EPSY 490 OL Essays
Metacomprehension Metaphor
Metacomprehension is being aware of your understanding of the text while reading. A metacognitive reader is constantly assessing if they understand what they are reading. They will recognize if they do not understand a word and seek out its meaning. They will recognize if they are familiar with the topic and who or what is being talked about while they are reading. If this understanding is not there, they will go back and look for clues to help them form an understanding of the text and then read on. An example of this would be to ask questions like, “Does that make sense?” or “What is this about?” or “What are they trying to tell me?” It is a conscious effort to ensure that you comprehend what you are reading.
What makes it meta is that brain power that is used to actually read the text is also used to assess the reading comprehension. It is another layer of thinking that assesses the first layer. What the metacognitive reader is doing is using brain processes not just to read the text but also to be aware of their understanding of the text. They are reading words, interpreting sentences, assigning adjectives to nouns, adverbs to verbs, and at the same time using other brain processes to evaluate their understanding of the reading. With this extra level of thinking going on they are able to make adjustments to their reading while in the process.
A metaphor for how metacomprehension works can be found in our new government administration. President Obama last month appointed a new position to government, Chief Performance Officer (CPO). The CPO will work in the Office of Management and Budget. (Nancy Killefer was appointed to the post but recently withdrew her name because of tax issues.) The position is popular in very large corporations. In essence the CPO is responsible for assessing the effectiveness of the organization. In the case of the President’s CPO he or she will be responsible for continually assessing if the government is working effectively and efficiently, spending money wisely, passing legislation, helping the American people, and keeping the country safe. The CPO will analyze the procedures and strategies that are working and will look for reasons why some strategies fail. Based on the CPO’s insider understanding of the goals and processes of government, he or she will ask the questions necessary for the government to assess its effectiveness. They will continually report to the president and appropriate parts of government to keep them aware of how they are doing.
The government will become more aware of their processes because of a government employee. The government is self-assessing and making adjustments based on how they are performing as government. The metacognitive student does the same thing when reading. He or she is using their insider information (a clear knowledge of how their own brain operates) to assess the effectiveness of their reading. They can learn about strategies that work like highlighting words, repeating parts out loud, reading while pointing to the words, and continue to develop those strategies. Just as the CPO is looking at failures, the metacoprehensive reader will recognize sentences that were not understood and go back to look for the meaning.
Just as metacomprehension uses the brain to be aware of and assess the brains comprehension, the CPO position is the government assessing the government’s performance and effectiveness. In each case it is a matter of an entity self assessing. In the case of the reader there is no teacher asking them questions along the way, it is up to the reader to do his own assessment. In the case of the CPO President Obama promised more self regulation and this in certainly the case. It is not a separate lobby group or special interest organization that is making these assessments and adjustment for the government, but rather the government actually self-regulating.
REFERENCES
Standiford, S. M. (1984). Metacomprehension: ERIC Digest. (ERIC Document
Reproduction Service No. ED250-670) Retrieved February 12, 2009, from ERIC
database
Cognition. (n.d.). Retrieved Febrary 8, 2009, from Wikipedia: http://en.wikipedia.org/wiki/Cognition
Standiford, S. N. (1984). Metacomprehension. Retrieved February 8, 2009, from ERIC: http://www.vtaide.com/png/ERIC/Metacomprehension.htm
In Learning and Instruction, Mayer defines metacognition as the “knowledge and awareness of one’s own cognitive processes” (2003).
Mayer, R. E. (2003). Learning and Instruction. Upper Saddle River, New Jersey: Pearson Education, Inc.
Standiford, S. N. (1984). Metacomprehension. Urbana, IL: ERIC Clearinghouse on Reading and Communication Skills. (ERIC Document Reproduction Service No. ED 250 760)
Writing Curriculum
The class that I plan to implement this writing curriculum is in a 9th grade algebra course. These are students in their first year of high school who are in need of motivation to practice and understand math. The writing would be designed to have the students explore their own methods of how to solve various math problems. We try to emphasize metacognition in solving problems. We want the students to think about the steps that they are taking to solve problems. For so many students entering high school there is a notion that to be successful in math it only takes memorizing some formulas or making sure worksheets are filled out one way or another. What we struggle with everyday is convincing students that being successful in math involves becoming proficient at problem solving. They need to be able to understand the problem that is presented, understand what kind of answer needs to be produced, understand what processes might work to accomplish this, and understand how to go through these processes correctly to come up with a solution. While a base knowledge of facts and formulas is important, mathematics is more about a process that the students must go through to solve problems.
