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

Posts tagged ‘Classroom observations’

Communicating with Parents


Mentor teacher: Mr. T

In student teaching with my mentor teacher, I have had the opportunity to observe several conversations he has had with parents of his students. Of the conversations that I have observed, all of the parents have come with the same intent: to discuss their child’s grade in the class and determine how it could be improved. Mr. T exhibits an exemplary attitude in discussing students and their grades with parents.

Positive statement

He often begins conversations with a positive statement about the student. For example, “First of all, Johnny is a nice boy. He pays attention in class, and is never a problem. I never have to ask him to be quiet or stop distracting others.”

Addresses reasons for suffering grade

Then Mr. T will address the reason for the student’s suffering grade. “Johnny is too nice. He is rather quiet and is very hesitant to really engage in classroom discussions or ask me questions. If he doesn’t understand something, he keeps it to himself.”

Reminds parent and student of opportunities to grow

Mr. T proceeds to remind parents of the opportunities he gives to students to keep their grades up and provide a safety net so they do not fall too far behind. Each of his opportunities involves students taking ownership of their own education and taking initiative. In this way, Mr. T communicates to parents how he values their child and the future of their child’s academic career. Some of the opportunities he offers include open classroom hours during lunch period and after school for questions and individual instruction, test retakes, additional homework practice, and encouragement to ask questions and dictate the pace of the class by “managing the teacher”.

Assures both of his desire for “A”

Mr. T’s philosophy is founded on the principle that students should get an A if they work hard and grow in their understanding of mathematics. His philosophy gives all students the chance of getting an A, but again, requires that the students take personal responsibility for their own learning.

Story telling: Basketball

In conversations with parents, Mr. T often uses analogies for his teaching philosophy. In one particular case, the student was a basketball player and Mr. T compared his math class to a basketball game. “In the game of basketball, you need to work hard to see results. If you never go to practice, you can’t expect to go to the game and get put in to play and succeed. However, if you practice hard, work with your coach, and use your team as a resource, you will be sure to see much better results and maybe even score!”

Moral of the story: “With work comes achievement.”

Mr. T’s philosophy can be summed up in one phrase, “With work comes achievement.” As he ends the conversation with parents, he has gone through the process of addressing the problem, explaining solutions, and finally, expressing a team-like collaboration with student, parents, and teacher. He has deflected any idea of “Teacher vs. Parent” or “Teacher vs. Student” and has established the sentiment that he wants all his students to succeed and, like a coach, will provide opportunities for them to be challenged and grow.


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.

Teacher Observation 1


Teacher Observation Reflection


Setting: Middle School Math Classroom

The teacher I am working directly with, we will call him Mr. T, demonstrates excellent teaching techniques and classroom management methodology.

Mr. T primarily uses differentiated instruction to enable the students to take ownership and responsibility for their own learning. The format of his class period might start with a 10min instructional period where he provides students with new material, then 15-20min of collaborative work on assigned problems (while he formatively assesses and answers questions while working with struggling students). After this, he would have 10min for students to demonstrate their work to the class on the projector, and finally the remaining time will be spent getting feedback (exit slips) and answering or asking questions. This format is student centered and very much follows a differentiated instructional approach.

Mr. T pushes students to take ownership of their learning by insisting and reminding them to ask questions, to see him during lunch for further clarification, and come talk to him after class if necessary. He teaches them to ask specific questions, slow the teacher down, and “manage the teacher” instead of allowing the teacher to “manage the student”. Furthermore, he sets high expectations for them. They are to bring their own supplies, (i.e. calculator, ruler, pencil) in this way, preparing for their learning. Students are also required to take notes and write key terms and important ideas in their math journals. By requiring students to practice good note-taking, Mr. T is preparing them for their future high school classrooms. He will sometimes stop the “math lesson” to discuss a reason for the classroom norms and how they will help the students in their future lives. For example, Mr. T has said, “Ladies and gentlemen, I see a lot of people looking down at their notebooks or out the window and Student1 is answering one of my questions. Now, here, the expectation is that when someone is talking, you look at them. You do this to not only hear what they are saying, but to show them honor. In this way, you communicate your respect for them and what they have to say.” Discussions like these are a proactive approach to classroom management. In this scenario, Student1 was talking, and while the other students were not talking over Studen1, they were not paying attention to what was being said. Mr. T uses opportunities like these to reiterate the classroom norms and to encourage positive behavior. Additionally, Mr. T takes the time to provide positive feedback when students are demonstrating the desired classroom behavior. For example, the other day a very shy student (Student2) raised her hand to ask a question during an instructional segment of the lesson. Mr. T stopped and thanked the student for asking the question. Later, as Student2 was working during a collaborative work time, Mr. T made it a point to go tell the student that he was proud of her. When she asked why, he simply said he was proud she had been brave enough to ask him a question.

So then, Mr. T uses his teaching time and classroom norms to create a positive environment of where the students are responsible for their own learning.

Classroom Management


Here is my Classroom Management Plan.

Making Purple: A lesson in 6th grade Probability

Red+Blue = Purple !

This is a 6th grade lesson on experimental and theoretical probability. Attached are the following

1) Lesson Plan Part 1-5: Probability Lesson Plan 6th grade

2) Text pages: probability scan

3) Blank Worksheet: making purple blank worksheet

(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.

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.


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.