Oral Defense Portfolio
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School
Western Governors University *
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Course
MFT2
Subject
Mathematics
Date
Feb 20, 2024
Type
docx
Pages
14
Uploaded by CorporalInternetSeahorse14
HANNAH BROOKS
WESTERN GOVERNORS UNIVERSITY
Masters of Arts, Mathematics Education (K-6)
MFT2
P
ORTFOLIO
O
RAL
D
EFENSE
MFT2: PORTFOLIO ORAL DEFENSE
A.
Provide an overview of your teaching philosophy in math by doing the following:
1.
Explain how your approach to math teaching promotes a positive learning environment.
My approach to teaching mathematics promotes a positive learning environment by centering each math task around the students’ abilities, learning
styles, and interests. For each math lesson, I first model a similar task, complete a guided task, and then monitor students closely as they work alone, with a peer,
or in a group. While I model, guide, and monitor, I set the expectations for the task so that the students are knowledgeable of what is required of them for the lesson. The students in my classroom effectively learn in a variety of ways, auditory, kinesthetic, and visual. I support each type for each lesson. For example, during a lesson on shapes, I support auditory learners specifically by playing songs with rhymes that relates to the standard, such as the ‘Quadrilaterals Song’ by Numberock on YouTube. To support kinesthetic learners during a lesson on shapes, I allow students to play with shape manipulatives. They can sort them into categories based on the attributes and combine different
shapes to create composite shapes. To support visual learners, I create anchor charts for the students to refer to. Aspects of the YouTube video, manipulatives, and anchor charts can benefit more than one time of learner at a time. Additionally, I promote a positive learning environment by building tasks that include student names and interests. The learners in my classroom particularly enjoy animals, sports, and video games. Students enjoy solving tasks that represent themselves and their peers. 2.
Explain how the positive learning environment from part A1 promotes student learning, including
one
specific example from the environment.
1
MFT2: PORTFOLIO ORAL DEFENSE
The positive learning environment in my classroom promotes student learning by targeting students’ individual needs to help them be successful in math. When students feel successful, they are typically more engaged, perform better, and have a positive attitude towards learning. I specifically take this into account when creating math tasks for my learners. In my classroom, I serve a wide range of student skill levels from students who are unable to read directions
and word problems to students who score advanced on the Math Inventory. One specific example from the learning environment is reading directions and word problems aloud. I have two students who are unable to read, so during math, I read the directions and each question aloud. When this occurs, the two students can be more successful with the task, which then encourages them to keep trying. 3. Describe
two
goals you have for your elementary math students. Identify the grade level you are teaching or will be teaching.
In my third-grade math class two main goals that I have for my students are, becoming fluent in the math operations; addition, subtraction, multiplication,
and division, and using strategies to show their work. I have chosen these specific goals because adding and subtraction within 1,000 and multiplying and dividing within 100 are very important skills that third graders should master. These operational skills are needed to be able to master other math topics that are dependent on them, such as finding the area and perimeter of a shape. I chose the second goal of using strategies to show students’ work because I have found that students tend to make errors and are unable to correct them when they solely rely on mental math when solving complex expressions.
a. Explain how
both
student goals from part A3 have affected or will affect your teaching.
2
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MFT2: PORTFOLIO ORAL DEFENSE
One student goal that affects my teaching is effectively using strategies to
show their thinking. Teaching students to use strategies is important because it fosters a deeper understanding of the concepts. This affects my teaching because as the teacher, I introduce students to specific strategies for addition, subtraction, multiplication, and division. While teaching these strategies, students are able to determine which strategy works best for their skill level, so it’s important that I teach different strategies for each concept. The use of strategies, such as model drawing and using manipulatives, will facilitate conceptual understanding. The second student goal that affects my teaching is for students to become fluent in mathematical operations. After students have a conceptual understanding of math topics, then they are able to become fluent with their math facts. To encourage fluency, I plan math games with small groups, flashcards, number talks, and drill practice.
4. Describe
two
professional development goals you have for yourself as a math teacher.
The first professional development goal that I have set for myself is to integrate more technology into teaching math. I am currently in a technology leadership cohort for my district, and we have been encouraged to find new ways
to integrate technology in all subject areas. Technology integration is beneficial for all learners because technology is becoming more vital in our world and education, particularly with virtual learning. I have discovered many virtual manipulatives that can be embedded into our learning platform, Canvas, discussions can take place in the form of comments on Padlet, and interactive lessons can take place using Nearpod. The second professional development goal
that I have set for myself is to dissect each math standard to become more 3
MFT2: PORTFOLIO ORAL DEFENSE
familiar with the vocabulary that is used, have a better understanding of what students need to master, and the progression of standards throughout k-6.
a. Explain how your goals from part A4 have affected or will affect your teaching.