Here is where a writing component works perfectly. Having the students write about the processes that they go through would re-enforce the idea that mathematics is more about that process. It is more important to pay attention to the process that we are going through rather than worry about the answer. Many teachers including myself grade in such a way that the work shown on a test counts more than the final answer. I have even given tests that have the answers on them already and all the students have to do is show their work. I want the students to think much more about these processes. I want them to be problem solvers.
A writing curriculum in an algebra would come in as a review writing assignment in each unit of study. After each section the students are required to write about the process that they take to solve a particular problem. According to Hayes and Flower the three processes of writing included planning, translating, and reviewing (Mayer, 2003). These will come in to play in a somewhat unique way when writing about mathematics.
The planning process would involve students thinking about the steps that they need to take. From their long term memory they will have to recall all the necessary information and steps needed to solve the problem. This can be done by showing how to do an example problem. Students may need to look at old problems that have been worked out already if they can not remember. What this forces the student to do is look at a problem and ask themselves, "What is going on at this step?" This is exactly how we want everyone to be thinking about each problem. It forces student to think about the steps and think of what is actually happening. They can write notes to the side on what steps they are doing to help in the translating phase.
In the translating process students are required to turn these steps that they took to solve a problem into a general script to solve all types of problems of this nature. They will have to fully understand what was necessary in doing a step and why that step needed to be taken. This is where the writing process will help build enduring understanding of the material. If they are able to take what they did to solve a problem and translate it into a general process for all problems then they are showing a strong understanding of the content.
To ensure that this process that they wrote about works it will need to be reviewed. General text editing will be needed such as grammar and punctuation but also the students will have to see if the process works for all types of problems. They will be given alternative problems that have something different like a negative number where a positive was before and check to see if their process still works.
This writing component in algebra supports school wide efforts to increase reading and writing in all subject areas. Traditionally there is not a lot of writing in a math class because of time constraints, the emphasis on solving problems for multiple choice questions, and lack of expectations from students and teachers. I believe that a writing component in math can be fit in and would end up saving time in the long run. The increased understanding and stronger connections to memory that these kind of assignments produce would result in less reviewing of old material in later courses. Many students forget about a lot of these processes from year to year. A writing component would help fuse these concepts into long term memory.
References
Mayer, R. E. (2003). Learning and Instruction. Upper Saddle River: Pearson
Misconceptions
There are two main categories of misconceptions that I see in school everyday. One category has to do with misconceptions about the concepts that we are learning in class. In mathematics there are many misconceptions about the way we represent things with variables and how these can be manipulated. There is another category of misconceptions in our school. This other type of misconception is that learning is something that happens to a student rather than by a student. Unfortunately this second kind of misconception is shared by fellow teachers when trying to learn new technological tricks.
Algebra students are full of misconceptions. Some will struggle with positive and negative numbers. They will say that -11 is greater than 3. This kind of misconception can be dealt with using a number line. If students get used to visualizing these numbers on a number line than they can successfully manipulate the numbers. A student who can clearly see that -11 is to the left of 3 will be able to accurately determine that -11 is less than 3. The student who only perceives the number and does not worry about the negative sign continues on with this misconception. This gets progressively worse when the student needs to perform calculations on these numbers. Adding and subtracting negative numbers can be a nightmare for students who hold onto this misconception. Simple memorization tricks can help when multiplying and dividing but that will not help with the misconception. Students need to understand what negative means to be successful in mathematics.
Another common misconception in algebra is combining unlike terms. Students given 2x + 3 will sometimes simplify this to 5. The student does not see that they are separate terms that can not be combined. This misconception can wreak havoc in algebra because of all the calculations that need to be done with terms that have different variables. While it is necessary to think of 2x + 3 as "two x's plus three" this is very often just thought of as "two plus three." This misconception gets at the heart of algebra. We are using variables to represent different unknown values. If this is not understood at first the misconception will continue. The student will need to deal with his or her understanding of what a variable is for before then can start manipulating equations.
The list of content misconceptions goes on and on but there is another category of misconceptions that affects students of all ages. This misconception is when the student sits and waits for the information and understanding to be handed to them by a teacher. This student does not think of learning as something that they have to actively participate in. They expect it to happen by the teacher saying something to them, or by them getting a worksheet filled out one way or another, or by getting the notes copied down, or by just sitting in class. Max Roosevelt wrote in the NY Times about the changing expectations of college student. He described this same phenomenon at the college level. He even mentioned a survey at UC Irvine where a third of the students think they deserve a “B” for attending lectures (Roosevelt, 2009). This is a difficult misconception to deal with because it involved an attitude change. The student needs to see that it takes a genuine effort to activate the brain enough to synthesis materials together and create a learning experience.
