Conclusion
Implications
Through this research I sought to learn the effects of using portfolios as a summative assessment in a math class. Specifically I was interested in the following questions:
Implication #1:The impact of summatively using portfolio assessments that emphasize conceptual understanding, procedural fluency, and problem-solving on students’ overall mathematical understanding.
As I reported in Phase 2 Findings, I was unable to assess 43% of my students’ mathematical understanding from Portfolio 2. This was due to the fact that the responses these students wrote did not construct evidence of their understanding. Rather than being specific about the mathematics they understood, my students vaguely referenced their work. The lack of observable mathematical thinking made it so that I could not determine whether my students possessed or did not possess the understanding. I believe this was due to an oversight on my part. Although I provided my students with the opportunity to construct evidence of their understanding, I did not adequately support them to do so. My students did not have the skills necessary to express and reflect on their learning because it was such a new task. I am inclined to believe that my students’ would have been more successful if we had more time to spend developing these skills.
I am unable to speak to the impact using portfolios as a summative assessment has on students’ mathematical understanding. I am not ready to rule out or rule in favor of them. I believe that more exploration needs to be done. Teachers cannot simply implement Portfolio assessments as I did. If they wish to do so they must also support their students to become aware of, be able to express, and analyze their learning. I do not recall reading about this in my literature review. Although several sources substantiated the use of portfolio assessments, I did not read about effectively preparing students to be assessed by portfolios.
Implication #2 The impact portfolio assessment that emphasizes metacognition has on students’ dispositions toward mathematics.
The Findings from Phase 1 and Phase 2 exhibited my students developing more positive dispositions toward math. I believe this is due to the fact that through the Daily Reflections and the Portfolios, my students were becoming aware of their learning. These activities allowed them to tap into their learning and witness themselves grow intellectually. This reinforces Powell’s (2013) argument that portfolio assessments that emphasize metacognition allow students to better understand their learning in a meaningful way. My findings propose that all teachers should incorporate metacognitive activities into their classroom routines. They do not have to be Daily Reflections or Portfolio assessments, but the opportunity to become aware of their learning will benefit all students.
Implication #3 The impact portfolio assessment has on students’ perception of what it means to be good at math.
My Findings from Phase 1 displayed a shift in what my students think it means to be good at math. Before this research began, 59% of my students believed that being good at math is determined by passing a math test. After Phase 1, in which the summative assessment was a portfolio, only one student held this opinion. 35% of my students shared the belief that being good at math means being able to solve problems. The other 60% had differing ideas about being good at math. These included being able to understand the whole process and being able to teach someone else. These changes in perceptions of what it means to be good at math showed me that portfolio assessments positively impacted my students. This implies that if teachers wish to support students to expand their perceptions of mathematical proficiency, they should consider incorporating portfolio assessments.
- What impact does emphasizing conceptual understanding, procedural fluency, problem-solving, and mathematical reasoning through portfolio assessment have on students’ overall mathematical understanding?
- What impact does portfolio assessment that emphasizes metacognition have on students’ dispositions toward mathematics?
- What impact does this portfolio assessment have on students’ perception of what it means to be good at math?
Implication #1:The impact of summatively using portfolio assessments that emphasize conceptual understanding, procedural fluency, and problem-solving on students’ overall mathematical understanding.
As I reported in Phase 2 Findings, I was unable to assess 43% of my students’ mathematical understanding from Portfolio 2. This was due to the fact that the responses these students wrote did not construct evidence of their understanding. Rather than being specific about the mathematics they understood, my students vaguely referenced their work. The lack of observable mathematical thinking made it so that I could not determine whether my students possessed or did not possess the understanding. I believe this was due to an oversight on my part. Although I provided my students with the opportunity to construct evidence of their understanding, I did not adequately support them to do so. My students did not have the skills necessary to express and reflect on their learning because it was such a new task. I am inclined to believe that my students’ would have been more successful if we had more time to spend developing these skills.
I am unable to speak to the impact using portfolios as a summative assessment has on students’ mathematical understanding. I am not ready to rule out or rule in favor of them. I believe that more exploration needs to be done. Teachers cannot simply implement Portfolio assessments as I did. If they wish to do so they must also support their students to become aware of, be able to express, and analyze their learning. I do not recall reading about this in my literature review. Although several sources substantiated the use of portfolio assessments, I did not read about effectively preparing students to be assessed by portfolios.
