The Journey of a Lifelong Learner
By: Christine Sherwood
During my second year of teaching 5th grade, I decided I wanted to further my education by working towards my master’s degree. My goal was to continue to improve my teaching practices. I wanted to be able to work full time while taking graduate courses. I achieved a Bachelor of Arts Degree in Elementary Education at Michigan State University. Since I had an amazing educational experience at MSU, I applied to their Master of Arts in Education online program.
Original Thoughts
When I began this online master’s program, I was concerned about its structure. I have always enjoyed interacting and getting to know my professors and being able to ask them questions and discuss my thoughts and ideas. However, I knew I would be successful since I am organized, driven, and an extremely hard worker.
I decided I wanted to focus on mathematics and technology. Math has always been a passion of mine throughout my life. While attending high school and college, I truly enjoyed tutoring and assisting my peers on the mathematical concepts being taught. Conversely, I was not as confident in the realm of technology. I knew the importance of technology in society and concluded that it would be imperative to further my education in this area.
Before beginning this master’s program, I had many goals that I wanted to achieve. I had a strong desire to become a more effective, meaningful, and inspirational educator. My goal was to strengthen my ability to teach for conceptual knowledge. Therefore, I needed to become a more effective inquiry based facilitator and create more authentic learning experiences for my students in order to instill an enthusiasm and passion for learning. I am striving to have my students become more critical thinkers, questioners, and problem-solvers. I realized the importance of learning about a variety of technologies and having a deeper understanding of them so I would be better equipped to integrate the latest technology throughout the curriculum. This would enhance my students’ learning through a more creative and enjoyable process.
Benefits of the MAED Program
Once I was accepted in the MAED program, I was excited about the flexibility of the program and how many course choices there were to choose from. It was beneficial to have the freedom to work on the assignments when it fit my schedule, since I was working full time. It also required me to get more familiar and comfortable with new technologies since I was actively participating and exploring them. By integrating these technologies into our MAED coursework, I gained a greater knowledge and understanding of how to implement these systems with my students.
Throughout all the online courses that I have taken, I was able to establish personal relationships while being connected electronically. There were many avenues available to establish relationships with my professors and peers. I participated in group and partner projects and assignments as well as class discussion postings. These relationships built trust, allowed for critical feedback, and the sharing of ideas. I was able to learn a great deal from my classmates and the feedback from my professors. My initial concerns with this program were quickly resolved and I truly enjoyed the content and process of this online program.
Each course that I was enrolled in brought me a wealth of knowledge and enlightenment. These classes taught me a variety of valuable information that I was able to apply to my daily teaching. The courses that had the greatest impact and influenced on me were TE 855: Teaching School Mathematics, TE 831: Teaching School Subject Matter with Technology, CEP 805: Learning Math with Technology, and CEP 810: Teaching for Understanding with Technology.
Conceptually Understanding Mathematics
Reflecting upon my experiences as a math student, I remember learning the steps and procedures of how to solve the problem. I never had a thorough understanding of why those procedures worked. Now as a teacher, I realize why many teachers would just teach the procedures. It is much easier and quicker for the teachers to instruct and the students to learn. However, my TE 855: Teaching School Mathematics course with Kristen Bieda taught me a great deal about teaching mathematics for conceptual understanding. From this course, I learned many strategies and methods for teaching mathematics.
Mathematical reasoning was a central focus of this course. I learned several strategies to help students be able to reason. First, students need to feel safe and comfortable to share their thoughts and ideas amongst their peers and teachers. Therefore, one must establish a safe and caring classroom environment. Secondly, the tasks or problems given to students need to be of a higher-level of demand. Also, teachers need to help their students make connections between isolated topics in order to make math reasonable. In addition, the types of questions teachers ask are very crucial. It is essential that teachers ask open ended questions and focus on the student’s thought process rather than the right and wrong answer. Students will be more willing to share if they are not afraid of saying the wrong answer. Having class discussions is a very important aspect of math reasoning. Students can learn a great deal from each other.
A particular quote that is important to me is “reasoning is one of the principal instruments for developing mathematical understanding and for constructing new mathematical knowledge” (Ball & Bass, 2003, p.30). Real life issues do not occur in an easy straight forward problem that can be solved with a set procedure. One needs to be flexible to be able to solve problems in a variety of ways and apply their knowledge to new situations. In order for this to be accomplished, students need to have good mathematical understanding and be able to reason through the problem. In addition, it is imperative for students to be able to justify their thoughts, ideas, strategies, and solutions.
