Planning:
Target P1: Effective planners exhibit a positive disposition toward learning and doing mathematics by identifying essential learning outcomes bases on content and process standards and knowledge of adolescent learning, development, and behavior.
P1- Unit Plan Reflection
The unit plan for Quadratics demonstrates my ability to exhibit a positive disposition toward learning and performance of mathematics. First, we identified learning outcomes based on content and process standards with knowledge of the adolescent learning, development and behavior. After reviewing the common core state standards with my cooperating teacher, another teacher assistant; we created the learning targets for the quadratic unit. We were able to establish six learning targets for this unit. The learning targets are listed in the second column of the unit plan. The learning targets align with the various lessons. For example, “Finding the Axis of Symmetry,” “Finding the Discriminant,” “Quadratic Notes” and “Quadratic worksheets” support the learning target 6.6. One can find solution(s) to a quadratic function by utilizing the quadratic formula.
In order to motivate the students and promote their engagement into learning, we created the following lessons and worksheets for this unit: Zero Product Property Multiple Intelligence lesson plan and “Exploring the Vertical Motion Model” worksheet. These activities allowed students to become active learners and gave them an opportunity to develop their understanding of the content. As found in the content of the Zero Product Property Multiple Intelligence lesson plan, the students had a choice of how they wanted to demonstrate their proficiency by deciding how they wanted to present their project to their classmates. As in the “Exploring the Vertical Motion Model” worksheet, the students were allowed to use their cell phones to scan various QR codes and were able to watch videos as they answered questions of the situation. Also, they were able to scan the QR code to check their answers. We discovered with both activities, the students understood which learning targets matched since they had to write the learning target number on their worksheet as well as on their table of contents for the unit. The students were engaged with each lesson since they were able to use technology and were able to apply their personal learning style. This allowed the student’s to combine the lessons and thus this allowed them to form connections with the content.
I strongly believe that it is important to engage the students and keep the students interest in mind while planning the unit since it provokes motivation to learn. We purposely selected various YouTube clips throughout the unit to engage the students. For example, we played YouTube videos demonstrating a person diving off a platform and also shown a video of a person shooting a basketball which demonstrated examples of the vertical motion model. The students were really engaged with these lessons when they saw relevant examples of the content, which allowed them to take ownership of their learning. The students saw the connections with the relevant examples by aligning the learning targets and common core state standards with the lessons which promoted motivation and engagement with the learners.
The unit plan for Quadratics demonstrates my ability to exhibit a positive disposition toward learning and performance of mathematics. First, we identified learning outcomes based on content and process standards with knowledge of the adolescent learning, development and behavior. After reviewing the common core state standards with my cooperating teacher, another teacher assistant; we created the learning targets for the quadratic unit. We were able to establish six learning targets for this unit. The learning targets are listed in the second column of the unit plan. The learning targets align with the various lessons. For example, “Finding the Axis of Symmetry,” “Finding the Discriminant,” “Quadratic Notes” and “Quadratic worksheets” support the learning target 6.6. One can find solution(s) to a quadratic function by utilizing the quadratic formula.
In order to motivate the students and promote their engagement into learning, we created the following lessons and worksheets for this unit: Zero Product Property Multiple Intelligence lesson plan and “Exploring the Vertical Motion Model” worksheet. These activities allowed students to become active learners and gave them an opportunity to develop their understanding of the content. As found in the content of the Zero Product Property Multiple Intelligence lesson plan, the students had a choice of how they wanted to demonstrate their proficiency by deciding how they wanted to present their project to their classmates. As in the “Exploring the Vertical Motion Model” worksheet, the students were allowed to use their cell phones to scan various QR codes and were able to watch videos as they answered questions of the situation. Also, they were able to scan the QR code to check their answers. We discovered with both activities, the students understood which learning targets matched since they had to write the learning target number on their worksheet as well as on their table of contents for the unit. The students were engaged with each lesson since they were able to use technology and were able to apply their personal learning style. This allowed the student’s to combine the lessons and thus this allowed them to form connections with the content.
I strongly believe that it is important to engage the students and keep the students interest in mind while planning the unit since it provokes motivation to learn. We purposely selected various YouTube clips throughout the unit to engage the students. For example, we played YouTube videos demonstrating a person diving off a platform and also shown a video of a person shooting a basketball which demonstrated examples of the vertical motion model. The students were really engaged with these lessons when they saw relevant examples of the content, which allowed them to take ownership of their learning. The students saw the connections with the relevant examples by aligning the learning targets and common core state standards with the lessons which promoted motivation and engagement with the learners.
Target P2: Effective planners design focused, coherent sequences of connected lessons [that show a progression of learning over time toward proficiency and understanding].
P2- Unit Plan Reflection
The unit plan for Quadratics demonstrates my ability to design a focused, coherent sequences of connected lessons. The learning targets are the main concepts of the unit, which we would be measuring the student’s proficiency. The learning targets are clearly stated in the unit plan. With the learning targets in mind, we were able to create a backward design lessons which connect the concepts form previous lessons to the new concepts. In the unit plan document, we identified the learning targets and common core state standards for each lesson as well integrated the concepts from the previous lesson into the next worksheet. For example, “Finding the Axis of Symmetry” and “Finding the Discriminant” worksheet allowed the students to connect the previous concepts in their past lessons on factoring and apply them together in the quadratic formula worksheet.
While planning the unit plan, we created lessons based on the learning targets. For example, each lesson of the unit plan matches with the learning target, which allows the student to know what they should be learning in this portion of the unit. Therefore, this allowed me connect lessons together with the content as well as show the progression over the learning over unit. In each lesson, the students will use the previous content and apply it to the new material in quadratics. This will allow the students to make connections in mathematics. We wanted to engage every student, thus we created differentiated instructions which allowed every student to participate in the lesson. For example, the exploring Vertical Motion Model and the Zero Product Property Multiple Intelligence lessons encouraged the students to become active learners and take responsibility for their learning. The students had choice thus giving them an opportunity to demonstrate their learning over the previous content.
