All It Takes Is A Little Love

I just spent an hour or so attempting to master a method for factoring quadratic functions that made me more and more livid as I attempted to understand the purpose behind the exercise. I’ve been teaching Algebra I and Algebra II for years and I have developed ways for helping my students to understand both the purpose for doing so and how and why certain methods work. The one that was baffling the student whom I tutor is the so called tic tac toe method. 

I don’t have any problem finding a sure fire way for students to do mathematics in an easier manner but it really has to make more sense that just repeating a set of rules to reach the answer. Sadly the tic tac toe way of doing things was more confusing than helpful based on the materials that the teacher gave to the student. It had little to do with understanding the art of factoring compared to other methods. 

The real difficulty came about because the original teacher of the Algebra II class left the school after only working there for a week. She was young and perhaps not aware of the challenges of teaching math can be so she just left.

It took until November for a full time teacher to be hired while a series of substitutes kept the class going. Sadly most of them had little or no experience teaching higher level mathematics so they were not particularly gifted in explaining how and why things work. The result is a large number of very confused students who have so much catch up work to do in a short amount of time.

There is always more than one way to perform different calculations and processes so there is nothing innately wrong with using a method that is less complicated than guessing and checking but it has to be presented in a manner that makes sense. While surfing the Internet to learn how to use tic tac toe I found other ways of factoring that were explained so well that I picked up on the whys and wherefores of them in less than five minutes. Little was present for tic tac toe until I finally found a slide presentation that at least clarified the methodology even if it never bothered to explain why it works. Soon I was tic tac toeing my way to factor heaven but I knew that many other ways of doing so are available and most of them make way more sense. 

One of the problems with mathematics in general is that one will always hit a wall if he or she has only memorized an algorithm. Sooner or later the difficulty level will rise to a point where even the slightest change will send the person into a panic of confusion. I decry so-called shortcuts that don’t take to time to demonstrate the logic and beauty of mathematics. 

One of the things that I love most about how most modern day math teachers provide knowledge is that they use words, examples, visuals and physical manipulatives that literally show in concrete manners what the different concepts are. They bring in real life examples of how math is used and why it matters the know that the slope of a line represents a constant rate of change, not just a slanted line on a paper. 

Some students figure out such things on their own but all too many people report in adulthood that they always hated math and felt confused and frustrated most of the time. I often wonder how many folks who might have proven to be excellent in mathematics gave up on themselves early in the game because a teacher or teachers were unable to show them the wonderful connections between mathematical ideas.

I’m picking up the pieces with the student that I am presently tutoring. He has also taken the initiative to meet with an experienced teacher dury study hall time at school. He is a very bright young man who is frustrated right now and anxious to master what he has missed. I have taught him before and know that he usually catches on to new information very quickly. The fact that he is showing papers with half of the problems blank tells me that he is in a very bad place mentally and it may take a great deal of effort on his part. the new teacher, and me to help him fell one hundred percent confident again. 

I don’t think that there would be as many problems finding good teachers for every school if we valued educators as a society. Sadly many Americans have totally unreal beliefs about the lives of teachers. They imagine teachers lolling around swimming pools once the clock strikes three and having no more work to do until maybe nine the next morning. They speak of all the holidays that teachers have and the long summer vacations. The truth is that the average teacher brings home work every single night and works long after most people have gone to bed. 

School hours are not just compacted into an eight hour day and those summers are much shorter than most people imagine. Many teachers are lucky to have six weeks of vacation time once all of the demands for new learning and preparations for the coming school year are met. Sadly their salaries are based on a ridiculous belief that they don’t really work as long and as hard as others and so they are still grossly underpaid for the skills that they have to offer. Add to that the audacity of advice from so called experts whose only connection with schools has been going to them as a children. It is not to difficult to understand why so many teachers are leaving he profession. 

I’ll be going in a few minutes to pick of the pieces of destruction that have rattled the student that I sometimes tutor. I will do my best to help him understand that most of this was not a reflection on his intellect. Our society is neglecting and insulting our schools these days and it really is a shame. In the meantime if you find yourself needing help understanding how to factor with a tic tac toe grid just call me. I have figured it out even as I am not so sure that it is as helpful as it was meant to be.

Traveling is relaxing, educational, absolutely fantastic but returning home can turn into a multi week readjustment period. Our recent journey home was very much a rude awakening to reality beginning with the fact that we first flied from London to Frankfurt, Germany where we had to spend the night. Luckily there was a hotel attached to the airport. Not so luckily our home for the night was a very long walk in an almost empty airport where everything was closed at a time when we had not had anything to eat for at least nine hours. What might have been convenient and not so bad under other circumstances became a long walk followed by a growling stomach. 

