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

Posts tagged ‘Historically informed’

H5- Honor student potential for roles in the greater society

H5- Honor student potential for roles in the greater society

Teacher-candidates prepare students to be responsible citizens for an environmentally sustainable, globally interconnected, and diverse society.

This means that teachers should teach in such a way so as to guide students to be responsible people in diverse society. In the math classroom, this includes thinking critically so as to solve real-world problems (such as environmental sustainability).

As a math teacher, there has been numerous times in which my classes have engaged in problem-solving exercises and activities. As a warm up before starting a unit on algebraic functions, I used a youtube video about the Enigma Machine. This machine was used in World War II to encode and decode messages by the Germans. The video, along with explaining the mathematics surrounding the machine, provided historical background and global facts surrounding the machine and its uses. The clip also explained how different countries had attempted to crack the code so as to intercept messages.

Four-rotor German Enigma cypher machine, 1939-1945.

This short film allowed students to think of mathematical topics as globally interconnected- a universal language. Following the films, students worked collaboratively to solve coded problems (functions with inputs and outputs) and determine the code (function rule). In working collaboratively, diverse students gained insight from multiple perspectives and were encouraged in their mutual respect for the skills of others (responsible citizenship).

Through using the video as inspiration and encouraging group work, I learned the power of collaboration among students and effective ways of motivating student learning. In the future, I would like to use this video as an inspiration for students to write more about what they learned and express their understanding in written reflection.

Cultural Beauty in Education

Jewish School Visit

I recently had the opportunity to visit a private Jewish school and observe several math classes in progress. This was a fantastic experience and unlike any observation I have done in the past. Walking into the school was like entering a completely unique culture and community of learning.star of david

The school was for early-childhood through 8th grade and as such exhibited many characteristics of an elementary school with art and student work throughout halls and entryways. Signs and labels were written in beautiful handwriting or text in both Hebrew and English. The walls and floors were colorful and lively.

communityClassrooms could be described as what you might see in any elementary or middle school except for the added Hebrew phrase here and there. However, the culture and community in the classrooms were quite unique. Class size was considerably small which gave opportunity for a comfortable and familiar atmosphere. Some classes had as little as two students! In this case, the teacher was able to work directly with individual students, customize lessons, and present unique challenges.

Because of the fluid transition from elementary age classes to middle school, several elementary school characteristics were present in 6th and 7th grade classes. For example, one teacher had her students take their math textbooks and notebooks and circle up on the floor facing a floor whiteboard. In this less formal setting, the teacher proceeded to review vocabulary words and previously discussed material.

Another unique aspect of classes at this school is that class periods are much shorter (38 min) than the typical public school time block. This shortens the instructional time considerably, and yet the teachers are still expected to keep up with the state standards and timelines.  The reason for less time per period is the additional Jewish cultural classes taught during half of the day. Students at this school spend extensive time learning about and partaking in religious traditions, studying Jewish history, and learning Hebrew. In this way, students’ cultural backgrounds are deeply honored and provide the foundation upon which their education is based.

Because of the school’s strong religious and cultural bonds between curriculum and learning community, parent and familial support is very strong. Faculty and administrators of the school regularly inform, involve, and collaborate with family and community members in each student’s educational process. Social justice projects and multicultural field trips are peppered throughout the students’ academic career.

This school’s commitment to their faith and cultural roots allow faculty to create a beautiful harmony of family and education. Though the set of values may be different per school, I believe other schools may take a lesson from this and strive to create a similar culture of student value and community outreach.

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.

 

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.

 

Film Review: As American as Public School 1900-1950

This post reflects on the film: As American as Public School 1900-1950. Through these reflections, the following three questions will be answered:

1) What is the focus of the era?

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

3) Who are the key players in society?

What is the focus of the era?

Initial Goal: Make every working man a scholar, and every scholar a working man. Changes to: Documentation of academic progress.

  • School was the place where the American dream was nurtured
  • Among the general population, there was tremendous pressure to get an education
  • Thousands of students attended school part time for lack of space in school buildings.
  • During the depression, many children worked instead of going to school, approximately 2million.
  • As these numbers became known, progressive Americans suggested that too many children were working as opposed to going to school- they suggested creating and enforcing labor laws.
  • Schools, under progressive ideals, became a place of training rather than memorization.
  • The training in school caused students to “fall in love with America”
  • 1920’s schools grew to become more than just teachers. Secretaries, mentors, counselors, janitors, cooks, and administrators where just a few of the positions necessary to run a school. This turned the “one teacher” classroom school into a multi-level bureaucracy.
  • It was at this time that career tracking was first introduced introduced. People thought of going to school as a way of getting a job.
  • Intelligence tests sorted students into categories for tracking.
  • IQ tests were used to determine the quality of people by ethnicity, race, and class even by the military to decide who got desk jobs and who had active duty.
  • Segregated schools often placed students of diverse ethnicity into industrial schools.
  • 1940’s: Life-Adjustment curriculum sought to teach relevant lessons to daily life.

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

  • Older children were seen to be “good students” if they started working at 15 to support the family.
  • Tremendous pressure to get an education
  • Children learning by doing.
  • Students were seen as the future, intelligence tests sorted students into categories for career tracking.
  • Progressive schools heavily invested in the lives of students, yet tracking did not provide all students an equal opportunity of learning. Often women were taught home-making skills, while men were taught a trade. Minority students were taught simple routine tasks which prepared them for factory work.

