Barb's Presentation

This presentation caught me off guard.  Going in I did not realize that Barb was non-verbal and has Tourette's.  I assumed she would be physically talking about her life and her book.  This obviously did not cause any issues because she was able to communicate through her I-pad.  This leads me into the use of facilitated communication.  For those who are not familiar with facilitated communication; "it is a process by which a person referred to as the "facilitator" supports the hand or arm of a communicatively impaired individual while using a keyboard or other devices with the aim of helping the individual to point and thereby to communicate" (Wikipedia).  The presenter that helped Barb was the "facilitator" as Barb used her I-pad to communicate to the audience.  At first, this seemed to be amazing; and it was interesting to see someone with autism an apraxia to use this technology.  After seeing facilitated communication first hand, I decided to do a little research about this practice.  The following article submitted by the American-Speech-Language-Hearing Association (ASHA) discusses the intent and implications of facilitated communication.  FC has drawn skepticism and left me doubted after seeing and researching.  It was hard for me to understand how it could be possible for a person that does not speak or read to develop the capability to spell out words in a diverse vocabulary.  Barb seemed to understand what was going on and could actually type using the technology, but with the facilitator's help it seemed she was being led into what words to type.  The words that the facilitator wished to speak, not necessarily the words that Barb thought.  The support of a hand on the back was obviously helping Barb to regain focus and deal with her apraxia.  However, it seemed like her hand remained in the same position as the facilitator moved her to the necessary letters on the keyboard.  We were told that she is capable of typing emails and this method has allowed her to open the lines of communication to many people.  This I believe is her own words and thoughts.  Other words that I felt like was truly hers during the presentation were the constant announcement of "goodnight".  I know she has Tourette's, but to me 'goodnight' was what she was trying to tell everyone, she was tired and ready to go home.  I do not intend to take away with the possibility of someone with autism communicating and having their own thoughts.  It just seems outlandish that an 'aut' could develop answers to questions completely on her own.
     The presenter, forgive me for forgetting her name, talked about psychology and the expectations that are set for students and persons in general.  Her analogy of the rose and other types of flowers through testing seemed to be a little askew.  I agree that we hold students to norms, but these norms are created by using tests that are given to everyone, not some made up standards that cannot be met by most individuals.  She used the example of a rose being the "premier" flower with other types of flowers falling short and considered as lesser flowers that have issues.  These norm-referenced scores are calculated into a bell curve that is used to evaluate everyone.  However, the presenter made it seem like these tests had no validity or relevance.  I understand the complications with norms but it remains a standard way to assess, not a test that is pulled out of thin air.
   

#8

In this high school case study senior history students are uninterested and misbehaving.  Due to the time of the class and the age of the students they do not pay attention are causing a distraction to other class members.  Some students are paying attention and would like the opportunity to learn but this opportunity is being minimized by the disruptive students.  A behaviorist could tackle these issues in two different ways.  First, the disruptive students could be handled by administering punishment.  Because they are behaving in ways that need to be eliminated, the teacher could give more homework, take away fun things, or physically "call out" these students in the middle of class.  Another way of handling this situation is to address the students that are behaving properly.  You want to encourage their actions and hope that the other students will take notice of the treatment that the well-behaved students are receiving.  In order to reinforce the well-behaved students, you can present negative or positive reinforcements.  You can give these students less homework (negative reinforcement) or you can give a reward for their good behavior (positive reinforcement). 

The main difference between the way a behaviorist and a constructivist would handle this situation is addressing the behavior or addressing what is causing the behavior.  I would assume that a constructivist would attempt to get the entire classroom's attention by changing the instructional strategy.  The behavior must be addressed but not necessarily punished or reinforced.  Instead of calling out individuals, you could address the situation as a class and talk about what problems the misbehavior is causing and why it needs to change.  This website talks about different ways to address behavior issues in a classroom from a constructivist perspective.  It is important to realize the repercussions that may occur from always punishing bad behavior or always positively reinforcing good behavior.  Sometimes good and bad behaviors can be overlooked individually and the whole class can benefit from a group discussion.  I believe that constructivism will play a larger role in my classroom due to my level of expectations for my students.  I hope that my students will use the knowledge that I provide them and the things that they learn from the class to create their own ways of thinking and learning.  This will promote higher level thinking and help my students understand concepts within math.

Metacognition Lesson

The first thing I came across during a google search was this web page that leads to an activity a teacher did in her 2nd grade class.  I think this activity is amazing and could work at many different ages.  The activity described helped me come up with an activity that would be useful in my high school math class.  Sometimes math can be hard to understand, point blank.  However, I believe using different techniques and activities can help students relate to the material.  In a geometry class, I could use a meta cognitive activity to help the students understand.  A lower level geometry class would require students to be able to construct different polygons via angles.  I could start a lesson by reviewing angles with the students.  This will allow the students to question how much they remember about angles and if they need further explanation.  Once the angle review is completed, I would move into the actual lesson.  I would have the students construct different polygons using their knowledge of angles.  Hopefully, I would have access to different materials to have my students construct the shapes physically, rather than simply drawing.  This activity will require true understanding of the rules and laws associated with angles and shapes.  If the students do not fully understand, they will have trouble constructing more complex polygons, i.e. something other than a square or triangle.  However, the knowledge of triangles and squares can help them create a different object.  In essence, this activity will require constant use of meta cognitive skills.