Of course this is undoubtedly a first world problem so I don’t want to complain too much. Perhaps the biggest difficulty was that my knees do not work so well without pauses from walking here and there, but in this particular situation there was no place to sit along the way so I had to push through until we finally made it to the inn. 

The hotel itself was incredibly nice but the key card that we received was just another annoyance that blocked our ability to fall into bed in response to the way we were feeling. Soon enough a very kind soul who worked in the place had us inside where we saw that the room was exceptionally nice and the huge bed beckoned. Still, we both knew that we needed some sustenance so I headed out like a gatherer of old in search of any kind of food that might be available. 

I finally found a little store inside the hotel that had some sandwiches, chips and drinks that were far more tempting than they might otherwise have been. I felt as though I had made a great discovery in finding something to fill our tummies. Suddenly I believed that everything was going to go well at last. While the food was nothing to brag about it did its job and we were soon sound asleep.

Early the next morning we retraced our steps back to the airport. With rest it felt like a much easier trek than it had the night before. With no problems at all we were soon sitting at the gate where our final leg of the journey would begin. We munched on some coffee and baked goods feeling more than ready to get the trip going. 

Once again we had Premium Economy seats and they were as comfortable they had been on the way over to London. The food was excellent and everything went without a wrinkle. After many hours we were landing back in Houston, unaware that we would be greeted by hot weather. We had become so accustomed to cool days that it felt out of sync to be in a place that still had temperatures in the nineties but everything else about being home again was oh so pleasant. 

I began washing clothes almost immediately because I would be teaching my homeschooled students the following morning and I was out of everything that I would need to be presentable. I also knew that my father-in-law would be returning as well. What it did not know is that he would bring two weeks worth of his own laundry because he had not understood how to get it done in the place where he had enjoyed respite care. 

Somehow we had our usual craving of Tex-Mex that seems to be the first thing we want to eat when returning from out of the state. After a quick meal we visited the grocery store to stock up with essentials like milk and bread, fruit and vegetables. Then we realized that we were exhausted as jet lag took over our bodies. 

I must have spent the next five days washing and folding clothes. I’m surprised that my ten year old washing machine kept working with precision. Somehow I found the energy to keep working until we were no longer in a state of chaos which was fortunate because we were scheduled to attend a high school reunion event for my husband. 

A point came when I felt as though I was moving on autopilot. I had no idea where I found the energy but I made it through the first week before I crashed. It was only then that I took care of myself and found the time to recall how wonderful our trip had been and how fortunate we were to be able to travel. Now that a few weeks have passed I have no doubt that given the opportunity I would do it all over again.

All good trips eventually come to an end and so it was with ours, but first we decided to have a glorious day in London doing little things here and there that made us happy. 

Our first stop was at the site of the last time that the Beatles performed together. We hired a car to take us to 3 Saville Road which had once been the site of the Apple records offices. It was there that the Beatles climbed to the roof and began what would become an epic but short-lived concert for anyone who happened to be on the street that day. It was January 30, 1969 and the Fab Four had drifted apart but on that day they played and sang as brilliantly as ever only to be stopped by police before their unique performance was complete. Years later a documentary would show them writing music, rehearsing and finally performing. 

My husband and I had followed the documentary in a state of awe. It was a very honest and personal look into the lives and interactions of the four Beatles who had sat at the pinnacle of success before deciding to break apart as a group. With both George Harrison and John Lennon gone it took on even more meaning because there could never be another moment when they would perform their magic together. 

Standing in the street below and imagining the sounds of Get Back emanating from the roof was magical. I had dressed for tea time in a blue frock that somehow seemed to be a throwback to that time and my youth when I was only twenty one years old. I was almost as giddy as a school girl. 

After reminiscing about how much we had enjoyed the Fab Four we sauntered down Saville Row and peered into the tailor shops famous for producing bespoke clothing. The pattterns and completed suits and shirts in the windows reminded me of my mother’s sewing that was so incredibly meticulous. She tried to teach me how to create dresses as beautiful as hers guiding me in the process of beginning with fine fabrics and then carefully measuring and cutting patterns. She insisted that my seams be precise and would not settle for a crooked line or threads that did not lie flat. I became good friends with a tool that allowed me to rip open my work and then begin again and again until it was exactly right. Sadly I did not have the joy for such tedious work that she had but I learned how to fully appreciate the artistry of well made clothing. Seeing the tailors on Saville Row doing their work was quite exciting for me. 

