Part III: Presenting the Total PACKage
Context:
I am a high school math teacher at Fraser High School in Fraser, Michigan. Our school consists of about 1700 students and we are the only high school in the district. We are very lucky to have an extremely supportive and tight knit community and school district! I currently teach algebra 1, geometry, and algebra 2 to about 150 students each semester. Depending on the type of class, my class sizes have ranged from anywhere between 20-36 students.
Our day is based on a block schedule, meaning we see our students every other day for 90 minutes each block. A typical day is 4 blocks long, and along with their classes being every other day, they also have a 90 minute seminar every other day, where they have the time to complete homework, visit teachers to make up missed work, and make up tests (kind of like a 'home room'). |
We are fortunate to have access to an abundance of technology, such as promethean boards, active inspire clickers, over head projectors, elmos, computer labs, and soon one-to-one correspondence with iPads. Within my classroom, we use the promethean board daily for deliverance of notes, student interaction, and everything in between. I have a pretty structured class that consists of a daily warm up, homework correction, notes, and classwork, within a block. This is something I am hoping to transform more with the one-to-one technologies in the near future. I would like my classroom to be more of an open concept with students working on multiple facets of the lesson while working together on collaboration and having the one-on-one time with me directly.
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Content:
I want my students to use writing as a way to show a deeper knowledge of the understanding of mathematics, and in this unit, dealing with quadratics. I want them to have an understanding of quadratics and be able to verbalize their thinking and process they use to solve problems. My students should not only have a computational understanding, but I want them to have and be able to verbalize their conceptual mathematical understanding of quadratics.
I aim to have my students have the ability to write and express their thought process for solving problems, specifically quadratics. The students should be able to demonstrate their understanding and apply it to different situations and thoroughly explain their reasonings for their process. I want my algebra students to be able to relate such concepts of mathematics to real world context and be able to clearly articulate their thinking process.
My students should be able to verbalize their thinking and the process they use to solve quadratics and factoring problems both in classroom context and real world context. For the content, I plan to pick a few 'main' standards to hit, and elaborate on them to try to deepen the students understanding of those specific concepts. From here we will be able to get an understanding of what is expected from the writing, what I hope for the students to explain and touch on, and then continue this process in future units.
I think many students struggle connecting the math from the lesson to outside problems and situations. In order for students to get a more conceptual understanding, it is important to relate these problems to outside context situations and ask them to explain their thought process as to how and why they chose this 'path' to solve the problem. This will allow an easier determination of where specifically they are making mistakes and allow us to be able to more clearly target those areas on an individual basis. This will allow us to see misconceptions of ideas they may have from previous beliefs and understandings that they have acquired over time and work towards understanding 'why' they have those misconceptions and see what we can do to try to correct them.
I aim to have my students have the ability to write and express their thought process for solving problems, specifically quadratics. The students should be able to demonstrate their understanding and apply it to different situations and thoroughly explain their reasonings for their process. I want my algebra students to be able to relate such concepts of mathematics to real world context and be able to clearly articulate their thinking process.
My students should be able to verbalize their thinking and the process they use to solve quadratics and factoring problems both in classroom context and real world context. For the content, I plan to pick a few 'main' standards to hit, and elaborate on them to try to deepen the students understanding of those specific concepts. From here we will be able to get an understanding of what is expected from the writing, what I hope for the students to explain and touch on, and then continue this process in future units.
I think many students struggle connecting the math from the lesson to outside problems and situations. In order for students to get a more conceptual understanding, it is important to relate these problems to outside context situations and ask them to explain their thought process as to how and why they chose this 'path' to solve the problem. This will allow an easier determination of where specifically they are making mistakes and allow us to be able to more clearly target those areas on an individual basis. This will allow us to see misconceptions of ideas they may have from previous beliefs and understandings that they have acquired over time and work towards understanding 'why' they have those misconceptions and see what we can do to try to correct them.
Technology:
There are a few technologies that I think will be useful throughout this process. The first, most basic, technology will be the use of paper and pencil. This will allow the students to demonstrate their thought process through writing. Paper and pencil is something that is easy to incorporate because it is something we use on a daily basis. Our other technologies will help us do more with paper and pencil than we have in the past.
Along with writing, it is important to have a clear outline of what is expected from the students and a rubric is necessary for the grading and understanding of grading process that we will be working on. I will be using rubric created on http://rubistar.4teachers.org/index.php to help students understand what I will be looking for and what they will be looking for within each other's work. This process will help us in our peer editing for both whole class, group, and partner activities. |
The Promethean board is a technology that is already utilized daily, and will be something that will be incorporated into this process as well. At first the process in which we take and walk through of rubrics will be presented and altered on the Promethean board. From here, we will use this technology for future gallery walks, ideas for corrections and revising processes.
The final technology that as a school we will be incorporating, so I will be using it within this process, are iPads. There are many apps that can be used to help with writing, evaluating, and collaborating with each other, and this is something else that will be incorporated within my classroom during both individual, partner, group, and whole class activities. This will be a nice introduction into the everyday use of iPads, and get us used to working with them and see different ways to incorporate them into my other everyday curriculum!
I think the most important thing to remember is that "integrating technology is not about technology, it is about learning" ~ L. Cuban. So while it is great to use these technologies, it is really more important that I have repurposed them to be useful and meaningful to the learning and understanding of mathematics. Having these different options, would allow me to mix and math for what I need.
The final technology that as a school we will be incorporating, so I will be using it within this process, are iPads. There are many apps that can be used to help with writing, evaluating, and collaborating with each other, and this is something else that will be incorporated within my classroom during both individual, partner, group, and whole class activities. This will be a nice introduction into the everyday use of iPads, and get us used to working with them and see different ways to incorporate them into my other everyday curriculum!
