceiling, tiny un-staffed libraries, and under qualified teachers that line up with my stereotype of inner city schools. The contrast he illustrates between these disintegrating and under-funded facilities and the majority white schools a few blocks away is enough to make the most uncaring individual stop and think. Why does this happen? Why does such blatant and crippling disparity exist in our “beautiful” and “free” and “equal opportunity” nation?

I don’t think anyone is really okay with this, yet somehow it doesn’t change. I was reminded of a comment my grandfather made during his most recent visit to Washington D.C. He looked out over the city, and pointed out the amount of buildings, parking lots, and roads that make up the US Department of Defense.  He then turned and pointed to the single unornamented office building that houses the US Department of Education. “That says a lot”, he commented, “about this country’s priorities.” I’m sure our Defense Department does much for our country and I am thankful for security, however, I can’t help thinking that our nation would see some amazing progress if a tenth the amount of funding and support that our military receives, was aimed instead at our education department.  It would be amazing to watch how truly equal-opportunity education would revolutionize and empower our nation. Imagine every child having access to music lessons, technology, motivating teachers, team sports, AP classes, and yes, free and APPROPRIATE education.

So what do us teachers do while we wait for the government to come through with something that actually helps students?

For a while in high school, I was obsessed with reading books about or by teachers in inner city schools who faced unimaginable odds in their classrooms. I loved the descriptions of the students who sat behind the battered and graffitied desks, bringing with them experiences, attitudes, and social connections that the teacher had to work through in order to reach their minds. I eagerly scrutinized the student-teacher exchanges, looking for tricks or strategies that enabled the teachers to reach and engage their students. What I found was that all these teachers had in their favor was their strong characters and big hearts. All of these men and women who went into a neighborhood, often far from their homes, and met the challenges of discrimination, low pay, under staffed schools, antagonistic co-workers and parents, and children from less-than-desirable home situations; went with the belief that they could make their classroom an epicenter of positive change, despite the surrounding climate. They were daring, willing to take risks, okay with confronting their students in unique ways, and above all, motivated by an intense love for each student. I can’t image that schools where I teach will present this level of challenges, but I know that this level of love and commitment is my strongest answer to the challenges facing our schools today.

Role Models

apple and hands                                                                                                            (image from Pinterest)

I think everyone has a favorite teacher, and looking at the similarities between people’s descriptions of their most amazing teacher ever can provide meaningful insights to what makes an effective teacher.  As part of a recent class assignment, I interviewed three individuals who have very different perspectives on education about their ideas and experiences with school and wanted to share their responses to my question: “who was your favorite teacher and why?” Natalie is a 60 year old mother of four and retired physical education teacher. She did not have to think hard about who her favorite teacher was, but she had a hard time telling me why. “She was just fun,” she said. This fun included classes held outside in the woods and most importantly, a personal connection with each of her students. This testimony shows me that being a mother figure to my students is not just an ideal situation, but is beneficial to their learning and enjoyment of school. A student will put in more effort when he or she values the teacher’s attentions and wants to please them.

Tiana is a seven-year old second grade student who does not find academics particularly easy. Her favorite teacher is strict and makes students redo their handwriting if it isn’t neat enough. That says something for that teacher: Mrs. Welks can be a favorite teacher by making her students re-do their handwriting practice. That is one awesome teacher. I doubt that the strictness is what makes this teacher loved, but Tiana could tell that her teacher cares about her work and wants to see her best effort. Gaining my students’ admiration has nothing to do with being soft on them or lowering my expectations. On the contrary, children seem to thrive with adults who challenge them in a supportive way.

Stephanie is a twenty-two year-old studying information technology. Stephanie’s favorite teacher was her enthusiastic and caring fourth-grade teacher who showed her students that she loved each one individually. This teacher is also remembered for her personal interest in each student and her enjoyable methods of inspiring learning.

My favorite teacher introduced me to college level writing in high school but did much more than that.  Mr. Hudson will remain an example of the teacher I want to be. He demanded a lot both academically and emotionally but he gave us the same level of effort and personal openness he expected of his students. I have never taken such a difficult and formative class in my life. From Mr. Hudson I learned to play on the students’ interests to motivate and inspire participation, show my students that their story is important to me, and encourage students to meet challenges of all kinds with conviction.  One of the most important things he taught me is to use valid criticism as a useful guide, and unfounded criticism to strengthen my beliefs and personality. This will be key to learning from other experienced educators and from my students. As I dive into education theory and instructional methods, I want to remember that a personal relationship with my students will be the best tool I can use in my classroom.

