Looking back on my journey
By Sophia Borden
Towards the end of my student teaching, I was looking for a new journey. One that would help me grow as an educator. My student teaching had gone well. The students had built a lot of conceptual understanding of fractions, ratios, similarity through the use of varied assortment of tasks and teaching strategies. The only thing I was disappointed with was my use of technology in my lessons. My school had a technology abundance: clickers, tablets, computer labs, test creation tools, document cameras, graphing calculators, and interactive projectors. The problem wasn’t access to technology, it was how it was being used. My students loved using clickers and always wanted a chance to use the tablet to write on the board from their seat, but in terms of student learning, not much was changing. The clickers promoted test taking skills to an extent, but in terms of building conceptual knowledge, the questions that were available were limiting. The tablet was just a fancy way of writing on the board from across the room and didn’t add any educational value to the lessons. The computer labs would run Microsoft Word and some specific websites, but any applications requiring Java or something else would not work, making many of the resources allowing students to manipulate tools online to learn math unavailable. As my student teaching was ending, I was constantly thinking about how I can find and use technology in my classroom, not so I can just say that I use technology regularly in my classroom, but to improve my students’ learning in mathematics. I mentioned this issue to one of my professors and he suggested that I apply for the Master of Arts in Educational Technology (MAET) program so that I can learn how to evaluate the pieces of technology that I find and use in my classroom to see which ones effectively build a better understanding of mathematics for my students. As I was already searching for a Master’s program to start after my student teaching, I thought it might be a great opportunity to improve my teaching by tackling this issue head on.
CEP 811, Adapting Innovative Technologies in Education, helped me start to achieve my goal of finding technology that I can effectively use to teach mathematics by giving me the tools to evaluate new pieces of technology. The first tool that I learned was the Technology, Pedagogy, and Content Knowledge (TPACK) framework. TPACK was a tool to help explore the intersection of the technology being used, how the technology supports the teaching strategies being used, and how those affect how students perceive the content knowledge. Using this framework, I could then predict the effects that a certain piece of technology would have on a lesson and revise the lesson if needed. To analyze the specific properties of each piece of technology, we also learned about the Universal Design for Learning (UDL) guidelines which is a tool to outline the potential features and barriers of including a certain piece of technology in a lesson. This helps to see what exactly what the piece of technology that I want to use brings to the table. Some aspects of the technology may be a benefit and help students considerably understand the concept while others may potentially create misconceptions or confusion among the students. In addition to TPACK and UDL, we also looked at other pieces when designing lesson plans with technology including how the lesson relates to real-world applications, the social aspect of the lesson and how students are communicating with each other, the motivation that the piece of technology may bring to students, and the necessary equipment and planning needed to enact such a lesson. Using this set of tools, I started to understand what pieces of technology were useful and which one were just for show.
Now that I had the tools to evaluate technology and see its usefulness or potential problems, I had to then learn how to introduce technology in my classroom to enhance student understanding. In CEP 812, Applying Educational Technology to Issues of Practice, I was pushed to apply the frameworks that I had learned about evaluating pieces of technology to attempt a solution to a challenging problem encountered in my teaching experience called a “Wicked Problem”. The problem that I chose to focus on was the difficulty that many middle school students have regarding fractions in both a conceptual and procedural sense. Fractions come in a drastically different format than whole numbers and that format makes comparing numbers with fractions and fraction operations much more difficult. As Tirosh said, (as cited in Cengiz 2011) “Division of fractions is often the most mechanical and least understood topic in elementary school.” The problem was that teachers tend to teach fractions as more of a procedural skill instead of building a conceptual understanding of fractions so that students know what they are doing when they add or divide fractions. The reason why they do this is because of the standardized testing’s focus on only the procedures and teachers focus on the procedures because it tends to be much easier and more efficient. Skemp (1976) explains how teachers fall for this trick of teaching students fractions procedurally (what he refers to as “instrumental”) as opposed to a more conceptual understanding (“relational”): "Within its own context, instrumental mathematics is usually easier to understand; sometimes much easier. Some topics, such as multiplying two negative numbers together, or dividing by a fractional number, are difficult to understand relationally. 'Minus time minus equals plus' and 'to divide by a fraction you turn it upside down and multiply' are easily remembered rules. If what is wanted is a page of right answers, instrumental mathematics can provide this more quickly and easily." However, even though students tend to pick up fraction operations quickly, they also tend to forget just as quickly and do not understand when to apply these operations. I tackled the problem by introducing a few interactive simulations that students to could use on the internet that involve visual models of fractions that students could play around with. With teachers as facilitators, guiding students to make their own conceptions of what it means for fractions to be added, multiplied, divided, students build a greater understanding of fractions in general and are more likely to remember when to use certain operations.