At the end of the unit, the students took a final summative assessment and they were scored on the individual learning targets. As both summative learning techniques were utilized (quizzes and test) the teacher was able to measure each student’s progression of learning. We monitor the student’s growth from the students quiz grades and the final summative assessment measured the students cumulative proficiency of the unit’s learning targets. This unit plan demonstrates my ability to connect each lesson with each other in order to create a sequence for learning. This concept allowed the students to see the big idea (main purpose) plus it allowed me to continually evaluate the students understanding throughout the unit.
The unit plan for Quadratics demonstrates my ability to design a focused, coherent sequences of connected lessons. The learning targets are the main concepts of the unit, which we would be measuring the student’s proficiency. The learning targets are clearly stated in the unit plan. With the learning targets in mind, we were able to create a backward design lessons which connect the concepts form previous lessons to the new concepts. In the unit plan document, we identified the learning targets and common core state standards for each lesson as well integrated the concepts from the previous lesson into the next worksheet. For example, “Finding the Axis of Symmetry” and “Finding the Discriminant” worksheet allowed the students to connect the previous concepts in their past lessons on factoring and apply them together in the quadratic formula worksheet.
While planning the unit plan, we created lessons based on the learning targets. For example, each lesson of the unit plan matches with the learning target, which allows the student to know what they should be learning in this portion of the unit. Therefore, this allowed me connect lessons together with the content as well as show the progression over the learning over unit. In each lesson, the students will use the previous content and apply it to the new material in quadratics. This will allow the students to make connections in mathematics. We wanted to engage every student, thus we created differentiated instructions which allowed every student to participate in the lesson. For example, the exploring Vertical Motion Model and the Zero Product Property Multiple Intelligence lessons encouraged the students to become active learners and take responsibility for their learning. The students had choice thus giving them an opportunity to demonstrate their learning over the previous content.
At the end of the unit, the students took a final summative assessment and they were scored on the individual learning targets. As both summative learning techniques were utilized (quizzes and test) the teacher was able to measure each student’s progression of learning. We monitor the student’s growth from the students quiz grades and the final summative assessment measured the students cumulative proficiency of the unit’s learning targets. This unit plan demonstrates my ability to connect each lesson with each other in order to create a sequence for learning. This concept allowed the students to see the big idea (main purpose) plus it allowed me to continually evaluate the students understanding throughout the unit.
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].
P3- Multi-Genre Project Reflection
My multi-genre project demonstrates my ability to the plan a research based teaching unit and learning practices to support their planning. The planning of the multi-genre project allowed gain a better understanding of how students can learn the significance of pi and the role of pi in mathematics in a Geometry classroom. I wanted to plan a unit where student felt they had control of their learning through inquiry. The project allows students to grow and develop their own perspective of mathematics from different genres and lens as they explored pi in this research based teaching. The research based learning improves the instruction in the class since it provides students an opportunity higher level of thinking to research in detail the significance of pi. For example, the students explore pi in each of the artifacts and they learn why pi is significant in mathematics. As the students began to explore pi, this project could be another avenue in which to instruct the class and the focus would be different as found in a traditional lecture based classroom. Instead, the students are engaged in the various genres and allowed to form their own opinions about the topic from their reflections. For example, the students bake pi after solving for the radius and area of the circle problems. I plan this project where the students can research pi and demonstrate their understanding of pi through reflections. This project encourages students to think critically and encourage creativity throughout the project. For example, the students can create a pi collage and explain the symbolism of the piece. Also, research paper encourages the students to demonstrate their knowledge and reflect each assignment as they explored and collaborated on pi. This lets students to view pi in the real world situations as well as in their real life environments. Thus, the students will create their own response and integrate their knowledge from the seven documents and use their own research to argue their perspective of the role of pi in mathematics. As this learning environment allowed students to collaborate problem solving and integrate the different genres, it also facilitated the students to discover the significance of pi in mathematics. Therefore, I feel my multi-genre project is a collaboration of various media, and resources, which promotes learning through inquiry and research based teaching since it provides the student a higher level of thinking opportunity to research in detail the significance of pi.
My multi-genre project demonstrates my ability to the plan a research based teaching unit and learning practices to support their planning. The planning of the multi-genre project allowed gain a better understanding of how students can learn the significance of pi and the role of pi in mathematics in a Geometry classroom. I wanted to plan a unit where student felt they had control of their learning through inquiry. The project allows students to grow and develop their own perspective of mathematics from different genres and lens as they explored pi in this research based teaching. The research based learning improves the instruction in the class since it provides students an opportunity higher level of thinking to research in detail the significance of pi. For example, the students explore pi in each of the artifacts and they learn why pi is significant in mathematics. As the students began to explore pi, this project could be another avenue in which to instruct the class and the focus would be different as found in a traditional lecture based classroom. Instead, the students are engaged in the various genres and allowed to form their own opinions about the topic from their reflections. For example, the students bake pi after solving for the radius and area of the circle problems. I plan this project where the students can research pi and demonstrate their understanding of pi through reflections. This project encourages students to think critically and encourage creativity throughout the project. For example, the students can create a pi collage and explain the symbolism of the piece. Also, research paper encourages the students to demonstrate their knowledge and reflect each assignment as they explored and collaborated on pi. This lets students to view pi in the real world situations as well as in their real life environments. Thus, the students will create their own response and integrate their knowledge from the seven documents and use their own research to argue their perspective of the role of pi in mathematics. As this learning environment allowed students to collaborate problem solving and integrate the different genres, it also facilitated the students to discover the significance of pi in mathematics. Therefore, I feel my multi-genre project is a collaboration of various media, and resources, which promotes learning through inquiry and research based teaching since it provides the student a higher level of thinking opportunity to research in detail the significance of pi.
