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

Posts tagged ‘Cultural Awareness’

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 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.

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.



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.


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.


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.



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


Action Project- Diversity Experience

Below is a paper written about my experience through an “Action Project.”

For my Diversity in the Classroom class, I given an assignment in which I was asked to dress out of the norm, even to the extreme, so that I appeared different from all of those around me. The assignment was to go to a public place for 2 hours and observe how I was treated and how other chose to view me. The experience was eye opening. I was different from the crowd for only 2 hours, yet I was more than greatful to change into normal attire and blend in with the crowd. This experience gave me a very small taste of what it is like to be a minority in the crowd. Something that will prove useful in the classroom.


Action Project at North Gate

In order to get a sense of what it feels like to be stand out in a crowd, to be different from those around me, I changed my appearance to be drastically different than the social norm. First, I painted large black spots on my face. One spot even encompassed my right eye. Next, I arranged my hair so that I had four short “pony-tails” sticking out in various directions. Finally, I dressed in a grey poka-dot sweater and black –spotted boots.

Once my costume was complete, I headed out to the North Gate Mall where I knew I was sure to draw attention from the multitudes of Saturday afternoon shoppers. The mall was busy, and I was able to walk from store to store and be observed by people from all backgrounds. I spent two hours in the mall, plenty of time to feel the stares and second glances of those around me.

            As I walked around, I could feel people looking at me. Some did a double take and attempted to pretend that I wasn’t anything out of the ordinary. Those of the older generation gave me looks of a more sympathetic nature as if to say, “Poor girl doesn’t realize how silly she looks.”  What I did not expect was the occasional positive attention that I received. There were a few times when people made comments about how, “more people should dress like you” or “I like your face”. This was rather strange, but as I began to think about it, I realized that I stood out. I was not “ordinary” but unique.

Regardless of the looks and comments of the crowds, I felt different. I couldn’t enter a store without feeling uncomfortable and self-conscious. I felt beneath others. I would have much preferred to look the same as everyone else. I was constantly attempting to avoid eye contact and pretend that I could fit in with the other shoppers. I can’t quite imagine having those feelings all the time. It would be emotionally draining. I think I would feel as if I needed to put up some sort of “front”, masking my feelings and pretending as if I didn’t feel any different.

This activity will definitely impact how I choose to address diversity in my classroom. Cultural awareness is one subject that I will highly value. As a math teacher, I will not have quite as much freedom to explore multiculturalism through the school curriculum, yet there are a few ways that come to mind which I will attempt to implement.

Equal, fair, and respectful treatment will be sought for each student in my classroom. The use of racial, religious, or cultural slurs will not be allowed. Such behavior and words hurt students and parents in ways damaging to their self-esteem and self-image and is similar to a slap in the face (Oesterreich). Students will treat each other with respect regardless of their differences. 

It is my hope that the classroom setting will be one of community. Students will work together on projects and group assignments.  This will not only promote learning from social interaction, but will provide opportunities for students to learn from one another. People of different cultural backgrounds may think differently or describe events in different ways. This will allow for students to broaden their perspectives and appreciate other points of view.

Though sometimes parents are the last on the list of issues involving multiculturalism and diversity, it is important to recognize the home life of each student to understand them better. Differences like first languages, traditions, parent literacy, and even common foods in the household will affect students and their learning. It will be important that I am a student of culture, even as a teacher. I will be meeting with parents regularly and communicating their child’s academic progress. By being a student of culture, I will be able to better communicate and understand reactions and feedback I get from parents.

The Action Project has shown me that it is not always fun to be “different” or “unique” when you feel like it would be much better to be like everyone else. Unlike in my case, students cannot change the way they look with soap and water. Instead, they must adapt to their surroundings. Often it seems many students will try to draw the attention away from their differences by what they wear, the make-up they apply, or even the jokes they tell. Rather than try to ignore the differences in my classroom, I hope to engage students in their uniqueness by drawing attention to their strengths and abilities, and equipping them with tools to develop their minds. 

Specifically in the math setting, the history of certain math concepts can be used to introduce people of different cultures. For instance, the Pythagorean Theorem was derived by a man named Pythagoras, a Greek who lived in the 6th century B.C. (Haenisch 80). Using this a discussion topic, I further describe the time and society in which Pythagoras lived and compare it the community in which we live today. This is just one example of a single mathematician, yet there are many men and women from different cultures and backgrounds who contributed to our knowledge of mathematics. Teaching students about these people will give them an understanding that they are learning about a worldwide subject that extends beyond the classroom. 

To build on the universal understanding of mathematics, I would very much like to engage my students in a math project which would affect other students of a different nationality. At the mathematics conference that I attended in October of 2010, I attended a session in which a teacher described how he and his class of junior high students created, designed, and published a small math textbook which they then sent to a foreign country where math textbooks were scarce. This not only allowed for the students to reach out and help other students in need, but provided an opportunity for them to learn about other cultures and what school looks like in other countries. Projects like these will help students to recognize and appreciate the beauty of diversity.

The Action Project at North Gate gave me perspective of what it is like to be different. I only looked different for a few hours, but knowing that some of my future students may have the same feelings of embarrassment and discomfort motivates me to make my classroom a place of community.  I hope to use this experience effectively in my classroom to show students the value of differences in people and model equal, fair, and respectful behavior towards others.   


Haenisch, Siegfried. (2004). Lesson 9: The Pythagorean Theorem. Algebra. (pp. 80) Minnesota: Algebra.

Oesterreich , Lesia. (1995). Insensitivity to Physical, Racial, or Ethnic Differences. The National

Extension Service Children Youth and Family Educational Research Network. Retreived from :