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Positioning Paper Academic Systems ® Algebra A multimedia curriculum designed to help faculty increase academic success Published by PLATO Learning 10801 Nesbitt Avenue South Bloomington, MN 55437 800.44.PLATO Table of Contents Academic Systems® Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 A Partnership for Academic Success . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Collaborative Community . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 PLATO Learning Team . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Professional Services . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Summary of Typical Course Content for the Academic Systems Algebra Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 The Mediated Learning Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Instructional Design of Academic Systems Algebra . . . . . . . . . . . . . . . 5 Explain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Apply . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Explore. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Homework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Academic Systems Algebra Instructional Design: Summary . . . . . . . 11 Special Features of the Multimedia Lessons. . . . . . . . . . . . . . . . . . . . 12 Personal Academic Notebooks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Instructor Customization Features. . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 PLATO Learning Environment™ (PLE™) . . . . . . . . . . . . . . . . . . . . . . . 14 Section Progress Reports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 Learner Progress Report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 Results: Success for Students, Faculty, and Campuses . . . . . . . . . . 15 Mathematics Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Implementation Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Appendix I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Appendix II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Academic Systems ® Algebra Academic Systems® Algebra is for faculty who are committed to helping students succeed and who are looking for proven, innovative methods to help students learn mathematics. A comprehensive series of educational software courses, Academic Systems Algebra was developed by PLATO Learning in collaboration with faculty from colleges and universities around the country. Academic Systems Algebra is composed of highly interactive educational software, a new and powerful instructional management system that provides assessment and feedback to students and instructors, and print materials for students and instructors. Academic Systems Algebra’s flexible and engaging assemble lessons in any order that suits their design meets the diverse needs of today’s preferences and the instructional needs of their institutions, from the classroom to distance learning students. implementations. The lessons cover, thoroughly and With Academic Systems Algebra, faculty can rigorously, the curriculum offered in basic mathematics, provide a diverse population of students with a more prealgebra, elementary algebra, and intermediate individualized learning experience. Students can algebra courses in colleges and universities. The access more learning resources when they need them material is modular and can be customized to fit and at the level they require. Faculty can better utilize course requirements. The modular approach to lesson valuable resources—including their expertise and their development and organization makes it possible for time—and gain more flexibility in the way courses are individual mathematics departments and faculty to offered to meet the demands of today’s students. A Partnership for Academic Success PLATO Learning’s goal is to work in a collaborative Academic Systems Algebra brings together all of the partnership with faculty and administrators to achieve resources needed to make instructors successful both success in three areas: on campus and off: high-quality instructional materials, a new model of partner support, and a collaborative Increase student academic achievement community effort that values the experience and PLATO Learning is dedicated to working with faculty expertise of faculty. to create more motivated and more engaged students who learn better and learn more. Faculty using Academic Systems Algebra materials are reporting Collaborative Community higher pass rates, fewer repeating students, and Interactive multimedia instruction requires a broad greater student retention. array of skills and people to successfully develop, implement, support, and continuously improve Increase faculty flexibility and impact instructional materials and implementation models. Faculty are freed to focus more of their time on high- While PLATO Learning contributes many of the needed impact activities—providing timely feedback, supporting resources, we do not do it alone. A key element of their online students, developing specialized instruction, PLATO Learning’s approach is the collaborative and working with students either in small groups, community which brings together a team of PLATO one-on-one, or via the Internet. With Academic Systems Learning experts and faculty and administrators using Algebra, faculty have more flexibility in structuring their Mediated Learning across the country. courses to meet their own needs and the needs of their students. Faculty using Academic Systems Algebra With each group focusing on their expertise, and with report that students are more successful because all of us cooperating, the collaborative community instructors are better able to meet the diverse needs provides interactive multimedia instructional solutions of the