Action Plan
Research Purpose
Recent interactions with my students have made me realize that the math assessments in my classroom do not effectively measure mathematical understanding, that there are gaps in my students’ mathematical understanding, and that they are not cognizant of their learning. Through this research, I hope to improve these conditions within my classroom.
From my review of the existing literature I found several implications for my plan of action. I learned that to be proficient in mathematics, students must demonstrate their competency in the strands of mathematical proficiency (Kilpatrick et al., 2001). For my students to develop this strong understanding, it is necessary that I engage them in learning experiences that incorporate the five strands and the mathematical practices. Implementing the five strands into the learning that takes place in my classroom must be paired with introducing an assessment tool that allows my students to interpret and prove their mathematical understanding in terms of the five strands. One alternative assessment, portfolios, allow students to construct evidence of their learning, which allows teachers to truly see students’ achievements.
I have decided to explore the effects portfolio assessments have on students’ overall mathematical understanding, dispositions toward math and perceptions of what it means to be good at math, while also supporting my students to develop their mathematical proficiency in terms of the five strands. There are three distinct interventions that will take place within my classroom during Phase 1 of my research. These are
From my review of the existing literature I found several implications for my plan of action. I learned that to be proficient in mathematics, students must demonstrate their competency in the strands of mathematical proficiency (Kilpatrick et al., 2001). For my students to develop this strong understanding, it is necessary that I engage them in learning experiences that incorporate the five strands and the mathematical practices. Implementing the five strands into the learning that takes place in my classroom must be paired with introducing an assessment tool that allows my students to interpret and prove their mathematical understanding in terms of the five strands. One alternative assessment, portfolios, allow students to construct evidence of their learning, which allows teachers to truly see students’ achievements.
I have decided to explore the effects portfolio assessments have on students’ overall mathematical understanding, dispositions toward math and perceptions of what it means to be good at math, while also supporting my students to develop their mathematical proficiency in terms of the five strands. There are three distinct interventions that will take place within my classroom during Phase 1 of my research. These are
- Mathematical content
- Daily Reflections
- Portfolios
Interventions
Intervention #1: Mathematical Content
I hope that at the end of Phase 1, my students will be well on their way to developing their proficiency. Recall that “mathematical proficiency” refers to students’ competency in terms of Kilpatrick’s five strands of mathematical proficiency--conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition. For this research project I have decided to narrow what I mean when I mention “mathematical proficiency.” Rather than encompassing all five strands, I will only be addressing the first three strands:
I made this decision because I feel as though they are the foundation of mathematical proficiency. In other words, before students are able to adaptively reason and have a productive disposition toward math (strands 4 and 5), they must first comprehend mathematical topics (conceptual understanding), be skilled in carrying out procedures (procedural fluency), and have the ability to formulate and solve mathematical problems (strategic competence). Additionally, I feel as though addressing all five strands will become unmanageable throughout this research project. As a result, I have prioritized the first three strands.
Note: From this point on, I will use the terms “procedural fluency” and “procedural understanding” interchangeably. Also, I will use the term “problem-solving” in the place of “strategic competence.”
During Phase 1, I strive to support my students to develop their mathematical proficiency. To do this, I must create learning experiences that expose my students to the three strands and to the mathematical practices. I have decided to use the unit from Connected Math 3’s Curriculum entitled, “It’s in the System,” because it covers Linear Equations and Linear Inequalities (the logical next step in our progression). (Note that the previously used curriculum could not be used during this research project because it focused only on procedural fluency.) I chose to use this curriculum to guide my students’ interactions with mathematics because of its nature and structure. Connected Math 3 focuses on big ideas and making connections between mathematical topics. Additionally, learning is constructed by students as they interpret rich problems. The structure of Connected Math 3 emphasizes cooperative learning, discourse, and learning through problem solving, while balancing conceptual and procedural knowledge.
