The paths to "Eureka" moments: Teaching Mathematics in Secondary Education

Archive for March, 2011

Showcase Lesson Plan – Functions as Literal Equations

As a result of the conclusion to my first quarter in the Education Program at Seattle Pacific University, I have completed my first showcase lesson plan!

Please view it, and give me your feedback!

Attached are four documents which make up a showcase lesson plan centered around a lesson titled: Functions as Literal Equations.

The documents are as follows:

1) Unit Plan Alg1

2) csc function lesson

3) Functions as a Machine of Literal Equations Rational

4) Function Lesson

Service Learning Project

One of the requirements in my Introduction to Education class was to participate in a service learning project. My own experience took place at Coe Elementary School in a 3rd grade classroom. I was an aid to the teacher once a week for a total of 21 hours.

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Below is a paper written describing how this experience has changed my understanding of the four pillars: Service, Leadership, Competency, and Character.

Service Learning Paper: Where I Was and Where I Am Going

As I reflect upon my time spent at Coe Elementary during my service learning hours, I am able to compare my initial understanding of how service, leadership, competence, and character, are seen in the classroom, to my previous understanding.

On the first day of Intro to Education, I wrote the following four definitions as they apply in the classroom setting. First, service is observed in a classroom when the teacher understands that teaching is not about his/herself, but about the student. A service minded teacher will make sacrifices for the students to promote better learning. Secondly, leadership is demonstrated when the teacher leads the class both instructionally and as an example. A leader recognizes the skills of those who follow him/her, and seeks to enhance those skills. Thirdly, a teacher seeks to promote competence – the ability to understand the subject matter. This involves problem solving and not simply memory recall. Fourth and finally, a teacher develops character in the classroom. Responsibility, integrity, and creativity are all elements important to education.

After having spent eight weeks in a third grade classroom, my views have become enhanced by the experiences I have had and the interactions I have observed.

As a teacher, service not only takes place inside the classroom, but in the community and among educational faculty. This can take the form of anything from an after school program like refereeing a student football game, to spending hours at night working on prepping for an in-class Mother’s Day project. A leader in the classroom knows the abilities of the students. A leader is able to multi-task, teaching new information to the entire class, but also providing individual feedback to students, asking them questions and challenging them at a personal level.

A competent teacher not only knows the subject matter to be taught, but knows it well enough to teach excellently. In order to ensure competence, a good teacher will continue their own education. This may be pursued by working to get a higher degree or through attending educational conferences and classes. Teachers must also promote competence within their classrooms. One way I observed this being accomplished in the third grade classroom was through peer discussions. Students explained to their neighbors what they had learned and their partners either added to or disagreed with what the first student had said. In this way, students were getting immediate feedback as well as demonstrating their understanding of the topic. Finally, character should be demonstrated by the teacher and encouraged within the student body. Teachers can be the example in character, by teaching “to the student”, not the test, and having organized lessons for efficient time management. Teachers can also encourage moral character within the student body through classroom policies and school-wide programs. Respect is one characteristic that must be shown to students in order for them to follow the rest. When teachers have the respect of their students, other important traits such as integrity, trust, and responsibility will follow.

As I conclude my volunteering at Coe Elementary, I plan to continue learning and growing in the four areas of service, leadership, competence, and character. In service, I will grow as I serve as the Sports Ministry Coordinator for Youth Missions International. Through Y.M.I. I will have the opportunity to work at sports camps, coaching elementary and middle school children. While the academic quarter continues, I will seek to serve my peers and colleagues here at S.P.U, striving to live a service-minded lifestyle on and off campus. As a staff leader with Y.M.I, I am constantly being challenged to grow in leadership skills. One particular challenge is how to assign volunteer leaders to the different camps in the Northwest. As the coordinator, I must assess the abilities and gifts of the volunteers and place them where they will work best. I will continue to grow in competence as I finish out my mathematics major and secondary education program here at S.P.U., but my education will not stop here. After I have graduated with my B.A, I will continue to learn about my field and how to be a better teacher. This will most likely take the form of a Masters degree. As a Christian, my education of character is never complete here on earth. As I continue in these last few years at SPU, and look forward to my career as a teacher, I will mold my character after the Greatest Teacher.