students in Mediated Learning classes. that significantly increase the effectiveness and efficiency of student learning. As a partner, each Increase resources and reduce budget constraints campus and its faculty become part of this collaborative community and will realize many benefits, well beyond By accelerating student achievement, increasing the scope of their entry-level mathematics courses. student retention, reducing the number of students repeating courses, and enabling students to learn more efficiently—both on campuses and via distance PLATO Learning Team learning—Academic Systems Algebra can free up PLATO Learning brings to the community a unique resources in the mathematics department and on and multi-faceted team with experience and expertise the campus. It can even open up new avenues for in three critical areas: mathematics instruction and generating revenue. In the face of persistent fiscal instructional design, software and networking pressures, Academic Systems Algebra provides an technologies, and faculty and technical support. In alternative to increasing faculty workloads, cutting combination, these strengths make PLATO Learning costs, and raising tuition. the leader in interactive multimedia mathematics instructional materials and implementation models for college mathematics courses. Professional Services Based upon 12 years of implementation experience, • How to take advantage of an environment where we and our partners have learned valuable lessons faculty know the progress and performance of each about how Academic Systems Algebra can best be student daily. implemented in a variety of college and university • How to customize the instructional modules to best settings to maximize student learning. meet the objectives of specific courses and the needs of individual students. together we have learned: • How to take advantage of network technology to • How to implement Mediated Learning in a variety of extend access to mathematics courses beyond campus settings, taking into account facilities, the classroom to support expanding and highly technology, staffing, and scheduling. in-demand distance learning implementations. • How to best utilize a combination of instructional methods in a Mediated Learning environment. Summary of Typical Course Content for the Academic Systems Algebra Series Academic Systems Algebra consists of 21 topics in 62 lessons covering 111 concepts. The following examples show how some campuses structure the Academic Systems Algebra courses. The material is modular and can be customized to fit your campus’ needs. BasIc MatheMatIcs/PrealgeBra eleMentary algeBra InterMedIate algeBra • Whole Numbers • Essentials I—Preparing for Algebra • Essentials II—A Review of • Proportional Reasoning I • The Real Numbers Elementary Algebra • Fractions • Solving Linear Equations and • Introduction to Graphing • Decimals Inequalities • Graphing Linear Equations • Introduction to Graphing and Inequalities • Proportional Reasoning II • Graphing Linear Equations • Solving Linear Systems • Ratio and Proportion and Inequalities • Exponents and Polynomials • Percent • Solving Linear Systems • Factoring • Signed Numbers • Exponents and Polynomials Factoring • Rational Expressions • Geometry • Rational Expressions • Rational Exponents and Radicals • Interpreting Data • Rational Exponents and Radicals • Quadratic Equations • Units of Measurement • Quadratic Equations • Functions and Graphing • Graphs • The Exponential and • Introduction to Statistics Logarithmic Functions • The Real Numbers • Solving Linear Equations and Inequalities For more detailed information, see Appendix I. As we and our partners know, faculty play a central role Armed with detailed learner progress reports, faculty in shaping the continuous improvement of instructional can intervene with customized instruction. Mediated materials and implementation models. The Mediated Learning provides faculty with a powerful tool for Learning approach enables faculty to integrate powerful enhancing the learning success of students. Faculty new technologies into their courses without requiring partners report that Mediated Learning allows them to them to become technologists. The Mediated Learning teach the way they would want to, if it were not for the environment focuses on learning, not on technology, constraints of time, budgets, and tradition. and so discussions among our partner faculty focus on instructional issues, not technical issues. In a Mediated Learning environment, students learn by drawing upon faculty expertise and by working with the In the following description of Academic Systems multimedia lessons and printed materials. In a Mediated Algebra, the instructional materials, methods, and Learning environment, learners shift from being passive support models result from the combined efforts of this receptors of delivered instruction to actively engaged extensive collaborative community. Together we are learners. Students can work individually, in pairs, and successfully improving the academic lives of students in groups in class or online, guided by faculty who and faculty. have the tools to provide the situationally appropriate assistance each learner needs to succeed. The Mediated Students have individual learning styles, motivations, Learning Model and preferences, as well as different rates of learning and varying levels of prior knowledge and skills. Mediated Learning is a faculty-guided, learner-centered By having more interaction with instructors, in person approach to instruction and learning founded on the or online, and by actively learning in an interactive research of current learning theory of the last few multimedia instructional environment, students in a decades and informed by the wisdom of practice of Mediated