The goal of integrating technology has affected my teaching and student learning because I have been exploring different ways to teach math concepts. Instead of creating pencil and paper tasks, I now create gamified lessons on Nearpod and Kahoot. Since adding more technology into math lessons, I have noticed my students are more eager to participate and stay on
task. The goal of dissecting each math standard will affect my teaching because I will be able to understand what exactly I need to teach better, which will in turn help the students become more successful with each standard. Knowing how standards progress throughout k-6, I will be able to accurately pull-out prior knowledge and set them on a course to master the next progression. While reviewing standards, I plan to use the more accurate vocabulary while teaching and create math vocabulary anchor charts. 5. Describe
one
formative and
one
summative assessment you use to understand student learning in mathematics, including
one
specific example of
each
type of assessment.
One formative assessment that I use to understand student learning in mathematics is having math “closers” and planted questions. At the end of math workshop, I select individual students, partners, or groups to close out our math lesson. Students display their work on the smart board and describe the strategy they used to solve a math task. This allows me to see the thinking of the student presenting, misconceptions they may have, and areas they are successful in. At the end of the presentation, students ask planted questions such as; why was a specific strategy chosen and higher-order thinking questions that are related to 4
MFT2: PORTFOLIO ORAL DEFENSE
the task. One summative assessment that I use to understand student learning is
exit tickets. During math workshop, students work together so at times it is difficult to see what a student can do independently. When using an exit ticket, I give similar questions to the day’s math lesson, have students complete the task independently, and have them show their thinking through a strategy. a.
Explain how the assessments from part A5 are a valid measure of student understanding.
The formative assessment of having closers for math workshop is a valid measure of student understanding because I am able to observe the student sharing their work with peers and listen to them explain in detail how they solved a problem and respond to planted and spontaneous questions from other students. If a student understands the math objective, then they are able to accurately describe the steps that were taken. If a student made an error and is unable to identify the error or fix it, then I can make note of what the student may have a misconception about and address it during the next lesson. The summative assessment of having an exit ticket is also a valid measure of student understanding because I am able to see what the student
can do independently and the strategy they used. If a student makes an error, I highlight the problem and have them fix it later. This can show me if the student made a simple error or does not understand the content. B.
Discuss how national or state mathematics standards build student understanding of
mathematics as students progress through grades K–6, including
one
specific example.
The Georgia mathematics standards build student understanding of math as students progress through grades K-6 by laying the foundation for concepts in kindergarten and increasing in complexity as they move into upper elementary and 5
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beyond. For example, geometry begins in kindergarten with learners identifying and describing simple shapes. In first grade, learners build onto the prior knowledge of identifying and describing shapes to distinguish shapes based on their defining attributes. In second grade, learners begin to recognize and draw shapes when given a specific number of angles and faces. After being able to recognize and draw shapes, learners in third grade begin to understand that shapes with shared attributes belong to specific categories and subcategories and are introduced to finding the area and perimeter of rectangles. In fourth grade, students go more in-
depth with shape attributes and can classify the shapes by the properties of their lines and angles and apply the formulas for the area and perimeter of these shapes. By fifth grade, learners can successfully classify 2-d shapes in a hierarchy based on attributes and are introduced to finding the volume of 3-d shapes. In sixth grade, students are able to represent 3-d shapes by using nets and finding the surface area
for those shapes. They are also increasing the complexity by finding the area of shapes other than rectangles, and the volume of prisms using formulas. C.
Identify an instructional model or models that align with the way you teach math, and explain how the instructional model or models you identified benefit math students.
The instructional model that I use in my third-grade classroom is the Math Workshop model. At the beginning of the math lesson, I introduce the standard, create or review anchor charts, and model a task similar to one that the students will
work on with student input such as; background knowledge, questions, and ‘notice and wonder’. Then students are given the instructions and solve tasks with a partner
or group. While students are working I observe them so that I can assist students who are struggling and ask higher-order thinking questions to those who can be pushed further. As I observe, I choose students to close the lesson by sharing their 6
MFT2: PORTFOLIO ORAL DEFENSE
work and thinking with the rest of the class and plant questions for other students to
ask the closer. In a lesson, I attempt to pick three students or groups who 1) have mastered the task, 2) used a unique strategy to solve the task, and 3) had a common misconception. The Math Workshop model is beneficial for students because a similar task is modeled and the expectations are known, they are able to work with peers to discuss the task and strategies, and students take ownership of their work by sharing out. Students also benefit by watching and listening to how the
closers solved their tasks. Students can ask questions and make connections at the conclusion of the lesson and listen to the answers to the planted questions. D.