Implication #2 The impact portfolio assessment that emphasizes metacognition has on students’ dispositions toward mathematics.
The Findings from Phase 1 and Phase 2 exhibited my students developing more positive dispositions toward math. I believe this is due to the fact that through the Daily Reflections and the Portfolios, my students were becoming aware of their learning. These activities allowed them to tap into their learning and witness themselves grow intellectually. This reinforces Powell’s (2013) argument that portfolio assessments that emphasize metacognition allow students to better understand their learning in a meaningful way. My findings propose that all teachers should incorporate metacognitive activities into their classroom routines. They do not have to be Daily Reflections or Portfolio assessments, but the opportunity to become aware of their learning will benefit all students.
Implication #3 The impact portfolio assessment has on students’ perception of what it means to be good at math.
My Findings from Phase 1 displayed a shift in what my students think it means to be good at math. Before this research began, 59% of my students believed that being good at math is determined by passing a math test. After Phase 1, in which the summative assessment was a portfolio, only one student held this opinion. 35% of my students shared the belief that being good at math means being able to solve problems. The other 60% had differing ideas about being good at math. These included being able to understand the whole process and being able to teach someone else. These changes in perceptions of what it means to be good at math showed me that portfolio assessments positively impacted my students. This implies that if teachers wish to support students to expand their perceptions of mathematical proficiency, they should consider incorporating portfolio assessments.
Limitations
Implementing this research project had several limitations. Some of the limitations were external (e.g., time, end of the year scheduling), while others were created by me. In retrospect, I feel as though I tried to change too many factors in my research. First, I wanted to address the procedural focus issue. To do this, I replaced the previous curriculum (which focused on procedural fluency) with one that emphasized conceptual understanding, procedural fluency, and problem-solving skills. This change alone is far greater than it sounds. With this change, I was working against eight years of traditional math focus; my students had been conditioned to understand that learning math meant completing a procedure or computation. The new curriculum I implemented challenged their understanding of what math is. Although it was necessary, it was a heavy change to make. I made some attempts at supporting my students to interact with math with regard to the three strands in Phase 2. However, as I explained in the Lingering Questions of Phase 2, I still do not know how to effectively do so.
Second, I wanted to address the assessment issue through my research. To do this I replaced the traditional pencil and paper test with a portfolio. Students compiled portfolios from pieces of their work as well as reflections/analyses of how those artifacts exhibited their learning. Expecting students to reflect on and analyze their learning when they have never done so before is difficult. They require the appropriate scaffolds and support in able to do so successfully. I did not learn this until after Phase 1. However, I was able to provide a few supports during Portfolio 2 to support my students more effectively.
Implementing these two changes simultaneously is quite difficult. However, doing so at the end of the school year, specifically at the end of 8th grade was arduous. When my students returned from Spring Break, which was two weeks before Phase 0/Pre-Phase 1 began, they were ready for the end of the year. Additionally, they were looking forward to graduating from middle school and moving to high school. As is the case with many students at that time of the year, it was difficult to get my students to focus or be motivated to engage with the content. To overcome this, I tried to connect each day’s objectives to important skills necessary for high school.
The combination of the internal and external challenges we faced made it difficult for me to pinpoint the specific effects portfolio assessments have on students’ mathematical understanding, dispositions toward math, and perceptions of what it means to be good at math. As I have explained throughout Phase 1 and Phase 2, I was able to gain insights into the effects, but I am unable to definitively state the impact my students experienced.
Second, I wanted to address the assessment issue through my research. To do this I replaced the traditional pencil and paper test with a portfolio. Students compiled portfolios from pieces of their work as well as reflections/analyses of how those artifacts exhibited their learning. Expecting students to reflect on and analyze their learning when they have never done so before is difficult. They require the appropriate scaffolds and support in able to do so successfully. I did not learn this until after Phase 1. However, I was able to provide a few supports during Portfolio 2 to support my students more effectively.