Learning environment can receive the outstanding faculty from across the country. Mediated individualized support they need to succeed regardless Learning draws upon the best elements of traditional of whether they attend class on campus or online. instructional methods—lectures, seminars, and tutoring—and incorporates a new element: interactive Mediated Learning is informed by the wisdom of multimedia instructional software, enabling faculty practice—the wisdom of faculty with years of experience to support both on-campus and distance in the classroom and online helping students learn learning courses. entry-level mathematics. Experience and research on learning are clear: students need to be active learners, In a Mediated Learning environment, faculty find they need to apply concepts to real-world problems, that they can now draw from a variety of instructional and they need timely, individualized feedback. As the techniques, choosing which is appropriate at the time. Mathematical Association of America recommends, Faculty can involve students in collaborative projects students in developmental mathematics courses in person or online, lecture to present special material, “should participate actively and receive frequent and provide customized tutoring to respond to each personal attention.” learner’s unique needs. Freed of many routine and standardized instructional, assessment, and administrative tasks, faculty focus their valuable time on teaching activities with the highest impact—providing timely, individualized feedback, developing specialized curricula, and working with students in small groups, one-on-one, and via the Internet. Mediated Learning represents a return to the traditional Mediated Learning environment, students spend less and fundamental principles of good instruction. This time on concepts they already understand or learn approach enables instructors to be the kind of quickly and more time on problem areas. Some faculty instructors they want to be and their students want allow students who demonstrate mastery of the them to be—more accessible and more informed week’s material in a pretest to proceed directly to about each student’s individual learning needs. the next lesson. This flexible, interactive, multimedia software design, coupled with the increased impact Mediated learning Model of faculty in a Mediated Learning environment, makes Mediated Learning effective and valuable for students of all abilities. Instructors Text Instructional Design Learners of Academic Systems Algebra applying the Mediated learning Model to Mathematics. Academic Systems Algebra’s Interactive Multimedia Instruction & Assessment comprehensive instructional materials include three integrated elements: interactive multimedia lessons, Personal Academic Notebooks (PAN), and an integrated learning environment. • Instructor role. The instructor in a Mediated Learning class provides direction, guidance, and individualized Interactive Multimedia lessons. Academic Systems instruction. Algebra has been designed for the faculty-guided, learner-centered environment of the Mediated Learning • Student role. The student in a Mediated Learning approach. The interactive multimedia lessons class is an active learner, working individually, with a accommodate students’ individual learning styles. partner, or in a group, drawing upon the most effective Students control the pace and the order of instruction resources as needed. within a lesson, with recommendations from the • Media and text. Mathematics content is presented in program and direction and individualized support a stimulating fashion, utilizing a variety of pedagogical from faculty. methods appropriate to each student’s needs. A Mediated Learning course provides students with flexibility, but it also provides more structure, guidance, and support than self-paced independent study courses. Students work within a faculty-created syllabus, meeting or exceeding stated class goals each week. But each student allocates his or her time and effort differently in order to increase the efficiency and effectiveness of their own learning. For example, in a Sample Pretest Question Academic Systems Algebra covers 21 topics in 62 score for each concept covered in the pretest, and lessons. Each lesson consists of six modules designed based on these scores, the student receives a to instruct students and assess their progress customized learning plan. The learning plan helps the throughout the course: Overview, Explain, Apply, student guide and focus his or her study throughout the Explore, Homework, and Evaluate. These six modules lesson by indicating for each concept whether it is perform the key tasks of assessment and feedback, optional, recommended, or strongly recommended. instruction, and the assignment of homework. Each lesson also makes use of special features and student score learning Plan for mathematical tools incorporated into Academic on a concept that concept Systems Algebra. < 74% strongly recommended 75% to 89% recommended real-time assessment and Feedback. Students > 90% optional receive assessment and feedback before, during, and after each lesson. The learning plan is designed to provide students with Pretest. Each Overview contains an optional pretest, information to help them decide how to spend their and all students can take a pretest for each lesson. For learning time most effectively and efficiently. The each concept presented in a lesson, there are usually learning plan recommendations appear on students’ four test items, so a typical pretest consists of between menus throughout the lesson to remind them of their eight and sixteen questions. Test items are presented in course of study. random order so that two students sitting side-by-side will not see the items in the same order. Questions take The pretests are diagnostic and prescriptive several formats and may ask students to type a number, instruments designed to support and guide student expression, or equation; plot a point; draw a line or study and are not intended to contribute to a student’s curve; select the correct symbol, expression, equation, grade in the course. However, depending on how description, number line, graph, coordinates, point, faculty customize their course, students scoring over theorem, or region; or complete a table. 