BG: When you are preparing to teach a new course each year, say, in the summertime, what is the first thing that you do to prepare.
MS: Well…I ask other people who have taught the course about the pitfalls and approaches to the curriculum….No! Wait! First, I take a look at the printed, or at least published, curriculum. I look at what the state is expecting me to teach. Then I try to find out what the district wants me to teach. Then I ask colleagues. Then I start planning.
BG: Interesting…
MS: What do you mean by “interesting”? It sounds like you think that there is something missing.
BG: Very perceptive of you. I DO think that there are things missing.
MS: Missing? Like what?
BG: Well, you included the state, down to the district, down to your school and then other teachers. What do you, or who do you think, is missing?
MS: When you say it that way, I see you are talking about students and parents. But how do I ask them? I don’t have contact with them in the summertime. Am I supposed to call them and ask? I don’t think that their focus is on that sort of thing in the summertime. We are probably the only ones thinking about that.
BG: You are absolutely right; we, as teachers, are just about the only ones thinking about what to teach the following fall. But that is where our experience and imagination comes into play. We probably can’t have in-depth conversations in reality with these groups but we can converse with them in our heads. We have talked with enough parents and students to know how they are going to react. So, what I am saying is, that you can know their desires as long as you have a dialogue using your best imagination. I think it’s really important that you have your students’ desires in mind.
MS: I agree about the students’ perspectives but isn’t that reflected in the curriculum and other teachers’ advice?
BG: Really?! Can you hear yourself?! Students views reflected in state curriculum?! That’s probably the biggest gap in education!
MS: You’re right. I get it. That’s not what I meant. I meant it in a more roundabout way.
BG: How did you mean that then?
MS: The bottom line for parents and students is the SAT and the game getting them into “a good college.” Part of the game is taking the SAT and doing well on it. That means doing well on a test based on the national curriculum imposed by most, if not all, states. State curriculums are a good source for knowing what’s required of the student.
BG: Good point about intention. It is what most parents are tapping into and, as a consequence, students. However, that game is designed for the elite students, economically strong parents and other small factors. Many students and their parents play this game but there are very few winners. The losers suffer many psychological consequences. I am more concerned with larger population that will not get into those choice universities. They are the ones who refuse to play that game or are disappointed with the school they “had to settle for.” I am also concerned for the many kids who get into those schools and find out that they don’t really fit in there.
MS: That’s very noble but how do you expect to help them?
BG: On the short scale or the long scale?
MS: Let’s take care of our “right now.” Let’s shoot for the small scale.
BG: Good call…The first thing we need to do is to convince them that everybody ends up in “the right school.” It may not be what they want but we always end up at the right place. We just need to realize that it is the right place for us and learn from the experience.
MS: That’s a tall order. It seems to me that is more of the big scheme of things. What do we do from place we are right now?
BG: I agree. I slipped onto my soapbox. Sorry.
MS: So, what can we do at the individual planning stage.
BG: Right! I got a little lost….I think that the key to all of this, for ALL students and parents is to ask why we teach what we do. From the broad reasons to the very minute reasons. From the logical reasons to the altruist reasons. We can’t really look at anything else until we look at that.
MS: Wow! That’s a lot to look at!
BG: It is a lot but it is a very important, to my mind.
MS: Where do we start?
BG: I believe that it is important to start broad and work our way down to the minutia.
MS: Okay. Makes sense. How broad do we start?
BG: I believe a great place to start is the general purpose of education for teenagers.
MS: Okay….
BG: If we look at our country’s history and education, different times called for different types of education. If we can ignore the elitism in education for a moment, education mostly met the needs of the time. We’ve had basic education modes that matched rural situations and liberal educations that matched the needs who had the resources and influence to attend college. As a result of the industrial revolution, we designed the schools to help teenagers to prepare for factory jobs.
MS: True enough…
BG: Nowadays, almost everybody goes to college. Not all of them are cut out for college but most of them go. On top of that, colleges and universities have become training grounds for technical jobs, rather than places of innovation and deep thinking, like they were in the recent past. That is, this happens at the undergrad level. The innovation happens more at the graduate level today, but not at all disciplines.
MS: That sounds like education inflation. That’s not too bad. It’s just that a new Master’s Degree is equal to an old Bachelor’s Degree. More expensive route but not terrible.
BG: First of all, it is terrible when that new Bachelor’s Degree cost $100,000….We’re getting distracted again. The main point here is that innovation is not happening at the undergraduate level but it is happening with people of that same age that are not in college programs. The sad thing is that most of these innovators are not being guided by mentors that a post-secondary situation could provide. As a result, innovation is rather chaotic and inefficient. Innovators are doing things on their own, without the resources that a post-secondary entity could provide. These innovators are forced to sell their product as pitchmen; and that may not be their strength. As a result, ideas fade away or taken over by salespeople looking for a profit. This results in ideas that have lost their passionate pursuer. This is bad for everyone but the profiteers. Then again, these profiteers could get a more lucrative product if the passion was not removed from the equation.
MS: I feel you! But what do you think the solution is?
BG: The solution, as I see it, is to give teenagers the avenues to pursue the lives that they want to pursue and give them all the guidance they need that a school district can provide.
MS: What if they all want to be basketball players and/or rappers? They can’t all go into the same field.
BG: You mean like they can’t all be engineers?!
MS: Touché! I get your point.
BG: What I mean to point out is that, no matter what field they choose, they are closer to their passions and what they were born to do. By picking the wrong career, they learn ideas and skills that will most likely help in their Life’s Calling. When one follows their heart, their true purpose can’t be far behind.
MS: Okay, I get it about the uniqueness of each student’s inherent purpose. However, the problem is that our school has 1,800 students. You certainly can’t expect a staff of 125 to take on 1,800 different curriculums.
BG: No, that would be crazy. But what we can do is offer a lot more choices. Instead of a mathematics teacher teaching 5 math classes, he or she could teach four classes and one mentoring class. In the mentoring class, the teacher could guide the students in what the teacher is at good at, other than mathematics. In that way, student and teacher can share things that they are passionate about. The student could sign up for 6 classes and one mentor.
MS: Interesting idea…
BG: Now, this is just one idea. There are probably dozens of others. The point here is that, with a little creativity, we can serve the unique natures of 1,800 kids at one time.
MS: I see; First, we must serve what the student feels his or her needs are. Then we can build upon that.
BG: Right!
MS: I hate to do this but we need a reality check here. These are great ideas but our school district is not going to allow this by August.
