Introduction
Through this student teaching experience, I've gained an understanding of my own beliefs in education as well as skills and techniques that help all students reach understanding in my class. I was handed classes with students from all different backgrounds and skill levels however I found one overarching theme in students who struggle: lack of confidence. This is the core of my philosophy. To inspire and empower students through math, not to practice math but to gain something deeper from it. After conquering a topic in math, students should know all of the real problems they can solve and the innovations they can contribute to. This semester has allowed me to apply this philosophy into everyday lessons and what I've seen as an effect is students becoming more confident and comfortable to try new things and trust the power of their own mind. This is what drives me to be a teacher.
Quality Standard 1:
Teachers demonstrate mastery of and pedagogical expertise in the content they teach. The elementary teacher is an expert in literacy and mathematics and is knowledgeable in all other content that he or she teachers (e.g., science, social studies, arts, physical education, or world languages). The secondary teacher has knowledge of literacy and mathematics and is an expert in his or her content endorsement area(s).
Element A: Teachers provide instruction that is aligned with the Colorado Academic Standards, their District's organized plan of instruction and the individual needs of their students.
Artifact: Lesson plan that exhibits the standard as well as values from the MYP curriculum
Rationale: The following lesson plan is aligned with the CDE Standard 2 element c. subsection (i) and the MYP curriculum by giving a good foundation of knowledge and connecting the standard to intriguing and applicable topics. The historical context of geocentric space models gives content more depth and a global perspective which are major values within the MYP and IB curriculum.
Element b: Teachers develop and implement lessons that connect to a variety of content areas/disciplines and emphasize literacy and mathematical practices.
Artifact: Exponential functions lesson that has use of text from a book about Math.
This text is an excerpt from a book that uses creative analogies and drawings to explain presumably dull math concepts. This book and readable, intriguing and easily accessible to all students. This is why I used it in my classroom to give literacy a role in exploring new math concepts. This book gave way to discussions that students could connect to, for example: could you imagine a truck carrying a thousand earths? That's the difference between 2x and 2^x, what other analogies can we think of? During this lesson, I read this text out loud and led discussions about the topic.
Element c: Teachers demonstrate knowledge of the content, central concepts, inquiry, appropriate evidence based instructional practices, and specialized characteristics of the disciplines being taught.
Artifact: Lesson on introducing e^x as more than a number but a fundamental growth constant within nature.
Rationale: This lesson exhibits not only my understanding of the subject but an extension of depth within the exponential functions. By extending the simple concept to ideas that span across multiple content areas and connect to the fundamentals of nature students are able to connect to the ideas on a deeper level. My role as a teacher is to not be a textbook but be able to show students how the content is related to the world and this lesson exhibits that depth of knowledge for the content.
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I feel proficient is this standard because I have an extensive background in math and I'm able to connect the content to multiple disciplines, use literacy to gain student understanding and expression of math and be able to give a worldly perspective of the content. The biggest growth I've encountered within this standard finding disciplines outside of math that relate to the content and include some form of literacy. However, what I've found is that when I find that connection I'm more invested in the lessons and my students are bought in. I've seen my students directed affected by this when they see a lack of literacy/ outside discipline connection they are easily frustrated by why they need to learn the content. To them, it starts to feel meaningless and disconnected from their life. WIth that my professional goal is to find connections no matter the content, even if I'm teaching a little theorem that seems meaningless I am responsible with injecting meaning.
Quality Standard 2:
Teachers establish a safe, inclusive and respectful learning environment for a diverse population of students.
Element a: Teachers foster a predictable learning environment characterized by acceptable student behavior and efficient use of time in which each student has a positive, nurturing relationship with caring adults and peers.
Artifact: Letters from student after having a discussion about respectful behaviors in the classroom
The following letters are examples of reflections from students on how respect plays a role in the classroom. After these letters were received the level of positivity and respect has made a major shift. After addressing the letters in class anonymously, students know that I appreciate their feedback and always listen to their thoughts either in class or through letters. This type of managed conversation promotes healthy student-teacher relationships as well as a sense of a unified structure. The feedback from the students showed me how much the standards for behavior are appreciated even when that isn't seen face to face.
Element b: Teachers demonstrate an awareness of, a commitment to, and a respect for multiple aspects of diversity, while working toward common goals as a community of learners.
Element: Show the use of agricultural examples to make content relatable.