Implementing these two changes simultaneously is quite difficult. However, doing so at the end of the school year, specifically at the end of 8th grade was arduous. When my students returned from Spring Break, which was two weeks before Phase 0/Pre-Phase 1 began, they were ready for the end of the year. Additionally, they were looking forward to graduating from middle school and moving to high school. As is the case with many students at that time of the year, it was difficult to get my students to focus or be motivated to engage with the content. To overcome this, I tried to connect each day’s objectives to important skills necessary for high school.
The combination of the internal and external challenges we faced made it difficult for me to pinpoint the specific effects portfolio assessments have on students’ mathematical understanding, dispositions toward math, and perceptions of what it means to be good at math. As I have explained throughout Phase 1 and Phase 2, I was able to gain insights into the effects, but I am unable to definitively state the impact my students experienced.
Reflection
From my experience implementing this research project there are several implications I have realized that impact me as a math teacher. These personal implications have to do with students’ recording and reflecting on their learning, authentically responding to students’ needs, and positioning students as the intellectual authority.
Personal Implication #1 Students recording and reflecting on their learning in the moment solidifies it in their minds.
I learned this through the positive effects my students’ experienced as a result of completing the Daily Reflections. From several students I was informed that recording and reflecting on their learning each day made them review the content an additional time. Also, explaining what they did, what they learned, and what they struggled with during the learning activity helped the content stick. Moving forward in my teaching practice, I will keep this in mind. I like the idea of making Daily Reflections a norm in my classroom. I believe that in doing so, I will support my students to recognize and take ownership of their learning. Needless to say, I think all math students would benefit from a similar practice. Thus, math teachers and teachers of other content areas should implement regular reflection times into their teaching practice.
Personal Implication #2 Positioning students as the intellectual authority positively affects their learning experience.
During Portfolio 2, I provided my students with the opportunity to determine what makes a strong portfolio response. This activity supported my students to take ownership over their learning and the evaluation criteria. Additionally, it equipped them with the confidence and skills to complete their learning activities. Moving forward with my practice I will remember this experience and position my students as the intellectual authority so that they can benefit from its positive effects.
Personal Implication #3 I am not an expert at teaching math effectively.
I also learned that although I have a degree in Mathematics, and I have completed one year of teaching math, I need more practice supporting students to interact with math in ways that help them learn. In Phase 1 of my research I simply introduced content I thought would help my students develop their mathematical proficiency. I quickly learned that I needed to do more. In Phase 2 I tried to support students to create their understanding of the new content through the “Focusing” method. I learned that although this was a step in the right direction, it was not enough to support my students in the ways they needed. As a result, I need to determine different effective ways to support my students to truly learn math.
Personal Implication #4 In order to support students to learn, I must authentically respond to the students.
Going into this research project, I was interested in implementing a curriculum that emphasized the three strands and an alternative summative assessment. I recognized the downfalls of the previous curriculum and assessment and I wanted to improve them. After a bit of reading about what the literature says in regard to these areas, I set out with a plan without considering the needs of my students. As their teacher I was able to determine the areas in which they required extra support, but I did not consult them as to what kind of supports would benefit them the most. In other words, I went in to my classroom with the plan that we would interact with the new curriculum and then my students would compile a portfolio. I did not ask them how they wanted to demonstrate their mathematical proficiency. As a result, Phase 1 was a confrontational time. I believe that if I had gone to my students with my notices and together we had created a plan for assessments, they would have experienced far greater benefits.
The most important thing I learned about myself through this research is that what my students think, want and need is very important to me. During Phase 1 my students and I disagreed. I thought the interventions I planned to implement would benefit them; they did not agree. What resulted was an incredible amount of tension. On my end, I doubted the my efforts and intentions. I was not confident in the changes I enacted. Looking back, it has become apparent to me that I doubted myself because I was going against everything my students thought, wanted, and possibly needed. The way I felt during Phase 1 tells me that what my students think, want and need must influence the decisions I make for them in the classroom. If I want to have strong relationships with my students built on trust and respect, I have to take into account what they think, want and need.