The in-class activities and homework assignments during Phase 1 and Phase 2 will come from “It’s in the System.” Phase 1 will take place while we work through Investigation 1 and Investigation 2 of “It’s in the System.” Because Connected Math emphasizes conceptual understanding, procedural fluency, and problem-solving, my students will be prepared to demonstrate their mathematical proficiency by compiling their portfolios at the end of Phase 1.
Throughout this school year, my students would learn about a particular mathematical topic by completing assignments intended to develop their understanding of the topic. The in-class activities allow students to explore the topic, while the homework assignments allow them to practice applying their new skills. This will remain the same during the interventions with the implementation of the chosen curriculum. One change to the normal in-class activities will be Daily Reflections.
Intervention #2: Daily Reflections
After my initial needs assessment, my literature review, and a great deal of reflection, I decided to meet with a content expert to gain some perspective about my ideas. I chose to meet with Dr. Jennifer Gorsky. She is a mathematics professor at the University of San Diego. I took many of her classes as an undergraduate in mathematics at USD. I sought her feedback with the development of my action plan because she is well-versed in metacognition and mathematical learning. One main point from our conversation was that if I expect students to reflect on their learning as a whole (which will occur with the portfolios), I must permit them to reflect on their learning in the moment. Students must have the opportunity to record and interpret their learning each day if they are to put the piece of each day together later on and analyze the whole. Additionally, it will benefit them if they quantify their learning--if they discuss their struggles and their successes. As a result, I plan to implement Daily Reflections into our daily math activities.
At the end of each day, my students will reflect on the learning that took place. The Daily Reflections will allow students the opportunity to become cognizant of their learning. The questions students respond to will include:
Intervention #3: Portfolios
My students will spend the first two weeks of Phase 1 developing their mathematical proficiency with respect to Linear Equations and Linear Inequalities through the new mathematical content, while also interpreting their learning through the Daily Reflections. At the end of these two weeks, my students will assemble their overall learning for the unit from different pieces of their learning. This assembly will take the form of a portfolio. As I explained in my literature review, as a teacher implementing portfolio assessment, I must ensure that the portfolios are created as purposeful collections of students’ work and self-assessments/reflections. I have decided that for the Portfolio Project in Phase 1, my students will complete the following tasks for the following reasons:
Interpreting the learning done within Investigation 1 and Investigation 2 will deepen my students’ overall understanding of Linear Equations in terms of their conceptual understanding, their procedural fluency and their problem-solving skills. This is due to the fact that through completing the Portfolio Project, they will be constructing evidence of their understanding that is meaningful to them, while also documenting and reflection on their learning experience. Through becoming aware of and interpreting their newly cosntructed knowledge, my students will deepen their overall mathematical understanding.
The Portfolio Project Overview shows the assignment as it will be delivered to students in its entirety.
I hope that at the end of Phase 1, my students will be well on their way to developing their proficiency. Recall that “mathematical proficiency” refers to students’ competency in terms of Kilpatrick’s five strands of mathematical proficiency--conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition. For this research project I have decided to narrow what I mean when I mention “mathematical proficiency.” Rather than encompassing all five strands, I will only be addressing the first three strands:
- conceptual understanding,
- procedural fluency, and
- strategic competence.
I made this decision because I feel as though they are the foundation of mathematical proficiency. In other words, before students are able to adaptively reason and have a productive disposition toward math (strands 4 and 5), they must first comprehend mathematical topics (conceptual understanding), be skilled in carrying out procedures (procedural fluency), and have the ability to formulate and solve mathematical problems (strategic competence). Additionally, I feel as though addressing all five strands will become unmanageable throughout this research project. As a result, I have prioritized the first three strands.
Note: From this point on, I will use the terms “procedural fluency” and “procedural understanding” interchangeably. Also, I will use the term “problem-solving” in the place of “strategic competence.”
