MATH TOPICS EXPLAINED: A DISCORD CHATBOT FOR COLLEGE ALGEBRA STUDENTS
Senior Honors Capstone Project Proposal submitted in partial fulfillment of requirements for the Norbert O. Schedler Honors College by
Excalibur L. Bunker
University of Central Arkansas Conway, Arkansas Fall 2023
Proposal Committee
Advisor: Dr. Loi Booher
Instructor: Dr. Adam Frank
Abstract: The increasing use of technology has significantly impacted mathematics education, particularly in visualizing complex concepts and providing step-by-step solutions to problems. However, many of these tools are paywalled, limiting their accessibility. This project aims to develop an application that combines the benefits of technology with the ability to break down foundational math concepts, allowing students to refresh their understanding and solve more complex problems.
INTRODUCTION:
The increasing use of technology has affected many aspects of the classroom, from the ability to quickly search for assignment answers to having access to information at students’ fingertips. Teachers and professors have seen technology used to explain complex concepts into digestible bits.
Mathematics has seen a significant impact, as it has become increasingly easier to display advanced math concepts, from asymptotes to graphing complicated equations to even showing derivatives creatively. Visual representations, such as plotting endpoints to display equations, can enhance the understanding of abstract mathematical concepts by providing students with a tangible representation of the concepts. This is why tools like Desmos have become increasingly popular in many classrooms to display other parts of an equation visually.
Another way technology has been used in mathematics for students is the ability to show the steps to complicated problems using tools like Mathway or Wolfram Alpha. These tools allow students to see the reasoning behind the methodology and help students understand the concepts more deeply with a breakdown of the steps to reach the correct answer. The issue with these tools and others available to students is that most are put behind a paywall that hides the solution steps, which can become frustrating for students trying to understand how to work the problem.
This project aims to combine the usefulness of technology with the ability to break down early mathematics concepts to refresh students’ understanding to solve more complex problems. One challenge in teaching is that students that have a gap in prerequisite knowledge will struggle as they move on to more advanced skills. This means that a student who does not understand multiplication will not truly understand division. Mathematics is structured to build upon concepts, going from what is considered essential to more complicated, using the concepts learned as tools to evaluate more complex problems.
For my capstone project, I plan to create an application to help students catch up on foundational skills. By allowing students to be able go back to different concepts that may have been forgotten but also break down the steps to solving these problems. This means having the methodology/reasoning for those concepts but also allows users to put in their problems and get a breakdown of the steps. This would enable students to refresh their knowledge on some of the prerequisites required for more complicated problems, for example, multiplying fractions by breaking it down to first understanding fractions and then the concepts of multiplying. It would also be a valuable tool for students struggling with a particular concept by being able to go back and refresh their understanding to solve that current problem.
LITERATURE REVIEW:
Engaging, meaningful, and socially interactive learning models are essential for effective applications.
Using iPads and other technologies in the classroom has increased over the last 20 years, giving kids access to a wide range of learning resources and applications to help enrich their learning and motivation (Harrison & Lee, 2018). From the early stages of education to even later education at the high school level and beyond, it is seen that technology increases retention if the application follows a particular design, this being engaging, meaningful, and socially interactive learning models for effective applications (Hirsh-Pasek et al., 2015). An application that does not engage the user or is perceived as meaningful can create a disdain for that application and remove any benefit it may have had. This creates problems as the students do not benefit from the added supplementary learning material to help enrich the student’s understanding of different concepts. The increase in the presence of tablets will enable teachers to select students with either learning disabilities or at risk of failing to use different methods of bridging the gaps between students (Zhang et al., 2015). Supplementing the current curriculum using these applications allows students to have a lecturer approach with hands-on practice using engaging and fun tools. An example is an application created that uses the ability of touch to teach kids addition and subtraction using numbers and images and allows teachers to see the progress of each of the students (Masood and Hoda, 2014). Another illustrative example is the video game MathDungeon, which employs engaging animations, hints, and interactive elements to facilitate the learning of college-level math concepts like the quadratic formula and factoring. A study involving the implementation of MathDungeon in the classroom revealed a significant improvement in students’ understanding of quadratic formulas. (Faghihi et al., 2014). The application was fun and allowed for students to have a creative way of learning math to help with their coursework.
Applications solely focused on demonstrating problems may hinder independence and critical thinking.
