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).


P1 – Intentional Inquiry and Planning

P1 – Practice intentional inquiry and planning for instruction. This means that classroom teacher plans instruction around a learning target and creates a lesson which encourages students to critically think about the function of the learning target. Within the realm of mathematics, students should build intuition around how mathematical processes and can therefore build from current understandings to unique situations in the future. For a teacher, building this intuition must be well planned.

Student Work Matrix POGILStudent Work Matrix POGIL2Student Work Matrix POGIL3 Student Work Matrix POGIL4

Student Work Matrix POGIL5Student Work Matrix POGIL6

In the images, I’m presenting the work of a group of students who completed a group inquiry activity that was monitored me. While POGIL (Process Oriented Guided Inquiry Learning) activities are highly structured and I lack the training to adequately design a true POGIL, this is my best attempt at guiding students through mathematical concepts using discovery as the motivator for the lesson. This POGIL is about matrix multiplication, the purpose of this activity was to build on their prior experiences of matrices, create intuition about mathematical practices, and assist students in making meaning behind matrix multiplication. Many students know the procedure, yet few understood how this process was applicable in the real world.

This classroom activity was built and designed by me, although I used a textbook to find problems with student interest in mind and adapted the questions to fit my instructional goals. Since this activity was designed by me, this demonstrates I am able to ask students good questions which lead to conceptual understanding. This also shows my ability to plan for 100 minutes of instruction and facilitate an activity, probing students for more advanced thinking.

While planning this activity, I learned about how challenging it is to create clear questions which lead students to understanding of the learning targets. Since I teach multiple sections of the same course, after each class, I revised my questions to ensure each question challenges students and leads them to more complete understanding of matrix multiplication. Students also state they enjoy the POGIL’s as a learning activity. Students get to work in groups and ask questions to their peers. Providing group based activities, students break the routine of back to back 100 minute learning segments. Additionally, this provides students the opportunity to practice new skills without the traditional “drill and kill” of many math classroom. Practicing with inquiry also helps students create meaningful understanding rather than the process of symbol manipulation alone.

When designing lessons, it may be useful within my lesson plans to prepare questions each day which probe at the students understanding. Also, I think that creating a classroom goal everyday (and actively writing it down in the lesson plan) will help lead to a meaningful result from the lesson. With a goal like “Students can understand the meaning and operations of matrix multiplication,” I can create quality lessons, ask questions which probe for understanding, and measure the effectiveness of my lesson.

Inquiry, Teaching and Assessment Methods II Reflection

E1- Exemplify professionally-informed, growth-centered practice. Teacher candidates develop reflective, collaborative, professional growth-centered practices through regularly evaluating the effects of his/her teaching through feedback and reflection. This standard means that teachers will use student feedback and formative assessment to guide lesson plans and class activities to meet the needs of students.

Parametric POGIL Student Work Sample

The document included is a student work sample from an activity which demonstrates some implementation from the Understanding by Design unit plan structure and implementation of teaching based on formative assessment. While this document is not from coursework, it demonstrates that I can take what was learned in the course and implement a lesson where I am designing activities from pre-established goals and finding acceptable evidence to show that students have met the goal. The student work sample is a class activity which was implemented after some feedback was given by students. During my internship, I noticed that students were not completely understanding the ideas of parametric equations and the importance of the location of the “T” in the equation. My mentor teacher and I discussed various forms of evidence which would allow students to demonstrate their understanding. After learning the POGIL (Process Oriented Guided Inquiry Learning) lesson strategy for group work, I decided this would be an appropriate way to formatively assess students again to see if they can distinguish differences between parametric equations which have “T” in different locations. Additional goals were for students to build some intuition about what parametric functions would look like when graphed on paper or their calculator and make sensical choices for plot windows.

This piece of evidence demonstrates my application of designing a lesson with the outcomes in mind and to address student concerns discovered through one on one student conversation. My engagement in this activity has taught me several important key concepts about lesson plan and unit design such as planning with the goal in mind and creating activities which help students meet the goals. I have been challenged with identifying the true needs of my students and then finding (or creating) lessons which help students meet the needs. I have learned the importance of being in touch with my students and listening to their frustrations and needs. When they ask for help or sound confused on concepts, this is a clue for teachers to think about how activities are helping students meet pre-established goals for the lesson or unit. When teachers are careful about the intentions of their lessons, student have more to gain. The Understanding by Design structure for creating a lesson or unit helps teacher focus the class activities around the ending outcome. Teachers who use Common Core State Standards and the UbD lesson structure are sure to bring students to standard because the activities are structured around the goals.