BG: I realize that. My point is that we need to always keep the student’s Inner Purpose in mind as we design a class. We need to take opportunities to be a mentor to 30 kids at a time. We need a relationship and structure that allows the teacher to guide the student in a non-academic way.
MS: I see what you are saying! We can still teach the subjects we currently teach but also see ourselves as mentors and as experts in other areas of Life other than our subject area. That way we can guide them to their Life’s Purpose, or at least point them in the right direction to get there.
BG: Precisely! I know a lot of things about other subjects but I know zilch about rap music or really pop music in general. But I certainly have enough resources to know where to find out more about the business of popular music. In that way, I can teach the necessary mathematics for graduation but also guide the student towards his or her passion. In that way, we keep two worlds happy; the administrative world and the student’s world. Who knows, I may end up teaching some relatable mathematics. Even if I don’t, I have made a relatable connection with the students.
MS: Excellent! That’s great news! So, what are we saying our purpose for teaching is?
BG: Thanks! We have been all over the place and we need to put this all in perspective. Our purpose in teaching our subjects is to satisfy administrations and giving the students a vehicle to find who they are and what they need out of education. When they start to figure who they are and what they want, we can interject those lessons into the daily carrying out of our subject matter.
MS: How are these subject matters related to their daily lives? How does math…
BG: Hold on a second! I answered that question in one of my college papers. Let me find that….Oh, here it is.
“Many math teachers will tell you that you need this for college or for a job. I’m not going take that route (various personal communications). First of all, a very small percentage of high school graduates pursue a degree that involves a large degree of mathematics (U. S. Department of Education, 2011). Therefore, my job is not to turn you into mathematicians. However, mathematics, especially algebra, is about using and manipulating symbols (Lockhart, 2009). That is, to communicate symbolically. Therefore, it is apparent that a mathematics education is about learning to deal with abstract ideas and acting abstractly. Hence, my job is to teach you to master abstract thinking. Along those same lines, science is about learning how the world works, languages are about communicating clearly and history is about learning from the mistakes and accomplishments of humanity. For example, we have many people in this school who have earned PhDs, and probably none of them in mathematics. However, if we asked them to factor a polynomial, most of them probably could not do it. On the other hand, if we asked them to do something that dealt with thinking abstractly, they probably could do it because they do it every day. Therefore, my job is to help you think abstractly because you will use that skill the rest of your life.”
MS: When you say it like that, I can see our purpose in teaching what we do a little clearer. This helps to see how we can blend mentorship and education….This rally helps as we go into preparing for the school year. Do you think we should record this somehow? I mean, like a mantra or a mission statement.
BG: That’s a good point. However, I am not sure what to write to record this. Any ideas?
MS: The first thing that comes to mind is a mission statement.
BG: That’s a good thought in general but let me tell you where I am on this. I used to work at a school system that required us to write a mission statement at the beginning of the year. I felt that it helped me focus on what I am all about, educationally. Our teacher assessment process has us write down SMART goals at the beginning of the year. These are pretty good ideas but the follow-through is vitally important, as is the amount of personal investment in writing these goals. If we use this method, it is very important that we post these goals somehow and check into them occasionally.
MS: Okay, sounds like a plan….Wait a minute! You’ve got more on this subject, don’t you?
BG: Looks like you read me like a book! Yeah, I have more. I once had a mentor who was a organizational psychologist. He told me that he often recommends that a business have a company mantra, rather than a long mission statement that nobody reads.
MS: A mantra?!
BG: Yeah, a mantra; a brief statement that tells what you goal is from a deep level.
MS: A mantra, eh? That sounds like a good option. So, which one are you leaning towards, a mission statement or a mantra?
BG: In my mind, a mantra is too brief and small and a mission statement is too broad and large. I lean towards having a series of mantras that express our goals when we educate.
MS: I agree. A series of mantras that cover our goals. Should we keep a limit?
BG: Yeah, I think that we should limit it. How does 50 words sound?
MS: That sounds like a good starting point but we should keep this number flexible. We don’t really know if it is too large or too small until we read it.
BG: Good point. I agree. How about these;
Mantra #1: The teacher should see personal growth through mathematics in the student in May that was not evident in the student in August.
Mantra #2: The class belongs to the student, not the teacher.
Mantra #3: The teacher, as a paid professional, is in charge of all policies and routines of the classroom.
Mantra #4: Student feedback is vital to student growth.
Mantra #5: The abilities and purposes of the students are very diverse.
MS: You know that these are more than 50 words, right?
BG: Yeah. It’s about 60 but they feel right. How do you feel about them, once the number of words is out of the way?
MS: At first glance, they are okay but they are not the mantras that I would have chosen. With a deeper glance, they aren’t really measurable, are they?
BG: Agreed. As for your first point, my mantras are different because our approaches to teaching are different. That’s okay. As to the second point, these are mantras, not goals. Goals are considered, in my mind, as endpoints, not the journey. Mantras, on the other hand, are sort of confirmations in that they should be reminders of what we should be striving for every day. As a result, I believe that they should not be very measurable.
MS: Good point! I think that you are right about the difference between goals and mantras. I guess we will save goals until we look at daily lessons and unit overviews.
BG: I agree with that. When we get to that, I will share my views on measurable goals. I don’t want to get off track…Do you have any thoughts, in particular, on any of the mantras?
MS: Let me see…I mostly agree with mantra #1. Seeing student growth is an important thing to see. However, I see the math knowledge as separate from their personal growth. I thought that our job as teachers is to make them maximize their abilities in our subject area. You don’t agree with that?
BG: I agree with that but I believe we should be careful about the word “maximize.” When we as teachers look at that, we think of test scores and in comparison to everyone else in the school, district, state and country, and sometimes the world. That’s not my interpretation of the word. I see it as the student’s growth at its fastest possible rate. But not compared to others but to that individual student. In other words, the student’s personal improvement. Does that make sense? What about the other mantras?
MS: Yes, that makes total sense to me. All the mantras are not what I would have said but I believe that they perfectly make sense for what I know about your approach to teaching. As for the word maximize, I understand your approach to the word but, to me, it’s not very measurable. I have a little problem with that. I want to have ways to measure whether I am doing my job or not.
BG: I get what you are saying about it’s measurability but that’s not the catch-all of my thinking. I used to get caught up with that but I found out that there is more to the results than test scores and comparing these scores to other people and groups. These scores are part of the story but not the entire story. It ignores the deeper part of each individual.
