Planning
Target P1: Effective planners exhibit a positive disposition toward learning and doing mathematics by identifying essential learning outcomes based on content and process standards and knowledge of adolescent learning, development, and behavior. [Effective planners also incorporate knowledge of learners’ cultural and language diversity and select culturally relevant examples as a means to motivate and engage learners.]
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Narrative for P1 (Updated Fall 2014): The artifact I chose for this target was an activity that I did with my Algebra 1 students during student teaching that reinforced how to write linear equations in standard form and how to create and graph word problems with linear equations in standard form. This activity is aligned with the standard CCSS.HSA.CED.A.2 which involves creating equations in two or more variables to represent relationships between quantities as well as graphing equation on coordinate axes. I used this standard to write a learning target for the students. In designing the activity, I made sure to incorporate a number of the Standards for Mathematical Practice such as constructing viable arguments (by having students write out their steps and explain how their equations relates to their story problem), critiquing others (by having students walk around and "critical friend" their peers' completed work), modeling with mathematics (students modeling the equations using real-world examples), and attending to precision (by having students check their answers and "critical friend" with their peers to make sure their work is appropriate).
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Target P2: Effective planners design focused, coherent sequences of connected lessons [that show a progression of learning over time toward proficiency and understanding].
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Narrative for P2 (Updated Fall 2014): For this target, I chose to include a unit plan that I designed and taught during my student teaching semester. This unit was an introduction to functions and relations. I designed this unit with the necessary state standards and the knowledge of how students learn mathematics in mind. I made sure to provide students with plenty of real-world, concrete examples to help them develop a conceptual understanding of the key concepts of the unit. The lessons within the unit plan were designed to build upon the content of each previous content and make as many connections as possible to prior knowledge and real-world examples such that as students progress through the coherent sequence of connected lessons, they will develop deep conceptual understanding of the content.
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Target P3: Effective planners draw upon research-based teaching and learning practices to support their planning[, including print, digital, and virtual resources and collections from professional organizations].
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Narrative for P3 (Updated Fall 2014): I chose to include two different frames that I created. The Frame is an educational tool that has been researched and shown to be effective in helping students remember key concepts of the content they are learning as well as to help them develop a stronger understanding of these concepts. The first frame that is included was one designed during Teacher Assisting in my Universal Design for Learning Class. The second frame was developed and used in my Algebra 1 class during student teaching. Both of these frames helped me plan out my instruction (how I wanted to teach the material so students understood it the best) and helped students develop a deeper understanding of the material I taught by helping students better-organize their thinking.
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Instruction
Target I1: Effective teachers use questioning techniques to a) expose and explore misconceptions and b) to engage students in productive mathematical discussions[, and they provide opportunities for students to communicate mathematics in a variety of forms and for a variety of target audiences].
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Narrative for I1 (Updated Fall 2014): Being placed in a Project-Based Learning school during student teaching was a great experience and gave me a lot of freedom to use a variety of different teaching methods with my students. I am including a variety of different student work as my artifact for this target. Over the course of the semester, both of my classes completed a number of different projects. The end products for these projects were usually different each time. The students submitted their projects in a variety of different formats ranging from a memo in a Google doc to a presentation to an authentic audience, to a pamphlet that could be shared with a college students, to literacy activities that gave a detailed explanation of student work. This variety of end product formats for these projects helped expose and explore misconceptions (especially when students presented their projects in a presentation) and these misconceptions often spurred full-class discussions about the mathematics. For example, in my Algebra class, a group was presenting and in their presentation they presented something that was wrong (but many other groups had also had the same misconception). This spurred a productive mathematical discussion as to what the students did wrong and how it could be fixed. This variety of different formats for end products makes it easier to expose and explore misconceptions and to partake in full-class discussions about these misconceptions.
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Target I2: Effective teachers use connections to students’ prior knowledge within and outside of mathematics to help students develop conceptual understanding and procedural fluency[, and they provide opportunities for students to select and explore personally relevant problems from a mathematical perspective].
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Narrative for I2 (Updated Fall 2014): The unit plan that I developed and taught in my Algebra 1 class during Student Teaching drew upon students' prior knowledge in a number of different ways. The unit plan focused on several real-world examples/analogies such as a pop machine representing a function or a roller coaster representing the graph of a function. Students used their prior knowledge of these examples/analogies (outside of mathematics) to help them better understand the mathematical concepts. The unit also drew on students' prior knowledge within mathematics by requiring them to use what they have learned about variables to help them better understand functions and relations. These connections helped students develop both conceptual understanding of what functions and relations are as well as other aspects of functions (such as the graphs of functions) and develop the procedural fluency necessary to complete related practice problems and complete their ongoing unit projects.
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Target I3: Effective teachers a) provide equitable treatment of and have high expectations for all learners, and b) they use a variety of strategies, including strategies for differentiated instruction, to build conceptual understanding and procedural fluency for all learners. [They allow multiple and varied opportunities for students to demonstrate their understanding and fluency, and they persist in helping each student reach their full potential.]