Mathematics tries to follow an essential aspect in the classroom: guided practice, transition, and independence (Hoang and Caverly, 2013). An app solely dedicated to presenting mathematical problems without providing opportunities for practice and self-directed learning may be insufficient. Merely displaying problems without fostering critical thinking and opportunities to apply learned skills limits the effectiveness of such an app. The other problem is needing to be able to refresh on specific topics. If the user does not understand the prerequisite, it becomes increasingly more challenging to solve the problem.
Insufficient foundational knowledge can hinder problem-solving, as evident in scenarios where a user tasked with adding fractions lacks understanding of the principle of division or the rules of addition regarding fractions. Without this essential knowledge, the problem becomes nearly insurmountable, impeding the user’s ability to apply critical thinking. Similarly, increasing problem difficulty, such as in solving a system of equations, can further exacerbate the likelihood of the user abandoning the task. Emphasis on Calculation and Critical Thinking: Nursing education underscores the importance of both mathematical and dosage calculation skills, coupled with critical thinking abilities, as highlighted in the study “Nurse Education and Mathematical Competency: Implementation of an Online, Self-Directed, Prerequisite Model.” This notion is supported by a study that investigated the relationship between nursing students’ performance in calculus and precalculus courses, overall math GPA, and their success in nursing school. The findings revealed that nursing students with a stronger grasp of mathematical concepts exhibited a higher likelihood of success in their nursing education (Maley & Rafferty, 2019). Math is more than a course you are forced to take, it has a real bearing on the perception of the world around us, from being able to convert different measurements, to being able to break down problems into a mathematical understanding. This can be seen as ACT math average scores have decreased in the last five years by 0.5 points. This does not seem like a lot, but in perspective, the scores have stayed the same since 1998, as the average score was 20.6 (Gewertz, 2018). This is affecting the readiness for college-level math courses, as students who transition into college-level math classes have a hard time, as skills such as fractions and word problems are complicated. As students struggle the most with fractions and word problems in college, the university has to create remedial coursework to bridge gaps in student understanding to allow for more complicated concepts. Creating remedial math courses, using different placement policies specific to community college, the issue being that in some of these placement tests missing one question about fractions causes students to be placed in lower-level math courses. This can affect the student’s mindset which is not seen in other placement tests but only seen in math courses placement (Ngo, 2019).
Applications for higher education, such as Desmos and Wolfram Alpha, need more practice and review functionalities.
Observing apps that use math in fun and creative ways can positively influence students who are reluctant to do math (Calder and Campbell, 2016). The concept of utilizing creative, engaging, and enjoyable educational tools is well-established, with examples like BrainPOP Jr.’s engaging video content, Mathmateer’s interactive games designed to teach shapes, number recognition, and even complex concepts like multiplication (Lubniewski et al., 2018). This learning approach deviates from traditional classroom methods, aiming to enhance the material already being taught. For instance, the aforementioned application caters to early development, spanning grades 1 to 6. There are not many applications designed for high-school or college students that foster deep learning and spark engagement in complex math concepts. Some do exist applications like Desmos and Wolfram Alpha. However, these applications are lacking some important features such as the functionality to practice the different math concepts or a way to go back on concepts that may be forgotten. As for most applications, these features, if the application supports them, are put behind a paywall, forcing the students to pay for that breakdown of the problem.
Visual representations of math concepts can make complex problems more manageable.
The integration of technology to aid mathematics instruction, particularly in higher-level math classes, is not a novel concept. As early as 1975, the National Advisory Committee on Mathematical Education advocated for calculator use in grades eight and above (Overview and Analysis of School Mathematics, Grades K-12, pg 41). Today, the classroom still uses calculators with more advanced features, such as graphing, to solve more advanced problems and graph complex functions. Allowing for spatial visualization of different problems, instead of using a table to write down values X and Y and then plotting the points by hand, graphing calculators allow for a broader picture (Bardini et al., 2004). Calculators have shown effectiveness as a learning tool in precalculus and calculus courses, for their ability to assist with functions, graphing, and modeling. Calculators allow for a shift from a standard model of algebraic manipulation, such as plugging in numbers to evaluate and plot a function , to a graphical method allowing students to explore concepts of a function graphically (Penglase & Arnold, 1996). Even when looking at the different learning methods, the use of smartphones, laptops, and even tablets has features designed to allow for applications and the ability to show math visually. The use of graphing technology in classrooms can improve student learning when it makes complex concepts more manageable for students. Examples are asymptotes, end behaviors, and logarithmic functions, which are hard to understand solely by solving them by hand. So, allowing for graphing technology gives a more complex understanding, allowing students to have a better understanding and the ability to solve problems (Shahriari, 2019).