MS: I am not sure I know what you mean.
BG: This an idea that is expressed by Ken Wilber but it is also an idea I have learned over the past severals years. It is the idea that our society puts great value on the measurable, whether its individual or plural. However, it puts much less value on the things that are not so measurable but are very real, like sensations, emotions, etc. I have always given the analogy of considering a brick building with considering the mortar. That is, we look at the building and rarely look at the in-between stuff that holds the bricks together.
MS: I kinda see what you’re talking about. But the important people, engineers and building contractors give estimates of how much is to be used, right?
BG: True! Good point. Let me give a more precise example. On one of my visits to England with my wife, we visited one of the great old cathedrals at Cambridge University. It was vast and beautiful. It was hundreds of years old and it was still standing very solid. I then read that the cathedral was build with no mortar or nails. I was amazed. How in the world did it stay together, even through Nazi bombings? It was held together with three things; gravity, physics and friction. These were three ideas that were, at least at the time, unmeasurable. Yet, the building still stands with raw materials and concepts.
MS: I get why you’re sayin but I still feel uncomfortable with putting less emphasis on the measurable. Besides, we have jobs that are determined by measurable results. If we don’t produce, we don’t work.
BG: That is true but only partially. Yes, we are evaluated by our test scores. However, I firmly believe that, if we teach conceptually, then our measurable test scores will go up. And no school district is likely to fire a teacher with high test scores.
MS: So you are saying that you pay attention to test scores but it is not your focus.
BG: Precisely! But be careful about who you say that to and how you say it. I said that to one class and their parents went over my head and complained to the school district. It forced me to really explain myself on my school website. It was, overall, an uncomfortable experience. But a great learning experience.
MS: Great advice but I don’t think I’m there yet.
BG: That’s okay too. Just keep that in mind and maybe you can fully see and feel what I’m talking about. That’s the main reason our mantras look so different. You have to go for what is good for you.
MS: Good to know…So we have created some mantras, look them over and feel that they are good to go. What do we do with them? Are they for the teacher’s use, the student’s use or both? Or maybe they are used for something further than that?
BG: Well, that one is a judgement call, on the behalf of the teacher who created them. A teacher could just put them in a notebook and refer to them periodically during the school. He or she could post them by her or his desk and refer to them periodically that way. Even still, the teacher could also present them to their students, as an extra agreement. In my case, I plan on doing all of these plus one more. That is, I am going to post them by my desk and try to read them over about once per week. I am also going to going to post them in a place for all the students to see. On top of that, on the first day, when we are going over the class rules and routines, I will go over each mantra, lead a discussion and, if time permits, I will get students to write their own set of mantras. I may even go as far as requiring students to periodically to look at their mantras and report how close they are following them. It may be a closing assignment.
My Lifelong Relationship with Education
In my experience, when a writer talks about “education,” they usually refer to formal education. However, I find it difficult to talk about formal education without talking about the informal influences. I also believe it is important to reveal my educational background in order for the reader to know “where I’m coming from.” I often read articles about education and I wonder if the author’s background is similar to mine or if it is a very different perspective. I believe that the source of perspective is almost as important as the actual perspective.
In a response to this, I am going to tell my own educational history. Some of it is mythical; that is, it is the stories that my family told of me. I have no proof of these claims but I feel it is important to “put it out there” as to establish my egoist state of mind as a young student. This informal history will be followed with my perceptions as a student and this will be followed by some concrete facts such as GPAs and SAT results. By the end, I hope the reader understands my perspectives by knowing my experiences. In that way, the reader should better know the sources of my perspectives and, thereby, understand my flaws and unique views.
Some the legends of my youth are as follows;
• An extreme delay in walking and talking as a baby led my parents and my doctor to believe that I was retarded. An intelligence test proved that I had above average intelligence.
• My parents provided me with some self-teaching devices as a little boy. This led me to start school with a 5th grade reading level.
• My mother and her best friend communicated in front of me , as a toddler, by spelling out words when I wasn’t supposed to understand their gossiping. It was reported that I figured out these words.
• As a first grader, I remember feeling frustrated by my education, particularly telling time. At some point in my primary school years, the school wanted to advance me a grade. My parents apparently refused because of their worry of being socially intimidated.
• In 6th grade, we were reading a passage together. Inside my book I had the latest issue of Sports Illustrated. I was able to follow both texts at the same time. (This one I distinctly remember doing.)
• In 5th grade, I would often fail to be listening when the teacher gave math assignments. As a response, I would do far more problems than the teacher asked. I often read ahead sections in the book to anticipate the next day’s assignment. If interested, I often would do this with other grades, all the way through high school.
• By the time I got to junior high school, I really didn’t care that much. I would get good grades in Band and Math but gave just enough effort to pass in other subjects. I occasionally made honor roll but only after my parents offered a cash incentive.
• When I was about 9 years old, I got interested on the stats on the back of baseball cards. Over the next few months (summertime), I taught myself to calculate batting averages and earned run averages. (This was before calculators were very available so this was long division and multiplication.)
In my later years of high school and college, I remember some more definite numbers and events;
• I remember taking the Armed Forces Test and graded in some really high percentiles. As a result, I was always getting things in the mail recruiting me to different branches of the Armed Forces.
• I remember getting a recruitment letter from a college in New England that did nothing but mathematics. I also received an offer to attend the University of Virginia on a ROTC scholarship. (I was never in high school JROTC.)
• I took the Pre-SAT in high school. My math was in the 53rd percentile and my reading was in the 47th percentile. I never took the real SAT or ACT or the GRE.
• I graduated from high school with a 2.4 GPA. After a year of community college, my GPA was 0.25. I returned 15 years later and raised it to a 3.2 GPA. I transferred to major university and graduated with a 2.6 GPA. 12 years after that, I received a Masters’ Degree with 3.8 GPA and I have finished my PhD with a 3.5 GPA.
After these long lines of experiences, I have learned most of my education on my own. This is not to say that I have not experienced some masterful teachers because I have. Fortunately, I have found ways to get credit for all the things that I learned. As a result, I feel very impressed and connected to people who have basically educated themselves, like Ken Wilber, Joseph Campbell and many others.