Next we headed toward Jermyn Street where we hoped to find some dress shirts for our grandsons who are now engaged in jobs that often require finer dress that the casual styles that they tend to prefer. We found a wonderful shop that also featured a fall sale. The shirts were definitely a cut above most of the offerings in department stores, if not bespoke. We were excited with our purchases and looked forward to presenting them to our young men. 

Armed with our purchases we sauntered down a busy street filled with Saturday shoppers. Along the way we noticed an old church with a lovely courtyard. Feeling enticed by the cool shade we sat down under an enormous tree and noticed signs indicating that the church had been there for hundreds of years so we decided to go inside. There we stumbled onto a jazz concert that was surprisingly lovely. 

We listened for a time but we had reservations for afternoon tea at Fortnum and Masons, a department store that has been in London since the seventeen hundreds. It specializes in food, tea, coffee and tableware so upon entering we were mesmerized by the incredible variety of edibles tempting us to throw dietary caution to the wind. The store was a delightfully whimsical purveyor of treats like chocolate frogs and ladybugs stored in little matchboxes. There were biscuits in musical tens that played classical music. I was almost overwhelmed by the wonder of it all. It reminded me of my childhood when department stores boasted sections filled with candies, roasting nuts and popcorn.

We would eventually purchase gifts for neighbors, my students and one of my grandsons but first it was time to head for the tea room on the top floor. The splendor only became better up there where linen covered tables were festooned with flowers and happy patrons munched tea cakes and sipped tea. All the while a beautiful young woman in formal attire played on a glossy ebony grand piano. I found myself wondering if this it what heaven is like. 

We took our seats and fell into a state of total relaxation as we sampled sandwiches, scones, jams and a variety of tea. For once we did not have to hurry or scurry. The tempo was slow and relaxing. No king or queen might have received better treatment than the waiter was showering on us. Our wish was his command but we made few demands because everything was already perfection. 

I was filled with the sweetness of the feast and wished that I might stay there forever but it was time to relinquish our seats so that those waiting might enjoy their slice of comfort. We stopped at the Christmas shop and there were so many wonderful things that I was unable to decided on any one item to purchase. Then we found the afternoon tea blend that I had so enjoyed only minutes before which I knew that I had to bring home.

It was growing late and we still had to pack for the journey the next day which would send us on our way home. We found the nearest tube station, rode toward Embankment and carried our packages and our happiness to the hotel. On the way we saw that there had been yet another protest in Trafalgar Square. We smiled at the thought of freedoms being exercised right under our noses and knew that it was a sign of just how incredible our trip had been. 

We visited Westminster Abbey during our twenty seventeen trip to London but both felt that there was so much to see that it was almost overwhelming. We decided that we wanted to take the tour one more time now that we had a better understanding of the layout and much of the history. After leaving the Dickens’ Museum we got a ride to the City of Westminster and made our way to the famous cathedral where we waited for the time of our appointed reservation.

The audioguides of the present day were far easier to use than the ones that had left us a bit confused the first time around. We also felt far more comfortable and less overwhelmed my the majesty of the cathedral itself so we slowly made our way to each section knowing that nobody was going to rush us from one place to another. We took our time and let the history soak into our very skin. 

While we were there a mass was taking place and we decided to tarry for a bit and celebrate with others who had taken seats and were praying together. It made the cathedral feel more sacred and personal to see it first and foremost as a working church, not just a collection of historic artifacts. As a Catholic I noticed that resemblances between my faith and that of the Church of England. 

After the mass we continued our journey, viewing the final resting places of kings, queens and important figures in the history of Great Britain. Each story was so touching and personal that I found myself feeling reverence for the hundreds of years that the cathedral had been a place of worship more so than the pomp and circumstance of history. Itfelt a clearer understanding of journey that humankind has taken over the centuries. 

Soon we were at my favorite spot in the cathedral. Poets’ Corner, here famous authors are either buried or remembered for their literary contributions. I was like a kid in a candy store as I read off the names of so many of my favorite authors. Just as before I was in a state of awe, wishing that the English teacher who had first introduced me to these people were there to discuss the importance of each person. The world would have truly been a duller place without them. 

Next came the resting places of scientists, explorers and political leaders like Isaac Newton and Winston Churchill. There was even a plaque dedicated to Franklin Roosevelt whose partnership with Britain during World War Ii will never be forgotten. I was happy that we came back to this glorious place. I felt a clearer understanding of its in role in the history of Britain but also of the world. 

