Task 1 (1)
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Western Governors University *
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MFT2
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Mathematics
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Feb 20, 2024
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Kyle Clinedinst
Student ID-001029234
Mathematics K-6 Portfolio Oral Defense MFT 2
A. Give an overview of your teaching philosophy in math by
1. Explaining how your approach to math teaching promotes a positive learning environment.
My approach to teaching math deals with using hands on manipulatives and being the facilitator as much as possible. I am currently a 3rd grade teacher, and I firmly believe that young children learn by doing. I use many manipulatives in the classroom that range from counters, counting cubes, fractions strips and circles, base ten blocks and many more. I believe this promotes a positive learning environment because the students enjoy learning with manipulatives. They like to be in charge of their own learning, and nothing lets them be in charge like working hands on with objects. I also try to be the facilitator as much as possible. Early in my teaching career, I struggled with this, and I found it harder to motivate students. Over the years, I have learned to let students lead instruction as much as possible. This can be done in many ways, from small group activities, pulling sticks and having students give ways in which they solve problems, let students choose their activities, to instructional strategies with the teacher walking around adding input when needed. When the teacher is the facilitator, students are motivated because they are in charge of their own learning and have more opportunities to work together. 2. Explaining how the positive learning environment in A1 promotes student learning.
Include one specific example from the environment
Children often learn best from their peers. One thing I try to do is pair students in ways I
think will be most beneficial and that allows me to act as the facilitator. A lot of times, this means pairing lower-level students with students who are on level or above level. But there are times I pair above level with on level or above level students to challenge or enrich their learning. An example of this is when we do a math scoot. A scoot is when there are multiple questions at each desk, and students move from one to another to answer the questions. A specific one we did recently was a fraction on a number line scoot. There
were many fractions on a number line questions, and this concept is tricky for a lot of my students. Before the lesson, I paired children who I know would struggle with students who not only have a good understanding of the concepts, but also who I knew would be good teachers. I had them work together, taking advantage of peer assisted learning for 12 of the 20 problems. “The students can be paired with older students or
peers who have more sophisticated understandings of a concept.” -(
Van De Wallie & Karp & Bay-Williams, 2012, p.99)
Then, as an extension, I paired my high-level students together to complete 8 separate/ enrichment fractions. These were fractions greater than 1 on a number line. Example- 12/8 (twelve eighths). While they were doing the enrichment activities, the rest of the class finished their “normal” fractions on a number line scoot.
3. Describing two goals that you have for your elementary math students. Identify the grade level you are teaching or will be teaching.
Currently teaching 3rd grade math.
Goal 1: By the end of the first nine weeks, every student will have felt successful in at least one specific math area. (Does not have to be on grade level.)
Goal 2: By the end of the school year, 100% of my students will show measurable growth according to district assessments. a. Explain how both student goals from A3 have affected or will affect your teaching.
Goal 1: For my first goal, I want to make a point to recognize and celebrate every student for at least one math accomplishment early in the school year. For some students, this will be very easy. For those that struggle, this may mean working on below grade level standards in small tier 2 groups. But it is more valuable to recognize success for the “low” students because they often do not feel successful in math. If I can recognize them, this will boost self-confidence and hopefully encourage some motivation to be successful in the future. This will affect my teaching because I will first need to know every student's current ability level. To do this, I will use district data assessment, class summative assessment, and class formative assessment. Next, I will work on number sense concepts, (this is our focus the first nine weeks of school), at
all different levels. I will teach a tier 1 whole group lesson and work on tier 2 or even tier
3 modifications and enrichment lessons to reach all students. Finally, I will recognize individual students' accomplishments in many different ways.
Goal 2: My goal of having every student make measurable growth affects my teaching because in order to do this I have to focus on each student’s strengths and weaknesses. In order to grow each student, I need to teach them at their level as well as teaching the 3rd grade math standards as a tier 1. This means I will have to make modifications, find enrichment opportunities, work in small groups, and progress monitor
throughout the school year. Our districts use NWEA MAP to progress monitor 3 times a
year. I will use the first assessment to find specific math levels by standards. Then, as
I teach each unit, I will make modifications based on student needs. I will also use my class summative and formative assessments to progress monitor on a daily and weekly basis. 4. Describing two professional development goals you have for yourself as a math teacher.
Goal 1: Improve parent/teacher communication involving student math progress.