90% on all of the lesson concepts may choose to count the pretest score as the final score for the lesson. The use of cooperative learning strategies is also critical to providing positive learning experiences…as faculty take on the role of a coach, rather than that of an authority figure, and as students learn to work together, they will begin to realize the mathematical power they possess. AMATYC Standards for Introductory College Mathematics Before Calculus Individualized learning Plan. Students receive extended feedback based on the results of the pretest. Sample Lesson Learning Plan In addition to receiving an overall score, students are able to view the answers and see the explanation of each question. Most importantly, students receive a I am learning more because it is at my own As in Overview, at the end of the final quiz, students pace. The computer does a great job in can see their scores, review the test questions, and compare their answers with the solutions provided. explaining and gives repeated examples! I Instructors can select how many times a student can am finally starting to visualize the problems take the final quiz. All student scores are reported to as opposed to just learning equations. the instructor. Academic Systems Algebra Student, Oklahoma State University at Oklahoma City Instruction. Students receive a preview of the lesson concepts within the Overview module. Most of assessment during the Instruction. During the Academic Systems Algebra’s core instruction is three different instructional modules of Explain, Apply, provided to students in the following three modules. and Explore, students work practical exercises. As the student works each problem, he or she receives each module takes a different pedagogical approach: different forms and degrees of feedback and support, • Explain presents the lesson concepts, shows with the support being appropriate to the learner’s examples, and then asks the student to work situation and the pedagogy of that instructional module. examples, supported by prompts and selected At the end of each instructional module, the student assistance. is shown how many exercise problems they completed correctly and is given customized recommendations • Apply allows students to learn in a problem-centered for next steps. environment. Problems are presented first and then, as the student solves the problem, focused instruction Post test. Evaluate provides the final quiz for the and assistance are provided. lesson. Lesson quizzes are criterion-referenced tests • Explore provides students with a structured and are similar to the pretests in Overview. They are environment of modules and exercises that facilitate designed to check a student’s understanding of the student discovery of underlying concepts. lesson concepts and are intended to count toward a student’s grade in the course. Each of these models of learning appeals most strongly to different types of learners; used together they enhance and strengthen the learning process. Sample Evaluate Final Quiz Question Sample Evaluate Score Screen Explain Explain is designed to model, in a rich interactive multimedia environment, the teaching and guidance behaviors, strategies, and tactics of an expert instructor. It presents, explains, and demonstrates the most important concepts, procedures, and operations embedded in the planned lesson. Effective mathematics instruction should involve active student participation. In-depth projects employing genuine data should be used to promote student learning through Sample Explain Check for Understanding Screen guided hands-on investigations. AMATYC Standards for Introductory College Mathematics Before Calculus each Explain includes: • Introduction: A short video that relates the concepts in the lesson to real-life situations. • Explanation: The instructional core of the lesson uses instruction screens to convey the key concepts and procedures. • Exercises: During the explanation, students work exercises that check their understanding of the new concepts. Students have two chances to answer each Sample Explain Summary Screen question. If a student answers a question incorrectly on the first attempt, suggestions are provided. Students may then use this feedback to answer At the end of each Explain concept, the student sees the question again. Following the second try, a how many exercise problems they completed, the step-by-step solution is provided, whether the number and percent answered correctly on the first try, student has answered correctly or not. and customized recommendations for next steps. All students’ exercise results are reported to the instructor. • Other Explain features include: Lesson Summary, Helpline, Take a Closer Look button, Journal, and glossary words. Sample Explain Instruction Screen Apply Explore In Apply, students learn and apply the concepts and Explore helps students investigate mathematical skills introduced in Explain by solving a variety of concepts using tools such as the Grapher and the problems. Academic Systems Algebra provides Expression Editor. It reinforces the concepts introduced students with the ability to link directly to those pages in Explain and challenges students to extend their in Explain that teach the concepts