Introduction
Introduction
In recent years, United States’ lawmakers have expressed the desire to reform secondary education through passing laws, rewriting standards and offering more money for educational programs. The prevailing approach of many has been to treat secondary students very much like students in grade school, without enough consideration of their development and potential. The relevant literature suggests there needs to be a shift away from the failed methods currently used—as evidenced in a multitude of test results indicating poor standing of US students in comparison to students from both advanced and less advanced nations—to a new human-centered method. In this book, a new approach to teaching secondary mathematics is presented that has the student’s growth and best interests in mind. Far from than treating each student as a cog in an economic machine, this new approach supports the student to realize his or her own inner human potential through such techniques as Jung’s active imagination, which encourages the student to find inner purpose and motivation, in a creative context, and helps teacher encourage this growth and achievement as well as fulfilling the need to teach mathematics in a more effective way. Even though my teaching experience has been primarily in secondary mathematics, it should become apparent that these approaches could be applied to almost any level of education and any educational discipline.
Since these are somewhat different ideas, I decided to write this book with a different approach. Many of my ideas came through applying Carl Jung’s ideas of active imagination. I have also used this psychological method to aid me in much of my academic and psychological growth. In addition, I am currently reading Ken Wilber’s A Brief History of Everything and The Republic of Plato. The most interesting thing about these two books is that are written as mostly dialogues. This is very similar to the style of active imagination that I do. Through these experiences, I have learned that dialogues or conversations are my best way of communicating clearly.
As a result, I have decided to write this book in the following way. First of all, chapters are organized in the same way that I would teach a class the first time. It starts off with a motivation for teaching and then follows the process that I go through to organize a year of teaching something new.
In turn, each chapter is written in the following way; It starts off with a written concept about teaching high school and it is followed by a dialogue between two educators; the way I consciously teach and another voice that believes in a standard, mainstream way of teaching. The second character is a composite of all the educators I had conversations with that feel closely tied to the way things “have always been done.” These educators believe that the failing of schools, for the most part, are a result of groups not cooperating with their philosophies. For example, they are the type teachers who blame poor student on their lack of motivation.
At the end, a conclusion is written as an attempt to condense the discussion of the chapter.
Confused
It’s late May. School’s almost over. I am about to receive a PhD in psychology. The weather is nice. I should be happy but I’m not. It’s not that I’m unhappy. The best description I can make is that I’m confused.
I have been a high school mathematics teacher for about 14 years. I love teaching teenagers. However, I am starting to think that my mathematics teaching days are numbered. I used to think that I could answer any unknowns through mathematics. Now I am not so sure. I feel like I am losing my passion for teaching all things abstract, which is a big part of math…at least at the high school level…the way we are supposed to teach it.
On top of all this, I recently received the results of my kids’ mandated state tests. In previous years, my students performed these tests and were ranked in the 75th percentile. About 75% passed these tests. (This is not the metric that the state uses but I don’t really care about that.) This year was different. A few weeks ago I apologized to my students because I felt like I didn’t teach with “my A game.” I felt as if I failed them. Then came the test results and my fears were confirmed; my students percentile dropped to the 58th percentile. On top of that, only about 50% of them passed the test. It is a guilt that I am having a hard time releasing.
Now let me be clear about this; I am not a big believer in standardized testing. I believe that the SAT and the ACT are biased tests that tell us little about the student. No, I am not scared that these test results will get me fired. If they want to judge me on these results, then go ahead; they are not a measure of my self-worth. However, when mediocre scores are in line with my self-assessment of a mediocre performance, than I become worried that I am not serving my students well.
I know my students and their parents still love me and I know that administrators believe that my unorthodox methods are ineffective. (My department head is moving me up the mathematical ladder to teach juniors and seniors next year. I can’t help but think that they are doing this because I can’t hurt their state test scores next year.) I’m okay with that. But the bottom line is that I am starting to realize that my passion to teach mathematics is fading. I’d rather help these kids with their psychological issues, teach them non-mainstream psychology and help them with their personal growth. Maybe its time to switch from teaching math to teaching psychology or serving in some other psychological capacity. (I have decided a few weeks ago to take the test to be certified as a psychology teacher.)
This confusion is not isolated in my educational side. I recognized this in the past year and it is really gaining momentum. Next month, I am being awarded my PhD in psychology. I am very proud of this and the results of my dissertation. However, I am not sure what I am going to do with the degree. I enjoy teaching but I feel like I am growing beyond that and it is not the best position to help reform education. I have nurtured many ideas through me lately; teaching psychology at a college, helping to run a private school, teaching teachers an alternative way to secondary education, etc. My latest idea is to start a non-profit that does educational research with my unorthodox ideas. Non-Profits are a new idea to me and I am going to try to learn all I can this summer. My point is that I am not sure who I am as a professional.
I have asked myself this question every night I go to bed, hoping the answer will appear in a dream. I have received clues but I have made no conclusions. Then, it hit me. As I was walking home from Starbucks this morning, because I was playing hooky from school today, some deep questions entered my mind; “Where are you an asset and where are you a placeholder? If you’re placeholder, is it worth the effort to become an asset? If you are an asset, is it worth it to up your game?” It really got me thinking. That might be the answers I need to answer to grow and realize who I am professionally. I spoke to my wife not long after that and she agreed. She also helped me realize that this idea is not just in our heads. (She is dealing with similar issues at work.) But it is predicated on how people treat us. That is, do they treat us like a placeholder or an asset? I guess we will find out after some introspection.
From Education Evangelist to Change Agent
In my past posts, I have written posts that seem, in retrospect, a little “angry.” Not aggressive or mean but just angry. Not angry at the characters or issues of the post but angry at education in American high schools, in general. You see, my educational experience before graduate school was not a great experience. I have always loved learning but I have not always loved how it was presented to me. Yeah, sure, I had some good teachers along the way but they were too few. There were some good administrators but even fewer. My experiences as a student were terrible, at best. (I was dirty and quiet and socially poor.) Not that I couldn’t learn because I could learn anything I wanted to. The trouble was that I didn’t want to learn much of what was being taught. I loved mathematics and music. Not much else. As a native Virginian, I loved the drama of the American Civil War. But not the way it was taught in school. I loved athletics but not the way it was taught in school. When I became a teacher in my early 40s, I said to myself, “Let me see what the standard way of teaching is and then I can change it to my liking, so it is more effective than what I was taught.” In my 14 years of teaching, that statement has been my foundation. Then, in my 50s, I worked on a psychology PhD, with a focus on high school mathematics teaching.
