Class 10 refelection

I am proud to say that I have finished all the courses required for my transitional license.  It has been a long and arduous process but not one without merit.  I have taken a class geared toward teaching mathematics specifically, one that focused on in grating technology into the classroom and one that focused on special ed students.  After all this I can unequivocally say that Educational Psychology 401 has been the most difficult, painful and worthwhile one of them all.  There is no other class that covers the range of material that EdPsych 401 does.  Below, I will highlight some of my main takeaways from the class.

I really enjoyed the video by Ken Robinson.  He gave me new insight into the importance of allowing for creativity in the classroom. My blog post c6 concerns this and highlights many reasons why this is the case, especially in math and science. 

I was familiar with behaviorism before I entered this class but I was not familiar with the other learning theories. All of the theories have their strong points and learning about all of them can only help an aspiring teacher.  However,  I was particularly drawn to cognitive theory because I believe it gives the best account for how an individual learns complex things such as chess and mathematical equations.  It thinks of the human mind as an immensely powerful, but flawed, computer.  My CSEL paper is on this topic and is contains many useful ideas to help students learn.

Other points that I will remember are: Cattell's fluid vs. crystallized intelligence for its wonderful conception of expertise at chess, Piaget's cognitive stages and Vygotsky's Zone of Proximal Development.  This class has also made me think deeper about how to motivate students and about the correct type of assessments to give.  It also made aware of how some of my students feel when I load them down with work!  Of all the classes I have been required take, this one was easily the most comprehensive, and while that might have been frustrating at times, I believe that everyone in the class left as a better teacher than they began.  

Class 9 reflection

What I have chosen to do for this post is to make a handy list of ways to keep yourself safe as a teacher.  All to often, teachers find themselves in compromising situations with students.  Quite often this is because the teacher initiated the situation.  However, good, well intentioned teachers can find themselves in scenarios they never envisioned or facing false student accusations.  In my two years teaching I have been placed into uncomfortable situations by students on several occasions.  Fortunately, these situations were very benign and nothing ever happened. And even though I felt blameless in these situations I couldn't help but think I should have taken steps to mitigate the risk of such situations.

This is especially important for young teachers to remember.  Many education graduates end up teaching high school and are only a few years older than their students.  In my personal experience, and many others I have talked to, this can be an awkward situation.  When high school students have a young teacher they much more likely to ask that teacher personal questions.  These may include: Questions about alcohol and drug use or statements such as, "Do you have a boy/girlfriend," "Do you like to party." Many of these questions maybe simple curiously on the part of the students, or they maybe trying to gain insight into a part of their lives that they will soon be leading.  In any case, if these questions are humored by the teacher they serve to undermine his/her authority and increase the likelihood of and awkward situation occurring. Below is a list of some suggestions to insulate yourself from this.

1. Never answer questions about your personal life other than simple facts. (Where you grew up, etc.)

2. Never find a student on Facebook or any other social media device.

3. Avoid being alone in a room with a student if possible.  If this situation does occur, which it probably will at some point, leave the door open.

4. Set boundaries and make sure that your desk and your personal possessions in the room are off limits to students.

5. Don't play favorites.

6. This is the biggest one.  Instill a constructive, respectful environment in your classroom. If the students do not respect eachother's personal space, it is less likely that they will respect yours.  Also, establishing yourself as a serious educator will make students less likely to ask you those personal questions.

Fluid and cystalized intellegence c7

I found Cattell's theory of fluid vs. crystallized intelligence to be very interesting.  Fluid intelligence is the ability to think logically and solve problems in novel situations, independent of acquired knowledge.   It is the ability to find patterns and relationships that problems revolve around and then use logic to solve those problems.  This is especially helpful in math and science.  Crystallized intelligence is the ability to use skills knowledge and experience.  A person’s vocabulary and knowledge of mathematical concepts is contained in this form.  While this theory has great application to the field of mathematics, the class I teach were it holds the most pull is chess.

Chess, for hundreds of years, has been considered the ultimate game of strategy in dozens of cultures.  Why has this game been so pervasive and why has an ability to excel at it been considered synonymous with intelligence, even by those who do not play the game?  The answer is simple.  There is no other game that requires so heavily, and so equally, fluid and crystallized intelligence.  The fluid intelligence comes into play because there are more possible games of chess than there are atoms in the universe.  That being the case, a chess player is likely to be in a novel situation in almost every game he plays.  He must be able to recognize patterns and combinations and find creative solutions to the problems that face him. But what helps him recognize those patterns?  At natural ability to do so helps, but the clear answer is crystallized intelligence!  Even though a position in a particular chess may be completely novel, a player may recognize similarities in this novel position and between other positions he has been in before.  This knowledge of chess principles and patterns helps him use his fluid intelligence to get the upper hand on the opponent.