 

 

Film Review: Equality (1950-1980)

This post reflects on the film, Equality (1950-1980). Throughout the reflection, three questions will be answered.

1) Do you see any race inequalities in the film?

2) Is education a civil right?

3) What is our view of children and adolescents at that time?

Do you see any race inequalities in the film?

  • During the 1950’s segregation was a dominant theme throughout schools. Segregation was seen in:
    • Proms
    • Student government
    • Sports teams
    • School population
  • In many cases, schools were either all black or all white, depending on the location of the school.
  • Parents fought segregation of schools, wanting integrated schools
    • Boards thought they were separate but equal—this was not so.
    • Often the white suburban schools were well stocked and funded, while African American Schools were underfunded and without proper resources.
  • Beginning in 1930’s but continuing through the 50’s NAACP lawyers traveled to schools and inspecting to prove that African American schools did not have equal-facilities, resources, or environments.
  • In the late 1960’s many Mexican students were integrated into schools. Yet, most teachers were Anglo-American. These students were not allowed to speak Spanish in class, and textbooks did not reflect any positive aspects of the Mexican culture.
  • In Crystal City, school “walk outs” reflected a reaction to lack of equal education toward minority students. The action of going on strike was found necessary when the board of education in abruptly adjourned an educational meeting and debate in which students and protesters were voicing the needs of minority students.
  • As a result of the strikes, Crystal City schools became a laboratory for bilingual education.
  • At this time, several lawyers sued the San Francisco school district who taught English only. Equality of education requires different treatment to student of different languages.

 

Is education a civil right?

  • President Johnson- equal chance at education, meant equal chance at life
  • Civil rights act of 1964, banned discrimination on basis of race or ethnicity in any federally funded institution, including schools.
  • By the early 1970’s, feminist leaders pushed for movements which advocated women’s rights
  • At this time, it was legal for an educational institution to have a quota of women admitted to a graduate school.
  • Title 9 – 1973 had a groundbreaking precedent that if men and women were going to have equality in sports in schools, they should have equal funding.
  • Before Title 9, textbooks and reading books encouraged gender inequality by picturing boys as active members of society, while women stayed at home and cooked and cleaned.
  • Girls were discouraged from math/science, while boys were encouraged in sports
  • Title 9 said, you could not put men and women together in a sport and pick the best players (most often men), but there should be principals of equity in sports, (i.e. two sports teams, women’s leagues ect.)
  • As a result of Title 9, textbooks changed, sports teams for women were created, graduates of both men and women were close to equal, and job/career movements changed.


What is our view of children and adolescents at that time?

  • Movements of education representative of movements in adult life.
  • Children and adolescence became the training ground for change in society.
  • For the first time, all children and adolescence, both male and female, black and white, began to have the same rights and were given the same opportunities within school.

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This film is part of a series of four called:

School- “The Story of American Public Education”

It was produced by PBS and narrated by Academy Award winner Meryl Streep. For more information see link: http://www.pbs.org/kcet/publicschool/


Reflective Book Report: The Angel Inside Went Sour

Reflections on “The Angel Inside Went Sour”

Dr. Esther Rothman’s book, “The Angel Inside Went Sour” documents her position as the principal of Livingston School for girls in New York, beginning in 1959. Rothman, a well experienced teacher with a doctorate in psychology was highly qualified for any principal position by the time she was assigned to Livingston. This school was special in that it was the final destination for troublesome girls; a place where they were sent when they had been suspended from multiple public schools and even failed in the correctional schools. As a principal, Dr. Rothman drastically changed the daily routine and methods of Livingston. She hired teachers who could not only teach, but who loved teaching. Teachers at Livingston had to love learning from their students and be willing to put up with and love students who: used dirty language as their main vocabulary, acted without a sense of purpose, were frustrated with life, yet, fought to survive and keep above the water of hopelessness (Rothman 1972). She describes many examples and scenarios in which she both failed and succeeded in reaching out and showing girls that they were loved and could make something better of their lives.