Teachers who are asked to add technology to their classroom will sometimes have a similar misconception about learning. Because many of the tasks on computers are automated, there is a misconception that the computer needs only to be set up once by some tech and then it will continue to do exactly what it needs to do for the rest of time. This leads to trouble when a class roster needs to be updated in the middle of the semester or the folder where grades are saved has to be deleted because of a virus. Many things come up throughout the year that require a knowledge of the computer and the programs that run on them. Just like for the students it takes a genuine effort to understand how the programs work and how a computer store files and runs programs. When helping fellow teachers with I insist on them using the mouse and I just help them through certain tasks hoping that they will start to feel comfortable manipulating things themselves.
In my instruction I constantly ask questions. Mayer talks about guided discovery being better in the long term than expository instruction (Mayer, 2003) There is never a time when I tell someone an answer. Even throughout presentations of notes I will not spoon feed information to students. For example, before telling the class about the rules relating angles, arcs, and chords of a circle, I will present the class with a circle I can manipulate on the screen. Through a series of questions I will lead them to the discovery of rules. Many times in my class students will ask, "Why didn't you just tell me that in the first place?" I always reply, "I'm not here to teach you, you're here to learn!" I am fortunate to have a student response system for my class. Now I set up my presentations with questions that each student needs to answer. This way every student is forced into this discovery mode, and then challenged to apply the information we just learned. Each student needs to click in an answer during instruction. I set these questions up before presenting information to gauge prior knowledge and to get the students in the correct mind set. Then I will ask questions about the material presented to see if they can apply it right away. With the instant feedback from the student response system I can see if we need to spend more time on the material or not.
References
Mayer, R. E. (2003). Learning and Instruction. Columbus: Prentice Hall.
Mathematics Website - Arcademic Skill Builders
Right now I have about 30 different sites that I have used in one way or another in my math classes. (www.del.icio.us/hohmanprovement) I've been trying different ways to engage and motivate students. It is difficult to keep the interest of students who have had little successes in math up to this point in their education. I have used sites like Hippocampus, Agile minds, ALEKS, and NOVEL that are a complete curriculum with videos, practice problems and quizzes. These can work for dedicated students who are willing to spend lots of time on them, or if there is a lot of time set up in class to work on them. If this is not an option then just parts of them can be used to further explain certain concepts that the students might be struggling with. These websites take advantage of the computer being able to instantly grade quizzes and give immediate feedback to the students. They also are able to dynamically create questions so each student has a unique test or quiz. However, they do not take full advantage of the interaction allowed by the internet.
There are some fantastic manipulative websites that take advantage of programs like Geometers Sketchpad or Geogebra. Students can move parts of shapes around and discover how the angles or sides are changing with relation to each other. The National Library of Virtual Manipulatives has just about every basic manipulative activity that you would want for an algebra or geometry class. These sites really start to take advantage of the internet and it's interactivity.
Then there are gaming websites that are usually quickly accepted by the students. While they generally don't teach an entire curriculum they can take the place of practice that is so often overlooked in math. The website that I took a closer look at for this essay is www.arcademicskillbuilders.com.
The intended students are any k-12 student needing practice in basic math skills like addition, subtraction, multiplication, division, fractions, or ratios. There are also some language arts games provided. Students are expected to perform these basic functions in their head. So many students are tethered by their calculator when coming into high school. I have often taken calculators out of student’s hands when they go to punch in 5 + 8. Students get used to relying on the calculators for these simple calculations. They are denying themselves the conceptual understanding of adding, subtracting, multiplying, and dividing. This slows down their ability to grasp the larger algebra concepts that need to be understood. These games force students to perform these calculations without the aid of a calculator.
The way these games work are very similar to popular video games. There are racing games and "shoot-em up" games. For the racing games students are given a problem to calculate. If they punch in the right answer their vehicle goes a little faster. If they get it wrong they slow down a little. Another question quickly pops up to give them another chance to increase their speed. This creates an exciting and highly motivational situation where the students need to answer quickly. Games only take a few minutes and the students are quickly restarting the game hoping to go a little faster. They are getting better at the game by getting better at doing basic calculations in their head.
Interaction with this website is where it really takes advantage of the internet. Students are able to set up multi-player online games. They can race other students in the room or other students across the world. A public game can be created where anyone can join. In all the times we have done this other students from other schools have joined in. The website does not allow personal information to be shared, or inappropriate names to be used while playing. It is safe for all students. Private games can also be created where the students create a password so only the students in the lab join. Either way they are motivated to go faster and win the game. Competition with real people is another motivational factor that increases engagement.