Chess is a wonderful game revered the world over for its cognitive challenges and Cattell has helped to show us why.

Piaget and Vygotsky c8

I have been thoroughly introduced to the theories of Piaget and Vygotsky in Educational Psychology classes before. even though I believe there are some flaws and oversights by both men, I think their theories are worth noting and worth studying.

I particularly like Piaget's stages of cognitive development. Perhaps the ages of the stages are a bit off and perhaps they are not as universal as he thought but they do give us a good guideline. Teachers and parents alike can use these stages to help children advance more rapidly and completely.

Vygotsky, like Piaget, but to an even greater degree, placed an emphasis on play.  As someone who was once a child myslef, I find this to be an astute observation.  I often worry about the youth of the 21st century. Kids are encouraged to play...video games.  However, they are not put into situations where they must entertain themselves with mud or a tree or a ball, at least not as much.  I wonder what will happen to the future adults of this age who have had all the entertainment created for them. Will they be able to innovate? Will they be able to exist without constant support? These are questions that remain to be seen and questions that will continue plague me. 

I also enjoy Vygotsky's zone of proximal development (ZPD) It states that were learning occurs is in the middle.  What I mean by that is that if a task is too easy, learning does not occur.  Also, if a task is simply impossible, then no learning occurs either.  It is in those middle difficulty tasks were learning occurs.  I have found this to be true of myself and of my students and it is something that I will keep in mind during my future teaching experiences and during my praxis exam.

Creativity c6

I found Audrey and Georganna's presentation on Creativity to be especially interesting.  The part that I remember most clearly, and the one I thought had the greatest application to my teaching, is the distinction between convergent and divergent thinking.  According to a study that I heard about from Ken Robinson, a noted expert on education, 98% of kindergarteners are geniuses in divergent thinking.  This makes perfect sense because even a very simple, mundane object to an adult can provide hours of fun for a small child.  They tested the children as they got older and with each passing year their divergent thinking scores decreased.  Part of this may have simply been the process of growing up but the convergent thinking that is so heavily emphasized in schools is certainly a culprit as well.  After years and years of being told there is only one right answer no wonder divergent thinking, and as a result creativity in general, tend to fade with age. 

All this is especially troubling for me as a math teacher.  Math above all other subjects, at least it is commonly believed, has only one right answer.  While this might be true with regard to the more elementary aspects of math, the real-life math that helps us understand and manipulate the world around us isn't a multiple choice test.  It is a world filled with billions of problems and possibilities and a human race in desperate need of creative mathematicians, physicists and philosophers to solve them. The question remains, how can we teach technical subjects like math without destroying divergent thinking?

The best I have figured out is to put students in real world situations as often as possible in order to take what they have learned in the classroom and apply it in real life.  It is important that these situations not be contrived or gimmicky, but rather situations that students may actually face and ones where maybe even the teacher is not in full  possession of the solution. 

Creativity is not exclusive to art or music. It is an essential need for us a species and it is our job as educators to facilitate it whenever possible.

Cognitive Theory c5

Cognitive Theory

So far cognitive Theory is by far my favorite approach to learning.  Behaviorism and Social Learning Theories have their perks, but both are far too simplistic to really explain how a human being learns.

One of the main attributes of Cognitive Theory is that it gives detailed description of memory.  The theory breaks memory down into two basic parts.  1. Memory Storage  2. Memory Retrieval.  Both are important for learning.  In order for memory storage to occur several things must happen.  The subject must be aware of a stimulus, perceive the information and interact with it in some way.  This theory explains why so few of our experiences make it into our long-term memory.  We simply do not give enough attention to them.  It also explains why people learn in different ways.  The key point is that you must interact with the information in some way.  Interaction does not simply mean picking up the information and playing with it.  It means that the information has to have an affect on you.  What affects different people, and to what degree, is highly individualized.  This is why different people are classified as audio or visual or kinestetic learners.  A sound may have a lasting impact on one person and be completely innocuous to another.

The are many interesting facets to long-term memory retrival but I will highlight the most interesting, namely, interference.  Interference is believed to be the most common reason for forgetting and there are two main types.  1. Proactive interference occurs when old information blocks the retrieval of new information.  For example, your address may have recently changed and you keep putting your old address on forms.  2. Retroactive interference occurs when new information blocks the retrieval of old information.

As you can see, Cognitive Theory, at least in my opinion, gives a much more robust explanation of the phenomenon of human learning.

