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

Posts tagged ‘Collaboration’

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.



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.


E3-Exemplify and understanding of professional responsibilities and policies.

E3-Exemplify and understanding of professional responsibilities and policies.

Teacher candidates demonstrate knowledge of professional, legal, and ethical responsibilities and policies.

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As a student teacher, I have had the opportunity to act as facilitator at a math department meeting. With this responsibility, I collaborated with my mentor teacher to create the meeting schedule. Throughout the department meeting, I introduced faculty and provided necessary transitions as it progressed.


Attached is the department meeting schedule (without names for confidentiality).

Math Department Meeting Agenda

Throughout the meeting, I demonstrated professional respect and consideration by enforcing department norms as well as contributing to the different discussions. I learned the importance of trust and mutual respect among faculty as well as the reasons for department norms and meeting organization. In the future, I hope to be an instrumental member of a math department by being prepared and abiding by department norms.

Student Choice! Stations Lesson

H1-Honor student diversity and development.


Teacher-candidates plan and/or adapt learner centered curricula that engages students in a variety of culturally responsive, developmentally, and age appropriate strategies.

As a teacher, the content I teach must be accessible to all students of diverse learning profiles, readiness levels, and interests.

On the fifth day of our Algebra unit on functions, I decided to do a stations activity. The stations were designed to allow students to work on various ways of working with functions. The activity enabled students to choose the areas where they felt they needed additional practice.

Functions day 5

The stations were:

1)    Domain/Range: Worksheets with multiple ways of representing given information.

2)    Input/Output: Worksheets with many different functions and problems where students are asked to find either specific inputs or outputs.

3)    Graphing: Students are given several related functions (shifted along either the x or y-axis) and asked to graph them on different coordinate planes. (See graph paper)

DomainRange Worksheet     function_output      graphing_coordinate_plane 

As with other workdays, students were encouraged to work collaboratively and use dry-erase markers on their tables to demonstrate their work. “Go-to” people were designated at each station as peer leaders to whom students could direct questions before asking me.

After the stations activity a differentiated quiz was given to all students. The quiz had two versions based on student readiness level. The only difference between the quizzes was the complexity of the math involved; the function content was the same. Prior to giving the quiz,  I explained why I was giving two different quizzes. “Those who showed an understanding of functions (based on pre-assessment) receive a quiz with more complex math as well as functional notation. This is to challenge each student, not to label one group “smart” and another “dumb”. All students received the same type of questions, just different levels of math complexity.”

Functions Quiz 1   Functions Quiz 2

This lesson was planned so as to be learner centered. It allowed students to work with the content in a variety of ways and from multiple perspectives. Students were able to work collaboratively- challenging each student in a developmental way. Finally, the quiz was given in such a way as to give each student the opportunity to succeed and demonstrate their academic knowledge.

In creating this lesson I was able to grow in my understanding of how to differentiate instruction and assessments. I focused on individual student readiness levels and was able to formatively assess where students had strengths and weaknesses. By giving students the choice of which stations to work at, they were responsible for their own learning and quiz preparation.

In the future, I will continue to strive to make my lessons student-centered, differentiating my instruction to meet students where they are at developmentally.

Math Riddles- Collaboration within the school!

E2- Exemplify collaboration within the school

Teacher-candidates participate collaboratively and professionally in school activities and using appropriate and respectful verbal and written communication.

As a teacher, I regularly engage in activities, meetings, and school events in a positive and professional manner.

IMG_20130205_150637One way that I have been able to communicate and interact with students outside of the classroom and in different grade levels is through the creation of “Math Riddles”. In articulating mathematical concepts in a fun and engaging way, I have given students a way to put their problem solving skills to use and see math as associated with fun! Each week I have posted a new math riddle outside the cafeteria with space for students to sign their names after presenting me with the correct solution. Rewards have been given to the first few students to answer correctly. At first the riddles were solved by student in my classroom, then, after a few weeks, several students from other classes began to solve them as well.

While this is just one way to reach out and connect with the student body as a whole, (I am also volunteering with the track team, regularly participating in staff events/meetings, and collaborating on lesson planning with other math teachers and in sharing resources) I believe it is an important source of connection.

In creating the math riddles, I am making math more accessible to students as well as making creating a specific reason for IMG_20130205_150657conversations with other students. I have learned to use games and riddles such as these to present math in a respectful and engaging way. Just this week, a student presented me with a math code that he had created, after looking it over I asked if I could use it as my next math riddle. How exciting to be able to not only challenge students, but use student designed material to do so!

In addition to presenting math in a new way, this supplemental material communicates my desire to be present in the school and be more than just a teacher confined to the classroom.

IMG_20130205_150644In the future I will continue to make my presence known at the middle school through additional math riddles, volunteer opportunities, and in collaboration with school staff and students.