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

Posts tagged ‘Diversity’

P2- Practice Differentiated Instruction

P2- Practice Differentiated Instruction

Teacher-candidates apply principles of differentiated instruction, including theories of language acquisition, stages of language, and academic language development, in the integration of subject matter across the content areas of reading, mathematical, scientific, and aesthetic reasoning.

This means that as a teacher, I construct my lessons by student interest and readiness, carefully integrating new vocabulary and academic language. I have done this by creating an engaging activity in which student learn new concepts around quadratic formulas. In their reflections on the activity, students were able to use their newly acquired vocabulary with the language function of “describe”. This lesson, as well as the student reflections, gave students the opportunity to develop fluency of the academic language surrounding quadratic functions such as parabolas, projectile motion, and vertex. In order to integrate the theories of language acquisition, this activity used principals 3 and 4. The exit ticket limited the forced output during the initial stages of learning new words as well as limited the forced semantic elaboration during the initial stages of learning new words.

Differentiation

 

The student work sample demonstrates how students have used the new vocabulary and language function to show their understanding. The rocket portfolio packet demonstrates how students were given the opportunity to choose their role in the group activity. In this way, the lesson was differentiated by student interest. The lesson was also differentiated by individual readiness as I created the collaborative groups to be mixed ability leveDifferentiation 3Differentiation 2

As I created this activity, I learned how to engage students in math content and inspire conversation around quadratic equations in a safe learning environment. Students were able to learn the real-life applicability of quadratic equations by shooting a rocket and using an equation to describe its height. In the future, I would like to build on student reflections, by giving them personalized feedback.

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Functions Bingo!- Just One of Multiple Instructional Strategies

H2- Honor Student Access to Content Material

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Teacher-candidates use multiple instructional strategies, including the principles of second language acquisition, to address student academic language ability levels and cultural and linguistic backgrounds.

As a teacher, I use differentiated instructional strategies to target students’ different learning styles. I am also conscious of my academic language when presenting new vocabulary. In introducing new vocabulary, I used the principles of second language acquisition as a guide so as to meet students at different readiness levels.

For the last week we have been working through the algebraic concept of functions. To many of my students, this is a brand new concept. There are many different terms of vocabulary associated with functions and thus care was needed in teaching students this material. First, I had all student copy definitions into their math journals and phrase them in their own words. With each new day, we reviewed these terms through conversation and applied their meanings to new content and perspectives. In this way, I implemented the first of Barcroft’s Five Principles of Effective Second Language Vocabulary Instruction: Present new words frequently and repeatedly in input.

To differentiate the instruction by learning style, I used several different methods of instruction. One of the latest lessons I did consisted of students playing Functions Bingo! A few days ago we had a half day of school and as I was discussing the upcoming day with one of my students and suggesting we play a math game, he offered that we play bingo. As I thought about it, I found that bingo could easily be adapted to be an effective kinesthetic and visual way of reviewing input/output vocabulary associated with functions.

Bingo Functions   3by3 Bingo board

I gave each student the same bingo board (conventionally, in bingo, each person has a different board) and a different function (of the form: f(x)=3+x ). Students were given colored chips to place on their boards. In the front of the room, I had two dice: one red for negative numbers and one green for positive numbers. When I rolled both dice on the document camera, students were asked to determine the sum of the numbers and use the sum as the input of their functions. For example, if I rolled -1 and 3 students needed to determine the sum to be 2 and use it as the value of  in their function f(2)= … if the output of the function, given the specific input, was on their board, they could place a chip on that space. Once one student got a bingo, (three in a row/column/diagonal) I had all students dump their chips of their board and start again with a new function. The first student(s) to get three bingos won candy.

In this way, students were evaluating many functions at different input values through the context of a competitive, kinesthetic and visually stimulating activity. Additionally, with each dice roll, I used the words “Use this input and determine your function’s output, if you put this in, what comes out?” Thus, I frequently used functional vocabulary throughout the game.

Through the game of functions bingo, I have been able to introduce the concept of functions using multiple instructional strategies to meet students of different learning profiles and readiness levels. In the use of a verbal and collaborative game, I have also implemented principles of second language acquisition to address student language ability levels.

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.

Student Diversity Honored in Design of Application Activity

P-1 Practice intentional inquiry and planning for instruction.

Teacher-candidates plan and/or adapt standards-based curricula that are personalized to the diverse needs of each student.

As a student teacher, I create curricula based on standards and the readiness levels of my students.