Who are the key players in society?

Progressivism vs Traditionalist Math and Science

  • “The School and Society” –Dewey- Father of Progressive Education. Dewey believed that if schools were anchored in the lives of the child, things would be different. Schools would be hospitable toward children.
  • Gary, Indiana Schools: These were extreme progressive school. One specific school, Emerson School,  had large athletic fields, playground, zoo, and a lagoon with swans. At Emerson School, students moved from class to class each hour. Under this system, students were not stuck to a desk hour after hour as they had been in more traditional schools.  Other schools had such commodities as a Metal Forge, Auto-mechanics center; as well as places dedicated to art, nature, animal care, and recess. Under the Gary program even reached into health and hygiene. However, many immigrants were convinced through propaganda that the Gary plan prepared children for industrial work- not professional careers. As a result, schools returned to the more traditional teaching methods with an emphasis on American patriotism.
  • Theodore Roosevelt: “America has room but for one language.” With this philosophy, New York began a new radical “English Only” philosophy in its schools.
  • Sputnik spoke volumes about the Russian education. To Americans, it said that Russian education was better than that of America. After Sputnik, math and physics courses became top priorities.

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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/




Film Review: The Common School 1770-1890

This post is a review of an educational film viewed in my Educational Psychology class at Seattle Pacific University. In this brief post, the following three questions will be answered:

1) What is the focus of the era?

2) What do we learn about schools then?

3) Who gets to learn?

What is the focus of the era?

To build an independent, patriotic nation.

  • In school students became something larger than themselves or their families, they became part of one nation. Students learned about the meaning of democracy itself.
  • At that time, only the larger towns in New England were required to build schools, outside of this area, education was neither free nor public. Most schooling was closely tied to the Protestant Bible. With the Bible as a core part of the curriculum, school was about saving the soul.
  • Aside from using the Bible, the most common school book was the New England Primer.
  • When Noah Webster claimed that the 1st step in forming a new nation was to remove England’s textbooks- national history had to be formed on the founding fathers.
  • General education will enable people to keep their own freedom. Survival of independence relied on the education of all Americans. With this in mind, Thomas Jefferson drafted a proposal of a three year education for all children in America. Additionally, he would send on the very brightest youth to universities.

What do we learn about schools then?

Schools widely differ depending on location and private funding.

  • 18th century schools were formed in a manner so as to keep the status quo; children would replace their parents in society.
  • Men were teachers, not women.
  • There is an average of 82 days of total school in a year.
  • Jefferson said at this time,  “People have more feeling for roads and canals than for education, they are leery of taxation for education.”
  • Horace Mann, the Secretary of Education, had little previous authority or background in education before attaining his position as secretary. He reviewed facilities and town-to-town education equality. He found that wealthy students could go to school for longer, and poor couldn’t go at all. He reported on the conditions of the school buildings. Rural district schools were out of shape and in disrepair.The materials were inadequate, readers were terrible.
  • At this time, children of all ages went to school, teachers acted as a ring master to keep multiple children working on all different subjects focused.
  • Schools had very strict rules and used punishment (often physical) as a form of discipline.
  • People began leaving public schools for private schools. Mann held a series of meetings for what he called common schools. These common schools would teach from a common curriculum. This system would “know no distinction between rich and poor.” Mann believed in equalizing school. Common,  meaning: all coming together.
  • Critics of Horace Mann were opposed to state control of schools as well as the taxes that came with it.
  • Furthermore, Mann recommended resources for classrooms:  a blackboard, standardized textbooks, chairs with backs on them, and in general, more teacher regulation. He got free, tax supported education, to be available to every class. Each citizen was to be equal to any other in politics and rights.

Who gets to learn?

A select few until …progress leads to more opportunity

  • Under Thomas Jefferson’s proposal (early 1800’s), girls were alloted three years of schooling, while no education was permitted for slaves. Male students were given the most opportunities and more was expected from their education.
  • By the mid 1800’s many of the students seeking education were immigrants. However, most schools were protestant (bad news for the Irish Catholics). John Hughes, the Catholic priest, called for movement of Irish children to  not go to schools that had books which would indoctrinate Irish students against their personal religion. He wanted a just proportion of the funds from the common fund to be given to the Irish to start their own schools. The city, New York, denied Hughes’ request.
  • In 1843 Bible riots broke out, leaving 13 people dead and the Catholic Church burned to the ground. Protestant textbooks spoke about the Catholics as a different race of people in offensive and derogatory language. However, after much opposition from the Protestant movement, most offensive statements toward Catholics were removed from textbooks.
  • During this time, 2/3 of the black population lived in the south, and were severely punished for any attempt of education. In 1840 African Americas were still restricted to segregated schools.
  • Inspired by Fredrick Douglas, supporters requested desegregation as a part of equal and common curriculum. Despite the requests, segregation continued even in the event of terrible school conditions of black schools.
  • In 1849 the case was heard at the Supreme Court. Denied again, the case was taken to the state legislator where it was passed.
  • 1865- The Civil War ended.  Now all were free to pursue an education.

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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/