Now the PhD is complete and next month I become Dr. Jungian Educator. With this, I feel it is time to “slow my roll” and be more precise about what I believe education should become. During my PhD experience, I had a trusted mentor tell me that I was writing “too bombastic.” I obeyed this advice but I felt deep down that I was expressing my passion about the state of education. I am now ready to truly follow that advice. I will use this forum to explore, “Who am I professionally?” I ask myself this every night, with the hopes that my dreams will help me to answer that question.
In my conversations with my dissertation committee, the three wise professors urged me to write a book on education from my unique view point. I assured them I would and I am going to test out these ideas through this blog. I am hoping the ideas will come fast and furious…and clear. As you hopefully read them, remember that 90% of these are teaching ideas are to be tested later. The ideas are based on my education and experience and instincts as an educator.
When friends find out that I have finished a PhD, they ask me that question, “What do you plan to do with your degree?” I tell them that I have several options; keep on teaching, write a book and/or doing talks about how to teach better. When I thought about these ideas, I realized that my ideas are just conjectures at this point. Well-thought-out conjectures but definitely unproven. As a result, I am thinking about an additional option; an educational researcher. I have given some thought about starting a non-profit organization and to start getting grants to do some educational research independently. At this point, it is just an idea and will keep feeding it until it starts to take its own shape. Wish me luck!
Random teacher thoughts…
I am trying to write about teaching every day but sometimes it’s hard. I think about teaching every day…a lot. But sometimes I can’t really put it in coherent series of thoughts. Today is one of those days. So here are my random and incoherent thoughts about today’s American education;
- I recently wondered if I am making a difference in modern education. My Inner Self immediately responded with a resounding Yes! I asked a trusted colleague and he assured me that I am making a difference. This was reinforced by a student telling me that I have made “a huge difference to so many students.” This forced me to rephrase my question because I wasn’t satisfied. The new question was; am I in the best place to make a difference in our kids’ education? I’m still waiting for that answer but I’m leaning towards No.
- I sometimes wonder about the over regulation of public school teachers. Is this the result of being a public employee? Or is it because schools are way too big? Or is the pursuit of a cost-effective template? Or are administrators, for the most part, prostituting us out for their lust for power? My mind says that it is because schools and their governing districts are just too big. I agree with Jackson Kytle when he wrote that schools should be limited to 400 students and 25 teachers. Wouldn’t that be awesome?!
- What is our real purpose as educators? Getting kids into the best colleges even if it doesn’t fit them? Getting them the best job we can even if they’re better at running a YouTube channel? Helping them to find who they are and what they’re meant to do? Make them better people and better citizens? Is it enough to want them to have healthy minds and bodies for a lifetime?
- Are my classes chaotic this week because of a Fall Break coming up? Is it my excitement that is causing the disruption or is it theirs?
Thanks for listening. If I don’t get to sleep, the excitement will devastate all of us.
Schools and Sports
Everywhere I have taught high school and attended high school football was a big deal. When I attended high school in Virginia, football was what brought the community together on a cool Friday night. The atmosphere was one of my favorite scenes as a young man in Virginia. Even after I graduated, I was still attending many of my high school’s football games. It was entertaining and it gave me a sense of belonging to my roots.
As an educator in Georgia, it is a little different to me. Football in Georgia means producing players to play major college football. However, it is not quite the same here. Almost no school has their own home stadium. Where I currently teach, there is a stadium right in our “backyard.” However, it is a shared stadium with other schools. There are times when our school is actually considered the visiting team. At other schools I have taught at here in Georgia, there is no home stadium in sight. To me, this removes the whole idea of bringing a community together. While football is still important to the schools, it doesn’t have the connection that I am used to.
I am saying all this to bring up an issue we have happening at our high school. Last Spring, our school had an assembly for just our boys. It was used to try to recruit boys to play football. Apparently, we are having trouble getting enough boys to field a varsity football team, much less a JV or freshman team.
The football fan and traditionalist in me is astounded. The good sense teacher in me completely understands. I love the game of football. I love the collisions that it causes. I love the war-like strategies it employs. I love that it forces young men to grow up really fast.On the other hand, I understand the reluctance to play. It is a rough game that can cause many life-long severe injuries. I understand the fear of playing a game that can cause such severe brain damage.
Of course, it doesn’t help the cause that our team has only won a handful of games in the past few years. These facts are further confounded by the fact that a recent graduate of the school is now a player in the NFL.
You may ask why a passionate educator like me is even concerned with this, besides my love of the game of football. First of all, football can be the thing that brings the community together. I suspect this is why our principal believed that this was worth using school time on this issue. But the real reason I am mentioning this is because the state of sports at the high school level. I feel that sports are becoming less necessary for schools to run them.
Our school has the following varsity sports; football, basketball, baseball, softball, volleyball, lacrosse, track, soccer and tennis. Students are encouraged to play at least one sport. However, almost every sport is offered in club and travel team opportunities in the community. I have heard some students tell me that they have softball practices that are 4 hours long on the weekend. One particular student told me that she no longer enjoys playing the game because of these long practices. When I ask her why she still plays, she said that her parents hope that she gets a scholarship to help pay for college.
This is not how I have developed a love of sports. I played, and play, them for fun and growth. I loved running in the neighborhood and trying to find the nearest pickup game. That’s how I learned and made friends. It is the heart of my fondest and happiest childhood memories. There were great lessons in these games of non-organization.
I mention all of this because I have to ask why we still have high school sports teams. Does it enhance the education of our teens? Have these sports become too much of a distraction to education of our teens? Does it serve in bringing communities together? Is this another way that we chase the almighty dollar? I am not advocating an elimination of high school sports. I am just advocating letting these community coaches run their sports and let amateur coaches, like myself, get out of the way. It just makes me think of all monies spent on these sports could be better served by channeled them into more academic pursuits…Like maybe better teacher salaries and more planning time.
Walk Out?
I received an email from administration the other day. It was in reference to a proposed student walk out on Friday. The proposed national walk out calls for students to walk out at 10 AM and to not return. The email said that a plan was being worked that would be “an agreeable solution that will still permit instruction for a longer portion of the day.” It seems to me that the writer of the email doesn’t have an understanding of what a walk out is. It is a protest. It is not to be negotiated. To me, negotiating a walk out takes away the power and effect of a walk out. It is similar to the previous walk out; it was negotiated to the point where it was almost pointless.
What I would like to see is a parent supported protest. Now that would have some punch and power. I would like to see parents say to their kids, “Go ahead and protest. When you are done making your point, come home and we will go out and talk about next steps and how it feels to stand up for something. When the school tries create negative consequences, the parent can remind the school that this is a excused absence, like a doctor’s appointment.
