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Enhancing Understanding of Geometry Concepts Through Online Homework Assistance: A Comprehensive Guide
1. Introduction
1.1. Overview
Enhancing Understanding of Geometry Concepts Through Online Homework Assistance: A Comprehensive Guide serves as a valuable resource on many levels for students and educators alike. For teachers, the book will help them to gain a more comprehensive understanding of how students solve geometry problems and where they go wrong in the process. Teachers can then use this information to design more effective instruction in the classroom. Additionally, the authors hope that this book will provide insight into the reliability and efficacy of online homework help websites for geometry students. The authors intend that other researchers will take this study as a stepping stone and design similar studies to gauge the true efficacy of homework help websites in other content areas of mathematics.
In these included chapters, younger students will likely be said to mean geometry questions that would be found in a high school or lower level geometry course. Older students would be said to mean students that are currently taking a college or post-secondary level geometry course. Basic geometry questions would represent the foundational skills needed to understand geometry at younger and older student levels. Higher-order geometry questions would represent the skills and concepts that build upon the foundational skills of geometry as applied in younger and older level geometry courses. At each elementary, middle, and high school level or in geometry courses, we differentiate between reading, writing, and math levels to assist in classifying the students’ level of completion. The reading-fragment level represents the language complexity required in reading practice. The reading-lexical level shows the difficulty of individual words. Finally, the writing and math questions would represent questions that pertain to language or short-answer responses and the standard type mathematics that students would need to complete.
Much prior work stresses the importance of definitions, including drawing diagrams to depict the various geometric entities such as points, lines, rays, and angles. But of those definitions that I provide, the ones that are most important, in my opinion, are those I present below. Here, and in the successor sections where I introduce new mathematical concepts, I provide problems, examples, questions for class discussion, and even proofs that will assist them in the process of learning. I believe in building connections with or between such related concepts, not only through proofs, but also through everyday examples as well as through the judicious exposition of well-designed problems.
This elementary distance formula can sometimes be used to prove very interesting results about lines, points, and circles. Thus, teaching the distance formula has intrinsic interest to the students since it can be used to validate or invalidate their conjectures. Specifically, since the distance from a point A to line l is given by the formula, d(A,l) = | a1 + b1 + c |, a2 + b2 from the formula one can deduce that the segment that is drawn from the origin to the line is perpendicular to the line if and only if line l has a slope, m, given by m = – a2 / b2.
Online homework assistance is comprised of numerous tools and resources that learners as well as instructors may access through the internet. Such assistance is not purely comprised of tutorial materials and resources, but also of virtual or simulated environments that allow users to explore, experiment, and verify certain hypotheses and test various assumptions. Unlike routine practice of solving word or number problems, etc., the tasks involved in geometry should be more about learners gaining insights into the key features of particular geometric elements and then coming to logical, justifiable conclusions based on their insights. Therefore, in utilizing online homework assistance for guiding learners through geometry concepts, we should choose the right type of resources and tools for carrying out the tasks at appropriate levels, which may vary depending on the types of geometry concepts that we intend for learners to master.
From a learner’s perspective, varying his or her choice of geometrical elements can lead to different visualization or symbolic/pattern-based opportunities and insights at play in an active manner. For example, choosing a pair of congruent but distinct triangles may prompt the learners to detect and compare different features present in and absent from the pair of triangles. Consequently, they may become aware of differences such as the three edges of one matching the three edges of the other; and both by directly superimposing one on top of the other, the triangle edges are aligned at the points.
Enhancing understanding of geometry concepts through online homework assistance: A comprehensive guide. Successful students are not born; they are made through hard work and dedication. Students should learn both successful study habits and time management skills. These habits are cruise control for success. For instance, students benefit from taking thorough class notes, thus leading to active learning. Homework should not be a rushed-through activity completed on the way to class, just so that it can be handed in. Instead, students should view it as an accumulation of ideas from each class session, which are then built upon to illustrate what will be on exams – a repertoire of exercises to build content knowledge, application skills, and numeric and algebraic fluency, which can then be tested on exams, tasks, and projects.
Successful study habits also require the participation or patience to seek help when one does not understand a particular idea. It does not hurt to use active learning to get ahead either. In a course based in hand-held technology where content knowledge is built upon and is useful for tasks and discussions, homework quizzes helped students keep up, and so students experience daily success. Failure to practice math skills and exercises through daily homework could result in a student having to redevelop their whole skill set, which was discussed at the beginning of the article. Geometry is Logic Class – not Memorization Class. Geometry is a class that involves understanding new concepts and applying them in novel ways. Learning that is designed to involve exploration and can make the most of online content through applications is a valuable commodity nowadays. These explorations can be challenging as they may involve calculus ideas that the students have never seen before. Working with fellow students in the study of geometry is beneficial to understanding the material as it helps with the articulation of ideas used in different proofs. Finally, learning online provides you with a time resource that you can schedule study times to coincide with those times when you have performed your best learning.
Promote the use of intuitive strategies. Incorporating strategies that can be applied directly to both the problem and solution leads to new knowledge and deep understanding. Logical reasoning, evaluating simple cases, and analyzing the relationships between given information and constraints are elements of strategies used in this study. By engaging in intuitive strategies, students are propelled to think critically about what is being asked and how it can be addressed while concurrently recognizing the specific geometric concepts and relationships involved in the problem that must be considered and applied in the problem-solving process. To further support learning, ensure that the solution the student submits is subject to verbal and effective cognitive processing. When tutors construct and convert students’ homework responses into verbal and effective communication, the thesis serves as a feedback tool that advances a student’s geometric learning and understanding. Prompting students to reflect and engage in discussion about their understanding of the homework assignment from their thesis, combined with the coursework, influences the development of comprehensive knowledge.
Use a structured peer review process. Faculty should utilize effective teaching practices and communication strategies to involve knowledgeable peers in the student learning process. By collaborating with a peer when reviewing homework and problem-solving assignments, students receive further opportunity for development of their mental structures and evaluation skills for improved academic performance. One effective peer review tool utilized in this study is Impromptu Assignments. These assignments promote critical thinking skills, foster original thinking and creativity, and enhance academic learning and subsequent understanding of the geometric concept. As peers collaborate and share ideas, they build a larger bank of conceptual understanding that supports deeper knowledge.
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