The types of question teachers ask greatly influence students ability to reason and justify their solutions. Teachers need to stop asking for the right and wrong answers and focus more on open ended questions. The article “Questioning Our Patterns of Questioning” by Herbel-Eisenmann significantly helped me reflect upon the ways I question my students. When I analyzed my questioning patterns, I realized I had to make many changes to improve my questioning technique in order to help my students reach a higher level of mathematical reasoning. This article emphasizes the point that the teacher’s questions should guide “the students to make their thinking clear and articulate so that others can understand what they are saying” (Herbel-Eisenmann, p.486). My goal is to consistently use this focusing-interaction pattern in my classroom. When I made changes to my questioning patterns, I noticed some changes in my students’ reasoning abilities. I am no longer satisfied with just the correct answer. I continue questioning my students to push them towards reasoning and justification.
I also learned about the importance of the types of tasks or problems we give the students. Giving a student a worksheet of all practice problems does not help the student’s mathematical reasoning. The tasks should be real world problems. In addition, students should be exposed to a variety of problems in different contexts. This will expose them to a variety of different wordings and symbols which will aid in the student’s flexibility to solve problems. I have learned how important it is to revise basic problems in order to create higher-level tasks. Lastly, these tasks should be differentiated to meet the needs of all students so math can be reasonable at each individual’s level.
During this class, I also conducted a research project based on the following question: “How do teachers help students learn to convert between mixed numbers and improper fractions with reason rather than only utilizing procedures?” I did much research and learned a great deal from my literature reviews. I learned how important it is for students to be able to build with manipulatives, draw, label, and verbally explain what they are doing. They also need to be exposed to a wide range of visual representations. In addition, I read an article called “Reflecting on Learning Fractions without Understanding” by Philipp and Vincent that explained how important it was for students to learn conceptual understanding prior to procedural instruction. As a teacher, I often try to have the students discover the concepts and conceptually understand them prior to the class determining the correct procedures.
From observing the students during my classroom investigation, the students were able to gain a conceptual understanding of how to convert between mixed numbers and improper fractions. By having my students use manipulatives to build, draw, and label their fractions, they gained a greater understanding of why the procedures of converting between mixed numbers and improper fractions worked. Through their dialogue, I observed how their mathematical reasoning was improving. By having these students work through these problems together, they learned how to express themselves logically so their peers could follow and understand their thought process. As a result, these students were able to learn a great deal from each other.
Based on this course and my research, I will attempt to incorporate the concepts of teaching conceptually and with reason into my lessons whenever possible. I will expose my students to many manipulatives and representations to assist my students in a deeper understanding of the concepts being taught. This should improve my students’ conceptual understanding and allow them to remember and maintain these concepts. When students learn math conceptually, they will be able to do the following: retain it longer, apply it to new situations, be more flexible in solving mathematical tasks by using a variety of strategies, and be able to persevere with difficult tasks.
TPACK Theory and a Variety of Technologies
The first technology course that I took in this program was TE 831: Teaching School Subject Matter with Technology with Erik Jon Byker. This class exposed me to a variety of technologies in which we learned the importance of integrating them appropriately. There was a great deal of focus on a theory known as TPACK which stands for Technological Pedagogical and Content Knowledge Theory. TPACK has three essential areas of knowledge that include content, pedagogy, and technology which all must be understood and integrated to be successful. Teachers must know the content they are teaching, understand the technology they are utilizing, and be able to present the information to the students in an effective way.
We reviewed the NETS Standards for Teachers, digital literacy and citizenship, 21st Century Skills, digital storytelling, and Internet-based technologies that would be beneficial to integrate and use in the classroom. Some of these technologies include digital storytelling, voicethread, Glogs, Wordle, and class websites, wikis, and blogs. We analyzed the affordances and constraints of each technology in relation to using it within our classroom. We learned about each of these technologies by creating our own project that would benefit our students. This course was very valuable and positively impacted my students’ performance.
During this course, I was teaching a science unit on weather. In the past, my students had struggled with the concepts of clouds. It was hard for them to visualize the different types of clouds and learn the weather they each bring. Therefore, I created a digital story about the different types of clouds. The digital story that I created for this course was very helpful for my students. It provided a visual that was engaging and taught my students a great deal about the content and impact of the different clouds.
In addition, I created a lesson that incorporated technology. It was a reading lesson that focused on improving reading fluency using reader’s theater and flip cameras. One of my student’s reflections of the lesson stated, “I think that I improved in everything but volume. I improved because I put a lot of effort into it and practiced more. I watched myself in the flip camera and my only problem was volume. I need to work on speaking louder and not just look at the paper. If I work a little bit harder I will get there. This experience helped me learn to show more character in things like this and I can read a little bit faster.” By using the flip cameras, my students were able to evaluate themselves and reflect upon their learning. By integrating technology, I enhanced the learning experience for my students and improved my teaching practices.
