E1 – Professional Development Student Surveys

E1 – Exemplify professionally-informed, growth-centered practice. Teacher candidates develop reflective, collaborative, professional growth-centered practices through regularly evaluating the effects of their teaching through feedback and reflection. This means that teachers are making reflection a regular practice to improve instruction and student learning. In the Internship Seminar class we were asked to provide a student survey about our teaching practices. I already ask students to provide feedback at the end of each unit. student reflectionMy piece of evidence is another type of survey I incorporate into my regular teaching practices. After students take a unit test, I ask my students the following question to respond in their reflection journal: “In what ways can Mr. G improve the teaching of this unit?” This response was particularly representative of the whole classes responses and provided constructive feedback with positive behaviors to continue. When this student wrote this reflection, I saved it because their feedback was helpful to me, both positively and constructively.

This student’s reflection about my work as a developing teacher, demonstrates my growth in my teaching practices throughout the year. The student says, “He does great when he is showing all the steps to solving something. Her is also very good at keeping the class engaged.” Both of these have been points of emphasis as I begin my teaching career, particularly keeping students engaged in rigorous academic work. Research shows that keeping students engaged improved retention of material (Borich, 2014), I am excited that students recognize my efforts to keep them engaged in learning. I will continue to ask students these and similar questions to receive feedback that I can improve upon (such as improving group work protocols to optimize student learning when working in small groups).

This student work sample, along with my reflection to the assigned student survey, that aims at different teaching practices, help me target areas of success and areas of improvement. I can ask specific questions to measure my effectiveness as an educator. “In mathematics, several factors have been consistently found to exert a positive influence on student achievement gains: teacher coursework, degree attainment, and certification coupled with pedagogical training in how to teach mathematics (Hightower, et al., 2011, p.32 ).” Teachers play a crucial role in student achievement, the improvements I can make directly impact the student’s success.

In the past, since I have asked the same static question at the end of each unit, I would like to get more diverse feedback. As I work with the Knowles Science Teaching Foundation, I will be developing a long-term teacher inquiry questions for the first several years as a teacher. As this question develops and I work in collaborative work groups to help me establish steps towards meeting these professional goals, I would like to use the student surveys to ask my students questions as evidence towards those goals. The student feedback will help me assess if I am meeting my practitioner inquiry goals and can help me find next steps in any are needed.


Borich, G. D. (2014). Effective Teaching Methods (9th ed.). Upper Saddle River, NJ: Pearson Prentice Hall.

Hightower, A. M., Delgado, R. C., Lloyd, S. C., Wittenstein, R., Sellers, K., & Swanson, C. B. (2011). Improving Student Learning By Supporting Quality Teaching.


H1 – Honor Student Diversity

H1 – Honor student diversity and development. Teacher candidates plan and/or adapt learner centered curricula that engage students in a variety of culturally responsive, developmentally, and age appropriate strategies. This means that the teacher is planning for students needs based on experience or historical understanding of students. The teacher is adjusting lessons to engage students at an appropriate level to maximize understanding based on experience and student culture. One of my moral obligations as a teacher is to encourage students to go to college and help students realize avenues for achieving college, such as funding and support. Outside of the school environment, I associate with the College Success Foundation, a Washington State Organization which is aimed at helping students who would not traditionally attend college, find ways of pursuing higher education. The school where I work has an ethnic population of about 42% (Washington State Report Card, 2014). While working with these students, as a former scholar of the College Success Foundation and my learning of their contributions to divers populations, I can speak with students about the contributions of this organization and help students learn about options for higher education. This includes work with students who are undocumented United States Residents. For these students in particular, college is a challenging and scary path to pursue because many barriers block these students from higher education.

CSFlogoThis year, I have talked with all of my classes about my experiences as a College Success Foundation Scholar and the experiences I have received working with a diverse community. While sharing of experience for higher education is not formal instruction, many of these students are planning for higher education and need an experienced person to help them through the process. As a current college student, I have a lot of relevant knowledge that can directly help students.