CEP 805: Learning Mathematics with Technology explored the intersection of technology and mathematics. The main goal of the class was to evaluate different pieces of technology in a variety of topics in mathematics such as algebra, fractions, integers, and similarity. Using the TPACK framework, the UDL principles, and other guidelines, we investigated different resources including games, simulations, web quests, and videos. We also explored methods for teaching certain concepts that apply them to the real-world so that students can experience how different topics in mathematics are used in different careers as well as resources that supported active learning which involves students communicating, reasoning, and problem solving using the concepts that they are learning as opposed to the students just listening to the teacher. At the end of the course, we summarized what we had learned by creating a library of evaluated resources sorted by topic. This course helped me find a whole bunch of resources that I could then use in my own teaching that I had already evaluated to be more effective than other pieces of technology that I used in my student teaching and started a library of these resources that I can continue to expand.
CEP 800: Learning in School and Other Settings further expanded my ability to evaluate pieces of technology by focusing on several psychological perspectives on learning. Studying learning in a variety of different ways, helped me understand more about how students were interacting with the technology that I was using in my lessons. CEP 800 focused on different perspectives of learning such as adaptation, conditioning, social interaction as a means of co-constructing knowledge, and the information-processing model. The other focus of CEP 800 was to create powerful learning experiences for students using technology. Using the TPACK and UDL guidelines, as well as the psychological perspectives learned in this course, I learned how to develop lessons that created powerful experiences for students that could inspire them and engage them both cognitively and emotionally.
When I first entered the MAET program, I entered with the goal to learn how to effectively use technology in my classroom. Throughout the program, I learned a wide set of tools to evaluate the technology that I found including the TPACK framework with helped me analyze the intersection and interaction between the technology, the pedagogy, and the content. In addition, I learned how to use the UDL guidelines to understand the benefits and potential barriers of using such technology. Once I had the tools to evaluate technology, I learned how to apply those tools to find technology in order to address a problem in education by using those tools to predict how students will interact with the technology and what they will hopefully learn from using it. In CEP 805, I created a library of resources and technology that I could then use in my classroom. I then finally learned other ways to think about how technology affected my students’ learning by thinking about different models and perspectives about learning in CEP 807. Over the course of my journey, I have learned a great deal on how to effectively use technology in my classroom.
Cengiz, N., & Rathouz, M. (2011). Take a Bite Out of Fraction Division. Mathematics Teaching in the Middle School, 17, 146-53.
Skemp, R. R. (1976). Relational Understanding and Instrumental Understanding. Mathematics Teaching, 77, 20-26.
CEP 811, Adapting Innovative Technologies in Education, helped me start to achieve my goal of finding technology that I can effectively use to teach mathematics by giving me the tools to evaluate new pieces of technology. The first tool that I learned was the Technology, Pedagogy, and Content Knowledge (TPACK) framework. TPACK was a tool to help explore the intersection of the technology being used, how the technology supports the teaching strategies being used, and how those affect how students perceive the content knowledge. Using this framework, I could then predict the effects that a certain piece of technology would have on a lesson and revise the lesson if needed. To analyze the specific properties of each piece of technology, we also learned about the Universal Design for Learning (UDL) guidelines which is a tool to outline the potential features and barriers of including a certain piece of technology in a lesson. This helps to see what exactly what the piece of technology that I want to use brings to the table. Some aspects of the technology may be a benefit and help students considerably understand the concept while others may potentially create misconceptions or confusion among the students. In addition to TPACK and UDL, we also looked at other pieces when designing lesson plans with technology including how the lesson relates to real-world applications, the social aspect of the lesson and how students are communicating with each other, the motivation that the piece of technology may bring to students, and the necessary equipment and planning needed to enact such a lesson. Using this set of tools, I started to understand what pieces of technology were useful and which one were just for show.