The teacher only needs to show students the option of starting multi-player games. Once one game is started they are off. Students will call out that they are starting a race, others will join, and then there will be silence for 3 minutes while they are each concentrating on their basic math skills to win the race. Students are also very motivated to keep the games going as competition increases. While these kinds of races are not for all students, the teacher may direct other students to play their own single player games.
Assessment of student learning comes in back in the classroom when working on other problems. Many algebra and geometry problems end up needing simple calculations to move on. When student are able to perform these calculations without the aid of a calculator the learning is apparent. Arcademic Skill Builders is a powerful and simple website that fully takes advantage of the internet. It catches student’s interest with well developed games and interactivity.
Assertive Discipline
Assertive discipline is a classroom management technique developed by Lee Canter. In its essence it is the belief that rules are set for the classroom and those rules must be followed. If they are followed then students are rewarded. If they are not followed then students are given consequences (Assertive Discipline 2008).
The traditional form of assertive discipline takes a strong leader who is clearly above the rest who sets the rules. This is most likely the style of assertive discipline that adults remember. In many adult groups there is the notion that everyone is equal and there is no one person who is "above" the others. In this case there the only way assertive discipline is used would be through self regulation. Other groups have a leader whether it is elected or for some other reason. In these cases assertive discipline is more likely to be used. A strong leader with a clear vision will be able to enforce the rules because they are motivated by the end product. Leaders who are using assertive discipline just as a tool for management will not be as successful.
I have been a part of many different sports teams. The goals have always been different for each. Some teams have just been formed for the social benefit of playing on a team. In this case the there no clear leaders who need to use assertive discipline or a coach who employs those strategies for the team. Other teams that I have been on had goals of conference championships. In these cases there was a need for a strong leader. In some cases it was the coach and in other cases it was from a team member. In either case it was clear to the leader that the team had a clear goal to work towards. In was necessary to go to practice, eat well, play hard, communicate well, and so on. These were all necessary for the team to win. If a member was not doing one of these things there were clear consequences. A player who was late for practice was given a consequence like running extra laps, or sitting out the next game. Players who were always there and working hard were rewarded with playing time or other types of recognition.
When there are clear goals that require dedication to meet those goals, then assertive discipline fits well. If groups are only together to socialize then it is not necessary for assertive discipline.
In schools there is a need for assertive discipline but this can not be military style "do as I say" management. The use of strong assertive discipline with low emotional connection lead to poor behavior in children. Strong assertive discipline and high emotional connections lead to good socio-emotional competencies(Towe-Goodman.) We can not just use strong assertive discipline for disciplines sake. There needs to be a strong reason behind it and there needs to be an emotional connection with the recipient.
Assertive Discipline. (2008, May 4). CTER. Retrieved May 3, 2009, from WikEd Web site: http://wik.ed.uiuc.edu/index.php/Assertive_discipline
Active Listening
The idea of relating school material to students life has been around for some time. Apprenticsships have made real world skills a priority when instructing our youths. This direct relationship to the real world is lost somewhat in the new school model. It is important for use to make those connections to the real world. Glasser argues that we need these connections and the following needs must be met: survival, belonging, power, freedom, fun (Control Theory 2008.) In writing a curriculum I kept these principles in mind.
Curriculum
The algebra ciricullum is one that is best done in order so there is little ability to discuss this. However it can be determined by student surveys what special topics would be used and an overall theme for the various units.
Class Organization
Seating chart will be created by the students. The rules and regulations will be come up with as a group. They are created and voted on.
Activities to satisfy student needs
Student run presentations
Student led field trips around the school area
Field trips to various local organizations to show importance of education
Projects can be done in various forms: powerpoint, poster, song, dance, movie etc.
Classroom Rules
School-wide Discipline
Student surveys conducted to determine the most important rules
Student surveys conductied to determine the most appropriate consequences
Meetings will be held at the beginning of the year (after school rules are determined) and all staff will decide on how to enforce all rules.
Consistency will be most important when implimenting school-wide discipline.
Grading Procedures
At the beginning of the year students determine what will be the best percentage for major and minor grades.
The grading policy is then part of the contract for students to sign.
Grades will be posted weekly for students and parents to view.
Characteristics of a Quality School
All school policies are expressely displayed and communicated with the students and community.
There is consistancy across all subjects and grades in terms of what is expected of the students.
All staff greets students as they enter the building or classroom.
Control Theory. (2008, August 16). Retrieved May 2, 2009, from WikEd: http://wik.ed.uiuc.edu/index.php/Control_theory
SKEP - Classrooms where Student Responsibility and Contracting are Promoted. (2007, January 20). Retrieved April 18, 2009, from WikEd: http://wik.ed.uiuc.edu/index.php/SKEP_Classrooms_where_student_responsibility_and_contracting_are_promoted