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Real-World Problems Lutz Home
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About the Author
In 8th grade I had a math teacher who didn’t teach. He wrote examples down that were already in the textbook and assigned practice. I had always enjoyed math but this year I struggled. I went to my 6th & 7th grade math teachers for help to understand the content. I was disheartened and discouraged by the end of this year.
Moving into High School I was still disheartened and discouraged with math. Then I met Mr. A! He was by far the best math teacher that I have ever had. He took a constructivist approach to teaching that would naturally lead from one topic to the next, and I understood math again! It was enlightening and he inspired me to become a math teacher myself. I am always striving to be better and improve. This drive to improve my teaching skills led me into the Innovative Learning program at Touro University.
I began my teaching career in 2008, at American Canyon Middle School where I taught 6th grade math, 7th grade math and Accelerated Algebra 1 to 8th grade students. In 2014, I moved to Vintage High School. At Vintage I have taught Prep and Honors Integrated Math 2, Prep and Honors Integrated Math 3, Pre-Calculus, and Prep Calculus. At the time of this study and moving through the Masters Innovative Learning program I was teaching four courses of Honors Integrated Math 3 and one course of Prep Calculus. However, the action research contained in my study focused on my four Honors Integrated Math 3 classes during hybrid teaching due to COVID. I love teaching math and helping students to learn.
I have two children of my own. Kayla and Abigail are twins and at the time of this study they were in 3rd grade. They bring joy and frustrations to me every day as they test their limits and explore the world. I love them with all my heart. The experience of being a mother has only added to my teaching skills. As I see them grow and learn I understand and remember more about being a kid and about my own school experiences. I had teachers at all levels that made a positive impact in my life. My children have already had wonderful positive experiences with their teachers. I hope that I am also that positive influence in the lives of my own students.
Moving into High School I was still disheartened and discouraged with math. Then I met Mr. A! He was by far the best math teacher that I have ever had. He took a constructivist approach to teaching that would naturally lead from one topic to the next, and I understood math again! It was enlightening and he inspired me to become a math teacher myself. I am always striving to be better and improve. This drive to improve my teaching skills led me into the Innovative Learning program at Touro University.
I began my teaching career in 2008, at American Canyon Middle School where I taught 6th grade math, 7th grade math and Accelerated Algebra 1 to 8th grade students. In 2014, I moved to Vintage High School. At Vintage I have taught Prep and Honors Integrated Math 2, Prep and Honors Integrated Math 3, Pre-Calculus, and Prep Calculus. At the time of this study and moving through the Masters Innovative Learning program I was teaching four courses of Honors Integrated Math 3 and one course of Prep Calculus. However, the action research contained in my study focused on my four Honors Integrated Math 3 classes during hybrid teaching due to COVID. I love teaching math and helping students to learn.
I have two children of my own. Kayla and Abigail are twins and at the time of this study they were in 3rd grade. They bring joy and frustrations to me every day as they test their limits and explore the world. I love them with all my heart. The experience of being a mother has only added to my teaching skills. As I see them grow and learn I understand and remember more about being a kid and about my own school experiences. I had teachers at all levels that made a positive impact in my life. My children have already had wonderful positive experiences with their teachers. I hope that I am also that positive influence in the lives of my own students.
Reflections on my Journey
As I began thinking about my Capstone and what my driving question would be I considered many different paths. My interests ranged from teaching strategies, active learning, pressures from high-stakes testing, timed tests, and the why of learning mathematics. All of these interests morphed into the question that drove my research: “How can I build effective summative assessments that are equitable for all students in mathematics?”
My research focused on assessment design because it is an important topic to students, especially the honors students in this study. Assessments have a large impact on student grades which is the main motivation for many honors students (as found in the study). As a mathematics teacher, each year I redesign and update the assessments that I give for each unit. However, I have never been instructed in how to design assessments. I have built assessments up from scratch with no prior training. I wanted to learn how best to design these assessments in order to be equitable for all students and help them to be successful in my class, to be prepared for the next mathematics course, and beyond the classroom to be successful on high stakes tests like the CAASPP, SAT and ACT.
In order to delve deeper into the question of how to build assessments, smaller need-to-know questions were investigated during my research study. These centered around student performance on traditional vs. real world problems on assessments, students' depth of knowledge (DOK) around mathematical content, and students' attitude toward the value of learning the mathematical content that is taught. The process of investigating these led me on an intriguing journey with my students. I am thankful to remember this year of reflections and study in more ways than just distance learning due to COVID.