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Narrative for I3 (Updated Fall 2014): This is a lesson plan that I developed and taught during student teaching in the Fall of 2014. The lesson plan utilizes a number of different teaching methods and is great for students of all different learning styles and abilities. One important part of the lesson, where students work together to make human graphs in order to better understand transformations of parent functions, is a demonstration of how I provide equitable treatment of and have high expectations for all students. The activity required students to work together and thus I had the high expectation that students would be fully-engaged and willing to collaborate with their peers in order to get the most out of the activity. The lesson shows that I must treat each student equitably by providing each student with the necessary support they need in order to each get the best educational opportunity possible. The variety of strategies (direct instruction, demonstration, simulation, group collaboration, etc.) show how this lesson was designed to be adapted to fit the needs of a wide range of diverse learners in order to help each student develop conceptual understanding and procedural fluency of the concepts being taught in the lesson.
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Target I4: Effective teachers engage students in a) a sequence of developmentally appropriate and challenging learning activities in which they are actively building new knowledge, b) including investigations that use math-specific technology[, and they facilitate students’ ability to develop future inquiries that extend their past investigations].
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Narrative for I4 (Updated Fall 2014): The artifact I included here is a project that was completed in my PreCalclulus class as part of the quadratic functions unit during Student Teaching. Throughout the unit, students learned about various aspects of quadratic functions (including how to graph them, how to find the roots of a quadratic function by factoring, completing the square, and using the quadratic formula, and how to identify and explain different parts of a graph of a quadratic function). The ongoing project for this unit was the Catapult project which involved students designing and building catapults and then shooting the catapults to get data to model a quadratic function for the trajectory of their catapults. The progression of this project required students to complete a series of workshops and activities which helped them actively build new knowledge and develop conceptual knowledge of quadratic functions. After designing and building the catapults, students used either a GoPro camera paired with Tracker Software or a CBR 2 (Calculator-Based Ranger) to record the data for their catapult and then analyzed the data to create functions that modeled their catapults' trajectories. The students used math-specific technology (Tracker, CBR) to investigate the properties of their catapults' shooting as well as to assist in coming up with quadratic functions for their catapults.
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Target I5: Effective teachers make appropriate choices regarding when to use math-specific technology and manipulatives to support deep learning, and they recognize the benefits and limitations of such tools. [They also participate in professional learning related to current and emerging technologies that support math teaching and learning.]
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Narrative for I5 (Updated Fall 2014): This artifact was one that I created during Student Teaching in my PreCalculus class. I often times had students use technology to explore the mathematics instead of just listening to me lecture and having to take notes over it. This activity was one that served as an introduction to transformations of functions. I had students use Geogebra, which is a math-specific free software available to anyone with a computer. Students used an applet which was created in Geogebra and found on Geogebratube to explore and understand the different types of transformations that can be applied to a parent function. Students used the technology to help them make and test conjectures based on their findings. This hands-on exploration with the technology allowed students to get a deeper understanding of transformations. While the slider aspect of Geogebra was useful, it would have been better if students could have put their own parent functions in instead of just the one that was provided in the applet. The limitation of this is that students were not able to see that the transformations work for any parent function they could possibly put in.
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Assessment
Target A1: Effective teachers identify [and design] formative assessments that can inform instruction and monitor learners’ progress toward meeting essential learning outcomes.
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Narrative for A1 (Updated Winter 2014): I used a lesson plan that I designed and taught in my 8th grade math class during my teacher assisting semester. The three "checks for understanding" (thumbs up, thumbs down; back-to-back whiteboards; and exit slips) were informal activities done by me during the lesson in order to gauge students' progress toward reaching the learning targets of the lesson. The results of these formative assessments were used to help me decide if more time needed to be spent on direct instruction in the future or if we were ready to move on.
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Target A2: Effective teachers identify [and design] summative assessments that can accurately gauge students’ achievement of essential learning outcomes.
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Narrative for A2 (Updated Winter 2014): I chose to include the Selected Response Assessment that I designed for ED 337 because it is an example of a summative assessment that I designed. This summative assessment requires students to answer higher-level questions and also reflect upon their answers. All of the questions are aligned to at least one of the learning targets provided in the assessment. Students answering either correctly or incorrectly on the questions will show their success or failure in reaching the essential learning outcomes of the assessment. Although I did not use an SRA during teacher assisting, I plan to design and use at least one during student teaching.
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Evaluation
Target E1: Effective teachers use timely analysis of assessment data to accurately gauge students’ progress toward essential learning outcomes identified during planning[, and use this information to inform future planning, modify instruction, and increase student achievement].