Currently, I am reading a book called Teaching as Inquiry by Weinbaum et al. (2004), where in one vignette, a middle school english teacher is discussing how to encourage students to find a love for reading. She models her love of reading to the students by sharing the recent books she has read and shares a brief synopsis of the book she is about to read. This teacher is encouraging behaviors by modeling those behaviors in her own classroom. I am impacting students of diverse cultures by modeling what a good college student looks like, and sharing my experiences with an organization which caters to first generation, undocumented, foster and low income students who are interested in pursuing higher education.

I would like to implement more direct culturally sensitive material within my classroom, but haven’t had a good opportunity yet because of the current curriculum track we are using. When writing assessments (yes, my mentor teacher and I collaborate to write context based questions) I am sure to review the context of those questions to ensure we are not discriminating against a student who doesn’t understand the context of the question. For example, in order to introduce a question about golf and using words on an assessment such as “tee,” “fairway” or “green,” students need to be introduced to this before the assessment to ensure fair testing conditions for all students.


Washington State Report Card. (2014). Retrieved May 14, 2015, from http://reportcard.ospi.k12.wa.us/summary.aspx?groupLevel=District&schoolId=3601&reportLevel=School&year=2013-14

Weinbaum, A. (Ed.). (2004). Teaching as inquiry: Asking hard questions to improve practice and student achievement (Vol. 30). Teachers College Press.

H4 – Honor Family & Community Involvement

H4 – Honor family/community involvement in the learning process. Teacher candidates inform, involve, and collaborate with families/neighborhoods, and communities in each student’s educational process, including using information about student cultural identity, achievement and performance. This means that the teacher is making efforts and succeeding at communicating with parents, families, faculty and students outside of the classroom. To extend the learning process outside of the classroom, I am taking advantage of students access to technology. I have created and maintained a simple, yet content rich website (http://www.mrgermanis.com/precalculus/) which provides students with access to all class materials, handouts, notes, journal reflections and homework; all at their convenience. Additionally, through he online grading system, I regularly publish accurate records of students performance and comment when appropriate for reasons of student performance. Finally, I send email communication to some parents for students who standout in class as well as students who are struggling to make efforts towards classroom goals (i.e. they do not attempt homework which results in poor assessment performance).

All of these communication efforts provide resources for parents to assist in the students learning. Absent students are able to learn at home with a simple internet connection (even phone internet connections are sufficient). All classroom activities and links to those activities are published up-to one week early to provide advanced access. Additionally, parents and students can see upcoming assignments, test dates and quiz dates and the content of those assessments. Lines of communication are open and our teaching process is transparent to everyone involved. The administration can easily see what is happening daily in all of my classes by looking at our website. More communication is provided with parent emails, this alerts parents to actions to improve student performance in the class. Here is an example of an email sent to parents of students who are at risk for failing the course and steps to improving students performance:

I am writing to warn that low scores on the remaining assessments will likely result in a failing grade for the semester.  Please consider

  • Perform “test corrections” on Test 4.1—there are two opportunities tomorrow.
  • Complete all homework.
  • Work extra problems in areas of weakness.
  • Come in for help on concepts that are still unclear.
  • Prepare for the semester final exams. Optimize JR scores by writing full and complete responses.
  • Track progress on Illuminate.
  • Perform VERY WELL on the semester finals.

As always, all class information (activities, homework, content of tests, etc.) is on the class Website

– Mr. Germanis

By creating an open and public forum for sharing information about what happens in my classroom, I am learning to keep myself accountable for the work that happens within the classroom. Since parents, students, administrators and the community members can observe my lesson plans on my website, I am encouraged to prepare lessons more carefully and plan my instruction better. My website should make sense to someone who is not in my class and the classroom experience should enhance the learning. In communicating with parents, I have learned that they will only help with their students learning process if I provide specific tools to assist their student. My letter provides specific instructions for parents to help their student. I remind them of grades online, encourage parents to help their students prepare for assessments and help students make time to attend test correction sessions. One of the great joys I have is informing parents of the good things their students are doing. From these emails, I have experienced openness and have a chance to communicate with parents the good things their students are doing, the responses warm my heart and help me establish a positive communication with parents about their student.