What was most exciting to both me and my husband is that I had learned that there was going to me an Evensong that very afternoon starting at five. All we needed to do to partake in the event is show up around four thirty. We left to rest a bit in our hotel and to gather our coats knowing that nights became rather cool in London during October. 

At four thirty we were ushered into the cathedral with clear instructions that there would be no photography of any kind allowed. We learned that the event would include a special tribute to the ambassador of Fiji who was there with his wife celebrating their anniversary. Soon enough the sounds  of angelic voices filled the air as the choir processed into the church. I was immediately so moved that I was unable to keep tears of emotion from forming in my eyes.

There was an alternation between readings from the Old And New Testaments, sacred songs, and a homily. The whole event was moving and inspiring and I felt that we were part of something so much bigger than even the sum of all of our lives. It was a spiritual moment in time that bound us together with all of the souls who have gathered to praise God. It was so profound that I could hardly catch my breath. 

We all left the church soundlessly and once we were outside I turned to my husband who proclaimed his own reference for what had happened. It seemed such a fitting way to understand the true meaning of what Westminster Cathedral has meant to the people of Great Britain over time. 

We rode the tube from Westminster back to the Embankment Station quietly pondering what we had just witnessed. We followed with a lovely dinner that seemed to bookend the day perfectly. It had been glorious in every possible way.

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We were quite tired when we returned from our whirlwind one day trip to Paris and we were nearing the end of our vacation. I had purchased tickets to the Dickens’ Museum for the day after our Paris adventure and my husband was feeling squeamish about having to arise early in order to eat breakfast and arrive at the museum in the time slot that I had reserved. He rather meekly asked if I felt the need to go there rather than taking it easy in the morning. 

I suppose he saw the look of disappointment on my face when I reluctantly agreed that maybe it was a bit too much to ask him to rush around without a great deal of sleep. We were quite exhausted from rising before dawn to catch the the 6:00 train to Paris on time and it was after ten in the evening before we were back at our London hotel. Somehow what had seemed like a good idea on paper didn’t sound so wonderful in our exhausted states but I still hesitated and suggested that we play it by ear when we arose the following day. 

As would happen we managed to sleep like Rip van Winkle and awoke fully refreshed and ready for new adventures. After breakfast at our favorite cafe we we on our way to the Dickens’ museum as planned. Taking the tube would have required a great deal of walking so we used an Uber which turned out to be yet another wonderful interaction with Londoners. The driver was from Nigeria and his intelligent discussion of the world’s present situation including commentary on both the United States and Great Britain was like having a noted professor giving us a crash course in world politics. He was so interesting that I almost wanted to stay in the car even after we had arrived at the museum. Sadly he had another customer to serve and we needed to get inside to claim our reserved time. 

The Dickens Museum is housed in one of Charles’ Dickens homes and to say that it proved to be delightful would be an understatement. We began in the basement where the kitchen was housed and moved our way upward with delightfully crafted audio guides that explained the importance of each room as it related to the history and personality of Dickens. The information was interspersed with lovely readings from the novels that Dickens wrote. The whole experience made the house and Dickens’ time in it come alive. 

Some of the rooms additionally had live explanations from guides dressed in the clothing of the Dickens era providing personal details of what had happened there. One of the most touching took place in the bedroom of Dickens’ sister-in-law who died suddenly at a very young age with no real explanation for what had happened to her. She and Dickens had shared a very personal relationship and her death took its toll on both Dickens’ personality and his marriage. Some even hinted that he had been secretly in love with the young woman and that the tragedy was more than he and his wife could bear. Eventually their marriage fell apart. 

Each room was filled with wonderful stories as well as sources of the ideas that gave birth to the many novels that Dickens wrote. We learned about the hardships that he had endured as a child that lead him to have the great compassion for the poor that is reflected in his work. He was very much in tune with his times and so each book that he wrote seems to reflect the London of his era as perfectly as might be possible. 

The home itself was enchanting and there were moments when I fully expected Charles Dickens to walk in on our spying. The neighborhood around the house made us imagine what it would have been like when he was in his study writing the stories that have become so familiar. He would have known that Camden town where Bob Cratchit lived may have been nearby in distance but was hundreds of miles away in terms of difference. Dickens was haunted by his own success and its unevenness with the experiences of his youth. 

The top floor of the museum was dedicated to a study of all the times that plays, movies and television productions had turned to the works of Dickens for plots. He made his characters so human that their essences jump off of the pages and their stories seem as important today as they were back when they were first written. We sat for almost an hour enjoying clips of Dickens productions, making note of books that we want to read and shows that we want to view. It was with reluctance that we left even as we both agreed that it had been one of the most delightful moments of our trip.