or procedures knowledge via guided and open explorations in which needed to answer the specific question in Apply. students experiment to become familiar with a variety of mathematical and problem-solving tools. Specific feedback and tutorial-like assistance are provided for every student response, but not until after Guided explorations ask students to investigate and the student has attempted the problem. Each Apply write about an idea central to the mathematics in concept ends with a score screen similar to the one the lesson. ending each Explain and Explore. All results are reported to the instructor. Sample Explore Guided Exploration Screen Sample Apply Problem Question Screen Carefully constructed problem situations, directed use of the tools, and feedback support the student’s inquiry. After the students have finalized their thoughts and observations, they can save them as notes in their Journals. Sample Apply Score Screen Homework Academic Systems Algebra provides both online and offline homework. Offline homework assignments in algebra are customized for each student based on their performance in a lesson; the better a student’s performance, the more challenging the homework questions. In the Fundamentals Prealgebra lessons, the instructor assigns homework from an item bank of 72 to 96 problems per concept. The homework problems are located in the Personal Academic Notebook. Every lesson in the Personal Academic Notebook also includes a set of enrichment activities. These problems are more challenging than Homework problems and are Sample Explore Question Screen often open-ended. Explore questions, often built around the tools, Online homework is part of the Academic Systems challenge students to integrate concepts from the Algebra lesson and is automatically graded and reported. lesson. Feedback is provided for every response. It is available in two modes—instructional mode and test As in Apply, the Link to Explain button takes the student preparation mode. In instructional mode, students get directly to those instruction screens in Explain that immediate detailed feedback upon completing the teach the concepts or procedures needed to answer question. Test preparation mode simulates the Evaluate the question in Explore. quiz and provides students with detailed feedback after the problem set has been scored. The Explore summary screen reviews the key points covered in Explore. As students review the summary, they are encouraged to take notes in their Journals. Explore ends with a score screen similar to the ones in Explain and Apply. All results are reported to the instructor. For students who are developing their basic mathematics skills, Fundamentals lessons provide a different type of exploration. In these prealgebra lessons, Explore consists of one or more investigations that feature everyday applications of mathematics. The investigations are introduced on the computer and developed in the Personal Academic Notebook. Sample Homework Screen 0 Academic Systems Algebra Instructional Design: Summary Each lesson consists of six modules designed to instruct students and assess their progress throughout a course: Overview, Explain, Apply, Explore, Homework, and Evaluate. An open architecture enables instructors to customize their learning path by re-sequencing and/or including or excluding these modules. Students in turn may move through the materials in any order. Overview gives students a preview, an optional explore provides students with an open pretest, and an individualized learning plan based exploratory environment, investigations of on the results of the pretest. The preview provides everyday applications of mathematics, and an advance organizer for the lesson and usually guided exploratory experiments that faciliate ties the concepts in the lesson to real-world student discovery and challenge students to contexts and applications for the concepts integrate concepts from throughout the lesson. covered. The pretests are diagnostic and Explore provides students, as needed, with prescriptive instruments designed to support situationally specific instruction. and guide students’ study. The individualized learning plan helps students decide how to use homework includes both offline and online their learning time most effectively and efficiently. options. Offline homework assignments are customized for an individual student based on explain presents the mathematical concepts their progress through and performance in a and procedures, works simple and then more lesson. In the Fundamentals Prealgebra lessons, complex examples, and then checks students’ the instructor assigns homework from an item understanding through first simple and then bank of 72 to 96 problems per concept. The more challenging exercises. Using text, hypertext, Homework problems are located in the Personal visualizations, animation, graphics, video, and Academic Notebook. Online Homework is part of audio, the presentation of concepts captures each Academic Systems Algebra lesson and is the teaching and guidance techniques of an automatically graded and reported. It is available expert instructor. in two modes—instructional mode and test preparation mode. apply centers the learning process around specific problems and then provides students, evaluate provides the final quiz, or post test, as needed, with support and instruction specific for the lesson and is similar to the pretest in to the concepts to be learned. The screens of Overview. A typical post test consists of instruction utilize the same highly stimulating between 8 and 16 questions. techniques used in Explain. Special Features of the Multimedia Lessons helpline: The Helpline (available in Explain and link to explain: The Apply, Explore, and online Explore) offers students hints