Personally, I thoroughly enjoyed “The Angel Inside Went Sour”.  Through Dr. Rothman’s words, I was able to step inside the inner city school of Livingston and catch a glimpse at what real teaching is all about. At first, I was a bit shocked at the attitudes and vulgar language that the girls used; Rothman thoughtfully included word-for-word language of the girls for authenticity and honesty. But as I continued reading, I was thankful for the exposure to the everyday experiences that the teachers at Livingston had.

As an inner city school, Livingston was filled with girls from extremely rough home lives. Girls faced situations and experiences I could never dream of living through. I loved how Rothman took the school day and flipped it upside down by having the students choose their own schedule and which subjects they wanted to learn. This not only showed me the importance of giving students choices, but even a bit more control when they have none in their personal lives. I realize that this exact example is next to impossible for most schools, but in principal, the idea of breaking the mold, and molding education to fit the needs of students is revolutionary and very applicable to the classroom today.

Livingston was also a very multicultural school with the minority being white students. Rothman treated students of different ethnicities equally. She seemed to see race as a cultural boundary (Banks, 2010). Her staff was comprised of a mixture of races. Through her eyes, whether it be a student or teacher, she saw them as people. Dr. Rothman and her teachers did not simply overlook race and culture when teaching, they embraced it. They allowed the culture to change their curriculum so that it was designed specifically for their students (Banks, 2010).

I was continuously inspired by the way Dr. Rothman handled difficult situations and difficult students. Her methods were grounded in getting students to understand why they were hurt, why they felt the need to lash out at others, and how they might better fix the problem by being in control of themselves. She rarely “punished” girls. Punishment seems to be the easy way out of a problem, without really solving it (Rothman, 1972). Instead, Rothman worked through problems with students and found ways of rewarding those who were able to work through problems on their own.

As I continued to read, I was awestruck and challenged by the lives of the teachers at Livingston as well as by Dr. Rothman herself. They were able to see past the behavior of a student, and look deeper into the lives and hurts of students, in order to heal their broken self-worth. Students, no, people, came first. When a girl was at Livingston, she was not there to improve her reading, writing, or arithmetic; though she often did so. She was there to learn about herself, and hopefully come to the realization that she could be more. Teachers needed to be good at their subject. So good, so as to attract the attention and curiosity of girls who chose what they felt they should learn. But more than experts in their field, teachers needed to be invested in the lives of their students. They had to care more about the girls than they did about being cussed at. They had to care more about making a difference in the lives of their students than their test scores. These were real teachers.

When I am teaching, I hope to be able to model myself after the teachers at Livingston. They saw past race, social economic status, and reached out to hurting lives. Through respecting the students, and treating them like breathing, feeling, human beings, teachers were able to connect with students and make a difference. I want to put my students first. I will put their personal growth before my classroom agendas and be sensitive to the lives which they live. From a multicultural standpoint, I will defy racial and ethnic stereotypes and treat my students with respect. Doing this, I hope to also look through the behaviors of my students and dig deeper into the hurt causing their angel inside to be sour.

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References

Banks, J.A., & Banks, C.A. (2010). Multicultural education: issues and perspectives. Hoboken, N.J.: John Wiley & Sons

Rothman, E. P. (1972). The angel inside went sour. New York, N.Y.: Bantam Books.

 

Book Summary: Cry the Darkness

This summary is meant to inform readers of the plot and theme of Donna L. Friess’ book, Cry the Darkness.

  • Donna L. Friess, P.H.D.
  • 275 pp.
  • Appropriate for mature high school readers.

Donna L. Friess’ novel, Cry the Darkness, is her own story about the sexual abuse she and other female members of her family suffered from her father. Her story is one of working through the shame, and making a better life for herself and her family. When she learns that her little niece is also being abused Donna is given the much needed courage to bring her father to court. Though faced with extreme danger, Donna fights to stop the vicious cycle of rape. Read on to see what happens to her father, if justice brought forth, and if Donna is able to find peace.