Instruction:
Target I1: Effective teachers use questioning techniques to expose and explore misconceptions and 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].
I1- Open Ended Questioning/Formative Assessment Observation Reflection
During my observation and discussion with David Coffey, I gain an abundance of new information on the instruction process for teaching, especially with questioning techniques. I feel my in-class observation with Dave Coffey demonstrates my usage of questioning techniques and exploring student misconceptions since I learned the importance of open ending questioning throughout my instruction. During our discussion, Dave and I talked about the purpose of questioning as a type of formative assessment, which gives the teacher feedback on the student’s understanding of the new and old concepts. In the “So What” section of my reflection, I explained how I plan to ask open end questions throughout my lesson. I learned while instructing I need keep a list of questions with me and keep track the student’s response on an observation sheet. This will give me feedback as well as think where in my lesson where students will struggle and why they are struggling. In the “So what” section of my reflection, I learned how to ask appropriate higher level think questions to my students during discussion will give students opportunities to communicate mathematics to their peers. Lastly, from my “What” and “So what” sections of my reflection, I learned I need to create a list of open ending questions throughout my lesson. I need to think where students may have misconceptions during each portion of the lesson and how I can facilitated their learning by developing high level of questions to promote their learning. This will allow students to make their own connections as well as providing them an opportunity to communicate their understanding of mathematics to their peers and myself. Therefore, I need to keep open questions in mind as I walk into each class period in order to think of the student’s misconceptions of the content. The observation with Dave allowed me to understand how I can improve my questioning techniques in the classroom in order provide opportunities for students to communicate mathematics in a variety of forms and for a variety of target audiences.
During my observation and discussion with David Coffey, I gain an abundance of new information on the instruction process for teaching, especially with questioning techniques. I feel my in-class observation with Dave Coffey demonstrates my usage of questioning techniques and exploring student misconceptions since I learned the importance of open ending questioning throughout my instruction. During our discussion, Dave and I talked about the purpose of questioning as a type of formative assessment, which gives the teacher feedback on the student’s understanding of the new and old concepts. In the “So What” section of my reflection, I explained how I plan to ask open end questions throughout my lesson. I learned while instructing I need keep a list of questions with me and keep track the student’s response on an observation sheet. This will give me feedback as well as think where in my lesson where students will struggle and why they are struggling. In the “So what” section of my reflection, I learned how to ask appropriate higher level think questions to my students during discussion will give students opportunities to communicate mathematics to their peers. Lastly, from my “What” and “So what” sections of my reflection, I learned I need to create a list of open ending questions throughout my lesson. I need to think where students may have misconceptions during each portion of the lesson and how I can facilitated their learning by developing high level of questions to promote their learning. This will allow students to make their own connections as well as providing them an opportunity to communicate their understanding of mathematics to their peers and myself. Therefore, I need to keep open questions in mind as I walk into each class period in order to think of the student’s misconceptions of the content. The observation with Dave allowed me to understand how I can improve my questioning techniques in the classroom in order provide opportunities for students to communicate mathematics in a variety of forms and for a variety of target audiences.
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].
I2- Vertical Motion Model Multiple Intelligence Reflection
The vertical motion lesson plan demonstrates how students use their prior knowledge within and outside of mathematics as the students develop their conceptual understanding and procedural fluency. The vertical motion model lesson with multiple intelligence encourages the students to explore the vertical motion modern from a mathematical perspective. This allowed the students to demonstrate their learning by given them various opportunities, like creating a song/rap, creating a poster or story etc. for the students to form connections with the vertical motion model from their prior knowledge and apply their knowledge in a meaningful way to explain the vertical motion model to their peers. For example, one student created a song about the vertical motion model in which she described how to use the model in real word situations. Since the students create a creative song, the student will retain the concepts since he/she put meaning behind the concept. Each student has a choice in how they wanted to demonstrate their understanding of the vertical motion concept. For starters, the students picked a learning strategy, like visual, role play, rhythmic etc. in order for them to develop a deeper understanding of the vertical motion model. They started to form connections of their prior knowledge outside of mathematics in order to develop their own conceptual understanding and procedural fluency of the vertical motion model. Thus, the students to become active learners as they create their project by themselves or within groups by building from their previous knowledge and creating/new connections of the concept outside of mathematics in their project format. This allowed them to apply their knowledge to a new situation in order for the student’s to use their prior knowledge of the vertical motion model and quadratics as they make their own connections and how they can explain the process/importance in their learning style. This activity gives the students a learning opportunity to become active learners as they explore and demonstrate evidence of their learning. The students are given choice on how to demonstrate their fluency by giving them various learning styles as the students develop their conceptual understanding and procedural fluency of the vertical motion model to their classmates and teacher.
The vertical motion lesson plan demonstrates how students use their prior knowledge within and outside of mathematics as the students develop their conceptual understanding and procedural fluency. The vertical motion model lesson with multiple intelligence encourages the students to explore the vertical motion modern from a mathematical perspective. This allowed the students to demonstrate their learning by given them various opportunities, like creating a song/rap, creating a poster or story etc. for the students to form connections with the vertical motion model from their prior knowledge and apply their knowledge in a meaningful way to explain the vertical motion model to their peers. For example, one student created a song about the vertical motion model in which she described how to use the model in real word situations. Since the students create a creative song, the student will retain the concepts since he/she put meaning behind the concept. Each student has a choice in how they wanted to demonstrate their understanding of the vertical motion concept. For starters, the students picked a learning strategy, like visual, role play, rhythmic etc. in order for them to develop a deeper understanding of the vertical motion model. They started to form connections of their prior knowledge outside of mathematics in order to develop their own conceptual understanding and procedural fluency of the vertical motion model. Thus, the students to become active learners as they create their project by themselves or within groups by building from their previous knowledge and creating/new connections of the concept outside of mathematics in their project format. This allowed them to apply their knowledge to a new situation in order for the student’s to use their prior knowledge of the vertical motion model and quadratics as they make their own connections and how they can explain the process/importance in their learning style. This activity gives the students a learning opportunity to become active learners as they explore and demonstrate evidence of their learning. The students are given choice on how to demonstrate their fluency by giving them various learning styles as the students develop their conceptual understanding and procedural fluency of the vertical motion model to their classmates and teacher.