To improve my ability of being a growth centered, informed instructor, I need to constantly ask myself whether or not students are learning and if I am meeting my goals. Within the teaching profession, where teachers may repeat these lessons year after year, I can improve each lesson by assessing whether or not the activity really met my goal for the unit and revise for the following years. Growing as a teacher doesn’t end when I have taught for a few years, I am obligated on continue growing and improve my students learning every single year. I believe the key is intentional improvement and measuring student growth.

Technology Observation

Background Information

My school is fortunate enough to provide students with personal computers for use in the classroom and at home. Internet is provided to students in the building and is used to distribute information to students, write papers, perform research and similar educational tasks. Teachers are provided iPads to use in class which can be synced with the classroom display (60 inch LCD display). Additionally, classrooms are equipped with speakers which is attached to portable microphones which teachers may use to amplify their voice in the classroom.


In this class, the teacher distributes notes and scaffolds the class activities by distributing a OneNote document which is a note taking document by Microsoft. Teachers can add graphs, pictures, full documents and sound files to the OneNote file and easily distribute the information in an organized way to students.

During this class period, students were asked to type their responses to an initial thinking question and then the teacher debriefed student responses as a class. When interviewing a student, he responded that typing responses to the initial thinking question versus writing them allows him to express his thinking more quickly and can write more information down. The hope of the teacher using the OneNote is that students can take notes in between the information provided. The notes are not collected, but provide students a resource to be able to search their notes and include supporting documents between their notes.

Today, the activity was a lecture about living conditions on Mars, the document in the One Note was a table set up as Two-Column notes. The teacher scaffolded the lesson by providing the information on the left column (the topics covered in the lecture) and the right was to be filled in by the students during the discussion. When talking with the instructor, before the school had computers for students, she would have printed and distributed the notes outline to provide students a tool to learn from the lecture.

During the lecture, the teacher utilized her iPad. She had a PowerPoint Application which allowed her to control the slideshow remotely as she walked around the class. During the lecture, the teacher weaved in and out of the students to see what they were doing and take corrective action. This tool also had a laser pointer function that allowed the lecturer to highlight an area of the screen she wanted students to pay attention to more closely. Additionally, the use of the iPad and the many applications helped switch between tasks gracefully without significant transition time. Within 30 seconds, the teacher moved from her PowerPoint presentation to a Word Document (to inform students of what good research looked like) to an excel file to display team groups. I think this was a good use of technology to aid in classroom management.

Finally, one low tech piece of technology that was used in the class was a microphone to amplify the teachers voice. Microphones are used by many teachers at the school, they help create clarity of instructions and teachers don’t strain their voices to talk over students. One improvement I would make as the teacher using a microphone would be to repeat what students say a when the student is not using the microphone. This way everyone can hear students comments loudly and clearly.

One downside to the use of technology in the classroom is when the tools don’t work. LanSchool is a tool which provides teachers an overview of what students are looking at on their computer. This technology is currently unavailable so students easily take advantage of the computer use and look at non-school related sites. This can be challenging for teachers if they are not careful at monitoring student computer use. While technology has it’s benefits because students can access many sites for information, it also presents problems when trying to teach and students are off track. Students even claim that they computer use can be distracting, one student in particular claims he is easily distracted by his coding (Java Script). In all, technology has improved classroom culture and provides different learning opportunities, there are also unique new challenges that also detract from information. Many of these tools are classroom management tools and few are subject specific contributing to the unique needs of the specific lesson.

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.

Learners in Context Post-Course Meta-Reflection

[1] The Learners in Context course focused on two principals of HOPE, E1 — Exemplify professionally-informed, growth-centered practice and H1 — Honor student diversity and development. The standard E1 means that teachers are adopting best professional practices based on research and tested to maximize student learning. The H1 standard means that teachers are able to recognize that students are different and have very unique needs. Taking these differences into account, teachers are strategically thinking about their practices to improve student development.