This is less about the issues about guns in schools and more about, to my mind, about the power that a large protest has. The guns in schools is an important issue but a bigger issue is empowering teenagers in knowing the way the system is supposed to work. Stand up for what you believe in. Don’t just go through the motions. Really care about something and let people know your passions.
This should be just the beginning. I have always said that many of the problems in schools are due to teenagers being pissed at the system and wanting things to change through a unconscious revolution. It is my hope that teenagers (and their parents) will see the power of this action. When this issue is improved, I hope that some will think to themselves and say, “What else am I pissed about that needs to be changed? Why do we put up with the way teachers treat us? Maybe we can actually have a voice about the way we are educated.” Maybe this can be call for changes in education. It is my opinion that, when education grows, everything grows.
Wouldn’t be great to see a day like “4-20″change from an excuse to go get high to an opportunity to take all of us to a higher place? Instead of copying the disasters of Columbine on this day, people would copy protests for changes for the better. Wouldn’t that be cool?!
On the cutting room floor…
As I have mentioned before, I am in the last phase of earning a PhD in psychology and applying it to secondary education. In previous phases of my education, I have written many papers. Sometimes there is stuff you like that you wrote but it is deemed inappropriate for the paper I was writing. However, some of this stuff I liked so I saved it, hoping to use it at a later date. Perhaps in another paper. It never happened. So I thought I would share it here. It may be a little to autobiographical and maybe a little ego investment. However, I believe it reveals a little about my process and views towards education. I hop that you enjoy it and I would love some feedback on this experimental writing.
Land surveying is a good example of this practice outside of education. Land surveying is similar to teaching mathematics in several ways. First of all, the nature of surveying is 50% procedural and 50% concepts. Similarly, concepts lead to procedures, much like teaching mathematics. In the practice of land surveying in the field, all jobs can be done proceduraly, unless something unknown is thrown into the equation. For example, if a surveyor turns angle that hits a tree or a building, procedure must be broken and new calculation must be made. In this type of situation, the person in charge has two options; call an office engineer to recalculate the missing point or points or the field surveyor, knowing the concept, can recalculate the new point himself. Therefore, it is obvious which option is more expedient. In turn, it is most efficient if the entire crew knows the concepts behind the procedures they perform.
In most cases, many surveying crew members are only high school educated and are mostly poor high school math students. Occasionally, the concept could be explained abstractly and, since the crew member knew what was trying to be accomplished, the crewmember has an immediate understanding. However, often this is not the case. When this happens, the use of free-hand diagrams, walking the area to be surveyed, or using the provided maps and diagrams can further explain the concept.
However, the classroom had fewer natural opportunities for natural demonstrations, as compared to field land surveying. However, the student experiences are very similar. That is, there are few students that can understand a mathematical concept by just showing an abstract definition. For the rest, some physical demonstrations must be made. This when the teacher must be rather creative in giving demonstrations that match the concept. Similar to the survey crew members, some students require several layers of representations before the concept is fully understood.
Dreaming, Active Imagination and Me
When I started doing dreamwork in late 2009, I had never even heard of Active Imagination. However, over the next five years, it became probably my strongest tool of personal growth.
In the Fall of 2009, my wife was watching an episode of Oprah! On the show was an author named Rodger Kammanetz. He was promoting a book called The History of Last Night’s Dream. He spoke of the importance of respecting dreams and using them as a spiritual resource. During his talk, he mentioned an organization called North of Eden, located near Eden, Vermont. Part of the organization is a website with the address of NorthofEden.com. On the site, it offered the opportunity to have a dream analyzed for free. My wife immediately took the plunge. After some consideration, I followed suit in December 2009. When I started, I thought to myself, “This is kinda interesting but I have nothing I really need to work on.” I could not have been more wrong.
A few months later, I decided to take the work to a new and deeper level. I was invited to participate in Dream Retreat in Vermont. The experience was an eye-opening experience. All the participants met with each other the entire week. We discussed dreams. We acted out each other dreams. We discussed what was happening in our dreams and what they meant to us. We talked about lives, the good stuff and the terrible stuff. I was amazed by the honesty and the raw emotions. I was amazed where these interactions took me and where I made a conscious effort to avoid. I have never cried so much. I have never seen others cry so much. I met some people who seemed whole and balanced. I met people that seemed almost delusional. I met people who set themselves apart but having the best intuition I have ever seen. Some were just odd in my eyes. By the end of the week, I was really starting to see who were beginning a path to wholeness and who, like me, were mere novices. In the end, it gave great perspective of what this kind of work looked like and where we are intending to go.
Over the next five years, my dream work became the catalyst to many positive changes in my life. At the time that my dream work began, I working as a land surveyor for a city in Northern California. The pay and benefits were really good but I was very unhappy. I was doing a job that I could do well but I was not always doing my best. I believe something unconscious was causing me to make small mistakes in my work and have disagreements with my bosses, partly due to my immediate supervisor being a perfectionist, which was the polar opposite of what I was at the time. It was a job I could do but I had no passion for it.
Within a few months, I was convinced, through dreams and discussions with my dream mentor, that I should pursue a Master’s degree in Psychology, with an emphasis on Sports Psychology. This completely made sense because I had always loved sports and I really enjoyed the psychological side of sports. This marriage of ideas resulted in some great results; I received my degree within 18 months of starting and I graduated with a 3.9 GPA. (I graduated with 2.6 GPA in my undergraduate program, with a rocky 0.25 GPA to start my degree.)
After graduating, while continuing my career as a high school mathematics teacher, I looked for work as a sports psychologist. I could not find any that fit my current situation. In the meantime, I started coaching our high school’s volleyball and tennis teams. Using the things I had learned from my education and dream work, the teams I helped coach were rather successful. The volleyball team made the state playoffs for the first time in the school’s history and the tennis team won the first round of the regional tournament, also school’s first time.
A few months later, my mentor recommended that I apply to work on a PhD. When I heard this from him, I smiled because it felt good that someone thought so highly of my potential. However, inside of me, I felt unworthy of such a lofty goal. I was not sure if was trying to inspire me or he thought that I had a chance to do something great. It was something I could not see for myself. In any case, I asked for information from the University of Georgia, Saybrook University and Pacifica University. Georgia, my undergraduate alma mater and the nearest university to my home, never responded back. Meanwhile, Saybrook and Pacifica talked me into applying. My mentor told me, “If I was to do it all over again, I would go to Pacifica.” With that in mind, I applied to both schools. Within weeks, both schools accepted me. At first, Saybrook offered me a $1000 scholarship. I was still not sure. A few days later, when Saybrook offered me a $5000 scholarship, I was sold. (This was the first and only scholarship I have ever received.)