Theories of Learning c4

 Theories of Learning

Behaviorism

 Behaviorism is an interesting philosophical and psychological theory that I had never really applied to
 teaching or learning.  In fact, I still don't know how it applies.  It obvious can be very effective for teaching
and learning specific rudimentary behaviors but I don't know how it applies to more complex activities.  How can a knowledge of behaviorism help me teach a student math problems or chess or physics?  Perhaps there is something I'm not thinking of, but until I am shown other evidence I remain skeptical.

On the other hand, behaviorism can help a teacher with classroom management.  However, I don't know if this is way to go about it.  Using classical conditioning seems like training robots and even operant conditioning doesn't seem much better.

I do think that a large majority of the claims made by behaviorists are correct.  I also think they have provided a very simple but insightful way to view human behavior.  The reason I don't think behaviorism will be my paper topic is because of its limited scope.

Social Cognitive Theory

Social Cognitive Theory (SCT) is interesting because it incorporates learning from others.  The bobo doll experiment showed this. However, the theory didn't seem to say anything interesting.  Perhaps this is because the theory is so ingrained into the social consciousness, but it all seemed like common sense to me.  People, especially small children, imitate.  People who grow up in violent surroundings are more likely to be violent, and vice versa.  While I think this is a beautiful view of humanity, namely that we are not violent or selfish by birth but rather trained to be that way, It doesn't say anything interesting.  At least not to me.

Motivation c3

Motivation!

How do we motivate our students? This question, along with the side-effects of it, are the main reason teachers leave the profession.  Many teachers go in to the field because they love watching children learn and progress, or simply because they love explaining things.  However, this enthusiasm tends to wane when the glazed over looks of students are all one sees.  And this is if you are lucky!  Unmotivated students are much more likely to become disruptions and even initiate violence than motivated students. After several years of boredom, frustration and unruly behavior many teachers call it quits.

Perhaps, if they had better resources and training in this matter they could avoid the problems that unmotivated students cause. In the few paragraphs below I will describe the best way I have found to motivate students in my two and a half years of teaching: Hands-on activites

Hands-on activities are great because they are simply more fun than worksheets and also connect what the students are learning to real-life in a much more concrete way.  I am by no means an expert in student motivation but I can think of nothing more productive to do than sharing what has worked for me.  These will mostly be specific to teaching math, but I hopefully teachers of other disciplines can benefit as well.

1. When Teaching Probability use actual cards and dice and tie the learning into actual games.

These are objects that most of us grew up playing with.  Students often find it interesting to learn about the probability of games they used to, or perhaps still do, play.  A great web device is Johnnie's probability page. http://jmathpage.com/JIMSProbabilitypage.html It has almost 30 different games and activities.  Below is a picture of an activity I created using a game on that page.

 

2. When teaching geometry stay away from worksheets as much as possible!

Geometry is inherently connected to the real world. It is the study of angles, shapes and distances.  Why teach such an interesting topic with a worksheet. Below is a list of ideas.

 a. Use the tiles on your floor to teach perimeter and area. Most tiles in schools are exact 1 foot squares.
 b. Teach them the Pythagorean Theoremand then use it to determine distances otherwise unmeasureable.
 c. Get actual solids in the class when teaching volume and surface area.  Show them that a rectangular prism is just a box with 6 rectangles, get a coffee can and peal off the label in order to show that a cylinder is really 2 circles and a rectangle, etc.
d. When teaching medians and perpendicular bisectors of triangles have the students cut out actual triangles and fold them to learn the actual essence of the terms.

3. When teaching regressions in algebra use actual data that the students collect.

For example I had the students measure their heights and wingspans on the wall. We were able to run a regression which allowed us to make predictions.

There are many, many more examples but hopefully I have given you a taste of how hands-on activities can enrich a classroom.

Reflections on Class 2

Standarized testing!

Everyone's favorite topic. In reality it is a subject that is near and dear to me. I got into education as because of standardized tests.  Back in 2008 I took the GRE and scored extremely well and while I did not get into the graduate programs I was hoping for, (Philosophy grad school is immensely competitive) I did manage to get a job at Kaplan tutoring and teaching the GRE and the ACT.  Using this experience I was able to land a job a Austin-East High School as a Mathematics Teacher Assistant.  After six months of working in this capacity the administration asked me to take the Mathematics Praxis Exam over the summer. If I passed, they might have a job waiting for me.  My knack for test taking came in handy again, I scored very well on the test and was hired. During my 2 years of teaching I felt the sting of End of Course tests (EOCs) on an almost daily basis. The classes I taught which had an EOC were hectic, stressful, compressed, formulaic and boring. The classes I taught that did not have an EOC were fun, creative, interesting and interactive.  I am not alone in this opinion. This is not to say that standardized tests should be completely eliminated from schools.  There needs to be a way to hold students, teachers and schools accountable.  However, I'm not sure standardized tests are way to do it. And I'm completely sure that the current form of most EOCs is not the way to do it. I'm not as familiar with other subjects but I will briefly describe what happens in an EOC math class.  The problems are mulitiple choice and many of them can be solved by plugging answer choices in the calculator.  There are graphing problems - calculator.  There are table and chart problems - calculator. There are linear regressions - calculator. There are imaginary numbers - calculator.