My Teaching Story

If you had walked up to me during my senior year at high school and told me that I would one day be a certified elementary school teacher and loving it, I would have laughed in your face. At that point, I had not the slightest attraction toward teaching as a career. I was toying with the idea of occupational therapy or sales and marketing for a business I loved, but didn’t really have any clear idea about what I wanted to do with my life. It wasn’t until about a year after graduation that my current track came into view. The frustrating thing was that my parents, peers, and co-workers all knew that I would end up working with children. I had reasons for not wanting to be a teacher. First, I was done with working in the community garden and having swimming lessons once a week and both activities were part of the summer program in our communities’ schools. As a young female teacher I knew that that was where I was needed and that is where I would be. Second, in my mind, good teachers are funny, creative, and at least a little bit crazy; I did not see myself in any of these descriptions. Third, I was aware that being with children means dropping many of my personal peeves, being ready to change my plans to meet the class’s needs, and ultimately putting the children’s well-being above my own. This sounds terrible, but as a teenager I was not ready to do that. Finally, there was this sticky point that was kind of a product of the three previous reasons: I didn’t like being with kids.

So how did I get from “I don’t like being with kids” to enrolling in a five-year-teacher education program? Initially it was simple obedience. I live in a church community in which we share our income, material goods, our labor, and our faith. This means that I submitting my own wishes and plans to the needs of the world wide church community. During my first year after graduating, our church realized that we needed more certified educators, and I was asked if I would consider studying education. Of all the possibilities, this seemed relatively harmless, and at the time that this request was voiced, I had been working in the community daycare for nine months (also out of obedience) and was finding out how much I enjoyed working with children. I agreed to do the training and five months later was enrolled in a pre-elementary education.

Even before I knew I was heading in the line of education, I had plenty of experiences with children. In our school, fifth through eighth grade students were paired with a younger student for whole-school activities and I learned by observation of my peers and by trial and error what is effective in trying to convince a stubborn seven-year old to do what you tell them to do. As I mentioned, I also worked in a daycare with one-year-old children and a range of other ages as a sub or interim teacher. I also volunteered at the school where my mother taught fifth grade and as I observed her and her co-workers I always felt that they had something that I definitely did not have – something that made them selfless, creative, authoritative, and just so teacher-like.

girl-close-up

(image from Pixabay)

I believe in the teacher as a facilitator of knowledge – one who creates a supportive and stimulating environment that encourages children to seek out knowledge and take learning into his or her own hands. I see a teacher as one who must have a firm authority in the classroom, not to control her students, but to ensure that the classroom environment is happy, organized, and fully conducive to learning. Teachers are there to make each child aware of the capabilities and talents he or she possesses so that learning is exciting and intrinsically motivating.  The teacher does have knowledge for students to gain, but it should be transferred through some creative instructional medium that leads the students to discover knowledge on their own.

Co-Teaching:Real-Time

Since publishing “Collaborative Education” I have had an opportunity to put my observations into practice.

While on winter break, I worked as a substitute teacher in a private daycare. Having worked here before, I knew many of the children and teachers and felt at home quickly. My first substitute position was in the group of one-year-olds. This is the age with which I have the most daycare experience and I felt confident that the morning would be enjoyable. It mostly was. If there is one thing that substitute teaching has taught me,  it is that children love their schedule. Young children are happiest when their day conforms to a familiar and predicable progression of activities. The schedule gives them security, facilitates smooth transitions, and never becomes, as us adults would expect, simply boring. The presence of  a different teacher is upsetting to many children and this can be decreased by the substitute’s adherence to a familiar schedule.

The one-year-olds’ teacher knew this and had left a detailed schedule written on a  small piece of paper and taped the wall for quick reference.   This was a useful aid for timing potty breaks, nap-times, and lunch but once the children had arrived and were in my care I had many questions. “Where exactly in the room do the children use the pots?”, “Which child will settle quickly at nap time and which will need more supervision?”

While these are seemingly small details, I could that a change as small as the placement of the circle of pots after lunch affected the children’s demeanor. The children were more fussy, impatient, and uncooperative than usual and often I sensed that they were watching me closely.

My next assignment was  with a group of three-year-olds; an age that I have never taught for an extended period of time. I had the group on my own for an afternoon, patterning the schedule off a few words extracted from a previous teacher. I won’t say the afternoon was a disaster, but it had the potential to be one. My arrival in the classroom was perceived by the children as an invitation to test every boundary their teacher had set, attempt things they had been taught were absolutely not allowed at daycare, see how far they could get with outright disobedience and insolence, and do all this with an eye on me; calculating my reactions and anticipating chaos and collapse of authority. I survived the afternoon by “not seeing” certain behaviors, addressing only the most important issues, doing a lot of individual talking, and summoning other staff for back-up when needed.

The next afternoon was as blissful as the previous day had been trying. The children were relaxed, mostly obedient, attentive, and generally much happier than the day before. Why? What changed?

The second day, I was working with the teen volunteer who spent most mornings with the group of three-year-olds. While not a teacher herself, she had spent enough time in the classroom under the experienced normal teacher, to know the schedule and every detail of the day’s events. With her at my side, I followed the schedule the children knew, and the children responded to the girl’s presence, treating me with almost the same level of respect as they would their normal teacher. As they saw that the afternoon would be just the same as usual, despite the substitute’s presence, the children fell into their routine and relaxed, knowing that the expectations, activities, and repercussions of disobedience had not changed.

Here I learned another benefit of collaborative teaching for the very young children. Consistency when one or the other is absent makes a world of difference for both students and staff and convinces me further that collaboration is the way forward in education.