During Phase 1, I strive to support my students to develop their mathematical proficiency. To do this, I must create learning experiences that expose my students to the three strands and to the mathematical practices. I have decided to use the unit from Connected Math 3’s Curriculum entitled, “It’s in the System,” because it covers Linear Equations and Linear Inequalities (the logical next step in our progression). (Note that the previously used curriculum could not be used during this research project because it focused only on procedural fluency.) I chose to use this curriculum to guide my students’ interactions with mathematics because of its nature and structure. Connected Math 3 focuses on big ideas and making connections between mathematical topics. Additionally, learning is constructed by students as they interpret rich problems. The structure of Connected Math 3 emphasizes cooperative learning, discourse, and learning through problem solving, while balancing conceptual and procedural knowledge.
The in-class activities and homework assignments during Phase 1 and Phase 2 will come from “It’s in the System.” Phase 1 will take place while we work through Investigation 1 and Investigation 2 of “It’s in the System.” Because Connected Math emphasizes conceptual understanding, procedural fluency, and problem-solving, my students will be prepared to demonstrate their mathematical proficiency by compiling their portfolios at the end of Phase 1.
Throughout this school year, my students would learn about a particular mathematical topic by completing assignments intended to develop their understanding of the topic. The in-class activities allow students to explore the topic, while the homework assignments allow them to practice applying their new skills. This will remain the same during the interventions with the implementation of the chosen curriculum. One change to the normal in-class activities will be Daily Reflections.
Intervention #2: Daily Reflections
After my initial needs assessment, my literature review, and a great deal of reflection, I decided to meet with a content expert to gain some perspective about my ideas. I chose to meet with Dr. Jennifer Gorsky. She is a mathematics professor at the University of San Diego. I took many of her classes as an undergraduate in mathematics at USD. I sought her feedback with the development of my action plan because she is well-versed in metacognition and mathematical learning. One main point from our conversation was that if I expect students to reflect on their learning as a whole (which will occur with the portfolios), I must permit them to reflect on their learning in the moment. Students must have the opportunity to record and interpret their learning each day if they are to put the piece of each day together later on and analyze the whole. Additionally, it will benefit them if they quantify their learning--if they discuss their struggles and their successes. As a result, I plan to implement Daily Reflections into our daily math activities.
At the end of each day, my students will reflect on the learning that took place. The Daily Reflections will allow students the opportunity to become cognizant of their learning. The questions students respond to will include:
- Explain the Problem from today.
- How did you solve the Problem?
- What struggles did you have while solving the Problem?
- What exactly did you learn?
Intervention #3: Portfolios
My students will spend the first two weeks of Phase 1 developing their mathematical proficiency with respect to Linear Equations and Linear Inequalities through the new mathematical content, while also interpreting their learning through the Daily Reflections. At the end of these two weeks, my students will assemble their overall learning for the unit from different pieces of their learning. This assembly will take the form of a portfolio. As I explained in my literature review, as a teacher implementing portfolio assessment, I must ensure that the portfolios are created as purposeful collections of students’ work and self-assessments/reflections. I have decided that for the Portfolio Project in Phase 1, my students will complete the following tasks for the following reasons:
- Daily Reflections: Explain how the collection of Daily Reflections embodies their learning. This task is important because it provides the opportunity for students to look back on their learning as they understood it in the moment, reflect on its validity, and evaluate their actual learning.
- Three strands: Choose one piece of work from a given list for each strand. Explain how/why each artifact demonstrates their competency in each strand. This task is important for two reasons. First, it provides students with the opportunity to demonstrate their understanding of each strand. Second, students are able to interpret, defend and ultimately prove their learning.
- Overall Reflection of Learning: Reflect on the learning experience as a whole in regard to mathematical understanding. This task is important because it provides the opportunity for students to become aware of what they have actually learned.
Interpreting the learning done within Investigation 1 and Investigation 2 will deepen my students’ overall understanding of Linear Equations in terms of their conceptual understanding, their procedural fluency and their problem-solving skills. This is due to the fact that through completing the Portfolio Project, they will be constructing evidence of their understanding that is meaningful to them, while also documenting and reflection on their learning experience. Through becoming aware of and interpreting their newly cosntructed knowledge, my students will deepen their overall mathematical understanding.