You get my drift.

The terrible thing in all this is that students come out knowing how to manipulate a calculator but not actual math. Perhaps there could be a calculator section of the test (calculators are very useful tools and mastering them is important) and a non-calculator section of the test. This would force teachers to actually teach math and students to actually learn it. Perhaps there could be critical thinking problems that aren't multiple choice.  I realize this creates grading problems but if it was a minority of the test I believe it could work.

I understand that I did more complaining than solving but I wanted everyone, particularly math teachers, to realize what they are getting into and to open the discussion for possible solutions.

Reflections and takeaways from class 1

I greatly enjoyed the first meeting of Psych ED 401. I felt the overall dynamic between the students and the teacher and student to student was good.  The part of the new material that I found to be the most interesting was the discussion between the three main styles of teaching.  These include: 1. Expository - This is the traditional method of teaching. The teacher lectures about new material, students take notes and ask questions and then the students practice the new material.  2. Interactive and Collaborative - In this method of teaching the instructor generally does not lecture for extend periods of time.  Instead, students work together in order to achieve understanding and share knowledge. 3. Discovery and Inquiry - In this method students use their background knowledge in order to discover answers to previously unattainable questions and most importantly, ask question of their own and then develop strategies to answer them.

There was quite a bit of buzz after we were introduced to these ideas and we broke off into small groups for discussion.  Our task was to, "Pick the teaching strategy that you think is the most effective." Surprisingly, or perhaps no so, nearly every group said, "All of them!"  Having taught high school math for the last two and a half years I starting thinking about the really good lessons I have taught and also about the great ones I have seen others teach.  They all had one thing in common. Namely, that they used all three types of teaching methods.

My burning questions are these: 

1. How can we as teachers effectively implement all three teaching methods more often?
2. What percentage of each style should be taught in order to achieve the best results?
3. Does this percentage vary from subject to subject and if so, how could we go about evaluating this?

Class Review

I went into TPTE 486 with a fair amount of trepidation.  I have taken several college classes in the course of getting my certification with mixed results.  Another cause of my trepidation was the simple fact that I am not very adept with technology.  However, I went into the class with an open mind and the results have been great. I will list my two most important accomplishments below.

1. I was proficient using Smartboard before entering this class because that's what my current school uses.  On the other hand, I had absolutely no experience with Promethean boards or Activinspire software.  Now I feel confident that if I moved to Promethean school I would be able to adjust fairly easily.  Also, some of the features on Activinspire were so useful that they inspired me to learn how to use the same features on Smartboard.

2. I created so much material that I will be able to use in my classroom.  The diagram that I made using Inspiration software will be useful.  The Interactive white board lesson will help me get students more engaged in the Pythagorean Theorem.  The Imovie will be a great way to introduce surface area.  The Inquiry based activity on probability is a lesson that I will use almost exactly as it is written on my website.  The list goes on and on but suffice it to say, this class has been very helpful to my teaching career.  Below are some pictures of projects that I will be using in the future.





Visit my website for a full list https://sites.google.com/site/mcclainclass/technology-projects

Wiki Walk Through

I never used a wiki in my classroom or even really considered it.  However, after reviewing the Wiki Walk Through I have determined several ways to use them in my classroom.  A procedural wiki could be very useful. Students could post various ways of approaching a problem along with steps for completing that problem.  This would be a valuable resource as it would offer different approaches for different minds. An applied math wiki would also be wonderful. Students could receive extra credit for posting how they used the math they learned in class to solve real problems.  This would provide students with two types of motivation and would lead to a more engaged class.
The final and perhaps most productive way to utilize wikis would be with a class inquiry project.  The class could come up with their own advanced and detailed real world question.  One of the examples may include: "How many square feet is the entire school?" Each student could be responsible for a certain part of the school.  After a student determined the area for their given section, they could then post their results and process on the page.  If a student was having difficulty figuring their section out they could use other student's post to help them.  Eventually the class could take all of their findings, add them together, and get the actual total.
There are many ways to utilize wikis in the mathematics classroom.  I hope the examples I have given will provide others with inspiration.  My examples however, are only the tip of the iceberg.  Go to  http://www.teachersfirst.com/content/wiki/wikiideas1.cfm for a plethora of ideas.