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

Archive for the ‘H3’ Category

The Classroom as an Environment for Learning: A Holistic Approach

H-3 Honor the classroom/school community as a milieu for learning. When the classroom and school community are respected as places of learning, student success is promoted and learning is uninhibited by unnecessary restrictions.

In the lesson plan presented below, students are encouraged to work collaboratively within groups of 3-6 students to solve for recursive equations given a sequence. Each group was given a different sequence and asked to solve using dry erase markers directly on their tables before then copying their work into math journals. In this way, students teach each other by discussing and writing their work for each other to see. Having completed their assigned problem, groups were then asked to review the work of at least two other groups and writing the others’ results in their personal math journals. Finally, one group was selected to demonstrate their work and rational in front of the class.

Recursive Review Lesson

IMG_20130117_113030Students were uninhibited by the tables as work spaces since they were able to use as much space as needed. Students were also able to quickly erase mistakes and make corrections. When the groups were satisfied with their own work, they were asked to leave it on the tables for other groups to review.  In reviewing the work of others, students were able to look to the entire class of peers as a resource for learning. They could learn from the work of others, ask questions, and then take notes in their personal math journals.


Finally, one group of students was asked to come forward and present their work in front of the class. Though their work was observed by several groups, the specific sequence they were given was at a level of greater difficulty and importance. In this way, all students were able to benefit from a more instructional time of learning (peer to peer instruction). The teacher, instead of directly instructing, led the presenting group through a series of questions about how they had solved their problem and why they were able to perform the operations they did. Not only did the students presenting have the opportunity to grow in communication and further understanding of their own work, but the entire class benefited from their work without having to struggle through it individually.


Through this lesson, I learned the power of peer instruction and collaboration. The teacher need not be the only source of learning. When students are in an environment which promotes peer communication and creativity in displaying their learning, they are able to thrive and grow as learners.

In the future, table tops will be continued to be used as resources for displayed work and examples. Additionally, I plan to continue selecting students to present in front of the class to demonstrate their work. I will especially look to encourage less confident students to do so (in content they display proficiency). I believe this to be one way to promote a healthy learning community where all students are valued.


Classroom Management


Here is my Classroom Management Plan.

(Prove/Disprove) Desk + Chair + Whiteboard = Learning Environment ?

Does classroom furniture make a difference?

The physical arrangement of the furniture in a classroom can be either a help or a hindrance to student learning. It is important that a teacher be aware of how students react to specific classroom arrangements so as to create the most effective learning environment within the given space.

As a teacher, “You are a placemaker, an individual who creates a place that supports teaching and learning to the greatest extent possible” (McEwan 2006). This can be done through the classroom set up. Specifically, rooms can be set up so as to be territorial or functional.

The classroom I am observing this quarter is designed in a flexible, yet territorial manner. Specifically, students are assigned specific seating in rows of rectangular tables. Sets of two tables are pushed together to form one 4-student desk. There are 4 rows of the 4-student desks with 3 sets of desks per row. The students face the white board and can easily move their chairs to work in groups. This structure keeps students focused and attentive to the task at hand, while allowing for the flexibility of different teaching strategies.

To one side of the room, there is a “quiet space”. This provides any student the opportunity to remove themselves from the noisiness of the class and work independently in a less distracting atmosphere. In this way, my mentor teacher has created a space that is conducive to multiple learning styles and removes unnecessary distractions.

By changing the seat assignments regularly, she gives her students the opportunity to work with multiple people in the class. This not only builds camaraderie amongst students, but allows students to learn from different people throughout the school year.

As observed in the classroom, furniture arrangement and structure are pivotal in creating an effective learning environment.

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.


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: