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).


Station Learning Activity – Asymptotes

I wanted to try a station learning activity that was inquiry based. Too often asymptotes are taught to students without much consideration for how or why the functions behave in this particular way. Personally, I think asymptotes are interesting, but to students they are a strange phenomena that have no application. The approach with the inquiry is to help students find interest in an abstract learning segment. This lesson comes near the end of a unit about polynomials and we have just covered polynomial long division. This activity is geared to help students learn through the various aspects of polynomial division and what could happen. Since slant asymptotes are unique, we will cover these the next day of class.


Students have been studying polynomials for about a month and we are just exiting a section about the Fundamental Theorem of Algebra and complex roots. It is clear that students are weak in factoring polynomials, but I cannot afford to stop all learning to generate mastery. So, I have designed a 2.5 day mini-unit in which students will have lots of practice in factoring polynomials, reviewing polynomial division while exploring asymptotic functions. This mini-unit will hopefully tie a lot of somewhat random ideas together and help loop some previous learning so that students can practice skills they should already know and continue to learn new ideas.

On my website (link below, date Feb. 24) I have posted 4 worksheet activities for the day (I created these by the way). As students walk in, they will be divided into 1 of 4 groups. They will read start the entry task which should require them to access prior knowledge. Students will have about 30 minutes at each station to complete a short worksheet. Since the period is 100 minutes long, I expect that all students will get through about 3 stations.

I will be walking around to each group during the class to ensure students are grasping the important concepts at each station and catching some misconceptions along the way.

My personal goal in creating this station learning activity is to: 1) Get students moving in the classroom during a long period. 2) Engage student in an exploratory, inquiry based activity. 3) Differentiate instruction so that struggling students can achieve new skills. 4) Fold in prior learning (factoring, finding roots, polynomial division) so we can move forward in content and review prior knowledge.



(Block Day)
Entry TaskFor the function f(x) = (x + 2) ÷ (x – 1), describe as many of the following features as possible. DO NOT GRAPH!

  • x-intercept
  • y-intercept
  • end behavior of f (x) as x approaches positive infinity.
  • end behavior of f (x) as x approaches negative infinity.
  • function behavior when the input is close to 1.
Activity“Be Rational!” (Station Learning Activity)

See THESE notes to clarify information from stations.

Journal Reflection: Complete the JR for each associated station you visited today. Build a rational polynomial that:

  1. Has a hole at x = -10
  2. Has a horizontal asymptote at y = -5
  3. Has a vertical asymptote at x = 3
  4. Intersects the x-axis at (3, 0) and the y-axis at (0, -5)
HomeworkThis homework is due on 3/2.
Note: Some problems may cover concepts NOT at your station. During class, we will continue the activity. All problems should be solvable by the due date.Pg. 229-233 # 1, 2, 3, 4a, 7

Lesson Goals: Students will learn about basic asymptotic behavior that results from polynomial division including domain and range of asymptotic functions. Additionally, students will recognize a polynomial which results in a curve with a hole.

Post-Lesson Reflection

My lesson today went well! There are a lot of opportunities to observe students understanding (or not understanding) the ideas of the lesson. I noticed some problems in the wording of some of my activities which was challenging since I needed to talk individually with each group to clarify my writing.

I created groups of 4-5 students and strategically selected different ability levels in each group. Roles per group were also assigned to bring out the qualities of each student that I needed. For instance one group contained a student who generally asks good questions in class and another student who generally has a difficult time engaging in lessons and a third student who has a difficult time asking questions. In this group, I assigned the unengaged student the role of reader, the curious students the role of checker/questioner and the quiet student an arbitrary roll. With these students and roles in the group the quiet student and the unengaged student became members of a group and engaged in the lesson well attaining significant new knowledge. Overall, this strategy worked very well, only one group of higher level students complained about the group roles and didn’t follow the structure. As a result this group was unsatisfied and felt lost during critical parts of the activity.

Thinking about pacing, I am realizing that these activities require a lot of thinking and within a single 100 minute period, students may have a difficult time accomplishing even just three of these activities (the intent was for students to complete 3 of the 4 lessons). If I were to do this activity again, I would divide the problem into two days of station learning and have only two worksheets per day (even during a block day). This will allow me to debrief more quickly to ensure students are getting at the heart and the objective of each station.

Additionally, if I do this activity in the future, I will provide check in point where the document controller will report their groups finding to the teacher to ensure connections are being made and the objective is being met.

One task that should be shared with the teacher in particular are the generalizations of the findings of the activity. Many parts of the activity were examples where students were to uncover HOW asymptotes, holes or intercepts worked. Making generalizations will solidify these ideas and prepare students to apply this knowledge to new situations.


Opener and Closer Observation

Course: Precalculus

Period: 1

Each morning, students are expected to enter the class and start on the entry task (ET) which is posted on the display in the front of class and is also posted on the class website (each student is provided with an internet capable laptop). For this lesson, the ET stated, “Explain how similarity of triangles is related to trigonometry.” Students write their response to the task in their homework notebook and should be writing for about five minutes. During this time, the teacher took attendance and spent a few seconds preparing the lesson. After the writing period, the teacher interrupted the class to debrief. He asked students, “ What do you suppose todays activity is about?” the conversation lead to a short discussion of “similarity.” he probed students, “Why do we care about similar? and What else?” Students volunteer responses to these questions. After the debrief finished, the day’s activity was introduced and students began working.

The objective was never explicitly stated, although the introductions to start the class was a brief indication of the objective for the class period. During the lesson, I asked students what the objective for the day was and several were able to produce a sufficient explanation as to the goal of completing the activity, but it was not completely accurate. Today was the end of a unit lesson and I would say that the ET prompted students to reflect on previous classes and learning about the relationships of triangles to completely answer the question. Since this lesson was a summary of many lessons, the opener was more theoretical than it has been in the past, so the authenticity and engagement were slightly lower than more application style lessons, however, the ET made a strong segue into the objective of the day’s lesson. I would have liked to see more explicit indication of the day’s goals. If I were to teach this lesson, I would have written something down on the whiteboard. I really liked that the teacher had the students articulate the purpose and the objective of the lesson. This indicated that students were aware of the lesson and the purpose for the day’s activities.

About ten minutes before the class was completed, the teacher held a debrief of the activity, he asked questions such as, “What was The Sim’s activity about?” and encouraged a response which aligned with the objective for the lesson which was similar triangles and trigonometry. He then extended the question with “Anyone want to add anything?” which I liked because it gave students another opportunity to share their learning and responses.

Another regular routine for this class is Journal Reflection (JR) in a special notebook kept within the class. Students are aware that they are graded on the effort and thoughtfulness of these daily entries. The goal of a JR is to help students articulate their learning and misunderstandings from the days lesson. The JR is posted on the screen at the end of class. Students know they are expected to be writing on the topic for the last five minutes. The JR for this lesson was “Explain how to use similarity of triangles to solve for unknown parts of a triangle.” This particular closer helped students reinforce the practicality of similarity as a form of trigonometry. In fact, this JR helped summarize most of the unit and goals which followed the Understanding by Design model. During the students JR time, the teacher talked with single students which I think was a little bit distracting to the whole class and made the JR time less valuable. I did not like this because it took away from the reflection time for students who are easily distracted. After the class, the teacher mentioned to me that he wished the students had a more fundamental understanding of what trigonometry was and that even through this lesson, some students are struggling. This lesson was aimed to meet analysis and synthesis in Bloom’s Taxonomy. Students were tasked with recognizing patterns in the activity and the opener and closer helped them see more patterns and create more sophisticated conclusions based on their engagement with the activity.

I really liked that students reflect on their thinking and that they are engaged with prior knowledge to start and end every class. I particularly liked the debrief period because it engaged students and had them articulate their learning and the connections they were making rather than being provided the correct objective. Overall this class was well executed and the opener and closer helped motivate the days activities and facilitated strong learning on many levels of engagement.

A Day in the Life of a Student

Today’s goal was to follow the school day of a sophomore student throughout their day. To protect the identity of this student they will be called MW. The goal was for me to observe five different classrooms during a six period day. Within each class, I was looking for teaching strategies and tools to use in my own classroom. At the end of the day, I asked MW some questions about their day. While the student interview was only a case study, MW provides several helpful suggestions to improve their learning experience.

The morning classes include Math, English and Biology. Within all of these classes, I noticed good responsive listening. Teachers would ask student questions and then summarize what the student said and repeated the comment to the class so all could hear. In English, the instructor was careful about making smaller comments to encourage conversation in class. The activity in English was to analyze a short story, a topic which can be shallow or deep depending on the students’ understanding. The instructor contributed to the classroom discussion as well to prompt students to analyze the short story more deeply. At the end of the classroom discussion, the teacher make a more sophisticated analysis than the students were able. This exposed the students to higher expectations. The teacher used OneNote to distribute materials to students and students were able to access copies of the teachers journal.

In math class, students started with an entry task to summarize their homework and clarify questions. The class activity was to debrief a challenging problem from the homework and clarify understanding of the basic elements of trigonometric ratios. Students had questions to prepare for a quiz the next day. The activity included a worksheet where students needed to use prior work to plot data and discover a relationship of a sine wave. The end of class, summarized their understanding of “accuracy” and careful procedures for getting more reliable results.

Biology was a very busy class, the lesson was very engaging and highly differentiated. One comment about the lesson that I particularly enjoyed was the presentation of the entry task. The day’s objective was clearly posted on the board and students were able download a copy of class activities from OneNote. Student’s shared out the Initial Thinking questions by popcorn method, students would choose others to “keep the conversation going.” The instructor was clear about the importance of understanding the Carbon Cycle and other biological systems and stated that this would be tested on the End of Course Assessment (EOC). The class activities included a dice game and students would mimic a carbon molecule in the journey throughout the day. Students seemed to enjoy the activity and learned about the many processes of the carbon cycle. Students were able to articulate what happens to a carbon atom as it moves from the sun to plants and then into animals and back into the atmosphere. The activity was followed by a debrief so students could articulate their learning. After the debrief, students watched a video that repeated the material again. This instructor was very smart about providing many learning opportunities for important content. The class ended with an exit slip that informally assessed students learning from the day. Students were instructed to make a carbon cycle as homework to use to prepare for their EOC test in the spring.

After lunch, MW was schedules to attend Current World Problems, Spanish and Health. Mostly, this class period was work time for students to finish a group project about government systems since 1500. MW shared with me the group project and the required elements for a grade. Before work began, students the teacher had a student present a “SHIELD” which allowed the student to comment about their past present and future. The intention of the exercise if for the class to know each other better. Students can share about their interests and goals. Next the teacher gave instructions of work time, he was very clear about presenting a product at the end of the period and made suggestions for groups to produce exemplary work (i.e. Review each other’s papers, get organized and then work together to produce a product). Essentially, the teacher anticipated potential shortcomings and took preventative measures to work through the project. We also talked about some of the functionalities of the grading system to optimise its use.

Next was Spanish in which students entered the class and listened to the instructor through an immersion lecture. The teacher spoke little english when teaching the material, but frequently broke into english to emphasize important points. He continued to discuss why immersion was used and why he believed in this philosophy for language acquisition. Most of this period was direct instruction and lecture based. Students did not respond frequently and when they did, it was brief.

The last class was Health where there was a lot of individual work time. Some of the lesson was direct instruction where students had access to a OneNote document to help follow the lesson and take notes. The period was an introduction to nutrition and involved the explanation of a project. The teacher clearly displayed the objective and the required elements of the project so that students knew what was expected of them throughout the unit. Many students who were in previous classes were also in this class. It was interesting to note the difference in classroom dynamic because of these students. Those who were quiet in the morning, we not more rambunctious and hard to get back on task. Teachers should consider this when teaching.

Finally, after the day, I asked MW some questions about their day. This student liked the biology lesson because there was an activity where she could move. She mentioned this was uncharacteristic of her typical day, but when she moves around, she claims she remembers more. Typically, she enjoys her math class because there are clear instructions and she tends to work hard. MW is also in a robotics class (which I did not attend) but this takes up a lot of her time. Sometimes teachers don’t understand that this is a challenging workload. Along these lines, MW claims that she becomes overwhelmed when projects are overlapping and she does not have the tools to manage this better. MW recommended teaching students in advisory time management and note taking skills. She also would like a space after school to get some work done and manage her schedule. Throughout the day following the student, I realized that the school has very high expectations for the students and teachers don’t often repeat information. This school expects students to understand verbal instructions the first time, which is a challenging skill for many people, even adults.

E2 – Professionalism and Teamwork

bPortfolio E1

Online Registration System

E2 – [1] Exemplifies collaboration within the school. Teacher candidates participate collaboratively and professionally in school activities and using appropriate and respectful verbal and written communication. [1] E1 means that teachers must work together to create products with the interests of students and other staff in mind for both curriculum and non-curriculum related tasks. This standard also implied that professional communication should be mindful of staff’s needs to communicate important ideas. [2] The document linked here is a set of instructions, a list of club names and club descriptions which is presented to the entire student body to implement a new online registration system for student clubs. Each student is required to join a club as part of the schools mission. The screen shot is of the online registration system which I produced. This registration system will help reduce chaos from previous years sign up system and will provide a fair way for students to select their club.

[3] Staff members were able to choose their own club and provide a description. Many emails were sent by the Associated Student Body (ASB) advisor and me to the staff to collect preferred club choices. I was required to present my product to a leadership team to approve the process to use for the school. During my presentation meeting, I was able to clearly share the mission and the utility of the tool, provide solutions to problems and took initiative to solve anticipated problems. For example, one team member asked how the staff would learn the new system. I responded with a prepared powerpoint presentation to guide staff through the registration process. Organizing such a large scale project has taken a lot of communication with all staff and the ASB advisor.