Target I3: Effective teachers provide equitable treatment of and have high expectations for all learners, and 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.]
I3- Vertical Motion Model Multiple Intelligence Reflection
The vertical motion lesson plan demonstrates my ability to sets high expectations for all learners to develop and build their conceptual understanding and procedural fluency. As mention in the assignment, this lesson encourages students to demonstrate their learning in a variety of ways to match how students learn to their full potential. The objective for this lesson was to give students an opportunity to form connections with the vertical motion model from their prior knowledge and apply their knowledge in a meaningful way to explain the vertical motion model to their peers. For example, some students created a song or rap which explained the vertical motion model. As mention in the assignment, the students picked a learning strategy in order for them to develop a deeper understanding of the vertical motion model while the teacher set high expectations for the students during this multiple intelligence lesson. The teacher plan this lesson based on the learning profiles, readiness and students interest, and felt this activity gave the students an opportunity to demonstrate their understanding and fluency. This activity gives the students a learning opportunity to become active learners as they explore and demonstrate evidence of their learning. The students are given choice on how to demonstrate their fluency, like creating a poster, song, rap, story etc. by giving them various learning styles and high expectations for the students in class projects on the vertical motion model and they present their project in a meaningful way to their peers and the teacher.
The vertical motion lesson plan demonstrates my ability to sets high expectations for all learners to develop and build their conceptual understanding and procedural fluency. As mention in the assignment, this lesson encourages students to demonstrate their learning in a variety of ways to match how students learn to their full potential. The objective for this lesson was to give students an opportunity to form connections with the vertical motion model from their prior knowledge and apply their knowledge in a meaningful way to explain the vertical motion model to their peers. For example, some students created a song or rap which explained the vertical motion model. As mention in the assignment, the students picked a learning strategy in order for them to develop a deeper understanding of the vertical motion model while the teacher set high expectations for the students during this multiple intelligence lesson. The teacher plan this lesson based on the learning profiles, readiness and students interest, and felt this activity gave the students an opportunity to demonstrate their understanding and fluency. This activity gives the students a learning opportunity to become active learners as they explore and demonstrate evidence of their learning. The students are given choice on how to demonstrate their fluency, like creating a poster, song, rap, story etc. by giving them various learning styles and high expectations for the students in class projects on the vertical motion model and they present their project in a meaningful way to their peers and the teacher.
Target I4: Effective teachers engage students in a sequence of developmentally appropriate and challenging learning activities in which they are actively building new knowledge, including investigations that use math-specific technology[, and they facilitate students’ ability to develop future inquiries that extend their past investigations].
I4- Unit Plan Reflection
The unit plan for quadratics describes how students are engaged in a coherent sequence of connected challenging lessons which allowed students to actively build on their new knowledge. By keep the learning targets in mind, we were able to create a backward design lessons which connect the concepts form previous lessons to the new concepts. This allowed us to scaffold the learning within the unit and allowed the students to form connects between lessons. In each lesson, the students will use the previous content and imply it to the new material in quadratics. For example, in the “Exploring the Vertical Motion Model” worksheet, the students had to use their previous knowledge of finding the solutions and the vertex of a quadratic during the real world application. This allowed the students to make connections in mathematics. We wanted to engage every student, so we created differentiated instruction with in each lesson which allowed every student to participate in the lesson. This encouraged the students to become active learners and take responsibility for their learning. By planning the unit, this allowed me to understand the purpose of engaging students by scaffolding the lessons, which would allow the students to see the big idea (main purpose) of the lessons and invited them to question more about mathematics to extend their learning.
The unit plan for quadratics describes how students are engaged in a coherent sequence of connected challenging lessons which allowed students to actively build on their new knowledge. By keep the learning targets in mind, we were able to create a backward design lessons which connect the concepts form previous lessons to the new concepts. This allowed us to scaffold the learning within the unit and allowed the students to form connects between lessons. In each lesson, the students will use the previous content and imply it to the new material in quadratics. For example, in the “Exploring the Vertical Motion Model” worksheet, the students had to use their previous knowledge of finding the solutions and the vertex of a quadratic during the real world application. This allowed the students to make connections in mathematics. We wanted to engage every student, so we created differentiated instruction with in each lesson which allowed every student to participate in the lesson. This encouraged the students to become active learners and take responsibility for their learning. By planning the unit, this allowed me to understand the purpose of engaging students by scaffolding the lessons, which would allow the students to see the big idea (main purpose) of the lessons and invited them to question more about mathematics to extend their learning.
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.]
I5- Vertical Motion Model Worksheet Reflection
The vertical motion model worksheet allowed students to make appropriate choices to use math-specific technology and manipulated support within their deep learning. We nonetheless felt that each student should be engaged in an activity where they could utilize their cell phones for learning besides doing story problems. During this activity, the students were offered to use either a cell phone or a tablet to scan the QR code in order to watch the videos and/check their answers for this activity. The video had different examples of the vertical motion model, like the diving into a pool. The students were challenged to time how long it took the diver to hit the surface of the water and to see how high the diver was above the surface of the water. Once the students were able to construct their equations and find their answers, they could check their answers by scanning the QR code. Also, the students typed their functions into their Ti-Nspire calculators to check their solutions for each situation. The students were engaged in this activity since they could use technology as well as they were making connections between mathematics and the real world. The students finally understood how mathematics can be applicable to real world situations by using the vertical motion model, and they liked learning beyond the worksheet with the videos and their cell phones. They enjoyed integrating their cell phones into the classroom in order to promote deeper learning.