However, education was not the only change that was prompted by my dream work. I had some changes in my professional life. When I was early in my Masters’ degree, I was a land surveyor for a city in California. On the surface, my life was good; good-paying job, great benefits including plenty of vacation time and living in the most perfect weather I have ever seen. Despite all of this, I was very unhappy. I was always disagreeing with my immediate supervisor. I second-guessed just about every decision he made. Meanwhile, I had a few life-changing dreams.
First of all, I had several dreams where I was teaching in a school or I was on my way to get a teaching job. From these dreams, and some conversations with my mentor, that my true professional passion was teaching high school. I had left teaching a few years previous because I was disappointed about its low pay. However, in the years since, I really missed teaching and interacting with teenagers. I decided that I needed to return to teaching. Since it was now my passion expressed passion, I no longer cared how much I got paid. Through the dream work, I had learned that, if it was truly an expression of my inner Self, then things would work out to my highest advantage.
In addition, I had another dream where I saw in big letters (made of macaroni) a sign that said, “Go Home.” Although I was born in Norfolk, Va., I saw Athens, Ga., as the place that felt like home to me. After milling over these two dreams, my wife and I agreed that the wisest thing to do for us was to move to Georgia and get a teaching job. I applied to several school systems in Georgia and waited. I waited despite friends in Georgia telling us that some teachers were getting laid off there. One Sunday, as we were entering a restaurant for lunch, a region supervisor for DeKalb County School system in Stone Mountain, Ga., called and asked me how soon could I get to Georgia. I told her that I would we would be there in a month. That was September 2010 and have been employed by this district ever since. Despite all the struggles I have as a result of the move, it was probably one of the wisest things I have ever done. Every struggle I had I saw as an opportunity for growth. I owe so much to the discovery of Jungian dream work.
At the point where I first learned the basics about Active Imagination, I was finishing a Master’s degree in sports and performance psychology. During my pursuit of this degree, I started wondering how I could combine my loves at the time; sports and Jungian dream work. At the time, I envisioned becoming a sports psychologist and helping young athletes over their personal psychological issues as they tried to improve their performances in their sport. (Near the end of the pursuit of the degree, I was helping coach girls’ high school volleyball. As I watched the community coach do his work, I thought about writing a book describing how Carl Jung would coach a sport if he were not a psychologist.) I soon learned how hard it would be to break into sports psychology at my age and with no experience or exposure to elite athletes. It then occurred to me that it could be applied to my current career, teaching high school mathematics.
The Guynn Approach to High School Mathematics
With conventional teaching setting the tone and providing the model for my teacher, I started my teaching career in January 2000 in northern California. After working very hard on a degree in mathematics education for four years, I showed up to my first school, they handed me my class rolls and teacher edition textbooks, showed my rooms and kids and said, “Now go teach.” There were no fancy introductions or warnings. They just put me to work. After being taught all that theory, it really just came down to using my wits and my knowledge of mathematics. The only advice came from a seasoned math teacher who gave me the best advice I have ever received for teaching; “The key to teaching is showing that you love them without really saying those words.” I have varied that theme at times but that pretty much sums up my teaching philosophy.
The general structure of my classroom teaching is very similar to Marzano’s four-part lesson plan. The class starts with a warm-up, is followed by instruction, which is then followed by student practice and ending with a closing of some kind. However, in my case, this framework is a flexible structure that bends to the needs of the classroom and its human contents. Also, Marzano’s foundation is to teach only with methods that are backed by research and standard practices. The Guynn Method’s foundation is to teach with simplicity and flexibility and replace “research-based” with following one’s gut and common sense. Marzano’s system relies on logic, while the Guynn approach relies on heart.
The warm-up in a conventional mathematics classroom consists of several problems from previously learned math concepts. I feel that this intimidates and raises anxiety in most math students. It reminds them that they are in a place they do not really enjoy. Therefore, the Guynn approach takes an approach that is based on Lockhart’s math definition of “detecting patterns.” This is accomplished by presenting a dream, quote, song lyric, poetry or any type of visual art to the class. The students are then asked to respond to the art form with their own personal symbolic interpretation. This essentially warms up their minds and is, therefore, the student is ready to attack some mathematics.
The middle part of the class is almost the duplicate of the conventional classroom; instruction and practice. However, the influence of the opening changes the atmosphere of the class a little. By using the different type of opening, students tend to feel more comfortable in the classroom with the teacher. This leads to a more trusting environment because students feel that the work has been assigned for their benefit rather than an attempt to control them. This trust usually increases as the semester proceeds forward.
The next step in the classroom routine is the closing. With about 10 minutes left in the period, the students are instructed to write a journal entry. For these classes, a journal entry are given the following instructions; “On a piece of paper, give a description of what happened in class today, using your favorite mode of creativity. When I say creativity, I mean it can be a story, a cartoon, a joke, a dialogue with a concept or a part of you, etc. It will be graded 50% for its math content and 50% for its creativity.” (There will be more details on this later in this paper.)
It is also important to point out that this routine is not a template of any kind. It is only a loose framework. In my experience, there is never just one way to teach anything mathematical. There are several ways to present the concepts and sometimes many of these can be used on one class. By the same token, no two classes should ever be carbon copies of the other. The teacher should be able to change things whatever way she or he sees fit at any point.
The preceding paragraphs are about the structure and routine of the classroom. However, there are other things that make this approach different from others. First, the framework leaves room for other types of assessment other than paper and pencil testing. This is the first option but certainly not the only option. This method allows other types of testing like group testing, group projects (like a PowerPoint presentation) or mathematics-based group activities. Of course, it is also open to any other type of non-traditional testing.
Another part of this approach that is different from conventional teaching is the de-emphasis on standardized testing. The goal of teaching high school mathematics is not to become junior mathematicians, although this happens in many cases. The purpose of high school mathematics education is to build better citizens through using mathematics to show students how to think abstractly. State tests and college entrance exams are not necessarily part of that equation. However, if the education is done right, then it could lead to better scores as a secondary consequence. This is a truth that is hard many parents, students and administrators to accept but, in my experience and view, it is an essential truth.