Goal 2: Improve active participation from students and become more of a facilitator.
a. Explain how your goals from A4 have affected or will affect your teaching.
Goal 1: My first goal will affect my teaching in a couple of ways. First, improving parent communication starts with building a rapport with the parents. I feel this is something I have improved at over the years. I use different forms of communication such as class letters, phone calls (positive and negative), and class dojo. After a rapport has been built, then I can make suggestions to parents on how to better help their child. I would like to improve on specific content communication. This will give the parents an idea of what we are working on in the classroom, but also help them better work with their child at home, in turn, help improve their child’s skills. I have found that a lot of parents teach
math to their children differently than we teach common core at school. For some children, this is beneficial, but for many others, this only confuses the student. So, by improving my communication, I can help make sure the parents and teachers are on the
same page. Goal 2: Over my 10-year teaching career, I have learned that students focus better when they have more control over their learning. 2 years ago, I felt that I was doing a great job being the facilitator. Last year, our district adopted a new math program that is
very scripted and to me, seems very teacher led. Now that I have taught this program for almost a year, a goal of mine is to become more of a facilitator in the years to come. This will affect my teaching because the students will be more involved and engaged in the lessons. I will incorporate more peer learning and encourage students to share their
ideas. 5. Describing one formative and one summative assessment that you use to understand student learning in mathematics.
Include one specific example of each type of assessment.
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Formative Assessment- Partner pair and share work using white boards. During this time, I walk around the room listening to students' ideas and strategies. Example- Recently, we were working on comparing fractions with the same numerator and different denominator. During this time, I had students working in pairs. Each partner had a white board and marker and fractions strips. I would put 2 fractions on the board. (2/4 and 2/8) One partner would make the fractions 2/4 with fraction strips and the other would make 2/8. Then, they would discuss the fractions to determine a number sentence. During this time, I was walking around the room listening to conversations for key words such as, “the bigger the denominator the smaller the pieces”, “this one has bigger pieces” ....
This would let me know the students who understood the concept because they were able to explain their thinking correctly. Also,
I was looking for correct number sentences. (2/4 > 2/8) Summative Assessment- Every week, we work on what we call “Math Boxes.” -
(McCarthy, 2013) These are 4 common core problems a day, Monday through Thursday. This takes about 5 minutes and I use it as morning work. I pull sticks, and the students do one problem of their choice until we complete all 4. Then, on Friday, the students have 10 problems to work on as independent work. I take a summative grade from day 5 and use this data to drive my small group tier 2 lessons. An example of the max boxes is below and an explanation of how I use it to drive my lessons. Example-
From this assessment, I can see that this student needs a tier 2 lesson on comparing fractions and fractions greater than 1.
a. Explain how the assessments in A5 are a valid measure of student understanding.
Each assessment helps me measure the students' understanding differently. The formative assessment above helps me make a quick note of which students not only can write a correct number sentence comparing fractions, but more importantly who can
explain their thinking. I was looking to see if one partner was dominating the conversations, showing me that we either need to work on how to be good partners, or that students are unsure of the concept and need more instruction. The summative assessment is a great way to drive my future instruction. For example, if I notice that only a few students struggle with a specific question or concept, then I know I may need to reteach that concept as a tier 2. But, if I notice that the majority of the class struggles after we have had our lesson(s) on said concept, then I know the lesson wasn’t effective or that I need to go back and reteach the lesson to the whole group as tier 1. B. Discuss how national or state mathematics standards build student understanding of mathematics
as students progress through grades K-6. Include one specific example.
Thus far, a big takeaway from this K-6 Mathematics Master’s Program has been standard alignment. I have taught for 10 years, and each year has been in 3rd grade. Coming into this program, I was very comfortable with the 3rd grade math standards and fairly comfortable with the 2nd grade and 4th grade standards. Admittedly, I understood number sense and other math concepts at each grade level k-6, but didn’t know how they were taught and how the standards build on each other. I now have a better understanding of how math concepts are taught in k-2. This helps me see where my below level students struggle and how the concepts were taught in the grades before. Also, I now have a better understanding of what students will be doing in the future. I have always worked on 4th grade concepts with my above level 3rd graders, but I now know how the 3rd and 4th grade standards build to the 5th and 6th grade levels. This helps me better prepare my students for the future. Include one specific example.