The vertical motion model worksheet allowed students to make appropriate choices to use math-specific technology and manipulated support within their deep learning. We nonetheless felt that each student should be engaged in an activity where they could utilize their cell phones for learning besides doing story problems. During this activity, the students were offered to use either a cell phone or a tablet to scan the QR code in order to watch the videos and/check their answers for this activity. The video had different examples of the vertical motion model, like the diving into a pool. The students were challenged to time how long it took the diver to hit the surface of the water and to see how high the diver was above the surface of the water. Once the students were able to construct their equations and find their answers, they could check their answers by scanning the QR code. Also, the students typed their functions into their Ti-Nspire calculators to check their solutions for each situation. The students were engaged in this activity since they could use technology as well as they were making connections between mathematics and the real world. The students finally understood how mathematics can be applicable to real world situations by using the vertical motion model, and they liked learning beyond the worksheet with the videos and their cell phones. They enjoyed integrating their cell phones into the classroom in order to promote deeper learning.
Assessment:
Target A1: Effective teachers identify [and design] formative assessments that can inform instruction and monitor learners’ progress toward meeting essential learning outcomes.
A1- Formative Assessments Reflection
The Quadratic Lesson plan with formative assessment demonstrates formative assessment because I continuously assessing my students throughout the lesson in order to motion the students progressed toward meeting the essential learning outcomes. In the warm-up, I had the students write a one minute essay explaining how to find a vertex of a quadratic from a graph/table. Plus answer the question, “What does the vertex of a quadratic tell us?” This gave the student a learning opportunity to reflect from the previous lesson and explain the process to find the vertex of a quadratic. During the note taking and instruction, I often checked the student understanding of the subject by randomly using hand signals. This allowed me to have instantaneous feedback from my teaching as well see how well the students picked up the new material as well as form connections in mathematics. Often, I asked open-ended questions throughout the lesson to give the students an opportunity to explain to me what they understood from the new material as well as formative assessed them. For example, I asked the following questions to assess my students: What is the process for factoring? Explain the difference between factored and standard form. How confident are you with your answer? Have the students demonstrate how to factor with another student in their group.
Lastly, I had the students create two test questions. The students would turn in the questions with the answers before they left the classroom which could be used on their quiz review or on their quiz. For example, one student converted a quadratic from factored form to standard. The student also provided the answer in standard form, which was This offered me a great opportunity to check the students learning progress as well as check their understanding of the learning targets. From the various formative assessments, if I observed that the students were not fully grasping the content, I would discover another way to teach the students. Plus I would gain understanding what the student misconceptions are and thus I could plan the lessons and assessment with the student’s interest, learning profile and readiness in mind as I formative assessed my students.
The Quadratic Lesson plan with formative assessment demonstrates formative assessment because I continuously assessing my students throughout the lesson in order to motion the students progressed toward meeting the essential learning outcomes. In the warm-up, I had the students write a one minute essay explaining how to find a vertex of a quadratic from a graph/table. Plus answer the question, “What does the vertex of a quadratic tell us?” This gave the student a learning opportunity to reflect from the previous lesson and explain the process to find the vertex of a quadratic. During the note taking and instruction, I often checked the student understanding of the subject by randomly using hand signals. This allowed me to have instantaneous feedback from my teaching as well see how well the students picked up the new material as well as form connections in mathematics. Often, I asked open-ended questions throughout the lesson to give the students an opportunity to explain to me what they understood from the new material as well as formative assessed them. For example, I asked the following questions to assess my students: What is the process for factoring? Explain the difference between factored and standard form. How confident are you with your answer? Have the students demonstrate how to factor with another student in their group.
Lastly, I had the students create two test questions. The students would turn in the questions with the answers before they left the classroom which could be used on their quiz review or on their quiz. For example, one student converted a quadratic from factored form to standard. The student also provided the answer in standard form, which was This offered me a great opportunity to check the students learning progress as well as check their understanding of the learning targets. From the various formative assessments, if I observed that the students were not fully grasping the content, I would discover another way to teach the students. Plus I would gain understanding what the student misconceptions are and thus I could plan the lessons and assessment with the student’s interest, learning profile and readiness in mind as I formative assessed my students.
Target A2: Effective teachers identify [and design] summative assessments that can accurately gauge students’ achievement of essential learning outcomes.
A2- Assessments Reflection
The selected response assessment, extended response assessment and performance assessment demonstrated my understanding of the construction of summative assessments by accurately gauge student’s achievements on the essential learning outcomes. In my Education 337, Introduction to Assessments class, we had to write summative assessments which matched the learning targets and the standards. Throughout the assessment, I accurately engaged the students achievements with learning targets by asking formatted questions differently to allow the students to demonstrate their knowledge and conceptual understanding of Algebra, for instance; project based questions or extended written responses. The assessments engaged the students in various situations and allowed them to reflect their understanding of Algebra. For examples in my extended response assessment, the students have choices on which to answer questions thus reflecting their proficiency for each learning target for the short answer reflection. The problems includes various situation based problems from how many texts left in a month, amount of hours on online social network as well explain how they solved the problem. For example in my performance bases assessment, the students have choices on how they wanted to format their final project as a skit, music video or create a math rap on one of the learning targets for the Linear functions unit. The students decide on how they wanted to reteach to their classmates by demonstrating one of the learning targets and they will be assessed on their performance based on the rubric. Thus, as the assessment progressed, the teacher understood exactly how the students are evaluated and thus allowed the teacher to backward design their classroom from the learning targets. In conclusion of the assessment, I was able to match the assessment with the learning targets from the various activities and notes. The assessments will fairly assess the students understanding and challenge the students to monitor their growth of learning as well as their learning outcomes. By creating the assessments, the teacher could plan their unit with the learning targets in mind and give students decisions on what way they would want to be assessed in the classroom.