Now that I had the tools to evaluate technology and see its usefulness or potential problems, I had to then learn how to introduce technology in my classroom to enhance student understanding. In CEP 812, Applying Educational Technology to Issues of Practice, I was pushed to apply the frameworks that I had learned about evaluating pieces of technology to attempt a solution to a challenging problem encountered in my teaching experience called a “Wicked Problem”. The problem that I chose to focus on was the difficulty that many middle school students have regarding fractions in both a conceptual and procedural sense. Fractions come in a drastically different format than whole numbers and that format makes comparing numbers with fractions and fraction operations much more difficult. As Tirosh said, (as cited in Cengiz 2011) “Division of fractions is often the most mechanical and least understood topic in elementary school.” The problem was that teachers tend to teach fractions as more of a procedural skill instead of building a conceptual understanding of fractions so that students know what they are doing when they add or divide fractions. The reason why they do this is because of the standardized testing’s focus on only the procedures and teachers focus on the procedures because it tends to be much easier and more efficient. Skemp (1976) explains how teachers fall for this trick of teaching students fractions procedurally (what he refers to as “instrumental”) as opposed to a more conceptual understanding (“relational”): "Within its own context, instrumental mathematics is usually easier to understand; sometimes much easier. Some topics, such as multiplying two negative numbers together, or dividing by a fractional number, are difficult to understand relationally. 'Minus time minus equals plus' and 'to divide by a fraction you turn it upside down and multiply' are easily remembered rules. If what is wanted is a page of right answers, instrumental mathematics can provide this more quickly and easily." However, even though students tend to pick up fraction operations quickly, they also tend to forget just as quickly and do not understand when to apply these operations. I tackled the problem by introducing a few interactive simulations that students to could use on the internet that involve visual models of fractions that students could play around with. With teachers as facilitators, guiding students to make their own conceptions of what it means for fractions to be added, multiplied, divided, students build a greater understanding of fractions in general and are more likely to remember when to use certain operations.
CEP 805: Learning Mathematics with Technology explored the intersection of technology and mathematics. The main goal of the class was to evaluate different pieces of technology in a variety of topics in mathematics such as algebra, fractions, integers, and similarity. Using the TPACK framework, the UDL principles, and other guidelines, we investigated different resources including games, simulations, web quests, and videos. We also explored methods for teaching certain concepts that apply them to the real-world so that students can experience how different topics in mathematics are used in different careers as well as resources that supported active learning which involves students communicating, reasoning, and problem solving using the concepts that they are learning as opposed to the students just listening to the teacher. At the end of the course, we summarized what we had learned by creating a library of evaluated resources sorted by topic. This course helped me find a whole bunch of resources that I could then use in my own teaching that I had already evaluated to be more effective than other pieces of technology that I used in my student teaching and started a library of these resources that I can continue to expand.
CEP 800: Learning in School and Other Settings further expanded my ability to evaluate pieces of technology by focusing on several psychological perspectives on learning. Studying learning in a variety of different ways, helped me understand more about how students were interacting with the technology that I was using in my lessons. CEP 800 focused on different perspectives of learning such as adaptation, conditioning, social interaction as a means of co-constructing knowledge, and the information-processing model. The other focus of CEP 800 was to create powerful learning experiences for students using technology. Using the TPACK and UDL guidelines, as well as the psychological perspectives learned in this course, I learned how to develop lessons that created powerful experiences for students that could inspire them and engage them both cognitively and emotionally.
When I first entered the MAET program, I entered with the goal to learn how to effectively use technology in my classroom. Throughout the program, I learned a wide set of tools to evaluate the technology that I found including the TPACK framework with helped me analyze the intersection and interaction between the technology, the pedagogy, and the content. In addition, I learned how to use the UDL guidelines to understand the benefits and potential barriers of using such technology. Once I had the tools to evaluate technology, I learned how to apply those tools to find technology in order to address a problem in education by using those tools to predict how students will interact with the technology and what they will hopefully learn from using it. In CEP 805, I created a library of resources and technology that I could then use in my classroom. I then finally learned other ways to think about how technology affected my students’ learning by thinking about different models and perspectives about learning in CEP 807. Over the course of my journey, I have learned a great deal on how to effectively use technology in my classroom.
Cengiz, N., & Rathouz, M. (2011). Take a Bite Out of Fraction Division. Mathematics Teaching in the Middle School, 17, 146-53.
Skemp, R. R. (1976). Relational Understanding and Instrumental Understanding. Mathematics Teaching, 77, 20-26.