One specific example of how the standards align is relating 3rd grade multiplication standards up to 6th grade geometry standards. In third grade we teach multiplication properties, such as the associative property of multiplication. Students learn they can multiply 3 numbers in any order. For example (2x3) x 4 or 2x (3x4). Before, I thought this prepared students for order of operations, which it does. But I also see how this relates to finding the volume of a rectangular prism in 5th and 6th grade. Students in 5th and 6th grade learn that volume is (L x W x H). So, they learn how to multiply 3 numbers in 3rd grade and use this skill in 4th, 5th, and 6th grade geometry.
C. Identify an instructional model or models that align with the way you teach math. Explain how the instructional model or models benefit math students.
The instructional models that most closely align with my teaching style are interactive instruction and experiential learning. “ Interactive instruction relies heavily on discussion
and sharing among participants. Experiential learning is inductive, learner centered, and activity oriented.” -(Keesee 2015)
I feel like one model I use is the interactive instructional model because I like to have a number of different groupings, students working in pairs, and students sharing ideas and concepts. This model is beneficial to my math students because as we know, students learn best from their peers. I like to start my lessons as a whole group but take
time to share ideas with partners as we progress through the lesson. Then, I like to have children work in smaller groups or with partners to bounce ideas off each other and support each other as needed. For almost every lesson, I have what we call “share and show” activities. This is when two students work together on the daily concept. I try to pair my students so that a low student is with an on level or above level student. During this time, I try to act as the facilitator and listen to different conversations and add my input when needed. However, I could do a better job circulating the room. I have a tendency to focus on the students who I know will struggle and spend most of my facilitating time with them. This takes away from some enrichment conversations I could be having with the other students. I also like to use the experiential learning model at least once a week. I like this model because I like to have students up and moving and still learning once I have established
clear behavioral expectations. (I do feel that model is impossible if students don’t follow
class expectations.) Some ways I use this model is by doing classroom scoots, manipulatives, gallery hops, and projects. I like to have a lot of manipulatives when teaching math. I feel younger students learn best by interacting with concrete representations. We then take these concrete representations and turn them into pictures and visual representations. Another example of this is when I had my students do “A table for 20”. I got this idea from the geometry and measurement task 1 video. The students each got a 1-yard border paper to use as their spot at the table. They were to find the possible perimeters and the table that would have the largest and smallest area. After some discussion, planning, and sharing ideas, I let the students go and try to make the tables without me. They did struggle to do this when making the 5x5 table. They did a great job when making the 9x1 table. We were able to discuss how it’s ok to make mistakes when experimenting with mathematics, and how we can learn from our mistakes. But most importantly, the students love the experiential learning model and are motivated to learn.
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D. Reflect on three different
instructional strategies you observed or used in your AOA2, AUA2, and
AVA2 coursework by
1. Describing a scenario where you successfully implemented one instructional strategy. Provide enough detail that a non-math substitute teacher could replicate the strategy.
One instructional strategy I observed in AUA2 Task 1 was interactive instruction or practice by doing exercises. As described by literacy basics “
Interactive Instruction relies heavily on discussion and sharing. Interactive instruction allows for a range of groupings and methods, such as debates, role-playing, simulations, brainstorming, peer
learning, discussion and cooperative learning.” In this 5th grade lesson, “A Table for 22”, students used the interactive instruction to practice the learning goal with real world
applications. The learning goal was to find 2 rectangles with the same perimeter, but the smallest and largest possible area. Rather than giving the students graphing paper and having them draw it, the students were applying a real-world situation to this problem. They had to make the tables using border paper as their seats. This challenged the students to work together, share ideas, have mathematical discussions all at the same time. Not only did the students work with area and perimeter, but the teacher also incorporated other geometric standards such as right angles, parallel lines,
and properties of a rectangle. I teach area and perimeter in 3rd grade. After our area and perimeter unit, I implemented the same lesson, but called it a table for 20 because I have 20 students. I had my students start by reviewing area and perimeter as vocabulary terms with a partner. Then, we introduced the activity, and like the video, I had the students work in small groups to come up with a plan on how to make different “tables” with a perimeter of 20. As a class, we took all the tables, and decided which would have the largest area
and smallest area. I did this as a class because it's more of an abstract thought for 3rd graders. I kept the 2 tables with a perimeter of 20 and the largest and smallest possible
areas on the board for them to reference while doing the activity. After some discussion, I let them try to make the table with the largest area first. They were very close but could not make the 5x5 table. One side had 6 seats, and another only had 4. They knew it wasn’t correct but couldn’t figure out why. I took this as a learning opportunity. Then, I had them make a table with the same perimeter, but smallest area.