Reflect on
three
different instructional strategies you observed or used in your AOA2, AUA2, and AVA2 coursework and what you have learned, by doing the following:
1.
Describe a scenario in which you successfully implemented
one
instructional strategy. Provide enough detail that a nonmath substitute teacher could replicate
the strategy.
An instructional strategy that I successfully implemented during a fraction lesson is the C-R-A model, which stands for concrete, representational, and abstract. In the concrete phase of the model, we focus on hands-on manipulatives. For this phase, students made their own fraction strips and partitioned the strips by folding them. To show the units ½, students were instructed to fold their strip in half, draw a thick line on the fold, then label each section ½. The same concept was duplicated to show 1/3, ¼, 1/6, and 1/8. By doing this, my students were able to see that the whole does not change, only the amount of parts in the whole. In the representational phase, students are encouraged to draw representations. For this phase, students were instructed to draw models using dry erase markers on their desks by drawing rectangles, 7
MFT2: PORTFOLIO ORAL DEFENSE
partitioning them into unit fractions that represent the denominator, then coloring in the parts that represent the numerator. Students were able to draw different fraction models and compare unit fractions. In the abstract phase, students are urged to represent the fractions by using numbers and symbols. This was used when students compared fractions by using the greater than, less than, and equal signs. a. Explain why your implementation of the instructional strategy from part D1 was successful.
The implementation of the C-R-A model was successful because it gave students the opportunity to look at a concept in multiple modes. This model is particularly beneficial for students who are kinesthetic and visual learners. The concrete phase allowed students to manipulate the strip and see how the whole stays the same, but the unit fraction differs. The representation phase builds on the concrete phase by allowing students to represent the fractions strips that were created. After creating strips and drawing models, students can then use the abstract phase to compare fractions using symbols. 2. Describe
one
instructional strategy that was challenging for you to implement. This strategy must be different from the strategy you described in part D1.
The instructional strategy that was challenging to implement was integrating prior knowledge. This strategy was used in a lesson on data analysis because the third-grade standard for representing and interpreting data foundation is built into the first and second-grade standards. For this lesson, I introduced the standard and referred back to the standards and “I can” statements for first and second grade. 8
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MFT2: PORTFOLIO ORAL DEFENSE
a. Explain what made the implementation of the instructional strategy from part D2 a challenge.
I believe that the implementation of integrating prior knowledge was challenging because many of my students did not receive the appropriate skills due to being virtual and having limited technology at home during that time to actively participate in the lessons regarding data analysis. 3. Describe
one
instructional strategy you have used or observed that you feel is effective for promoting student learning, and justify why you believe the strategy
is effective using
one
specific example. This strategy must be different from the strategies you described in parts D1 and D2.
An instructional strategy that I feel is effective for promoting student learning is learning centers. This strategy was implemented in a lesson regarding
shapes. For the lesson, I set up 5 different centers. In the first center, students created 3-d shapes from play-doh. In the second center, students sorted 3-d shapes that were of different sizes and colors. In the third center, students were able to observe shape realia from photographs (buildings) and tangible items that are used daily (cereal boxes). In the fourth center, students were able to enjoy watching different instructional videos and songs regarding shapes. In the fifth center, students sorted foods that were in the shape of cubes, cylinders, cones, and spheres, then they were able to eat the foods. I believe that this strategy was effective because students were able to work in groups that were predetermined based on skill levels, which enabled me to modify centers based on the groups. For students who were able to easily grasp the topic, I was able to
add extensions into the center, such as combining two play-doh shapes to form a
new composite shape. For students who had other special needs, I could work more closely with that small group to provide additional support in their learning 9
MFT2: PORTFOLIO ORAL DEFENSE
environment. For the most part, the students were able to complete the centers without teacher help. By the end of the lesson, 87% of the students were able to successfully identify and describe shapes on the exit ticket. Note: “Practice” in part E entails instruction, planning, lessons, or any single component of your teaching.
E.
Reflect on the content of your AOA2, AUA2, and AVA2 coursework, your portfolio, and your personal practice by doing the following:
1.