Teachers’ perceptions of technology significantly impact application selection and usage.
One of the issues is for teachers to use the application in their classroom, as their perceived notions of the usefulness of technology significantly impact what applications are selected or even used at all (Domingo and Garganté). This can hurt any possible benefits that students can receive or find bad applications that do not either allow for student feedback or to be able to practice problems. Technology should be a tool that goes along with lesson plans, not the sole teaching method. When trying to find a reliable application, most teachers look for some assurance of value and quality—as with the countless applications presented out there, ensuring that the application has value and will benefit the student (Grant).
METHODOLOGY
I plan to create a Discord chat bot that will help math students in College Algebra. The application will be created using JavaScript, and a discord node library. This choice over other solutions is because it allows for the user to be able to use commands to put equations into the text box and get a response. Allowing for a more human response, creatively showcasing mathematics concepts by showing steps. The most important factor when designing this application is that everything looks cohesive and creatively designed. JavaScript allows for taking in complex math equations and transforming them using different algorithms that I will create. This application will focus on a foundational set of mathematics concepts but will have potential to expand the application into more complex math concepts.
The application will focus on the elementary mathematics skills and work upwards: addition, subtraction, multiplication, division,, fractions, and lastly linear equations and functions. he application will focus on key concepts that are necessary for student success in their College Algebra class and beyond—allowing students to refresh on key concepts that they may have forgotten so they can better learn more complicated problems. The application will be designed to have a start menu that allows students to select the concepts they are struggling with, including those mentioned above. Once a concept is established, it will have two options: first choosing pre-populated practice problems that will explain the concept in detail, and second, inputting in their own problems to see if their solution matches the correct answer. If the student’s solution is incorrect, the app will give step-by-step instructions on how to solve the problem, highlighting different parts of the problem and breaking it down. This allows students to learn the concepts and then place their problem to see if they got it correct. Lastly, once they feel comfortable, a quiz will review the selected concept to ensure they have refreshed enough knowledge and learned it. This application will be designed to allow at any point in the semester to be a refresher on different concepts.
At the start of a semester, two College Algebra classes will be divided into two groups: the current curriculum without adding the math tutor application and the other group with the application available as a resource for the students. As the semester progresses and quizzes and exams are given, we compare the results between the two groups, seeing if there are improvements in the grades between the group that has access to the math tutor application throughout their coursework and those that do not. The results will be compiled to see if there is a positive correlation between using a math tutor-like application and students’ grades in college algebra. Also, I will develop a survey to request feedback on how the application helped or not with student understanding of the concepts shown in college algebra, and to gather feedback to see if anything needs to be improved or changed for the next semester.
TIMELINE
January - December Timeline for 2024
January: Work on roughly developing the Discord chat bot and creating what I want outputted to the user
February: Refining the Discord chat bot by starting on the menu with the selection options
March: Start working on different mathematics operations given by the selection menu and develop how to teach the concepts. Also, work on getting IRB approval for the testing of the application for the fall semester.
April: Work on the test functionality in each of the mathematics operations sections
May: Finish working on user input and display the data nicely and with correct steps.
June: Work on creating a nice user interface and design for the Discord chat bot.
July: Beginning testing the application and refactoring the code to work correctly and more efficiently.
August: Add documentation to the application to be used in a classroom setting.
September - November: Testing period and data collection.
December: Look at all of the data and make a result section for the Capstone project.
CONCLUSION
The application will be designed to break down linear equations and functions into a series of arithmetic operations allowing students to better understand the mathematical concepts they need and creating confidence to approach increasingly complex problems in College Algebra and beyond. Math tutor applications have increased students’ understanding of simple and advanced concepts allowing for a better understanding of complex problems. If one of these key concepts is not fully understood it can cause issues when trying to think logically of how to approach the problem. The application I plan on creating will help bridge that gap of understanding by allowing the user/student to have an app to refresh and grow their understanding.
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