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Citation

Friess, D.L. (1993). Cry the darkness one woman’s triumph over the tragedy of incest . Deerfield Beach, FL.: HCI.

America’s Teachers, Chapter 5

This post is a reflective on assigned questions from Joseph W. Newman’s America’s Teachers: An Introduction to Education, Chapter 5.

Present a short argument for, and then, against the fact that teachers get tenured.

Pro-Tenure:

Teachers should have security in their job. Tenure protects experienced teachers from getting fired on the whim of their superiors. Teachers who have completed three years of teaching are given tenure, which requires school boards to prove that the teacher is unfit to continue their job before terminating their employment. This stabilizes teachers, and gives them the right to keep their jobs unless proven guilty of incompetence, insubordination, or immorality (Newman 2006).

Anti-Tenure:

Tenure often protects bad teachers. The status of tenure makes it difficult to fire teachers who do not teach at a high standard. Tenure gives teachers the ability to take school boards to court, costing schools to pour finances into court cases. As a result, teachers that have a low performance, but maintain tenure status, are often passed from school to school instead of being dismissed (Newman 2006). In this way, tenure is a hindrance to excellence in education.

What can cause a teacher to be liable for a students’ injury?

Teachers can be held liable for a student’s injury if the following four statements can be proven:

1. The teacher had a duty to be careful not to injure the student and to protect the student from being injured.

2. The teacher failed to use due care.

3. The teacher’s carelessness caused the injury.

4. The student sustained provable damages.

Note: These statements quoted directly from America’s Teachers, by Newman, pg. 157.

What are the limits of freedom of expression for teachers?

The freedom of expression for teachers can be viewed from several topics discussed in “America’s Teachers”. These topics include: academic freedom, right of public dissent, appearance while teaching, political activities, and lifestyle. All categories have seem to have one overall governing theme: the limitations set on teachers depends on how their expressions affect the classroom and academic learning of the students. Academic freedoms such as choosing controversial books or topics of discussion are limited, but these limitations vary from state to state. Often academic freedom will depend on the ruling of whether or not the discussion or book is age appropriate and handled in a non-disruptive manner. A teacher’s right to public dissent lies with the content of their voiced dissention. For instance, a teacher may voice an opinion regarding any issue that is of public concern, but not an issue that is heavily focused on the individual teacher. A teacher’s expression of appearance is limited to a more professional standard due to the fact that all teachers represent role models to their students and are called to “promote positive educational experiences” (Newman 2006). Finally, teachers are not limited in their own personal lifestyle such as living arrangements or sexual orientation so long as it does not affect the progression of learning in the classroom.

What is your personal position on teaching about sexual orientation?

Personally, the discussion on teaching about sexual orientation is a new consideration for me. So far, I have come to conclude that I hold all students to be created in the image of God, and thereby will treat all students equally and positively. As to teaching about sexual orientation, my role as a math teacher will most likely be a minor one. However, my position on teaching about sexual orientation is that teachers should give students truth. This truth should include the fact that homosexuality has been shown not to be a mental disease, that often HIV AIDS is contracted through homosexual men, and that using differing sexual orientations as grounds for bullying is wrong. It is my opinion that 6th grade students and above should be given some sort of introduction to sexual orientation from a purely informational standpoint. Once a student reaches the high school level, further information may be given. It is also my opinion that explicit details as to sexual activity be given with extreme caution, and by no means in an “encouraging” manner, but purely scientific. Concluding this topic, I believe that students, especially those in private Christian schools, should be encouraged, not in tolerance, but in love for humanity.

List 3 physical indicators and 3 behavioral indicators that you are very LIKELY to see (or have actually seen at some point) that would lead (or have led) you to suspect either physical, sexual, or emotional abuse.

Three physical indicators that would lead me to suspect abuse are:

  • Bruises, welts, cuts, or burns

Three behavioral indicators of abuse are:

  • Fear of going home, Habit disorders (biting, sucking, or rocking), and suicide attempts.

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Citation

Newman, J.W. (2006). America’s teachers: an introduction to education. White Plains, N.Y.: Allyn & Bacon.