As I have explained in this section as well as throughout my research I have learned a lot about teaching and learning math. More importantly, I have learned quite a bit about who I am as a teacher. Just as I mentioned in the Implication section, it is important for me as a teacher to ensure that the supports I make available to my students authentically respond to my students’ needs. Sure the research says that portfolios are a good way to assess students’ learning, but that does not necessarily mean that they will be the best way for my students to demonstrate their knowledge. Rather than trusting and implementing the good ideas I read in studies, I need to make sure the ideas are good for my students.
Although this research was difficult, and not always pleasant, I am glad I had the opportunity to experience it. I have learned so many things that will influence my teaching practice as well as the ways in which I interact with my future students.
Personal Implication #1 Students recording and reflecting on their learning in the moment solidifies it in their minds.
I learned this through the positive effects my students’ experienced as a result of completing the Daily Reflections. From several students I was informed that recording and reflecting on their learning each day made them review the content an additional time. Also, explaining what they did, what they learned, and what they struggled with during the learning activity helped the content stick. Moving forward in my teaching practice, I will keep this in mind. I like the idea of making Daily Reflections a norm in my classroom. I believe that in doing so, I will support my students to recognize and take ownership of their learning. Needless to say, I think all math students would benefit from a similar practice. Thus, math teachers and teachers of other content areas should implement regular reflection times into their teaching practice.
Personal Implication #2 Positioning students as the intellectual authority positively affects their learning experience.
During Portfolio 2, I provided my students with the opportunity to determine what makes a strong portfolio response. This activity supported my students to take ownership over their learning and the evaluation criteria. Additionally, it equipped them with the confidence and skills to complete their learning activities. Moving forward with my practice I will remember this experience and position my students as the intellectual authority so that they can benefit from its positive effects.
Personal Implication #3 I am not an expert at teaching math effectively.
I also learned that although I have a degree in Mathematics, and I have completed one year of teaching math, I need more practice supporting students to interact with math in ways that help them learn. In Phase 1 of my research I simply introduced content I thought would help my students develop their mathematical proficiency. I quickly learned that I needed to do more. In Phase 2 I tried to support students to create their understanding of the new content through the “Focusing” method. I learned that although this was a step in the right direction, it was not enough to support my students in the ways they needed. As a result, I need to determine different effective ways to support my students to truly learn math.
Personal Implication #4 In order to support students to learn, I must authentically respond to the students.
Going into this research project, I was interested in implementing a curriculum that emphasized the three strands and an alternative summative assessment. I recognized the downfalls of the previous curriculum and assessment and I wanted to improve them. After a bit of reading about what the literature says in regard to these areas, I set out with a plan without considering the needs of my students. As their teacher I was able to determine the areas in which they required extra support, but I did not consult them as to what kind of supports would benefit them the most. In other words, I went in to my classroom with the plan that we would interact with the new curriculum and then my students would compile a portfolio. I did not ask them how they wanted to demonstrate their mathematical proficiency. As a result, Phase 1 was a confrontational time. I believe that if I had gone to my students with my notices and together we had created a plan for assessments, they would have experienced far greater benefits.
The most important thing I learned about myself through this research is that what my students think, want and need is very important to me. During Phase 1 my students and I disagreed. I thought the interventions I planned to implement would benefit them; they did not agree. What resulted was an incredible amount of tension. On my end, I doubted the my efforts and intentions. I was not confident in the changes I enacted. Looking back, it has become apparent to me that I doubted myself because I was going against everything my students thought, wanted, and possibly needed. The way I felt during Phase 1 tells me that what my students think, want and need must influence the decisions I make for them in the classroom. If I want to have strong relationships with my students built on trust and respect, I have to take into account what they think, want and need.
As I have explained in this section as well as throughout my research I have learned a lot about teaching and learning math. More importantly, I have learned quite a bit about who I am as a teacher. Just as I mentioned in the Implication section, it is important for me as a teacher to ensure that the supports I make available to my students authentically respond to my students’ needs. Sure the research says that portfolios are a good way to assess students’ learning, but that does not necessarily mean that they will be the best way for my students to demonstrate their knowledge. Rather than trusting and implementing the good ideas I read in studies, I need to make sure the ideas are good for my students.
Although this research was difficult, and not always pleasant, I am glad I had the opportunity to experience it. I have learned so many things that will influence my teaching practice as well as the ways in which I interact with my future students.