My research focused on assessment design because it is an important topic to students, especially the honors students in this study. Assessments have a large impact on student grades which is the main motivation for many honors students (as found in the study). As a mathematics teacher, each year I redesign and update the assessments that I give for each unit. However, I have never been instructed in how to design assessments. I have built assessments up from scratch with no prior training. I wanted to learn how best to design these assessments in order to be equitable for all students and help them to be successful in my class, to be prepared for the next mathematics course, and beyond the classroom to be successful on high stakes tests like the CAASPP, SAT and ACT.
In order to delve deeper into the question of how to build assessments, smaller need-to-know questions were investigated during my research study. These centered around student performance on traditional vs. real world problems on assessments, students' depth of knowledge (DOK) around mathematical content, and students' attitude toward the value of learning the mathematical content that is taught. The process of investigating these led me on an intriguing journey with my students. I am thankful to remember this year of reflections and study in more ways than just distance learning due to COVID.
Lasting Learning from the Innovative Learning program
There is always a need to learn more! I have learned so much in this program about teaching, but it is important for me to continue learning and growing as an educator. This program has opened up a wide variety of learning opportunities for me. I was not aware of how interesting it could be to complete an Action Research Project. I have learned so much through this process and from my students and will continue to test new and innovative solutions. I have learned that I want to continue to incorporate real-world problems in my assessments, but on a balanced scale. Real-world problems are vital for students to understand for the high stakes tests (like the CAASPP, SAT and ACT) that exist in high school, but also in life. It is important for students to see where they may potentially use mathematics in the future and in what career fields.
Beyond the research, I have also learned so much about technology through this program. The technological skills and programs that I have learned about were invaluable during distance and hybrid teaching. However, they are also great skills to continue to use in the classroom moving forward. All of the tech programs like GoFormative, Quizizz, DeltaMath, PearDeck, Screencastify and EdPuzzle are a wonderful resource for teachers and students. I will continue to use these moving forward in my teaching. In addition, I will continue to look for new and innovative tech tools that may appear in the future. As teachers, I think that we often get stuck in our ways. However, technology is a wonderful resource that is ever-evolving. Teachers need to adapt as the technology also adapts.
Beyond the research, I have also learned so much about technology through this program. The technological skills and programs that I have learned about were invaluable during distance and hybrid teaching. However, they are also great skills to continue to use in the classroom moving forward. All of the tech programs like GoFormative, Quizizz, DeltaMath, PearDeck, Screencastify and EdPuzzle are a wonderful resource for teachers and students. I will continue to use these moving forward in my teaching. In addition, I will continue to look for new and innovative tech tools that may appear in the future. As teachers, I think that we often get stuck in our ways. However, technology is a wonderful resource that is ever-evolving. Teachers need to adapt as the technology also adapts.
My TPACK Journey
My capstone primarily focuses on assessments in mathematics. Due to COVID-19 during my research, technology has been applied in more ways than ever before including to assessments of all types. I have included technology in assessments in the past, however these were monitored in the classroom. During distance and hybrid learning, assessments were no longer monitored. This combined with the technological aspect of the assessments tempted many students to cheat through this last year since the information was literally at their fingertips as they took the assessments. Many of my students explicitly said it is easy to cheat. This also forced many teachers to design assessments with the assumption that students would use the technology available to them. This is a GREAT skill and one that will be required in the real world, as we can often look up the information that is sought in the real world. This method does truly bring content, pedagogy and technology together as the TPACK model is designed! It is amazing that we were able to function during this pandemic and thanks to technology we were able to still teach and many students thrived in this environment!
It is important that technology does not become a crutch for students. I have seen over, and over, and over again that students use a calculator as a crutch for simple mathematical operations. Just today My 9-year old daughter asked Alexa (Amazon’s Echo device), “Alexa, what is 4 plus 9?” I was shocked, she knows this answer! It is important to know operations like this, and my daughter was using Alexa as a crutch so that she did not need to think about it. However, the brain is a muscle and just like any other muscle it needs exercise in order to function well. Technology is a wonderful resource and a wealth of information. It can help to exercise our brains when used correctly. As we return to “normal”, educators need to adjust and find the balance between using technology to enhance our teaching and letting students use technology as a crutch.
I have learned so many wonderful tools this year (EdPuzzle, PearDeck, GoFormative) that I will continue to use in my teaching for many years to come. These are great resources to incorporate into our pedagogy as we teach content. I will also continue to use technological resources on assessments, but under monitorable conditions. This will allow me to better gauge where students are and how much of the content they have learned through my instruction. However, I will also return to some paper and pencil assessments. Just like finding a balance when using technology for instruction, there is also a balance when using technology for assessments.