I have a wide diversity of students including students from farming towns, Hispanic backgrounds, and more. The following is the use of agricultural context in a math problem. Showing this problem gave half the class confused looks and the other grins. This problem allowed students with a farming background or agricultural interest to speak out and share bits and pieces of their culture with the class. What came out of this problem was a well-rounded education of the subject with an awareness of the individuals of the classroom.
Element c: Teachers engage students as individuals, including those with diverse needs and interests, across a range of ability levels by adapting their teaching for the benefit of all students.
Artifact: Working with Lynny to advance her curiosity in the patterns of curved geometry.
Lynny came to me with the idea of crocheting a sphere so during 6th period we explored developing mathematical functions for creating continuous curvature and have figured out how to translate that into crochet. After succeeding in making spheres we are now crocheting hyperbolic planes.
. Creating the environment for every student to thrive within their own curiosity is something I strive to do and in this particular case, I've seen this student thrive.
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Element d: Teachers work collaboratively with the families and/or significant adults for the benefit of students.
Rationale: With the following student I worked with their parent to create a plan of success and celebrate good moments with their child.
Element: An email to a girl's parents about her improvment
Creating a safe inclusive environment is one of my top core values of teaching so this standard I'm particularly fond of this is why I see myself as proficient in this standard. Some things that are seen in my classrooms are group learning that teaches students how to work with people that are different from each other, talks about respect and how to treat others. One of my classes was notorious for disrespect and throughout the year we grew incredibly close and it now feels like we are a little math family. The impact this type of environment has been on my students is shown from how they've changed since the beginning of class. They used to sit spread out by themselves in rows, not engaged or making a peep. After giving them the gift of anonymity of groups they are engaged and have built friendships within the classroom. In the future, I strive to create that culture of engaged respectful students from the beginning.
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Quality Standard 3:
Teachers plan and deliver effective instruction and create an environment that facilitates learning for their students
Element a: Teachers demonstrate knowledge about the ways in which learning takes place, including the levels of intellectual, physical, social, and emotional development of their students.
Arifact: using the lesson of reflections to have students reflect on their lives, understanding when students have things going on in their lives and being a support in their learning
Rationale: Our objective for the day was to discover the rules of reflecting objects around a coordinate grid, however, I saw this an opportunity for students to dig deeper and talk about deeper social/emotional parts of their lives. In the warm-up students were tasked with reflecting on their high school experience such as: What would you tell your middle school self? What can you do to get closer to the person you want to be?
I saw these students start to open up to each other and really be intrigued about these topics emerging in a math class. In my role as a teacher, I was promoting healthy self-security and growth mindset while students were sharing their thoughts.And after this exploration we turned our attention to reflections in the context of math.
Element b: Teachers use formal and informal methods to assess student learning, provide feedback, and use results to inform planning and instruction.
The following is a graded test and the feedback I gave on it. This student, like several others in the class, performed all the transformations correctly but didn't write any notation which I vocalized was expected. After assessing this as a common thread, in the next project I added a section in the grading that specifically talks about notation and in the directions I show what my expectation is. Through this process, I was able to reevaluate my clarity to students and make sure that they know what is expected of them so nobody feels like they are shooting in the dark.
Element: Feeback on a test and the growth in my instruction from that.
Element c: Teachers integrate and utilize appropriate available technology to engage students in authentic learning experiences.
Rationale: This lesson utilized Desmos, this program allowed students to play with graphs then ask questions about their patterns. This use of technology freed students of having to graph many functions by hand and instead see many lines on the screen and have more moments of discovery.
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Artifact: Parallel and Perpendicular lines lesson integrating Desmos into the class
Element d: Teachers establish and communicate high expectations and use processes to support the development of critical-thinking and problem-solving skills
Rationale: The project shown is a summative assessment for students in college algebra to show their knowledge for financial models. In this project students were not only asked to show numbers, they were expected to answer what that number meant, they had to problem solve for a savings account that would fit their financial goal for the future and be able to express this knowledge well.
Artifact: college algebra financial planning project rubric and process for criticial thinking
Element e: Teachers provide students with opportunities to work in teams and develop leadership.
Artifact: Group Quiz
The following is a group quiz. Students work in teams on the group quiz, they can use each others notes, and ask each other questions. Only one students' quiz is graded and the rest of the group gets that grade so working collaboratively to make sure everyone has the same answers is very important.
Element f: Teachers model and promote effective communication.