The Portfolio Project Overview shows the assignment as it will be delivered to students in its entirety.
Assessment Plan
Phase 0/Pre-Phase 1
The first two weeks after Spring Break will be considered Phase 0 or Pre-Phase 1. Because the changes I plan to make in my classroom (Mathematical content, Daily Reflections, and Portfolios) differ so greatly with respect to the established norms, I want to ensure my students have time to get used to them before Phase 1 takes off. This time will be dedicated to students developing their understanding of the three strands and reflecting on their work through.
Making sense of the three strands
From the first needs assessment, it became clear that the majority of my students do not understand the three strands well enough to explain them, which is necessary for them to justify their competency in each strand. If someone does not understand the idea of procedural fluency in mathematics, it will be difficult, maybe even impossible, for them to explain how they have developed their procedural fluency. I plan to introduce the three strands through a simple example. Pieces of the Math Puzzle shows the introductory activity.
While learning how to write Linear Equations in different forms, which will be the current topic of study, my students will simultaneously develop their understanding of the three strands. They will do this by recording their learning with respect to each strand. For example, after interacting with a problem that has procedural and conceptual characteristics, my students will explain the methods they used to solve the problem (procedural fluency) and why/how they were able to solve the problem in that way (conceptual understanding). This practice will help my students realize that not just the answer, but also their thinking is important in mathematics. It will also expose my students to interacting with math via the three strands, which will make them more confident in doing so during Phase 1.
Student Reflection
At the end of Phase 0/Pre-Phase 1, once my students have a foundational understanding of the three strands, they will compile a practice mini portfolio. They will choose one artifact from their work on the current topic and reflect on that work in terms of the three strands and their learning experience. The task students will respond to includes the following questions:
This learning activity is intended to expose my students to the experience of constructing evidence of and reflecting on their learning. It is for those reasons that I chose to include the questions noted above. This practice portfolio resembles the Daily Reflections explained above. Question #1 allows students to formulate and recount their methods of interacting with the problem. Question #2 allows students to demonstrate their understanding of the learned mathematics. Questions #3 and #4 allow students to become aware of their learning.
Making sense of the three strands
From the first needs assessment, it became clear that the majority of my students do not understand the three strands well enough to explain them, which is necessary for them to justify their competency in each strand. If someone does not understand the idea of procedural fluency in mathematics, it will be difficult, maybe even impossible, for them to explain how they have developed their procedural fluency. I plan to introduce the three strands through a simple example. Pieces of the Math Puzzle shows the introductory activity.
While learning how to write Linear Equations in different forms, which will be the current topic of study, my students will simultaneously develop their understanding of the three strands. They will do this by recording their learning with respect to each strand. For example, after interacting with a problem that has procedural and conceptual characteristics, my students will explain the methods they used to solve the problem (procedural fluency) and why/how they were able to solve the problem in that way (conceptual understanding). This practice will help my students realize that not just the answer, but also their thinking is important in mathematics. It will also expose my students to interacting with math via the three strands, which will make them more confident in doing so during Phase 1.
Student Reflection
At the end of Phase 0/Pre-Phase 1, once my students have a foundational understanding of the three strands, they will compile a practice mini portfolio. They will choose one artifact from their work on the current topic and reflect on that work in terms of the three strands and their learning experience. The task students will respond to includes the following questions:
- Explain what the problems involved. What you were asked to do and how did you do it?
- Explain the mathematics behind what you did.
- Explain any difficulties you may have had.
- What did you learn?
This learning activity is intended to expose my students to the experience of constructing evidence of and reflecting on their learning. It is for those reasons that I chose to include the questions noted above. This practice portfolio resembles the Daily Reflections explained above. Question #1 allows students to formulate and recount their methods of interacting with the problem. Question #2 allows students to demonstrate their understanding of the learned mathematics. Questions #3 and #4 allow students to become aware of their learning.