Savings Problem

savings accountIn my 8th grade honors classes with Algebra students, we continued to work on recursive sequences using contextual problems to relate the concept to real life scenarios. I created a savings account activity and word problem where students were asked to determine how long it would take them to save $500 under different circumstances. Previous to this lesson, we had worked on recursive sequences for about 5 class periods and I had determined student readiness levels through formative assessments. In the activity, students were separated into 6 different groups and asked to solve one of two word problems. The two word problems were formulated for different readiness levels. The first problem was for those who were not quite proficient in finding explicit formulas and the second problem was for those who were proficient.

This activity was based on the standard:

A1.7.C Express arithmetic and geometric sequences in both explicit and recursive forms, translate between the two forms, explain how rate of change is represented in each form, and use the forms to find specific terms in the sequence.

Students were asked in both problems to find the explicit formula of the savings scenario they were given and then find the term when the balance reached $500. Those who were not proficient received additional aid in interpreting the problem as well as steps to finding the explicit formula. The sequence they were given was arithmetic and thus was less challenging mathematically than the second geometric sequence. In this way, students in the first readiness group were able to focus more on interpretation and application of their skills rather than the more complex mathematics operations.

Creating this activity provided me the experience of using formative assessment and knowledge of students’ readiness levels to plan for instruction which challenges students appropriately. I was able to isolate specific learning objectives and provide the opportunity for diverse students to be individually and collaboratively successful.

This activity allowed students to build on their prior understanding of recursive sequences through contextual examples. Additionally, students were able to collaborate in their groups, creating a learning community, and using their peers as resources for their academic growth.

Finally, this activity is exemplary of future lessons that I will plan to challenge diverse students. While this lesson was generated to meet student readiness levels, in the future, I will use similar strategies to fit diversity in learning styles, learning profiles, and multicultural backgrounds.

Teacher Observation #2: Ms. K

Teacher Observation #2: Ms. K

12442583961705917736smiley eyes.svg.medSpecial Education Teacher Ms. K is a true example of teaching through organized instruction and creating a safe learning environment.

Ms. K has an established classroom routine each day. The schedule is written on a board near the front of the room:

1.  10 Minute Warm-up Exercise

2.  Vocabulary Review

3.  Lesson

4.  3 Minute Break

5.  Individual Practice

6.  3 Minute Break

By strictly following this schedule, Ms. K’s students can be at ease throughout the day, knowing what is ahead and what they are to be doing at all times. The vocabulary words, learning goal, and examples given during the “lesson” period of the day are all to be written down in their personal journals. This expectation is the same every day so that students are familiar with what they need to do in order to be successful. These journals, along with all worksheets and warm-up exercises, are kept in personal files that are set out on their desks prior to each class period and then collected at the end. Collecting the students’ work each day eliminate the possibility of forgetting or misplacing important documents in between periods or leaving items at home. In this way, the focus is on academic learning and students are able to devote their energies to the subjects being taught without worrying about paperwork details. 

Organization and classroom management meet through Ms. K’s ticket jar system. When students are demonstrating positive behavior in staying on task, Ms. K gives them a ticket which they then write their names on and place in the ticket jar. On Friday’s Ms. K draws a ticket from the jar and awards the winner with a prize. The more positive behavior displayed, the more chances students have of winning. Rewards become large-scale (class wide parties) when entire class periods demonstrate positive behavior and excellent study skills. Classes that accomplish this get a star on the chart in the back of the room. The class with the most stars at the end of the month wins a party!

Along the same classroom management theme, Ms. K creates a safe and learning conducive environment with her classroom decor, atmosphere,  and posting of classroom expectations. Soft Christmas lights line the wall space above her large window on the far side of the room. Seasonal decor embellish plain tables and counter spaces as well as empty windows. Colorful posters and student work are neatly displayed on most walls. As Ms. K has gotten to know her students, she has asked their preferences on noise levels and light brightness. As a result, some classes have music playing softly during warm-up exercises and individual work times. Other classes have the lights dimmed during individual work time. Accommodations like these are class specific and only changed when students can come to agreements on what they want their learning spaces to be like.  Students continue to take ownership for their environment by determining their own classroom expectations and then writing them on posters which hang on the front wall. Expectations like, “Listen to others” and “Ask Questions” are phrased positively and encourage students to engage in the classroom.

Ms. K’s organization and classroom management techniques have given her students the freedom and comfort of learning in a safe space that promotes their specific learning preferences. I hope to implement similar strategies in my own classroom so as to encourage students to take ownership of their own learning and promote academic growth.

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.

 

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/