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Narrative for E1 (Updated Fall 2014): I chose two very similar artifacts for this target. I chose the learning logs that my CT includes in every lesson as a tool to gain insights into what students have learned from the lesson. Students are to fill out these learning logs (which consist of a questions related to the learning goal of the day). I chose to continue using these learning logs because they are a great tool that helps give me data on which students understand the lesson, which ones don't, and which ones are on their way to understanding the lesson. The second artifact, the exit slips, include the learning log question as well as a question asking the student to state which question was the hardest and why. By collecting these exit slips, I was able to get immediate data on which questions the students struggled with the most. This along with the responses to the learning log question helped me understand how well the students are progressing toward reaching the learning outcome(s) of the lesson. By looking at students' responses on the learning logs and the exit slips, I was able to make a list of students who had reached the learning outcomes of the lesson, those who were progressing toward the learning outcomes, and those who were falling short. I used this list to help me differentiate future instruction so to give additional help to those students who need it and to challenge those who have already reached the learning outcomes of the lesson.
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Target E2: Effective teachers use summative assessments to accurately gauge students’ achievement of the essential learning outcomes identified during planning[, and they determine the extent to which individual students’ mathematical proficiencies have increased as a result of instruction].
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Narrative for E2 (Updated Fall 2014): In both of the classes I taught during student teaching, my CT and I implemented a unique system for assessing. We would have students take a formative assessment halfway through the content and then another formative assessment toward the end before we reviewed. We would track students' performance on these assessments as they related to the standards and the learning targets for the unit. These would help us in identifying which areas needed to be emphasized more in future instruction and which students needed more help. We would then give a final summative assessment which assessed the same standards and learning targets as the first two quizzes. We would look at all of the data from both of the formative assessments as well as track how students' levels of understanding progressed over the course of the unit. This summative and formative assessment data helped guide my future instruction as well as helped to differentiate instruction. After looking at the summative assessment data, I was also able to reflect upon my teaching practices to fix any errors in the future.
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Professional Growth
Target G1: Effective teachers actively seek, engage, reflect, and share personally-relevant collaborative learning experiences[, and they apply what they have learned to enhance mathematical learning opportunities of their students.]
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Narrative for G1 (Updated Fall 2014): The first artifact that I have included is a blog post that I included in my personal blog toward the end of Teacher Assisting. Myself and the other teacher assistants had a chance to attend a panel discussion with current student teachers where we could ask questions and get a feel for what we would be experiencing during student teaching. This blog post served as my reflection of what I had heard from student teachers sharing their personally-relevant collaborative experiences over the course of the semester.
The second artifact I have included is the notes I took after attending the Fire Up Student Teaching Conference at Aquinas College. In October of 2014, we were invited to attend a student teaching conference where we were encouraged to listen to guest speakers (teachers, principals, professors, etc.) as well as actively seek out conversations with these speakers and other student teachers to share and discuss our experiences over the course of the semester. At this conference, I sought out different speakers and other student teachers to engage in conversations about many different aspects of teaching. The artifact I included is a list of takeaways from the conversations I had at the conference. |
Field Experience
Target F1: Effective teachers have observed [and implemented] a range of approaches to orchestrating the mathematics learning environment (e.g., task selection, discourse, and assessment systems), and they reflect on how those approaches may have been influenced by one’s beliefs about the nature of mathematics and how students learn mathematics.
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Narrative for F1 (Updated Winter 2014): I chose to include a blog post that I wrote during my teacher assisting semester that involved asking a fellow teacher at my placement to fill out a survey with similes about teaching and learning mathematics. This survey was meant to expose the teacher's own personal beliefs about the nature of mathematics and how students learn math. I observed this teacher's class as well as analyzed the teacher's responses to the survey to reflect on how the teacher's beliefs influence the teaching of mathematics. My blog post is a reflection of my observation as well as my analysis of the teacher's results to the survey.
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Target F2: Effective secondary teachers have demonstrated knowledge, skills, and professional behaviors in both middle and high school settings [and have communicated to other educators what they have learned from those experiences].
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Narrative for F2 (Updated Fall 2014): My teacher assisting placement was in a local environmental middle school in a 7th and 8th grade mathematics classroom. During that placement I was able to learn how middle school students behave, learn, and essentially survive in school and what kinds of teaching practices I need to exhibit to effectively teach middle school students. My student teaching placement was in a local Project-Based Learning high school in an Algebra and Pre-Calculus classroom. During this placement, I developed a greater understanding of different ways of teaching mathematics (through the use of the Project-Based Learning model) as well as learned how to better integrate technology into the classroom. Each of these placements were invaluable in giving me field experience with a wide range of students of varying ages, backgrounds, and levels of mathematical understanding. The completion of this content folio provides sufficient evidence as an artifact for meeting this target.
An artifact that demonstrates everything I have learned over the course of the Student Teaching semester as well as in previous semesters of my pre-service teaching career is a final reflective blog post to my personal blog. This blog post shows that I have demonstrated my knowledge skills, and professional behaviors in both a middle and, more recently, a high school setting. This blog post also serves as a communication to other educators what I have learned from my experiences as a pre-service teacher. |