The selected response assessment, extended response assessment and performance assessment demonstrated my understanding of the construction of summative assessments by accurately gauge student’s achievements on the essential learning outcomes. In my Education 337, Introduction to Assessments class, we had to write summative assessments which matched the learning targets and the standards. Throughout the assessment, I accurately engaged the students achievements with learning targets by asking formatted questions differently to allow the students to demonstrate their knowledge and conceptual understanding of Algebra, for instance; project based questions or extended written responses. The assessments engaged the students in various situations and allowed them to reflect their understanding of Algebra. For examples in my extended response assessment, the students have choices on which to answer questions thus reflecting their proficiency for each learning target for the short answer reflection. The problems includes various situation based problems from how many texts left in a month, amount of hours on online social network as well explain how they solved the problem. For example in my performance bases assessment, the students have choices on how they wanted to format their final project as a skit, music video or create a math rap on one of the learning targets for the Linear functions unit. The students decide on how they wanted to reteach to their classmates by demonstrating one of the learning targets and they will be assessed on their performance based on the rubric. Thus, as the assessment progressed, the teacher understood exactly how the students are evaluated and thus allowed the teacher to backward design their classroom from the learning targets. In conclusion of the assessment, I was able to match the assessment with the learning targets from the various activities and notes. The assessments will fairly assess the students understanding and challenge the students to monitor their growth of learning as well as their learning outcomes. By creating the assessments, the teacher could plan their unit with the learning targets in mind and give students decisions on what way they would want to be assessed in the classroom.
Evaluation:
Target E1: Effective teachers use timely analysis of assessment data to accurately gauge students’ progress toward essential learning outcomes identified during planning[, identify students’ zone of proximal development, and use this information to inform future planning, modify instruction, and increase student achievement].
E1- Analysis of Assessment Reflection
My main goal during my student teaching semester was to create and integrate various formative assessments. I wanted to utilize assessment data to accurately gauge the students’ progress toward essential learning outcomes and monitor their students’ progress throughout the “Expressions and Equations” unit. I utilized formative assessments such as: exit slips and open ended questions throughout the semester. I frequently created exit tickets or used socrative.com (SOC# 13366895) to gather formative assessments on my students with the lesson learning targets in mind. For example, while I taught solving multi-step equations to the students, I had them complete an exit ticket after our lesson. During our review for Simplifying Algebraic Expressions and solving multi-step equations, I had my students complete a student paced socrative activity which gave them instant feedback on how they solved the problem. The web site, Socrative sent me a report on each class reporting; how the students responded, and how well the students did on each problem in the socrative activity.
After comparing both formative assessment data, I was able to find where my students had misconceptions. They struggled with solving multi-step equations with unlike denominators. The majority of them made the connections that solving multi-step equations has the same process as solving one step and two step equations, and you just need to combine like terms to simplify your equation before you solve for your variable.
After analyzing the formative assessments on solving multi-step equations; I saw what I needed to modify for future lessons lesson since we were able to obtain information of where the students were struggling within the content of the learning targets. Also, I was able to identify the misconceptions the students had with solving equations. It allowed time to readdress the misconceptions during another portion of our class review and before the students took their summative assessment.
Throughout the semester, I created and used various diagnostic, formative, and summative assessments to check the students understanding. This allowed me to monitor the students’ performance in the classroom as well. By creating these assessments, I identified the student’s zone of proximal development and used this information to apply with future unit planning. Often I modified the lesson planning to promote student achievement. There were many opportunities in which I found many areas for teaching improvements. I often modified my lessons planning as I identified content weaknesses. I found that it increased the student’s achievement within the class as I learned how to analyze the assessment data. By monitoring the students’ progress during my student teaching and being able to integrate formative assessments to check the students understanding of the concepts allowed me to redirect misconceptions and achieve the Michigan core standards.
My main goal during my student teaching semester was to create and integrate various formative assessments. I wanted to utilize assessment data to accurately gauge the students’ progress toward essential learning outcomes and monitor their students’ progress throughout the “Expressions and Equations” unit. I utilized formative assessments such as: exit slips and open ended questions throughout the semester. I frequently created exit tickets or used socrative.com (SOC# 13366895) to gather formative assessments on my students with the lesson learning targets in mind. For example, while I taught solving multi-step equations to the students, I had them complete an exit ticket after our lesson. During our review for Simplifying Algebraic Expressions and solving multi-step equations, I had my students complete a student paced socrative activity which gave them instant feedback on how they solved the problem. The web site, Socrative sent me a report on each class reporting; how the students responded, and how well the students did on each problem in the socrative activity.
After comparing both formative assessment data, I was able to find where my students had misconceptions. They struggled with solving multi-step equations with unlike denominators. The majority of them made the connections that solving multi-step equations has the same process as solving one step and two step equations, and you just need to combine like terms to simplify your equation before you solve for your variable.
After analyzing the formative assessments on solving multi-step equations; I saw what I needed to modify for future lessons lesson since we were able to obtain information of where the students were struggling within the content of the learning targets. Also, I was able to identify the misconceptions the students had with solving equations. It allowed time to readdress the misconceptions during another portion of our class review and before the students took their summative assessment.
Throughout the semester, I created and used various diagnostic, formative, and summative assessments to check the students understanding. This allowed me to monitor the students’ performance in the classroom as well. By creating these assessments, I identified the student’s zone of proximal development and used this information to apply with future unit planning. Often I modified the lesson planning to promote student achievement. There were many opportunities in which I found many areas for teaching improvements. I often modified my lessons planning as I identified content weaknesses. I found that it increased the student’s achievement within the class as I learned how to analyze the assessment data. By monitoring the students’ progress during my student teaching and being able to integrate formative assessments to check the students understanding of the concepts allowed me to redirect misconceptions and achieve the Michigan core standards.