I think the most important thing to remember is that "integrating technology is not about technology, it is about learning" ~ L. Cuban. So while it is great to use these technologies, it is really more important that I have repurposed them to be useful and meaningful to the learning and understanding of mathematics. Having these different options, would allow me to mix and math for what I need.
Pedagogy:
One of the pedagogical strategies that I will incorporate is the use of the flipped classroom. With my classroom being flipped, we will be able to use more class time to focus on the computations and writings of our quadratics unit. This will also allow us to be able to spend more time working on quality evaluations and interpretations of misconceptions during our whole class, group, partner, and individual work time. "Effective teachers provide students with opportunities to work both independently and collaboratively to make sense of ideas" (Anthony & Walshaw, p. 9) and with the implementation of the flipped classroom, it will allow for more of these opportune times.
With the different levels within the classroom there will be more of an opportunity to be able to differentiate the information the specific ways the students may need. This will also allow me for more opportunity to learn what the misconceptions of the students are and work towards tackling what their specific struggles may be. At the beginning of each unit, the students will have a prompt to express their thoughts and ideas of the given question, allowing me to see their conceptual knowledge and misconceptions and plan/place them accordingly. |
Within the writing, instead of everything being a straight paper, I intend to allow the students to have some creativity in the way they present their thoughts and ideas. The students will have some straight forward writing prompts, but it is also important to give them the opportunity to use their creativity such as in a story, poem, lesson video, etc. Allowing the students these different outlets gives them the opportunity to not only be creative, but is "a new and different way" (Mishra & Kohler) and in order to accomplish the task at hand "they must fully understand the main idea" (Mishra & Kohler). This goes along with the theory that "effective teachers plan mathematics learning experiences that enable students to build on their existing proficiencies, interests, and experiences" (Anthony & Walshaw, p. 11). With giving them the openness of how they present their material and allowing them to build on existing knowledge, it allows them to incorporate some of their interests and experiences that they enjoy.
Another best practice that is important in this transformation is that fact that "effective teachers support students in creating connections between different ways of solving problems, between mathematical representations and topics, and between mathematics and everyday experiences" (Anthony & Walshaw, p. 15). Within this entire dreamit, it is my goal to allow the students to solve the problems the way they see fit, giving me an idea of their conceptual understanding. In the future of standardized tests, the answer is not as important as the process they use to get there, and this is a stance I am going to try to take throughout this process. It is really important for me to see the conceptual understandings, or misconceptions, in order to help them grow and build in the process of mathematics.
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Throughout the entire process of discussions, writings, analyzing, and evaluating their understanding, the best practice of "effective teachers are able to facilitate classroom dialogue that is focused on mathematical argumentation" (Anthony & Walshaw, p. 19), will be attended to. For the students to have an understanding of ideas and be able to verbalize them correctly, the classroom dialogue is one of the most important parts. They need to know how to explain their thoughts in the proper mathematical context, and as a teacher, it is my job to help facilitate that throughout the class at all times.
Throughout all of the writings, and discussions, it follows the path of explore, create, and share. It is important to explore the thoughts you have about the math at hand, be able to create your solution and thoughts behind that solution path, and then share it with others. The sharing is where we will be able to constructively discuss the ideas, allowing for their thought processes to possible change, if necessary.
Throughout all of the writings, and discussions, it follows the path of explore, create, and share. It is important to explore the thoughts you have about the math at hand, be able to create your solution and thoughts behind that solution path, and then share it with others. The sharing is where we will be able to constructively discuss the ideas, allowing for their thought processes to possible change, if necessary.
The Total PACKage:
Within my quadratic unit dealing with writing in the classroom to be able to demonstrate their conceptual understanding of mathematics, and specifically quadratics, the technology, content, and pedagogy all play an integral role. Within the class, there will be many strategies that help lead to the ability to incorporate all of these concepts on a daily basis, such as flipping some lessons, having more projects and activities planned during the class period, and allowing the time for reflection and understanding daily within the class. Being able to repurpose different technological tools will only help increase the motivation and engagement within the classroom, helping build the students conceptual understanding of quadratics.
Inquiry:When asking the students a prompt, they will think of how they would solve a situation, or answer a question. This will be using inquiry to to draw conclusions, or test ideas of what they think the best possible solution will be. Within this process they will have the iPads as a resource to communicate with each other and individually to try to answer questions. This will also allow them the opportunity to discover, ask, and answers questions for them selves of how and why they have chosen the path they have chosen.
Students will be able to use such technologies as: |
Construction:Throughout the writing in mathematics, the use of graphs and charts to display information or help construct the flow of their thoughts is vital. In math sometimes words aren't enough to explain your understanding and the visual representation of another resource such as a graph, can help describe your thought process.
Students will be able to use such technologies as:
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Communication:With the writing, the communication is vital. There will be access to the paper and pencil, which is a very useful technology in order to communicate their thoughts, ideas, and understandings. They will also have access to collaborate with others on some of the prompts, having access to their iPads to collaborate through email, google docs, etc. With the communication, the students will sometimes have free range of how they will present such findings and understandings of quadratic ideas. These could be presented via writing, poem, video, etc. allowing them the freedom to use their creativity.
Students will have access to use such technologies as: |
Expression:This is where the students will be able to express their ideas and thoughts whether it be through a paragraph, a video, or some other creative way to express their understanding. As a class, groups, partners, individually, etc. we will evaluate the writings using the given rubric of the fulfillment's that are asked for.
Students will have access to use such technologies as:
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