Research shows (Degner, 2013; Henderson, 2002) that students are more successful if the parents become involved at home. There is also evidence that parents are unsure of how to help their students, the role of the teacher is to help parents prepare their student for success. By providing parents with tools to help, the parent and community involvement is helping the student achieve success.

While parent communication is important, I would like to be more active in reaching out to parents in different ways. Most of my communication has been to parents though email contact. As I move into a more diverse community of students, some parents may not be best at communicating through email and I will need to communicate through phone or in-person more frequently. Additionally, I would like to be more proactive in communicating MORE good things that are happening in the classroom, especially when students are performing well. Because I have experienced positive feedback from parents after good communication, I would like to attempt to do this more frequently to establish a positive relationship with parents.


Degner, K. M. (2013). Demography as Destiny: The Role of Parental Involvement and Mathematics Course Taking Patterns among 9th Grade Students. Current Issues in Education, 16(3).

Henderson, A., & Mapp, K. (2002). A New Wave of Evidence The Impact of School, Family, and Community Connections on Student Achievement Annual Synthesis 2002. Southwest Educational Development Laboratory, 2002.

H5 – Applications of Learning Beyond the Classroom

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 the teacher helps students make connections between the mathematics taught in the classroom and the applications in the world around them. Students should be able to see the connection between the math and their surroundings, essentially answering the question “Why do I need to learn this?”

The evidence presented is a collection of activities which help students make connections between the mathematical concept and the world in  which they participate. Three units stand out as particularly relevant to my students. The first, was the use of polynomials, students were exposed to polynomials as they are used at Pixar animation and the United States Navy Office (USNO) to calculate the location of the moon and on a given day. The second application is for studying complex numbers. I provided students with access to a link which explains how trigonometry and complex numbers relate to spring systems in engineering. Finally, the most important is how exponential functions and the use of logarithms. On sample is to model how the human body decays drugs over time and another sample is how earthquakes are rated using the Richter Scale. For both, we discovered some shocking outcomes using mathematics. Making content relatable to students improves engagement and improved engagement increases learning opportunities.

Links to Evidence:

Each of these samples came from my own curiosity of how the content relates to the world around me. Generally, my students are interested in space, art, science, computers and engineering. In creating this content and hooking the students into participating in the activities for the real world application according to their interests, I have help students articulate the purpose for the content within their immediate future. For me, I learned about many applications of these tools too. For the Pixar Animation information, I contacted Tony DeRose, a Research Group Lead at Pixar Animation. I learned how to bring the world of mathematics into my classroom directly from the industry leaders themselves. With the creation of the Richter Scale Activity, I have become familiar with the common misunderstanding about how the Richter Scale actually works. Interestingly, a one point increase on the Richter Scale is NOT 10 times the previous energy, but rather about 27 times more energy. With Drug decay, students learned that theoretically, a drug will NEVER leave the body, its concentration just decreases.

Students benefit from the application because of their immediate use and interest in the topic. When students have some applications for the work they are doing in Mathematics, they become more interested in exploring more about the topic. I have become successful if I have interested one student to pursue a STEM career and they have used the tools learned through the application lessons in my class.

One area of weakness in helping students realize the potential for this topic is having them research the applications themselves. While I am truly interested in the matter, students will most benefit if they are able to do the research themselves and make the connections. One barrier is my fear that they will not be able to find inaccessible content because the mathematics is too advanced for their understanding. I could promote the learning by encouraging these students to do a project in which they find the application of these tools within the world and talk with an industry expert about the application of these tools themselves and ask questions to build understanding. This may pique their interest even more and teach them about the applications of learning beyond the classroom.