[4] During this process, I learned that some teachers are overwhelmed with many other needs and rarely have time to respond. I learned how to communicate through different mediums, both using technology and other methods to get answers. [4] I also learned that working with people who are overwhelmed is challenging and patience is an important disposition when working through frustrating experiences. [5] My school is particularly project oriented, students will see that teachers must also work together on projects. Students can learn that teamwork, professionalism and collaboration is a lifelong skill to acquire and is used during work. [6] Through this process, I learned about this particular staffs preference for online forms (Google Forms) only when time is allotted to complete these forms. Otherwise, the task will not be completed. In the future, I will create a Google Form before staff meetings and then request five minute of time to collect information. This will increase my professionalism by reducing the number of unnecessary emails to staff, ultimately reducing their burden and becoming more productive myself.

Introduction to Teaching Course Reflection

Discussion Post Entry: Education Reform

Discussion Post Entry: Education Reform

E1 – Exemplify professionally-informed, growth centered practice. This means that teachers have demonstrated an understanding of current educational and suggest strategies for improvement. The attached screenshot shows an assigned discussion post about recent reform in public education. Hunt (2005) discusses the problems with previous reform, (i.e. career education reform), as being over ambitious and under studied, claiming that reformists fail to anticipate long term affects when solving short term problems. My discussion post agrees that many reforms do not meet the needs and there is some concern for the Common Core State Standards as they approach full implementation. I suggest differentiated teaching as a potential solution to work around the many reform systems implemented in classrooms. This relates to the program standard E1 because teachers who are educated about policy reform can adjust their classrooms to best fit student needs while accommodating reform policies.

Since writing this discussion post, I have learned specific research based strategies for improving classroom instruction such as scaffolding lessons and teaching just above student understanding to maximize learning. From reading articles about education reform, I have learned how implemented systems intended to help the educational process are often challenged and rejected because of cost. An example of this was a class discussion of suggestions from “A Nation at Risk” where longer class days were suggested by researchers, but rejected by politicians because of costs.

Students have always been impacted by school reform. In the discussion post, I talk about my experience of the WASL throughout my middle and high school education and how I felt about standardized test reform. Hunt (2005) makes a strong argument in his article about how students change because of reform. One danger of the current standards based education is that low motivation students tend to complete the bare minimum to pass. On the other hand, the standards require generally require more rigorous understanding to meet expectations ultimately raising the level of general education. To improve my teaching and grow as an effective educator, I am pursuing professional development opportunities after earning my teaching credentials geared towards improving math and science teachers and retaining highly qualified educators in high schools. By becoming more engaged with my own professional development, I can collaborate resources with other educators to research and improve teaching to more positively impact student learning during immanent educational reform.


Hunt, T. C. (September 2005). History of Reforms: Education Reforms: Lessons from History. Phi Delta Kappan, 87(1): 84-89.

M6 Reflection: Social and Cultural Influences

H1 – “To demonstrate a positive impact on student learning, teacher candidates honor student diversity and development.” (Seattle Pacific University). This standard implies that each student has a unique set of personal and developmental differences where teachers can use recent and relevant research to positively impact student learning.

Students, Parents and Stress discussion post

Stress is a relevant and very real part of students lives. The impact of such stress has adverse effects on brain development and learning (Medina, 2008). Educators should use research based strategies to be aware of student stress and learn how to assist students in maximizing learning potential. The following screenshot is taken from a class discussion board which demonstrates my understanding of research showing stressful home live and the impact on student development within the classroom. In this piece of evidence, I discuss how creating an inclusive classroom community can negate some of the harmful effects induced by stress. This is relevant to the H1 program standard since unique home experiences can directly impact student learning and educators should address the effects of developmental challenges students face, even when they are beyond the control of the teacher.

In writing this post and discussing the impact on student experience, I made new connections with the importance of creating a classroom community to help students overcome stress from outside the classroom. When students have a safe classroom environment, even with uncontrollable stress, students can continue to learn and develop in content areas. Awareness of student stress and getting to know students can positively impact student learning. In my classroom, I will create a learner friendly environment to foster learning. Additionally, I will use best practices to engage my students with multi sensory lessons (Medina, 2008). By increasing engagement in learning, no matter the situation, students will learn more (Borich, 2014). Classroom communities and sensory integration in learning all provide opportunities for students to engage in the content and increases learning. There are many other social issues classroom teachers have the opportunity to impact. Using research based strategies to impact the community will positively influence student development.


Borich, G. D. (2014). Effective Teaching Methods: Research-Based Practice (8th ed.). Upper Saddle River, NJ.: Pearson Education, Inc.

Medina, J. (2008). Brain rules: 12 principles for surviving and thriving at work, home, and school. Seattle, WA: Pear Press.

Seattle Pacific University (n.d.). HOPE Standards. Seattle Pacific University School of Education. (Accessed Aug. 2, 2014).