Assessment during Phase 1
After the practice mini portfolio has been completed, Phase 1 will begin. After we have finished Investigation 2 students will compile their portfolio. During Phase 1 of my research I will rely on several sources of data to explain the effects portfolio assessment has on students’ overall mathematical understanding, dispositions toward mathematics, and perceptions of what it means to be good at math. I will not rely on any one data source for each area, but rather triangulate all the collected data in the hopes of answering my research questions. The table below shows how I plan to collect data during Phase 1.
Overall mathematical understanding
Through my research I am hoping to learn whether or not portfolios as a summative assessment tool more completely assess students’ overall understanding. Recall that this was in response to an assessment tool (traditional tests) I felt did not effectively measure my students’ learning. I must remain mindful of this as I move forward with Phase 1. Rather than relying solely on Portfolios to assess my students’ mathematical understanding, I must gather data from different sources, and analyze all the data as a whole. To assess my students’ overall mathematical understanding during Phase 1, I will rely on the portfolios, conferences with select students, and my teacher journal/observation notes. I believe that together the data I gather from all three sources will not only shed light on what my students have learned, but also on what they know they have learned and their experience in learning it.
Data source #1 Portfolios
The portfolios my students construct at the end of Phase 1will be used to assess my students’ overall understanding of Linear Equations and Linear Inequalities. Students will be evaluated using the rubric shown below. The score they earn from this rubric will be their summative score for the unit.
I adapted the rubric below from a Self Reflection Rubric I found here. This rubric is appropriate to use because it connects reflection and content learning. The original rubric measures Clarity, Relevance, Analysis, and Self-Criticism. For my purposes, only Relevance and Analysis will be measured. I decided to narrow the focus of the rubric I will use because my students thoughtfully reflecting on and analyzing their learning will produce evidence of their learning. Although clarity in writing and self-criticism are important criteria in self-reflection, I feel as though they do not reinforce the goals of my research. In other words, during Phase 1, I am more interested in my students’ abilities to thoughtfully and relevantly reflect on and analyze their learning, than I am in the clarity of their writing or their ability to critique “their own biases, stereotypes, preconceptions, and/or assumptions” (Self Reflection Rubric).
Note that in the rubric I will use to assess the portfolios, I changed the criteria “Relevance” to “Relevance and Thoughtfulness.” Also depending on the Portfolio Task, “learning unit goals” may be replaced with “conceptual understanding,” “procedural fluency,” and/or “problem-solving skills.” These adaptations will allow me to assess my students’ proficiency in each strand as well as the relevance, thoughtfulness and depth of their reflections.
Through my research I am hoping to learn whether or not portfolios as a summative assessment tool more completely assess students’ overall understanding. Recall that this was in response to an assessment tool (traditional tests) I felt did not effectively measure my students’ learning. I must remain mindful of this as I move forward with Phase 1. Rather than relying solely on Portfolios to assess my students’ mathematical understanding, I must gather data from different sources, and analyze all the data as a whole. To assess my students’ overall mathematical understanding during Phase 1, I will rely on the portfolios, conferences with select students, and my teacher journal/observation notes. I believe that together the data I gather from all three sources will not only shed light on what my students have learned, but also on what they know they have learned and their experience in learning it.
Data source #1 Portfolios
The portfolios my students construct at the end of Phase 1will be used to assess my students’ overall understanding of Linear Equations and Linear Inequalities. Students will be evaluated using the rubric shown below. The score they earn from this rubric will be their summative score for the unit.
I adapted the rubric below from a Self Reflection Rubric I found here. This rubric is appropriate to use because it connects reflection and content learning. The original rubric measures Clarity, Relevance, Analysis, and Self-Criticism. For my purposes, only Relevance and Analysis will be measured. I decided to narrow the focus of the rubric I will use because my students thoughtfully reflecting on and analyzing their learning will produce evidence of their learning. Although clarity in writing and self-criticism are important criteria in self-reflection, I feel as though they do not reinforce the goals of my research. In other words, during Phase 1, I am more interested in my students’ abilities to thoughtfully and relevantly reflect on and analyze their learning, than I am in the clarity of their writing or their ability to critique “their own biases, stereotypes, preconceptions, and/or assumptions” (Self Reflection Rubric).