HOPE Reflection H2 – Honor Access to Content

H2 – Honor student access to content material. 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. Many regard mathematics as a second language. Mathematica notation and use of mathematical vocabulary areLessonPlan LessonPlan 1essential to learning this topic. At the school where I work, all students are fluent english language speakers, it is unusual to encounter a language barrier in communication. Most of the language acquisition problems are through the understanding of mathematical language. To address this HOPE standard, math teachers must make the mathematical language more accessible by planning in vocabulary acquisition and teaching concepts and then naming the concepts.

The evidence I am presenting is two photocopies of some lesson plans where I am introducing two new topics. The first I am introducing students to sequences and series. In this lesson, students start with the Entry Task (ET) and are asked to complete “the list of numbers”. Since these are the teacher’s notes, the ideas are just brief notes. After the entry task, the plan is to formally put a name to “a list of numbers” which we will call a sequence. Similarly, as the lesson continues, I plan on clearly indicating and showing students the notation and the vocabulary for the notation about how to write a sequence. When I introduce combinations and permutations on the second lesson plan, I first mention “what are the possibilities of rolling two dice?” This removes technical language, the words “combination” and “permutation” and “the basic multiplication principle” are not even mentioned until the next day in class when students have acquired the conceptual understanding.

By removing the barrier of technical language students feel more comfortable with the content. The teacher will avoid the use of confusing language, but if a student uses improper language (such as the note about the difference between probability and odds in the lesson plan), the teacher will address the students misuse of language and avoid confusion of the vocabulary in the future. The HOPE standard is met because the teacher is planning for proper language acquisition and preparing students to understand content and then later naming that content when students struggle for a word to name the idea.

Over the course of my teaching internship, I have build knowledge and understanding of how to introduce new ideas to students without complicating the matter. From creating lessons that revolve around language acquisition and notation, I have learned that while I may have a deeper, technical understanding of mathematics, many students do not, and become intimidated by advanced language. By using lower level language, many of my challenged students become engaged.

Since many students are apprehensive about mathematics, this technique for introducing new ideas is helpful for students who are overwhelmed by math language and concepts. Providing instruction in an order that is helpful not to overwhelm students is important, especially in mathematics where there is a risk for pushing students away from the topic. To improve my understanding of this program standard, I will need to interact and prepare planning for more students who have different language needs, especially english language learners or those who lack significant mathematical skills. Since this HOPE standard is similar to Differentiation, I hope to address language acquisition, use of language and assisting english language learners as an improvement to my practices in differentiation.

P2 – Differentiated Instruction

P2 – Practice differentiated instruction. This means that teachers use a variety of instructional strategies or personalized instruction to help students acquire knowledge. Teachers will create opportunities for students to learn the same standards in different forms or with small modifications to fit the students’ needs.

The evidence is a series of mini-lessons presented over three days of instruction as outlined by a previous blog post found here. (LINK TO OTHER POST CLICK HERE) This post also includes some background information about the project, goals and outcomes. These lessons used student activities to help students to learn about and become familiar with vertical asymptotes, horizontal asymptotes, x- and y-intercepts and holes in a graph. Rather than providing students with direct instruction, the activities are built to facilitate student discussion around the topics and the teacher can target students with special learning needs during the activity. Each group was strategically selected to include students who brought different strengths (such as good communicator, critical thinkers in a single group). Group roles were assigned to draw out strengths or compensate for weaknesses of individual groups (quiet students were assigned as readers, critical thinkers assigned to questioner role).

Lessons 1 through 4 use student’s prior knowledge of polynomial functions to build on new understandings. Stations which revolved around asymptotes had students use limits by completing a table of values. For horizontal asymptotes, the values approached infinity and negative infinity. For Vertical asymptotes, the values approached a fixed value of x. Structuring groups with specific roles, students were able to converse and think critically about each of the four topics. Since the conversations were NOT teacher lead, students could explain to each other concepts they were unsure of. Most importantly, I would circulate the room during the activity to check on students progress and assess needs or misunderstandings with groups of about 4 students. I would target groups that were working fast to ensure they understood the intricacies of the activity and would provide challenge or extending information to groups who were able to build on more complex ideas.

