Foundations of Mathematics
FOR Geometry, Trigonometry, and Statistics
Our Foundations of Mathematics hybrid resource has been designed for students in business, trades and apprenticeship, health and nursing, and technology programs. It includes a comprehensive textbook, an interactive e-textbook, mastery-based online lessons, algorithmic assessments powered by a testbank with over 2,000 unique questions, solution manuals, animated PowerPoint presentations, and real-time performance dashboards to view individual or class performance.
The Foundations of Mathematics resource has been authored by Thambyrajah Kugathasan and Erin Kox in collaboration with college professors across the country. To view the information brochure, click here.
The Foundations of Mathematics resource is available in printed textbook format and etextbook format.
The following are the details to place an order for the resource:
- Textbook Package: $135 (ISBN: 978-1-927737-31-6)
- eTextbook package: $80
- The Textbook and eTextbook Packages will provide full access to the accompanying online resources, including lessons, assessments, PowerPoint presentations, and online solution manuals.
- Prices provided do not include taxes and shipping. These will be extra.
The Foundations of Mathematics textbook/etextbook contains numerous pedagogies and learning methods in addition to over 2,000 exercises and over 200 solved examples. The language used in the book is simple and straight-forward, while maintaining the required level of sophistication to thoroughly prepare students for the next stage in their academic and professional careers.
Numerous pedagogies and learning methods that have been developed and proven over 30 years are incorporated into the book. These pedagogies have succeeded in simplifying critical mathematical concepts and significantly improving retention of concepts. The alternative learning methods for solving problems have proven to be effective for students with a variety of learning styles.
The problems in the book are designed to test students on real-world, practical applications and are presented in increasing levels of difficulty. They are categorized into pairs of similar questions to provide professors with an opportunity to solve the even-numbered problems in class and assign the odd-numbered problems as homework.
The interactive lessons provide students with a unique Assessment for Learning experience. Through a step-by-step, mastery-based approach, students understand core concepts. The lessons contain numerous pedagogies that break-down concepts into micro-steps that help students to visualize, conceptualize, and enjoy the learning process.
The lessons are modular in nature and can be customized to a large degree based on the learning plan of each instructor or the course. Students will be required to unlock (master) key concepts, through built-in feedback mechanisms, before they sequentially proceed to understanding higher level concepts. This mastery-based approach has not only proven to help students to review concepts before tests and exams but also to prepare them prior to attending class.
Through an intuitive administration panel, instructors have the ability to select and customize lessons. They can set start and close dates, provide date extensions for individual students or for the entire class, set, download, or override marks. They can also view their student or class performance on any concept to tailor the in-class focus on concepts with which students are experiencing difficulties. This method has successfully proven to increase student retention and success at numerous academic institutions across the country.
Vretta’s assessments are designed to not only test students but also to teach them to solve problems using intuitive methods, illustrations, and pedagogies. The assessments contain interactive timelines, problems that are algorithmically generated, options to learn using alternative methods, and related reference links to concepts in the eTextbook and lessons.
In addition to providing students with the ability for unlimited practice on each question, the assessments contain unique features such as the provision for students to “Check My Answer”, “Ask My Professor”, and also receive dynamic feedback based on the entered answer. The assessments are built using an intelligent logic that provides students with an experience that is as close as possible to a real test. For example, in addition to unique error tolerances, if a student enters an incorrect answer by making a minor error (but has used the correct method to solve the problem), the system will recognize this and provide the student with a partial mark based on the extent of correctness.
Through an intuitive administration panel, instructors have the ability to select and customize assessments. They can set start and close dates, provide date extensions for individual students or for the entire class, set, download, or override marks. They can also view their student or class performance on any question to tailor their in-class focus on concepts with which students are experiencing difficulty. This method has successfully proven to increase student retention and success at numerous academic institutions across the country.
The solution manuals are available online for instructors and students. They contain solutions to problems using detailed step-by-step methods as demonstrated in the solved examples present in the textbook. The manuals are in a word format and can be downloaded and modified by instructors as required.
Instructor Solution Manuals
The instructor manuals contain detailed solutions to every section exercise, review exercise, and self-test exercise problem. The manuals also contain detailed solutions to the cases.
Student Solution Manuals
The student manuals contain detailed solutions to the odd numbered section exercise and review exercise problems. The manuals also contain detailed solutions to every self-test exercise problem.
The PowerPoint presentations (PPTs) are designed to teach every concept in the textbook. Steps in teaching concepts appear one by one through the creative use of animations to provide students with an inclusive learning experience. Instructors have the option of downloading and making modifications to any of the PPTs. Additionally, the PPTs are designed to be used with student response systems (clickers) to gauge the overall class comprehension of concepts.
The PPTs are available for instructors and students in the following formats:
- Instructor PPTs contain all of the solutions presented in the PPT.
- Student PPTs (also called handouts) contain only the questions. They do not contain solutions to the problems. Additionally, animations have been removed from the student PPTs so that they can be printed and distributed to students at the beginning of each class for them to be able to work through the problems during class.
- Delayered PPTs are the instructor PPTs without animations. These PPTs can be used on distance learning platforms that do not support animations.
Vretta’s dashboards provide a real-time visual understanding of individual student and overall class performance as they progress through the lessons and assessments. The dashboards are used by both students and professors to identify the areas of weakness, and to improve the in-class and self-study focus.
The assessment dashboard provides the highest mark and average mark secured on every question. This helps to identify the specific questions that an individual student or the entire class is having difficulty understanding.
The lesson dashboard provides the completion mark on every lesson. This helps to identify the specific concept that an individual student or the entire class is having difficulty understanding.
Professors can use the dashboard to export grades into their grade book.