#6

Skills are accumulating throughout each year a student learns math.  Everything in math builds on something that was previously taught.  In order for my students to truly learn mastery of the content, they have to master the basic skills and remember how to apply them.  Simple building blocks in math should be mastered at an early age in order to understand larger concepts in high school.  My job will be to reignite the information that the students may not remember from earlier years.  This includes simple things such as: order of operations, simplifying fractions, showing all work, etc.  These skills are necessary to carry over into higher mathematics and will prove worthy in mastering the content.  This blog discusses the importance of content mastery.  I realize this may not be the most credible source, but the information does seem to come from a high school teacher with quite a bit of experience.  She points out the significance of teachers' mastering content and being able to relay this knowledge to the classroom.

Memory

 

Because students learn at different rates and will retain some information quicker than others, it is the teacher's job to help the process.  At every age of life, our memory is tested daily.  Some things are remembered because of the importance level and others are memorized from silly mnemonics.  Although mnemonics may be silly, the strangest ones often are the most committed to memory.  We have learned different techniques to aid long term and short term memory retrieval.  As teachers, we must realize that each student is going to have different methods that work specifically for them.  While teaching math I will have to focus on helping students commit many formulas, strategies, etc. to memory.  This will be a daunting task, considering many high school students do not care about math.  I believe the way I teach will promote different types of memory devices that will help my students.  Mnemonics are used in all levels of math, from the simply "Please Excuse My Dear Aunt Sally" for order of operations to SOH-CAH-TOA for trig functions.  Simple classroom discussion can also trigger memory.  Thought provoking questions and questions that are directed towards students' interests can help the memory process.  This web page provides a nice table of strategies and characteristics for multiple age groups.  It is very important to remember that our instructional methods will greatly impact what students remember. I also believe that allowing students to collaborate and work on assignments together will aid in the understanding process. Sometimes, peers can explain the information in a manner that is easier to understand than any teacher.  Obviously, we do not want memorization for every detail and topic in the course, but formulas in math have to be memorized.  The idea is to help the students relate the given formulas to real applications and understand why each part of the equation works.  Having activities that ask students to explain the problem and answer will help with the application process.  My grand idea behind memory is that I don't always have to be thinking 'how can I get students to memorize this idea?'  Rather, I should be helping students apply the knowledge I have taught them and help them truly understand the idea. 

A little shout out to the music ed. folks.

Skills

My math class will require students to have a mastery level of many different skills.  These skills will build off of one another from the very beginning of the semester.  Vygotsky would consider my type of teaching as a scaffolding method.  I believe it is very important for math students to have the foundation and a strong network of knowledge and resources in order to become successful in mathematics.  I would hope that most of my students will be at a formal operational stage of most topics in math.  However, for those students who have not reached this developmental stage, I will have to backtrack and provide the instruction to bring them up to pace.  Once the students have reached a mastery level, they will be able to apply the skills they have learned to a real life situation.  This will help my students progress in their educational careers and their lives in general.

Assessment

At any level of Mathematics assessment is very important.  Everyone has heard the saying, "to learn math, you must do math".  As a high school math teacher I must remember that students will need to practice, practice, practice.  With that said, I must keep in mind that the practice needs to be evaluated.  There are many different ways to assign math work to students.  Considering the fact that a lot of students do not enjoy math, I must find ways to interest everyone.  Assessments can be good for the student but even more valuable for teachers.  Formal and informal assessments can be used throughout the year to monitor progress.  A very important informal assessment could be unannounced quizzes.  I feel like that checking students' progress via pop-quizzes will help me assure that students do not fall behind.  I do not feel that each quiz would be graded necessarily.  The purpose of such a quiz would simply be for me to check progression.  Another informal assessment could be checking homework problems occasionally.  Yet another way to assess informally would be to have the students write down a real life application of the theory or topic that I covered during the class period.  An exit pass could also be used to allow students to express concern, ask questions, or answer a brief question.You can check out more examples on this webpage.  Obviously, we have to use formal assessment to prepare students for the standardized tests and for grading.  The most used formal assessment could be a planned exam covering a certain unit.  The state and nation uses different standardized tests to place students in proper courses and to assess the knowledge learned over an entire semester.  In math I will more than likely have constant formal assessments in the way of worksheets or problems from the book.  I could mix formal and informal with these assignments by grading a pre-determined set of problems or not telling the students which problems will be graded for correctness.  I could also use different games as a formal assessment.  Grouping into teams and performing required skills could allow for kinesthetic involvement as well as a good way to assess the students' knowledge.