I start off the class by drawing a large circle on the board. About an inch inside the original circle, I draw another concentric circle. I label the area between these two circles as the Persona. I then draw a much smaller concentric circle inside the bigger circles and label that as the Self. I then draw a line that separates the larger circles into two regions such that the upper region is much smaller than the lower region. This line must not intersect the Self-circle at any point. I label the upper region as the conscious mind and the lower region as the unconscious mind.
I then start to define all the regions;
- The persona is the part of a personality that displays all the things about the person that he or she wants her outside world to know about. For example, the clothes one wears, the car that you drive, the house and neighborhood you live in and other things that are reflections that the person feels that they are. It is the layer that protects a person from the outside world that may judge the true contents in a negative way.
- The Self is area that holds all the things that are deeply important to the person. It contains what the person is really about and what its life purposes are. It is what a person strives to find out their entire life. Some people believe it is where God exists inside of them. For these people, this where the Soul resides.
- The conscious mind is all the things you have experienced and can remember quickly and on demand.
- The unconscious mind is all the things you have experienced and cannot remember. It many cases, the person believes that this information is gone forever. I point out at this point that, if you experienced it, it probably exists in one of those places. I also point out that some of the information there can never be retrieved.
After explaining the terms, I relate that Carl Jung (1969) once stated that there are only three ways to become aware of the contents of the unconscious; through dreams, fantasies and Active Imagination. With this as a backdrop, I then state that I believe that memories contained in the unconscious can be retrieved in a limited number of ways. The prominent of these are a deep needs and strong emotions. For example, if a person feels he or she will die or suffer pain if he or she does not retrieve certain important information, then the information quickly rises to the surface. Also, if the information is tied closely to love, hate or fear, then it can be quickly retrieved. Therefore, if one can find a way to love the subject matter (or maybe hate it strong enough), then it can be more easily retrieve for, say, a test.
I then tell them about something that I like to call “unconscious reading.” This is where I read things quickly without immediately comprehending it, at least not consciously. I let my unconscious mind read the passage and store it where it sees fit. Then, when I feel I could really need it, I can probably retrieve it for a paper such as this one.
Of course, these latter theories are of my own composition and may or may not be true. I have done little or no research, formally or informally, on the matter but my experience convinces me that these theories are at least partially true.
While I have planted the previous seed, I move onto the idea that, as the conscious mind retrieves more and more of the unconscious mind, the borderline between conscious and unconscious moved towards the bottom of the big circle. When it does this, part of the Self is revealed to the conscious mind. It is at this point that the person starts to realize his or her life’s purpose. Once again, this is a theory of mine that has not been proved or verified but is an extension of Jung’s views.
Creativity+living symbolically=effective problem solving
In my experience as an educator, there is a lot of opposition to learning mathematics. Parents (various private conversations, 2000-2015) know that it is a necessary part of a full education but they are often telling me, “I was never very good at math. I don’t expect my kid to do much better.” Some students question the relevance of mathematics in their daily lives. With this barrage of questions, it forces me to answer these questions for myself. If someone were to ask me if it was relevant in my life, I would answer with a resounding yes. I have loved mathematics from the first time it was introduced to me. I found it to be useful, exciting and interesting. I still find it to be all those things at different times. However, my love of mathematics does not convince some students that it is necessary and useful for them.
I am finding that the symbolic value and lessons from mathematics may provide a way in, for helping young people value these ways of thinking and knowing.
Mathematics Education. One may recall this formalism, and here is how it came to me as experienced educator. As an experienced educator, I needed to look outside myself to see why mathematics is so necessary for everyone. Or to find what parts may be most important, whatever a student does later with their life.
The first and obvious argument is “it is required to get into college programs” (Friedman, 2014) How central are high scores on the SAT or ACT? And at what level do students need to learn it. At one point in my life, I applied to get into pharmacy school. First-year calculus is a required prerequisite. When I asked my counselor about it, she told me that calculus wasn’t used in pharmacy but it was a way to weed out less dedicated students (personal communication, 1995). That is not a very convincing argument for people who are a little scared of math.
Another argument I have heard is that it is a great preparation for working in many occupations including the military or in industry. This is an argument used in federal programs’ documents (No Child left Behind of 2001, 2002, Common Core Standards Initiative, 2010, American Recovery and Reinvestment Act of 2009, 2009) If this is so, then what parts are central and are we educating students in a way that will last?
This brings up other issues about secondary education in America. It used to be when I was young that secondary education was required to get an industrial job. Now we are using colleges as training grounds for industrial workers and technicians in industries (Mayes, 2007, Zakaria, 2015). Consideration of such arguments and more—including increased student use of cell phones and technology for math applications once done “in one’s head” —led me to think long and hard about why educators in America stress the learning of mathematics to all of its citizens, and at what level and form this should take. Quantitative reasoning is presumably important in general and in life. But how do we frame this? All of this consideration led me to come up with the following type of speech for my students;
Many math teachers will tell you that you need this for college or for a job. I’m not going take that route (various personal communications). First of all, a very small percentage of high school graduates pursue a degree that involves a large degree of mathematics (U. S. Department of Education, 2011). Therefore, my job is not to turn you into mathematicians. However, mathematics, especially algebra, is about using and manipulating symbols (Lockhart, 2009). That is, to communicate symbolically. Therefore, it is apparent that a mathematics education is about learning to deal with abstract ideas and acting abstractly. Hence, my job is to teach you to master abstract thinking. Along those same lines, science is about learning how the world works, languages are about communicating clearly and history is about learning from the mistakes and accomplishments of humanity. For example, we have many people in this school who have earned PhDs, and probably none of them in mathematics. However, if we asked them to factor a polynomial, most of them probably could not do it. On the other hand, if we asked them to do something that dealt with thinking abstractly, they probably could do it because they do it every day. Therefore, my job is to help you think abstractly because you will use that skill the rest of your life.”
Despite delivering this speech passionately and with full belief of it, there seemed to be still something missing from my inner philosophy. I fully believed in many parts of it but it did not address how to implement such a plan. Besides, it did not involve anything about problem-solving as being one of the cornerstones of mathematical education. The theories of mathematics are great but, if someone cannot solve any problems with these theories, then it is almost useless in our everyday pursuit of our lives (Lockhart, 2009).
This is an excerpt from one of my academic papers. If you want the tile(s) of the references, please feel free to contact me and I will provide them.