Describe how you can apply what you have learned to your practice as a mathematics teacher, including
one
specific example. I can apply what I have learned about instructional strategies to my practice as a mathematics teacher. In my research regarding instructional strategies, I have been able to determine which strategies work well for my students and different strategies that pair well with specific content. Instructional strategies in math are very beneficial when applied appropriately. I plan to continue to use and research instructional strategies while teaching third-grade math standards. One instructional strategy that will reside in my classroom is using manipulatives.
I discovered that manipulatives foster conceptual understanding by offering students a way to personally interact with the math concept that is being taught. a. Explain how your application of what you have learned affected or could affect
students in your math classroom, including one specific example.
The application of implementing instructional strategies can positively affect students. While planning lessons, I will select an instructional strategy that pairs well with the content and for the students that I serve. Students will
benefit from the use of a purposefully selected strategy because it can encourage motivation and engagement. For example, the C-R-A method can 10
MFT2: PORTFOLIO ORAL DEFENSE
be used in a lesson for NBT. 2, fluently adding and subtracting within 1,000. For the concrete phase, students can use base ten blocks to solve expressions. In the representation phase, students can draw out the base ten blocks, using a cube for thousands, a square for hundreds, a line for tens, and
circles for ones. For the abstract phase, students can simply use the digits or symbols. I believe that using this instructional strategy would positively affect
my students by giving them different ways to experience the content, allowing them to be more successful and confident in their abilities. b.
Describe how your math teaching practice has evolved over the process of completing your coursework, including one specific example.
Over the process of completing my coursework, my math teaching practice has evolved because I have been able to understand the standards better, research instructional strategies that are best suited for my students and the content and focus on how my assessments relate to the standard, learning objective, and understanding the prior knowledge that the students should have from previous grades.
Of these practices, the one I feel that has most impacted my teaching is that I understand the standards better. While reading the textbook, Elementary and Middle School Mathematics: Teaching Developmentally, I have been able to identify why specific standards are important to student understanding and how a topic expands throughout K-6. For example, in a lesson about shapes, I included math vocabulary that was introduced starting in kindergarten up to third grade on our anchor chart. Having previous standards vocabulary posted in the classroom helped students integrate their prior knowledge into our current lesson. 2. Describe
two
weaknesses of your math teaching practice, and explain why these are weaknesses.
I believe two weaknesses of my math teaching practice are giving too much assistance and not asking effective questions. I have noticed that I am too eager to assist students. When a student is struggling instead of asking guiding questions, I tend to give the student the next step. If a student has an incorrect answer, I tell them it is wrong and how to correct the mistake instead of allowing them the time to review their work and check for an error. This does not allow 11
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MFT2: PORTFOLIO ORAL DEFENSE
the student to have a complete understanding of the content. I also feel that I lack in asking effective questions. When I do ask questions, they are more surface-level questions and do not require much thought beyond the original task. a. Explain how
both
weaknesses from part E2 could be addressed.
My weakness of giving too much assistance can be addressed by giving students more think time and instead of telling students how/why they are wrong or right, I can ask them to check their work and have them talk me through their thought process. In a previous math education course, we were given a problem to solve. The professor observed while we worked but did not
tell anyone if they solved the correctly, she would simply tell us to check our work. That process helped us have a more conceptual understanding of the content because we had to be able to show our work and explicitly describe our thinking. It allowed us to understand what we were doing and why we did it. I believe that I should give my students the same opportunity. My second math instruction weakness is not asking higher-order thinking questions while
students are working. I tend to only ask higher-order thinking questions at the
end of the lesson when students are closing our activity. I can address this weakness by pre-planning higher-order thinking questions and finding opportunities to ask them during work time. 3.
Describe how you can apply what you learned from earlier in this program in your
professional work environment outside the classroom. Include
one
specific example in your description.
In my coursework, I have learned that students are more engaged and motivated when activities are “gamified” and work with peers. I can use this knowledge in my professional work environment by providing gamified 12
MFT2: PORTFOLIO ORAL DEFENSE
professional learning opportunities. I am currently in a technology leadership cohort and STEM cohort, and I regularly have to provide resources and information to the teachers at my school. Instead of showing teachers something
I have learned, I can create a Nearpod that will allow the teachers to be engaged with the information I am sharing. For example, if I were to be sharing information about using ozobots in the classroom, I can create a Nearpod that includes a quiz to see who has used ozobots, embed an instructional video on ozobots, show examples of how they can be used in different content areas, have
ozobots for teachers to experiment with, then have a survey to see who would like to use this resource or want more information. I believe that teachers would be more open to this form of professional learning, than just listening to a teacher talk about something they learned about.
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