Throughout the unit, I will put a short timeline on the board so students know what is coming up and can prepare ahead of time. These excerpts of communication are seen on lessons as well as the dry erase board by the desk. TImelines like this gave students security that they know what's going on in the class and how they can prepare for sucess
Element: Look aheads for the week
I believe I am at "developing" with this standard because there's so much more that I want to learn and improve on within the art of instruction. Throughout this semester I feel confident in my ability to communicate clearly and concisely with every concept within my content. I've been able to create different types of lessons with different methods of instruction whether that being through a worksheet, group learning, technology, reading, etc. and from that, I feel like I have the tools to be more creative with content and bend to different methods. The effect that has had on my students has been transformational, at the beginning students had a hard time buying into the subject and through my development of instruction, students are more willing to jump in, more willing to suspend belief that math is cool and that has made the classroom a much more positive place. Moving forward in my career as an educator I want to get better at making my students thinking visible. I want to make easier ways to physically see their math and adjust in the moment, during a lesson. This semester I was able to develop some of those skills but they tend to be clunky or stressful.
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Quality Standard 4:
Teachers demonstrate professionalism through ethical conduct, reflection, and leadership.
Element a: Teachers demonstrate high standards for professional conduct
Artifact: Professional attire
The following is an example of my typical outfit for teaching. I exhibit high professionalism within my attire and in how I present myself as a teacher and mentor to students.
Element b: Teachers link professional growth to their professional goals
Element: journal entry about more worksheets in geometry
The following is a journal entry from the beginning of the semester. I was reflecting on the process of learning and how that could be improved in my class. Using some science of learning, I recalled that the core of learning is found within connections and my students struggle with that already. Using what I've learned throughout my time here I constructed a plan of action to make my teaching better for these particular students. What I found was that when I had lessons that were on worksheets with the homework students actually did the homework, and did it well. From then on I decided that my paper footprint was less important than students growth. I saw a lot of improvement in understanding after deciding to have worksheet guided notes.
Element c: Teachers respond to a complex, dynamic environment.
Artifact: Students seating petition
Rationale: Students were required to sit in the group seating chart every day. One day I came in and students had petitioned to sit in rows again. They even got signatures from everyone in the class! So we had a discussion about why I preferred for them to be in groups. My reasons were centered around engagement, participation, collaboration, and that I like for students to sit close to the front. In this discussion students explained how they would exhibit these values even outside of groups so we changed to rows and found that the students still upheld my values of the class. About 2 weeks later they moved back to groups because they wanted to be closer to their friends.
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Element d: Teachers demonstrate leadership in the school, the community, and the teaching profession.
Rationale: The following are students that I've privately tutored in various levels of calculus. These students are all veterans who haven't seen or used any high school math in a very long time. During this experience, I learned how to support veterans by scaffolding very heavily and always being ready to teach a lesson on fractions, rationals, and factoring at any given moment. This applies to the element because I've used education to contribute to the lives of veterans in the community.
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Artifact: Private tutoring for Veterans at CSU
I believe I'm "developing" in this standard. I strive to present myself professionally, always use appropriate language and more importantly I strive to instill these qualities in my students. I've grown in professionalism so much this semester and that alone has been a journey. In January I didn't feel quite like myself, it felt like I was dressing up every morning as someone else. With respect from students and other teachers, I became the person that I was dressed up to be. My students see me as a young but a teacher/ adult/mentor and a professional. Throughout the semester as I've become more comfortable in my professional self I've seen a lot of growth within my own students. They will still curse and act out but how they handle themselves afterward has been a huge development of the class. They've learned how to apologize and express why they acted out, they are reflective and are able to feel comfortable enough to have tough conversations with me. One of my goals for the future is being better at being more responsive in emails and having more active communication with parents.
Dispositions Reflections
I feel comfortable with my abilities within Tact and Judgment because I have strong social awareness and I'm confident in my ability to make strong student-teacher relationships. I also feel confident with my communication skills and being able to communicate well and clearly with any student regardless of background knowledge, language, and abilities.
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I would like to focus more on Initiative in the future, I wish that during my student teaching I became more interwoven in the school, for example: gone to games, volunteered at prom, helped in theatre, kaleidoscope, etc. The vision of the type of teacher I want to be is someone who is involved within the school and community, I want students to feel my support in and out of school and although I kept up with activities my students were part of I wasn't as involved as I wanted to be.
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These dispositions support my goals for having more initiative towards growth and awareness. They will help me to jump into learning the expansive methods and techniques within education that I've yet to learn and I know now that areas that I can lean on as strengths. My specific goal includes: being more integrated into school activities, being more time efficient in making lessons and learning more about navigating confidentiality and sensitive subjects around parents and other professionals.