America’s Teachers, Chapter 8

“Sorting” Students

Students can be sorted by ability in academics, preference of educational focus, geographical location, career goals, and age. Sorting of students is often used to put them in project or activity groups. This is best done when groups are equal, working cooperatively and not competitively.

Differences between Expectations

In public high schools in 2005, it was found that while 70 percent of upper and upper-middle class students were enrolled in college preparatory classes, only 25 percent of lower-working class students were taking those same classes. Conversely, there were no students of the upper and upper-middle class students enrolled in “track three” classes, yet 20 percent of lower-working class students took “track-three” classes (Newman 273).  These statistics are the reason many educators assume lower-class students should automatically place lower than upper-class students.

Tracking

As a home school student, I was not subjected to many forms of “tracking” in elementary or secondary school. I did work through several courses which were defined as “Advanced Placement (AP)” courses or “College Prep”. These courses, specifically calculus, biology, and chemistry were slightly more advanced and work intensive than the general courses in their respective subject. Through sports in the local public middle and high schools, I observed several of my peers and their involvement in “tracking” programs. One specific program I recall was called “foundations”. This was simply a euphemism for a repeated pre-algebra course in high school. Students in this class recognized their “failure” and assumed that they were not smart because of their enrollment.

Race or Ethnicity

In understanding students, ethnicity is far more significant than race. In knowing a student’s race, I simply am able to observe the color of his or her skin. However, if I am knowledgeable of the student’s ethnicity, I will understand his or her cultural background. This information is much more useful to me as a teacher. When I know that John is Hispanic American, I will better understand the traditions he and his family may participate in, as well as consider his abilities with the English language if any initial concerns arise. If I know that Cindy is Japanese American, I will better understand her social behaviors as well as her home expectations. Individually, knowing a student’s ethnicity will not answer all of my questions or concerns. Not all children from a certain ethnicity will behave in a manner considered the ethnic norm or generalization. Yet, by having a basic understanding of different ethnic cultures, I will be able to better know my students.

Segregation

The most common form of segregation that I have observed in schools has been that of De Facto. Students simply are attracted to people similar to themselves. In my years at Olympic College, the black students in my classes always sat together, even if they had never met before the first class date. A similar example is found in cultural segregation. Students who appeared to be from “the ghetto” sat next to each other, while those who came from the suburban more preppy areas also tended to group together. In both examples, students chose segregation. However, each group was represented in the larger class and interacted regularly with the other groups and benefited from cooperative learning.

Bilingual Education

Bilingual education is controversial because educators and the government are continually trying to close the achievement gap between English Language Learners (ELL’s), and those who already speak English as their first language. Basically, those with English as their first language are able to outperform ELL students to such a degree, that educators recognize that a change must be made. There are four types of bilingual education that educators have experimented with:  immersion, English as a Second Language (ESL), transitional bilingual, and bilingual/bicultural maintenance. Immersion places ELL students in the traditional classroom for the entire school day, though the teachers often speak a bit slower for better understanding. English as a Second language has ELL’s in the traditional classroom for part of the day, and then “pulls them out” to go to a special class with certified teachers in ESL to for the other part of the day. Traditional bilingual education  require bilingual teachers to work directly with ELL students to help them move along in the traditional classroom setting. The last method, bilingual/bicultural maintenance teaches all children two languages. There is still much controversy over this issue as no one method has been found to completely close the achievement gap.

Role in Gender Equity

As a teacher, it is my role to assist in closing the gender gap and maintaining gender equity in my classroom and school. This will occur through equal scoring, praising, and attention given to students. As a math teacher, I will encourage both boys and girls toward success in my classroom. It is my belief, that any student, regardless of gender, can learn the basics of algebra, trigonometry and geometry if they are willing to put forth the effort to learn. It will be my role to teach by example. I will equally respect both peers and superiors of both gender not only because it is the right philosophy to have, but because I am an example to my students through my life.

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Citation

Newman, J.W. (2006). America’s teachers: an introduction to education. White Plains, N.Y.: Allyn & Bacon.