They did this with no problems. a. Explain why your implementation of this strategy was successful.
This implemented strategy was successful because students were working together sharing ideas and the lesson was very rigorous for 3rd graders. The students were sharing ideas, learning from each other. I had a lot of good discussions where students were helping each other without just giving the answers. I had two boys who had
different answers for the table with the smallest area. Finally, after they discussed it without me, one student went “OOOHHH” and got a big smile because he found his mistake. Also, this lesson was very rigorous. They had a hard time making the first table with a perimeter of 20 and area of 25. This was because it was hard for them to visualize. After a while, I had to step in and help. But once they figured it out, they made the next table with a perimeter of 20 and area of 9 without any help from me. They learned how to visualize their idea! 2. Describing one instructional strategy that was challenging for you to implement. One instructional strategy that was a struggle for me was the questioning strategy in AUA2 Task 3. This was the True/False equation routine where 2 expressions are set equal to one another. The students are asked to look at the expressions and decide if true, they are equal, or false, they are not equal. As described in the video, students can do this by solving both sides or by looking at it relationally. An example of a student
looking at it relationally was the second equation she put on the board, ⅜ + 4/8 = ¼ + ¼
+ ⅛ + ⅛.
a. Explain what made the implementation of this instructional strategy a challenge.
This strategy was a struggle for my class because like the video, I had them sitting in front of the smart board working on true or false questions. I obviously didn’t teach the same equations or inequalities lesson to my third graders. Instead, we did equivalent or
nonequivalent fractions. My students struggled with this because they didn’t have their whiteboards and markers to draw the fractions to see if they were equivalent or not. My
top students did ok because they could visualize the fractions in their heads, but the majority of the class struggled. If I were to do this strategy again, I would definitely have
them bring their markers and whiteboards to draw the fractions. 3. Describing an instructional strategy you have used or observed that you feel is effective for promoting student learning. Justify why you believe the strategy is effective using one specific example.
One strategy that I have observed and used that promotes students learning in math is the use of concrete representations. As described by Van De Wallie & Karp & Bay-
Williams, 2012, p.100 the CSA (concrete, semi-concrete, abstract) model helps explain the students journey to abstract thinking. A goal of mine as a teacher is to teach my students how to visualize a problem or reading to improve comprehension. This is true for all subjects, not just math. In the younger grades, K-6, I believe that most students have to be taught how to visualize any scenario. A great way to teach this in math is by having students start by using concrete objects or representations. I always have my students draw what they create. For example, when we start multiplication, we create equal groups with counters or any objects. We learn to visualize the counters as the
objects we are multiplying. (Kim has 5 groups of 4 pencils. For this problem, I would have the students create 5 groups of 4 with the counters. Then I would say, “ok close your eyes. When you open them, these will no longer be counters, they will be pencils… 1,2,3 open.) They think this is funny and some play along and others think I’m crazy. But I want them to practice visualizing. Next, we work on the semi-concrete method. I will have them draw a picture of the same scenario. This time, they are to create 5 groups of 4, but really draw pictures of the pencils. They turn the counters into pencils. My goal is that this leads to abstract thinking on their own! E. Reflect on the contents 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. Include one specific example.
Through the AOA2, AUA2, and AVA2 courses, I have learned a lot. A few big takeaways from have been learning how all the state standards align from k-6, learning some new instructional strategies that get the students motivated to learn, and relating math to other academic subjects. One video that I really enjoyed and plan to use as a strategy in the future was the “Graphing with Colors” video. This lesson used concrete representations, think-pair-share, and peer learning as instructional strategies. The main aspect which I want to apply to my teaching is how the teacher related math to other subjects. I really like how she and the student make a connection between math and science. They did this by relating the clear pieces from their graphing activity to animals with camouflage in the wild. This activity could lead to a discussion on how animals have certain adaptations to survive in the wild which is a 3th grade science standard. a. Explain how your application of what you have learned affected or could affect students in your math classroom. Include one specific example.
One application that I put into effect because of this program was a bigger emphasis on vocabulary. I have also had students use a vocabulary notebook for math. But we usually write a word in the notebook with a definition and maybe an example, then the students never really look at it again. Through the lesson plan process and videos, I watched, I got the idea of making a vocabulary board for math. This has affected my students because now these words are not a “one and done” meaning they write them in their notebook and forget them. Now, they have a reference to these words and can look at the board whenever they want. I had one student get up in the middle of independent work and walk to the vocabulary board to check the meaning of a word. Before, this student never would have looked in his notebook, but now has a permanent
reference.
