by Lynda Cain (lcain3@gsu.edu), Assistant Professor of Mathematics, Georgia State University’s Perimeter College, and Marjorie Lewkowicz (mlewkowicz1@gsu.edu), Professor of Mathematics, Georgia State University’s Perimeter College
During the Summer semester, 2019, Lynda Cain and Margie Lewkowicz attended two workshops dealing with metacognition, sponsored by Perimeter College’s Center for Excellence in Teaching and Learning “Dig Deeper” faculty development series. Metacognition involves “thinking about thinking,” that is, understanding one’s own thought processes in learning. At the conclusion of the workshops, participants were asked to write down one new activity that they would utilize during the Fall semester to help students develop metacognitive skills. Participants were also asked to select an accountability partner to encourage one another to meet their predetermined goals. Lynda and Margie served as accountability partners and supported each other throughout the semester. Lynda’s goal was to incorporate educational technology to help students reflect on concepts that were previously taught or as a motivating tool at the beginning of the class. Margie’s goal was to implement weekly reflection in the classroom to encourage students to think about their own learning. The two projects are summarized below:
“Developing Metacognitive Skills: Beginning of Class” by Lynda Cain
Kahoot! is a game-based tool that allows users to readily create, play, and compete while engaging in active learning activities. Students may log into Kahoot.it from their cell phones or other web-enabled devices. They are provided a PIN that has been assigned to the Kahoot! session. Since class members often stare at their cell phones during class, I decided to grab some of that screen time in my Elementary Statistics classes!
The music in the tool is an attention-getter and is frequently changed, relative to the season or holiday. To spice up the Kahoot! visuals and support students’ learning experiences, I often include gifs, images, videos, and/or diagrams. The best part of using Kahoot! is that each student participates. Individuals who may not “speak up” in class will more frequently respond on their personal electronic devices. Students enter their own screen names. (Names must be “clean” and non-offensive.) Scores are assigned by Kahoot! based upon both speed and accuracy of each response. The top 5 screen names and their scores are presented after each question. Students enjoy competing with each other. “It’s a game!”
Most frequently, I create multiple choice questions in Kahoot!. After students submit their answers to a question, Kahoot! generates a simple histogram showing the frequency of each response chosen. We discuss each question immediately after the histogram’s results are displayed. Class members are asked to identify why a given answer is correct and why the other responses are not accurate.
I use Kahoot! at the start of class to get the juices flowing (reflecting on concepts that were introduced during a previous discussion) or at the end of class to assess students’ understanding of the day’s topics. In addition, students are often teased with questions on upcoming course content. Sometimes, the top 5 performers are rewarded with candy. Within seconds of recognizing the top performers, all students get the same treat.
Kahoot! provides reports (at the conclusion of each game) that may be used to assess students’ understanding of each question posed. An instructor may use this input to pinpoint concepts that require more attention. In addition, the instruction leader may identify specific students who need additional assistance, provided their screen names are identifiable. Report details may be utilized to organize small group activities.
While I have given thought to counting Kahoot! results as quiz grades, I have yet to determine the best way to do so. My classes are taught in a math lab. Most students use the lab’s workstations (with large screens) when playing Kahoot. A student can easily see the right answer if their neighbor responds before he does. Using a cell phone could be required. This would minimize the screen size; however, individuals enjoy showing neighbor(s) their cell phone displays.
The Elementary Statistics students appear to enjoy the element of gaming during class time. They actually discuss their right and wrong answers. Oftentimes, class members discover that they should slow down (a little) and read questions more carefully before responding. It is an enjoyable way to learn. In the future, I plan to require students to create Kahoots! as class projects. These projects will contribute to their course grades. Selecting and using student- created Kahoots! will not only show class members the value of the activity they created but also give them a sense of pride and ownership. Using Kahoot! in my Elementary Statistics class serves as a penalty-free environment in which everyone can comfortably “play” and learn.
“Developing Metacognitive Skills: End of Class” by Margie Lewkowicz
I chose my Math 2008 (Foundations of Numbers and Operations) class for this experiment, as this is the course designed for prospective teachers. Research has shown that providing students with the opportunity to reflect on their learning promotes ownership and can help students make connections between prior knowledge and new concepts.
Students in my Math 2008 class were given 3-5 minutes at the end of class to reflect on their work for that week. Students responded to a variety of questions including the following:
- What were the most important ideas or concepts learned in today’s class?
- What did you find most interesting about class today?
- What information appears to clash with your prior understanding?
- Where did you encounter difficulty and how did you handle it?
- What made you curious or excited today?
- What can I do to help you learn the material?