I also created a Glog that included many useful math websites that were beneficial to my students. Once I became familiar with Glogs and learned how to create one, I taught my students about Glogs. Glogs are an interactive poster that can be shared with others. One can include text, images, links, videos, special effects, and well as a creative and personal design. My students were so excited to create a Glog. I required all my students to create a Glog to present the key information they learned from their research paper. Then throughout the rest of the year, a Glog was always an option for presenting the information they learned. Several of my students would choose this option when available. They were able to present the information they learned in a fun, creative, and unique way.
Integrating Mathematics with Technology
TE 831: Teaching School Subject Matter with Technology emphasized the importance of integrating technology with subject matter. However, I felt that I struggled to integrate technology with mathematics. CEP 805: Learning Math with Technology with Ralph Putnam helped me greatly to integrate the two. Each week, we would study a different strand of the Principles and Standards for School Mathematics. In addition, we explored and analyzed different technologies that would help enhance the particular math strand. Again, this relates to TPACK in truly understanding the content you are teaching and the technology you are utilizing to enhance the learning of the students.
I created a math online resource library that will provide resources to my students and colleagues. My focus was on Number and Operations and Geometry. I chose these two strands since they are both a significant part of the 5th grade curriculum. This online resource library will enhance my students’ learning by providing them with a visual as well as practicing the concepts in a fun and creative way. For each technology, I analyzed the standard being addressed, the content being learned, the type of understanding, the role the technology plays, the instructional function, and the kinds of representations utilized. I now feel more confident analyzing the usefulness and application of specific technologies.
There was also a great deal of emphasis on having a balance between relational understanding and instrumental understanding. The PSSM article made a very important point. “One of the most robust findings of research is that conceptual understanding is an important component of proficiency, along with factual knowledge and procedural facility (Bransford, Brown, and Cocking 1999)” (PSSM, p.20). Therefore, teachers must incorporate mathematical understanding and problem solving skills in their daily curriculum.
Technology can greatly assist a student’s conceptual and procedural knowledge. This can provide a student with significant interactive and visual representations of the subjects being taught. Today, children have become accustom to immediate gratification. Therefore, the instant feedback that technology provides is extremely beneficial in meeting my students’ needs and desires. This immediate feedback will also enhance their learning since they will know if they are proceeding correctly. Many websites provide students with symbolic, graphic, visual, real-world objects, and dynamic representations. All these technological benefits greatly enhance the students’ learning capabilities.
Social Networking
Another essential class that I took was CEP 810: Teaching for Understanding with Technology with Susan Way. This class focused on Web 2.0 technologies that allow for self design, sharing information, and collaboration with others. Some of these technologies include RSS feeds, blogs, Google Docs, Google Calendar, social networking, social bookmarking, Twitter, and wikis. These web-based resources can be used to enhance the learning of students and teachers.
Social networking with colleagues, classmates, and other people in the field of education is essential. These networks can allow one to gain new ideas and insights, discuss a variety of topics, and share a wealth of information. There are many resources in my district in which people share information and resources. They provide blackboard courses, wiki sites, and a web site called C-MAPP where all essential resources for the county are located. The knowledge you learn from others can be very valuable. I not only network online but within my building. We meet with our Professional Learning Teams at least once a week to collaborate and analyze data to improve our teaching practices.
A quote from “Creating 21st Century-Ready Teachers” greatly impacted me. It states, ‘We cannot change how our students learn until our teachers are equipped to teach in new ways. It is unreasonable to expect that our students will ever gain the skills and knowledge to succeed in the 21st century if they are taught primarily by educators trained using a model developed in the 19th century’ (Creating 21st Century-Ready Teachers, School Reform in the New Millennium: Preparing All Children for 21st Century Success , p. 10). Teachers need to be lifelong learners themselves so they can prepare students with the most up to date skills that will prepare them for their future. One of my goals is to continue to improve and develop my 21st Century Skills in order to better meet the needs of my students. This class provided me with a variety of resources in which I can continue to learn from others. I would also like to expose my students to ways in which they can collaborate with their classmates. I am planning to create assignments in which they will have to work together and discuss ideas on either wiki or Google Docs. I plan to expose my students to as many technology resources as possible in the beginning of the year so they are able to utilize them throughout the year. Each year our district has teachers create a Personal Growth Plan. I will make sure to include a goal that incorporates technology. I now have a new passion and excitement for technology’s usefulness and enrichment.
Final Reflection
Overall, the Master of Arts in Education program was an amazing and profound experience. As I grew as an educator, these courses significantly impacted my teaching methods, strategies, and practices. The concepts that had the greatest influence on me were teaching for conceptual understanding, implementing the TPACK Theory, incorporating 21st Century Skills, learning math with technology, and collaborating and networking with others. My students were positively impacted by my new and improved teaching methods that I gained through this online program. I am committed to being a lifelong learner in which I will always be modifying and improving my teaching practices. My goal is to motivate, inspire, facilitate, and guide my students to also be lifelong learners.