Note that in the rubric I will use to assess the portfolios, I changed the criteria “Relevance” to “Relevance and Thoughtfulness.” Also depending on the Portfolio Task, “learning unit goals” may be replaced with “conceptual understanding,” “procedural fluency,” and/or “problem-solving skills.” These adaptations will allow me to assess my students’ proficiency in each strand as well as the relevance, thoughtfulness and depth of their reflections.
Data Source #2 Student Work
During Phase 1 students will take part in completing many learning activities. These include in-class activities, homework assignments, math journals, and quizzes. All of these will be used a formative assessments rather than summative assessments. I will track my students’ develop understanding of the content through these pieces of Student Work. I will analyze the thinking students demonstrate in this work to determine their mathematical understanding in terms of the three strands.
Data Source #3 Daily Reflections
As I have explained above, each day my students will record and reflect on their learning. This activity is intended to support students to become aware of their learning and their learning experience. These records can also be used as formative checks for understanding. At the end of each week I will collect the Daily Reflections and analyze them in order to gain insight into my students’ developing mathematical understanding.
Dispositions toward math
As was the case with assessing my students’ overall mathematical understanidng, I do not want to rely on one source of data to interpret the changes in my students’ dispositions toward math during Phase 1. Thus, I will use three different sources of data. The collection of the data I gather will allow me to understand the impact metacognition has on students’ dispositions toward math.
The three sources of data I will use are Teacher Journal/Observation notes, Student Conferences, and Post-Portfolio Feedback Form. The Teacher Journal/Observation Notes will be conducted in the way described above. However, different happenings will be noted.
In my Teacher Journal/Observation Notes I will keep track of the following:
Data Source #4 Student Conferences
For Student Conferences, I will meet individually or with a small group of students to gain insight into their experience. These conferences will take place during and at the end of Phase 1. These informal conversations will give me more detailed insight into the effects the interventions have on my students’ dispositions toward math and their perception of what it means to be good at math. I will consider any interaction with a student in which I seek them out to ask a specific question a student conference. To gather data about students’ dispositions toward math from Student Conferences I will inquire about the following :
Data Source #5 Teacher Journal/Observation Notes
In addition to the notes I take during the Student Conferences, I will take notes while I observe students working on math and as I reflect on each day in my teacher journal. These notes will be used to gather data about my students’ dispositions toward math, and perceptions of what it means to be good at math. To gain insight into my students’ dispositions toward math, I plan to keep track of the following:
Data Source #6 Post-Portfolio Feedback Form
This form will be given as a Google Form. It is very similar to the Feedback Form given as the initial needs assessment. As was the case with initial Feedback Form, students will be asked about their dispositions toward math, their perceptions of what it means to be good at math, and their understanding of math in terms of conceptual understanding, procedural fluency, and problem-solving. One difference is that the post Feedback Form will ask directly about the strands of mathematical proficiency in connection to Linear Equations. The other additions to the Post-Portfolio Feedback Form specific to students’ dispositions toward math include the following questions:
The three sources of data I will use to gauge the changes of my students’ perceptions of what it means to be good at math during Phase 1 will be Student Conferences, Teacher Journal/Observation Notes and Post-Portfolio Feedback Form. All three will be implemented in the ways explained above. However, specific qualities will be focused on.
During the Student Conferences I will inquire about the following items:
The questions the Post-Portfolio Feedback form that have to do with my students’ perceptions of what it means to be good at math are:
The data I collect from each of my data sources with respect to each area of interest will allow me to make sense of the ways in which my students as math learners are affected by the interventions in Phase 1.
Read on to learn about the implementation and findings of Phase 1!