[3] During the course I learned about the importance of exploration for students during their learning process. Medina (2008) talks about his learning growing up and his mother’s willingness to adapt to Medina’s changing needs as he explored his interests. Teachers must show willingness to adapt to students interests and work to encourage learning, not inhibit exploration through standardized testing. [2] Jamie Gephart is a student in our class and responded to a discussion post about incorporating exploration into learning while recognizing the requirement of testing, she writes

I had a teacher in high school that referred to his tests as a “celebration of knowledge”.  I know that may sound cheesy, but this subtle twist helped to relieve some of the pressure.  And in reality, shouldn’t this be the purpose of an exam?  Students have worked hard to understand and incorporate this new knowledge.  What if teachers presented exams more like game day, as an opportunity to show off all the hard work and practice they have endured? (Gephart, 2014)

[5] This matches the standard of H1 since it encourages student development through an effective way of allowing exploration and a creative way to test students without hindering natural curiosity. [4] From exploring and engaging in this discussion post, I learned that when students change their frame of reference from the testing frame to the game day frame their anxiety is drastically decreased and students can demonstrate their true knowledge. I have not needed to use these tools because I have been fortunate not to suffer from text anxiety, hover some students are not as fortunate. [6] In my classroom, I will try to frame tests as demonstrations of learning rather than a ritualized practice used to assign grades and create a classroom hierarchy.

Another point of learning from this course was Vygotsky’s Zone of Proximal Development (ZPD) and the use of scaffolding to guide students’ learning (Pressley and McCormick, 2007). [1] This aligns with HOPE standard E1 since Vygotsky has conducted significant research on human development and learning. [2] These two pictures from Pressley and McCormick (2007) have been incredibly beneficial to my understanding of the ZPD and how good educators should teach students to maximize learning.

Module 5 did not facilitate much discussion about the ZPD as much as the book or classZone of Proximal Development lectures, however, the concept was impactful. [3] The ZPD is an essential tool for teachers to know where students are located in the curriculum, the process of scaffolding provides an essential tool for teachers to implement and practice providing work to students which is in their ZPD. [4] Prior to this reading, I did not know how to best implement challenging material, Vygotsky’s research has explained the precise level of challenge to present to students. I learned a lot about scaffolding and how to present challenging material and provide a guide to full understanding by providing many resources to students. [5] Students benefit the most when teachers practice these techniques. By scaffolding lessons of Scaffoldingchallenging materials, students receive adequate help and can feel successful in their work while also learning. [6] Practicing using ZPD and scaffolding in my classroom will not be challenging, in fact this will be an essential tool. I will use to explain complex materials, especially during my internship while working with exceptional students and provide support to students where the content falls beyond their ZPD. Finding the balance between too challenging and not challenging enough will take the most amount of practice.


Gephard, Jamie. (2014, July 9). Module 3 Discussion Forum A-G. BlackBoard Discussion Post. (Web).

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

Pressley, M., & McCormick, C.B. (2007). Child and adolescent development for educators. New York, NY: The Guilford Press.

Micro-Teaching Reflection

Micro-Teaching Lesson Plan

[1] O1 – Offer an organized curriculum aligned to standards and outcomes. This program standard means that teachers will be thinking critically when writing lesson plans and will make sure that students are learning relevant material which meet state and national requirements. In teaching, curriculum should be easy to follow for maximum student understanding. [2] The attached document is lesson plan for my micro teaching lesson presented to the MTMS Cohort. The accompanying picture is a sample of student work from the micro teaching lesson. This lesson plan demonstrates my understanding of planning collaborative learning and inquiry based learning activities. Asking good questions and facilitating a collaborative learning environment increases student engagement and ultimately increases learning (Borich, 2014).Micro-Teaching Student Sample Work

[3] Within the lesson plan, I include questions which help students engage with the lesson and informally assess understanding. Students were also encouraged to work in groups where they could discuss their misunderstandings. The lesson clearly states the Common Core State Standards in Mathematics and the lesson aligns the learning activity with the learning target which helps students learn math concepts prescribed by the standard. [6] After teaching the lesson, I reflected on improvements I could make to improve the lesson or better achieve the learning targets. I would scaffold the learning more, my understanding of vocabulary relating to sets and subsets is strong, yet often times students do not have such deep understanding. I worked to scaffold the lesson with some vocabulary, although, if I were to teach this same lesson again, I would use direct instruction to introduce vocabulary and concepts and then use the activity to help improve understanding by allowing structured freedom. I would conclude by providing more independent practice. [5] The result for the student is that when lessons are highly organized and scaffolded well, their learning improves. The student will retain more taught information if we guide them towards independent thinking. [4] In summary, by constructing this lesson, I learned about scaffolding well, using student inquiry when teaching a lesson and the possible challenges associated with gauging student learning. [Extra Learning] An additional learning point during creating the lesson is how easy it can become for teachers to use powerpoint slides to dominate classroom instruction and how dangerous it is to overload students with words on slides.

Reference List:

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