After completing this activity, I learned that station learning can be valuable but should be thought through carefully. I would reconsider several processes to make this better.

  1. Allow more time for students to complete the activities. Some groups seemed rushed and were not able to complete ideas.
  2. Debrief with groups after each activity to ensure students understood the purpose of each question.
  3. Provide a little bit of direct instruction before turning to station learning activity to motivate the learning more.
  4. Remove the unit about holes since it is not a standard, but a good to know topic.
  5. I would remove the idea of making the students physically move around the room during the activity, this wasted time.

There are some pieces of learning that I thought were beneficial to the activity.

  1. Assigning students to groups to ensure there are a variety of learners in each group of learning.
  2. Assigning group roles to draw out strengths of students to benefit others in the group.
  3. Circulating the room to provide direct instruction as needed rather than lecturing at the front of the room. The dynamic of a teacher roaming helps students by providing small group instruction AND if the teacher is unavailable, groups must work together to problem solve before asking for assistance and receiving help. The delayed gratification is more effective because students are more receptive to the learning (Meyer, 2010).

While many of the suggestions above would help students learn and are keys to improving the instruction better for next time, I can continue to improve by learning and practicing differentiated instruction and providing alternate means of learning to students when station activities are not being used, such as times when direct instruction is used more. There is more research and practice that can be learned.

References: Meyer, D. (Speaker) (2010, March 1). Math class needs a makeover. TEDxNYED. Lecture conducted from TED Conferences, LLC, New York City.

HOPE Reflection P4 – Technology

P4 – Practice the integration of appropriate technology with instruction. This means that the teacher is actively using the tools within the classroom to extend student knowledge. The technology used may not be the most modern or advanced, but it must be accessible for students in the future and commonly used within STEM fields. Since the students at my school are highly interested in Math, Science and Technology, the utility of this skill is for engineering tasks and aviation are highly relevant to the task.

The evidence presented is a lesson plan that integrates the use of a graphing calculator to solve for unknown coefficients of a polynomial when given a set of points. Even advanced technology and regression techniques in computers cannot solve for a polynomial that is greater than degree 5 without significant  algebra manipulation. Students are confronted with this realization and are directed to create a system of linear equations and are guided to use prior knowledge of matrix operations to solve for the polynomial coefficients. After the lesson plan, there is a set of reflection questions for the teacher and responses which help justify many of the decisions made throughout the lesson. In this commentary I explain the benefit of using a graphing calculator (as opposed to any other form of technology) to help students make connections form mathematical concepts.

Technology Lesson Plan and Reflection Questions

The technology lesson plan meets the program standard because it differentiates for different groups of learners and their experience with a graphing calculator. This tool is most appropriate because ALL STUDENTS have a Texas Instruments graphing calculator (or may borrow one from the class set). Additionally, the use of this type of technology is relevant to students who will continue into college when solving systems of equations are important. To relate this to student learning, many engineer students or those interested in design must learn how to create a polynomial function to fit points on a line. Some students in my class are also taking a class in engineering when they use CAD computer design. The computer automates the mathematical process and this lesson connects the computer process to the math behind the computer.

In creating this lesson, I was able to be highly reflective of the lesson that I was designing. During my internship, I am continuously working to differentiate instruction. In creating this lesson, I was able to challenge advanced students and also support students with another piece of material to help them grasp the mathematical procedure. If I were to do this activity again, I would want to show students another type of technology to accomplish the same task, such as a computer programming language or other online tool. Another way I would like to change this activity would be to have less direct instruction and create a more engaging lesson that would lead students to arrive at the conclusion that matrix operations would be the solution to the problem encountered within the lesson (not being able to model a fifth order polynomial with calculator regression).