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b. Describe how your math teaching practice has evolved over the process of completing your coursework. Include one specific example.
As I stated earlier, I feel like I got away from peer learning and me being the facilitator early this school year because I wasn’t comfortable with the new district adapted math program. Once I started this course, I realized that I wasn’t doing a good job of being the facilitator and tried to change that. I have incorporated a lot of peer learning opportunities and use the think-pair-share model every day in all my academic courses, not just math. One specific example of me becoming more of a facilitator is when I created a lesson for this program that I used in my classroom. We were learning about the attributes of quadrilaterals, and I created a scavenger hunt lesson where I posted attributes of a quadrilateral around the room. First, I showed a quadrilateral on the smartboard and the students looked around the room for an attribute that matches. Next, they walked and stood under the attribute that matches. Then, the students discussed a real-life example of the given quadrilateral that they either saw in the classroom or have seen in their lives. This is a lesson I may not have done if it wasn’t for this program making me reflect on my teaching and how I could do a better job getting students involved and excited about math.
2. Describe two weaknesses of your math teaching practice and explain why they are weaknesses.
One weakness of mine is meeting and teaching the higher-level students at their level. With third grade being a testing grade, unfortunately I know that I focus more on the struggling student. I do a good job of collecting data on all my students to find their strengths and weaknesses. I do a good job of creating tier 2 lessons for my lower students and they make big gains. I also feel I do a good job of working with and meeting the needs of the students who are on level. I know I could do a better job of creating enrichment activities and meeting the needs of the higher-level students. This is a weakness because all students deserve to be met at their individual level. The second weakness of mine is incorporating other content areas into my math lessons. As any teacher knows, there just isn’t enough time in the day. We may create great lesson plans for all areas, but in order to execute those lessons, we would need more time. So, the only option is to incorporate other content areas into math lessons. Over the years, I have really worked on incorporating science and social studies into my
language arts lessons, but I know I could do a better job incorporating other areas into my math lessons. a. Explain how both of these weaknesses could be addressed.
The first weakness of meeting higher level student's needs could be addressed by me making a conscious effort to incorporate an enrichment activity into every lesson. I now have a better understanding of what will be taught in 4th, 5th, and 6th grade, so I see what these students need to learn. When working with any math concept, I could think about what they will need to know in the future and modify my lessons to accommodate these children. The second weakness of incorporating other areas into my math lesson could be addressed by me taking some of the ideas from the videos I’ve watched and applying them. For example, when the 1st grade students were making graphs, they were graphing facts about butterflies. This can be modified to 3rd graders making graphs about animal adaptations or graphing different properties of rocks. Too often, when I teach math, I only focus on math concepts. I need to broaden my thinking to incorporate other areas into my math lessons. 3. Describe how you can apply what you have learned earlier in this program to your professional work environment outside the classroom. Include one specific example.
I can take what I’ve learned from this program and apply it to my professional work environment by becoming a mentor for new teachers. This is my 10th year teaching and I’m starting to feel like a “veteran teacher.” My district has mentor teachers work with not only college students but new teacher hires. I can volunteer to be a mentor teacher and help new teachers with things I’ve learned in this program. I can help them learn the standards and how they relate to other math standards K-6. I can show them how to become more of a facilitator by letting them watch my lessons or sharing my lesson plans with them. I can show them how to collect accurate data and the importance of teaching children at their independent levels. I can be more involved in my district's math making decisions and share my input from what I’ve learned in this program. F. Acknowledge sources, using in-text citations and references, for content that is quoted, paraphrased, or summarized.
Bay-Williams, J.V.D.W.K.S.K.J. M. (2012). Elementary and Middle School Mathematics: Teaching Developmentally, VitalSource for Western Governors University (8th Edition). Pearson Learning Solutions. https://wgu.vitalsource.com/books/9781256957669
Erin McCarthy. (2013). Common Core Math 4 Today
. Carson Dellosa.
Keesee. (2015). Instructional Approaches
. Teaching Learning Resources. http://teachinglearningresources.pbworks.com/w/page/19919560/Instructional
%20Approaches
Instructional Strategies
. (2013). Literacy Basics. https://literacybasics.ca/training/instructional-strategies/
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