During Phase 1 students will take part in completing many learning activities. These include in-class activities, homework assignments, math journals, and quizzes. All of these will be used a formative assessments rather than summative assessments. I will track my students’ develop understanding of the content through these pieces of Student Work. I will analyze the thinking students demonstrate in this work to determine their mathematical understanding in terms of the three strands.
Data Source #3 Daily Reflections
As I have explained above, each day my students will record and reflect on their learning. This activity is intended to support students to become aware of their learning and their learning experience. These records can also be used as formative checks for understanding. At the end of each week I will collect the Daily Reflections and analyze them in order to gain insight into my students’ developing mathematical understanding.
Dispositions toward math
As was the case with assessing my students’ overall mathematical understanidng, I do not want to rely on one source of data to interpret the changes in my students’ dispositions toward math during Phase 1. Thus, I will use three different sources of data. The collection of the data I gather will allow me to understand the impact metacognition has on students’ dispositions toward math.
The three sources of data I will use are Teacher Journal/Observation notes, Student Conferences, and Post-Portfolio Feedback Form. The Teacher Journal/Observation Notes will be conducted in the way described above. However, different happenings will be noted.
In my Teacher Journal/Observation Notes I will keep track of the following:
- student engagement (in terms of on-task behavior and participation)
- individual attitudes toward and during learning activities
Data Source #4 Student Conferences
For Student Conferences, I will meet individually or with a small group of students to gain insight into their experience. These conferences will take place during and at the end of Phase 1. These informal conversations will give me more detailed insight into the effects the interventions have on my students’ dispositions toward math and their perception of what it means to be good at math. I will consider any interaction with a student in which I seek them out to ask a specific question a student conference. To gather data about students’ dispositions toward math from Student Conferences I will inquire about the following :
- what students enjoy/find interesting about math
- how reflecting on learning has made math more or less enjoyable
- how students’ feelings toward math have changed during Phase 1
- how students feel about the changes made during Phase 1
- which changes in Phase 1 worked well for them
- how the changes in Phase 1 helped students become better at math
Data Source #5 Teacher Journal/Observation Notes
In addition to the notes I take during the Student Conferences, I will take notes while I observe students working on math and as I reflect on each day in my teacher journal. These notes will be used to gather data about my students’ dispositions toward math, and perceptions of what it means to be good at math. To gain insight into my students’ dispositions toward math, I plan to keep track of the following:
- student engagement (in terms of on-task behavior and participation)
- individual attitudes toward and during learning activities
Data Source #6 Post-Portfolio Feedback Form
This form will be given as a Google Form. It is very similar to the Feedback Form given as the initial needs assessment. As was the case with initial Feedback Form, students will be asked about their dispositions toward math, their perceptions of what it means to be good at math, and their understanding of math in terms of conceptual understanding, procedural fluency, and problem-solving. One difference is that the post Feedback Form will ask directly about the strands of mathematical proficiency in connection to Linear Equations. The other additions to the Post-Portfolio Feedback Form specific to students’ dispositions toward math include the following questions:
- The last few weeks of math have been different that the rest of the year. What changes worked well for you? Why? What changes did not work well for you? Why?
- What is the best way for you to learn math?
The three sources of data I will use to gauge the changes of my students’ perceptions of what it means to be good at math during Phase 1 will be Student Conferences, Teacher Journal/Observation Notes and Post-Portfolio Feedback Form. All three will be implemented in the ways explained above. However, specific qualities will be focused on.
During the Student Conferences I will inquire about the following items:
- the student’s previous perception of what it means to be good at math (taken from the initial needs assessment
- the student’s current perception of what it means to be good at math
- the experiences that influenced their change in perception.
The questions the Post-Portfolio Feedback form that have to do with my students’ perceptions of what it means to be good at math are:
- What does it mean to be good at math?
- How are you good at math?
The data I collect from each of my data sources with respect to each area of interest will allow me to make sense of the ways in which my students as math learners are affected by the interventions in Phase 1.
Read on to learn about the implementation and findings of Phase 1!