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].
E2- Summative Assessment Reflection
During my planning for the student teaching semester, I created a summative assessment on solving one and two step equations, which helped me accurately gauge students’ achievement of essential learning targets for the unit on Expressions and Equations - 8th grade Algebra. My cooperating teacher gave me an opportunity to create my own assessment for this unit, and used the backward design process to make sure the questions on the assessment aligned with the lessons I planned for “Solving one and two step equations.”
After grading the summative assessment on solving one and two step equations, I discovered some misconceptions my students had while solving equations. Majority of the students stated that they understood the process of solving equations. However, there was a minority of 8th graders that did not understand the process when dealing with two step equations. They would not cancel out terms on both sides and/or did not understand the order of operations while solving equations in order to isolate the variable. A few students forgot they needed to have their answer is “x=” form. Some students forgot to put units on their solutions for word problems as well.
By creating my summative assessment for my unit on Equations and Expressions, I learned how well my instruction matched with the assessments and how the students became proficient with the learning targets and content. The feedback generated from each student’s performance from the learning targets and content indicated on how I could improve and modify my lessons for instruction for future lessons. I will continue my desire to increase students’ achievement in my class as I learn how to analyze the summative assessment data. During my student teaching assignment, one of my strategies was to mark their misconceptions on the answer key and writing down key ideas I will need to reteach or reiterate the importance of to my students when I reviewed the summative assessment. This assessment helped me complete the process of misconception and direct lesson planning.
During my planning for the student teaching semester, I created a summative assessment on solving one and two step equations, which helped me accurately gauge students’ achievement of essential learning targets for the unit on Expressions and Equations - 8th grade Algebra. My cooperating teacher gave me an opportunity to create my own assessment for this unit, and used the backward design process to make sure the questions on the assessment aligned with the lessons I planned for “Solving one and two step equations.”
After grading the summative assessment on solving one and two step equations, I discovered some misconceptions my students had while solving equations. Majority of the students stated that they understood the process of solving equations. However, there was a minority of 8th graders that did not understand the process when dealing with two step equations. They would not cancel out terms on both sides and/or did not understand the order of operations while solving equations in order to isolate the variable. A few students forgot they needed to have their answer is “x=” form. Some students forgot to put units on their solutions for word problems as well.
By creating my summative assessment for my unit on Equations and Expressions, I learned how well my instruction matched with the assessments and how the students became proficient with the learning targets and content. The feedback generated from each student’s performance from the learning targets and content indicated on how I could improve and modify my lessons for instruction for future lessons. I will continue my desire to increase students’ achievement in my class as I learn how to analyze the summative assessment data. During my student teaching assignment, one of my strategies was to mark their misconceptions on the answer key and writing down key ideas I will need to reteach or reiterate the importance of to my students when I reviewed the summative assessment. This assessment helped me complete the process of misconception and direct lesson planning.
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.]
G1- Professional Growth Reflection
On Monday October 20th, 2014, I attended the Fire Up! Student Teaching Conference at Aquinas College. This was my fourth professional educational conference. Within this past year, I have attended Fire Up! during Fall 2013, EDCampGVSU, Math in Action 2014 and EdCampGR. While at Fire Up, there were various sessions one could attend ranging from technology in education, classroom management, the hiring process and how to be an effective teacher. The objective of the conference was to allow me to become more familiar with the current topics in education and how to take steps to become an effective educator. Also, the conference was a great chance to meet and interact with other colleagues from other universities and colleges. I was able to attend sessions which appealed to me and take an opportunity to learn how to improve my teaching practice. After attending each of the sessions and talking with the presenters, I was able to connect to more educational colleagues. I asked them if I could connect with them on twitter and use them as resource in the future. This gave me an opportunity to collaborate and share ideas with other colleagues. Also, I learned that my digital educational imprint I have created online will help me to standout from other first year teachers with my professional twitter and online educational portfolio. I learned how I can use other resources from the presenters. I would like to implement them into my classroom and practice. For example, I learned how to integrate i-pads in the classroom, which will engage students with the various applications.
Also, by utilizing digital publications (blogging and twitter) within the classroom, this allows one to collaborate with one another and be able to share ideas to others. I plan on using the information from this conference for my teaching practice and looking forward to attending other professional conferences coming to Grand Rapids and Michigan, for instance, the EDCampOAISD and 2015 MCAUL Conference to continue my professional growth in education.
As an educator, I will continue to seek other professional development and leadership conference in mathematics and education. This will give me learning opportunities on how I can prepare students for their careers in the 21st century and what I can implement into my planning, instruction, assessing and evaluation. I plan on attending other math educational seminars/conference to prepare me for teaching mathematics. I would also like to attend some NCTM and MCAUL conference in the near future.
On Monday October 20th, 2014, I attended the Fire Up! Student Teaching Conference at Aquinas College. This was my fourth professional educational conference. Within this past year, I have attended Fire Up! during Fall 2013, EDCampGVSU, Math in Action 2014 and EdCampGR. While at Fire Up, there were various sessions one could attend ranging from technology in education, classroom management, the hiring process and how to be an effective teacher. The objective of the conference was to allow me to become more familiar with the current topics in education and how to take steps to become an effective educator. Also, the conference was a great chance to meet and interact with other colleagues from other universities and colleges. I was able to attend sessions which appealed to me and take an opportunity to learn how to improve my teaching practice. After attending each of the sessions and talking with the presenters, I was able to connect to more educational colleagues. I asked them if I could connect with them on twitter and use them as resource in the future. This gave me an opportunity to collaborate and share ideas with other colleagues. Also, I learned that my digital educational imprint I have created online will help me to standout from other first year teachers with my professional twitter and online educational portfolio. I learned how I can use other resources from the presenters. I would like to implement them into my classroom and practice. For example, I learned how to integrate i-pads in the classroom, which will engage students with the various applications.
