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

Archive for June, 2013

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.


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.

E2-Exemplify collaboration within the school

E2-Exemplify collaboration within the school

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

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

As a teacher, I must be able to work cooperatively with school staff and faculty. Throughout faculty interactions, I must not only be professionally appropriate, but also ensure that my tone and words communicate respect.

Throughout working as a student teacher, I have worked with my mentor teacher to create many student worksheets used either during lessons or as homework. I have also worked with math faculty to analyze assessment data in order to inform instruction. The school I student teach at is a pilot school for the Math Benchmark Assessment (MBA) and as such, the teachers are required to analyze their classroom data and provide feedback to the assessment creators. A “work in progress” is given in the following link. MBA Rational


This data analysis focused on one of the Washington State Standards and described the ability levels of students on that particular topic. Through the analysis, we worked to also describe the effectiveness of the district in providing instructional materials which aligned to the same standards.

In working collaboratively with faculty to create this analysis, I learned the power of multiple perspectives, gained insight from experienced teachers, and developed mutual respect for those I worked with. In the future, I feel collaboration will be key to my success as a first year teacher, but also as an effective member of the educational community.

E1-Exemplify professionally-informed, growth centered practice.

E1-Exemplify professionally-informed, growth centered practice.

Teacher-candidates develop reflective, collaborated, professional growth-centered practices through regularly evaluating the effects of his/her teaching through feedback and reflection.

As a teacher, I am to reflect on my progress and growth as an educator. This reflection, along with feedback from supervisors will help me refine my skills and become a more effective teacher.

One way that I have reflected upon my professional practices has been through the creation of a Draft Professional Growth Plan Documents (DPGP: Josie Becker Draft for DPGP). In this draft, I have reflected upon four rubrics and self-evaluated my skills and abilities in the corresponding categories. Following my reflection, one of my education professors gave my feedback in order to prompt for further details and deeper reflection. This enabled me to further dissect my skills as a teacher and determine areas for future growth.

In creating this DPGP, I had the opportunity to reflect on my skills as a teacher and determine areas of growth in order to teach more effectively. This directly relates to student learning as well, in that while I give them regular feedback, as a teacher I should look to get feedback from my students, peers, and superiors in order to continue be as soft clay, sculpted to best teach and serve those around me.


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.