Reflection can be a valuable means to help students focus and think more clearly, especially in more difficult problem-solving situations. Reflection allows students the time to step back and think about the problem. Reflection encourages students to delve back into their prior learning, as they consider which problem-solving strategies would be most helpful in any given situation. It also helps students become more self-aware so that they can identify their learning styles, recognize any obstacles they face, and develop ways of surmounting these obstacles. Some examples of students’ reflections in Math 2008 are provided below:
- “The most important thing I learned today was the how to change numbers from one base to another. I am in a computer science class this semester and I was super lost and confused when they started talking about base two. But today has cleared up what I was confused about”.
- “I didn’t know that there was a subtractive principle in the Roman numerals system. I was always taught to memorize that IV is 4 and VI is 6. No why or how, we just had to memorize the symbols. But after learning about the subtractive principle, it make the Roman numeral system so much easier to understand”.
- “Prior to this week’s lesson, I did not know about any other base system, other than ten. I didn’t know other bases even existed”.
- “Today clarified a lesson from another class. We began logic and mathematical proofs using p and q, and I was a bit confused. But this class helped a lot”.
- “It was interesting to see what I learned in philosophy to be used in a math class”.
- “It was fun learning how to change bases. I just have to switch my mindset that 10 is the only base”.
- “I struggle most with mental math because of my dyslexia”.
- “The most satisfaction I experienced today was remembering the math that I thought I forgot about”.
- “What was most satisfying for me today was learning that there are many different ways to solve a problem. I like to double check using different methods.”
- “It’s frustrating to not be able to use a calculator and rely on my own knowledge”.
In addition to weekly reflections, I utilized post-exam reflections as well. After the tests were returned to the students, I asked them to reflect on what grade they expected to receive versus what grade they actually earned. Further, I asked students to consider the areas that they lost the most points and to reflect on the reasons for missing the questions, such as lack of understanding of the concepts, careless errors, did not study that topic, etc. I also asked students to consider what they might do differently in preparing for the next exam. Here are some examples of the students’ responses:
- “I was confident about converting from one base to another, but I didn’t read the question (#4) properly. I just wish I had paid closer attention to my work and the directions”.
- “The most challenging for me is that I am normally really tired, so I was second guessing and triple checking my answers. I could do better by going to sleep a bit earlier the night before and managing my time better”.
- “I think that I should change my study habits. I used to make flash cards in other classes to quiz myself on the topics and it improved my grade. I will try to do this in my math class, especially when trying to learn the properties and divisibility rules”.
- “I tend to wait two days before the test to study and I bunch every bit of information I can into my head. I should try to study every day and spend more time in the tutoring center”.
- “My struggle is my procrastination. I even purchased a planner so that I can keep track of myself, but it’s hard to get over it, especially when the work piles up”.
Giving students the opportunity to process the information through reflection encourages them to make connections and also allows them to consider what they can do differently in the future. The process was also most beneficial for me as it provided valuable insight into how students view certain topics. It also afforded me the opportunity to develop teaching techniques to help clear up students’ misconceptions and help them become more effective learners.
During the semester, I made some anecdotal observations about this class and a prior Math 2008 class that I taught where reflection was not utilized. The grades in the semester where I used reflection were slightly higher than the class where reflection was not used. It is important to note that the sample sizes were small, so more study has to be done and more data must be collected. However, much more noteworthy than the average test scores is the fact that I have observed an increase in class participation and discussion in the class that utilized reflection. Students seemed much more engaged and were willing to communicate their thoughts about problem solving as well as share their strengths and weaknesses with their peers. This, in turn, led to students sharing the methods they used to overcome their difficulties.
Reflection can be a powerful metacognitive tool in the classroom. Reflecting on their work gives students a sense of their own growth and accomplishments. When I first considered using weekly reflections, I was concerned that in order to complete all the content in the course, I would not be able to spare any time at the end of the class for reflection. However, through this process, I discovered that the time spent on reflection actually enhanced learning. Students were more inclined to share their feelings and concerns. There appeared to be more camaraderie within the classroom when reflection is utilized. Although this is still a work in progress, I gained a lot of awareness of how students think about their own thinking. I feel that continued use of reflection can help students develop metacognitive skills which will not only enhance their understanding of course concepts, but will ultimately help them discover the joy and wonder associated with learning and doing mathematics.
Works Cited:
Arthur, P (2019, June). Metacognition, Growth Mindset, and Grit. Workshop presented at Perimeter College at Georgia State University.
Tanner, KD (2012). Promoting Student Metacognition. CBE Life Sci Educ 11, 113-120.
Kahoot! software available at https://kahoot.com