Also, by utilizing digital publications (blogging and twitter) within the classroom, this allows one to collaborate with one another and be able to share ideas to others. I plan on using the information from this conference for my teaching practice and looking forward to attending other professional conferences coming to Grand Rapids and Michigan, for instance, the EDCampOAISD and 2015 MCAUL Conference to continue my professional growth in education.
As an educator, I will continue to seek other professional development and leadership conference in mathematics and education. This will give me learning opportunities on how I can prepare students for their careers in the 21st century and what I can implement into my planning, instruction, assessing and evaluation. I plan on attending other math educational seminars/conference to prepare me for teaching mathematics. I would also like to attend some NCTM and MCAUL conference in the near future.
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.
F1- Observations of other Math Educators Reflection
F1- Observations of other Math Educators Reflection
After observing my cooperating teacher and analyzed other math educators at my junior high placement, I found each teacher had a similar approached with teaching, learning, and doing mathematics. I observed my cooperating teacher in the beginning of the semester and found she structured her class with 20 minutes for bell work, attendance, and homework check, 20 minutes for the lesson and 20 minutes for homework time for the students. In other math classes, the teachers had the same structure for their lessons. The teachers used the online resources from their textbook publisher in order to structure their lessons. Each math educator at Jenison Jr. High believed in doing mathematics through small group’s activities which are student centered. This allowed them to explore the concepts they have learned in class and apply them in a new task/objective. Each teacher centered their classroom management on Capturing Kid’s Hearts (Jenison Classroom Management Philosophy), which allowed them build a strong teacher student rapport and build their learning environment. This helped them build a positive, productive, and trusting student-teaching relationship. From the observations, I have similar mindset with my teaching and doing mathematics as I did in Mrs. Rockey’s classroom for 7th Pre-Algebra and 8th grade Algebra. I want to continue to change my focus of teaching from teaching centered and move it towards student centered so the students are more involved in doing mathematics.
Throughout the semester, I have been tweeting about my observations from my classroom and the discussions I’ve had with other math educators. Also, I post a blog post about my cooperating teacher classroom structure and procedures which has helped me get a better idea on how to structure my own classroom. Each of the educators have given me advice and feedback throughout the semester for me to grow as a lifelong learner. They told me to not to re-invent the wheel while lesson planning. Instead, focus on build relationships in your classroom so the students will be more engaged in your classroom and want to learn about mathematics. From this advice, I have gained a lot of experience as I implemented my teaching practice and plan to continue to learn from other collaborators as I become a secondary math teacher.
Throughout the semester, I have been tweeting about my observations from my classroom and the discussions I’ve had with other math educators. Also, I post a blog post about my cooperating teacher classroom structure and procedures which has helped me get a better idea on how to structure my own classroom. Each of the educators have given me advice and feedback throughout the semester for me to grow as a lifelong learner. They told me to not to re-invent the wheel while lesson planning. Instead, focus on build relationships in your classroom so the students will be more engaged in your classroom and want to learn about mathematics. From this advice, I have gained a lot of experience as I implemented my teaching practice and plan to continue to learn from other collaborators as I become a secondary math teacher.
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].
F2- Middle school and High School Field Experience Reflection
My completed math content folio consists of evidence of my teaching practice from both my middle school and high school field experience from my teaching assisting and student teaching.
During my teaching assisting and student teaching. I utilized share resources constructed diverse lessons with student centered activities and from other educators from twitter, http://map.mathshell.org/materials/index.php and mathalicious.com. Throughout my teaching assisting and student teaching, I have gained experience fromdialogues with other educators in person, at professional development seminars and online discussions on my professional learning network (via twitter). The past couple of years, I’ve been collaborating with other educators and joined educational chats via twitter (#msmathchat, #msmathstory, #miched, and etc.). This helped me build my teaching resources with other educators since they were willing to send me their resources; as well as guide me to relevant resources to “borrow ideas” to implement into my lessons for 7th Pre-Algebra and 8th grade Algebra. I was able to ask other educators who have been in the teaching profession questions about the various areas of teaching (planning, instruction, assessment, classroom management etc.). I plan to continue networking with educators through twitter.
During my student teaching semester, I was able to share my reflections and learning experiences from my classroom observations with my peers and other educators through my educational blog. These helped me to self-reflect on my lessons more in depth. I plan to continue to blog as I begin my teaching journey and have my own math classroom. This will allow me to publicize what I’m doing in my classroom and share my students work with others. I plan on continue to blog about my teaching and learning experience as I become a professional educator for mathematics and biology.
My completed math content folio consists of evidence of my teaching practice from both my middle school and high school field experience from my teaching assisting and student teaching.
During my teaching assisting and student teaching. I utilized share resources constructed diverse lessons with student centered activities and from other educators from twitter, http://map.mathshell.org/materials/index.php and mathalicious.com. Throughout my teaching assisting and student teaching, I have gained experience fromdialogues with other educators in person, at professional development seminars and online discussions on my professional learning network (via twitter). The past couple of years, I’ve been collaborating with other educators and joined educational chats via twitter (#msmathchat, #msmathstory, #miched, and etc.). This helped me build my teaching resources with other educators since they were willing to send me their resources; as well as guide me to relevant resources to “borrow ideas” to implement into my lessons for 7th Pre-Algebra and 8th grade Algebra. I was able to ask other educators who have been in the teaching profession questions about the various areas of teaching (planning, instruction, assessment, classroom management etc.). I plan to continue networking with educators through twitter.
During my student teaching semester, I was able to share my reflections and learning experiences from my classroom observations with my peers and other educators through my educational blog. These helped me to self-reflect on my lessons more in depth. I plan to continue to blog as I begin my teaching journey and have my own math classroom. This will allow me to publicize what I’m doing in my classroom and share my students work with others. I plan on continue to blog about my teaching and learning experience as I become a professional educator for mathematics and biology.