and alternative Homework screens allow students to access explanations of concepts in more colloquial terms. the relevant instructional screens in Explain on an as-needed basis. Students simply click a link the helpline is designed to: to Explain button to review the specific instructional • Assist students in choosing an appropriate screens that introduce the content in question. When approach to answering a question students have completed their review, they can easily return to their place in Apply or Explore. • Talk students through the first step in solving a problem the expression editor: A sophisticated answer- • Show a sketch of the problem situation processing tool designed to allow students to write complex mathematical expressions, equations, or • Remind students of the key mathematical inequalities. Thus, students can answer open-ended properties to use mathematics questions online as part of assessment • Work through a similar problem or instructional modules. For students who are developing their basic glossary Words: Students can click any underlined mathematics skills, Fundamentals lessons contain a word or phrase to see its definition and an example. Helpline that is “staffed” by one to four student helpers who supply multiple representations. Each student helper represents a different learning mode and provides hints and explanations accordingly. take a closer look: Students can learn more about a concept in Explain by clicking the Take a Closer Look button. This feature offers additional examples, alternative explanations, or other information to help students study a concept in greater detail. Personal Academic Instructor Customization Notebooks Features Personal Academic Notebooks allow students access Customization features give faculty the option to to the course materials when they are away from the design a course to match their syllabus and unique computer. This new form of instructional text replaces teaching style. the standard “one-size-fits-all-learners” textbook. • Instructors can fully customize student learning paths, Each online lesson has a corresponding lesson in allowing them to decide how to present the the Personal Academic Notebook. Based on the instructional content to students. They can also customized lesson plan, students are assigned upload their own online content and add Internet links particular sections of the Notebook in order to focus to further enhance instruction. their attention where it is most needed. • Faculty can control courseware access, assignment the Personal academic notebook contains due dates, and the order of instruction through the the following: creation of multiple assignments at the section, small • Summaries of all lesson concepts group, or individual student level. • Lesson checklists • Various instructional options allow faculty to choose online homework mode, the number of quiz attempts • Worked and partially worked sample problems available to students, and the types of questions • Offline homework problems (assigned by the shown on pretests and quizzes. computer) that give students practice while away • A flexible pre-validation grace period allows faculty to from the computer provide students with immediate online courseware • A lesson practice test which helps students prepare access the first day of class—prior to a student even for the final quiz purchasing their materials. The length of this grace period is determined by the instructor. • Cumulative review problems (provided at the end of each topic) that provide practice in all concepts • A test-generator enables instructors to create quizzes covered to date and can help students prepare for and exams using computerized test items correlated mid-terms and finals to the Academic Systems Algebra lessons. the Personal academic notebook is dynamically linked Communication is key. Instructors can utilize three to the interactive instructional lessons in three ways: communication tools to enhance instruction, inform students, and encourage collaboration. • Each instructional screen provides students with a link to the specific sections in the online version of the • Message Posting: Faculty can post a message to their Notebook that gives additional instructional section, small group, or individual students to share assistance on that specific concept. important class or assignment information. Likewise, students can post a message to their instructors. • Academic Systems Algebra creates a personalized learning plan that provides the student with guidance • E-mail Initiation: Faculty can initiate an e-mail to any on how to best use the Notebook to increase student number of students which will be delivered to the efficiency. student’s respective e-mail in-boxes. Students can also e-mail faculty. • Based on a student’s progress through and achievement in each lesson, each student receives • Threaded Discussion Board: Faculty can initiate a customized offline homework assignment in the threaded discussion topics to any number of students Personal Academic Notebook. to foster online collaboration. Students can contribute responses for all to see and respond to. PLATO Learning Environment™ (PLE™) Learner Progress Report The PLATO Learning Environment provides instructors The Learner Progress Report is a resource for both with timely, concise information about student faculty and students. It indicates the amount of time a achievement. This information gives instructors valuable student has spent on each module and module insights into the learning needs of each student, concept, the scores for lessons and modules, whether enabling instructors to more effectively intervene so as or not a student has reviewed individual concepts, and to maximize student learning. PLE creates multiple the dates on which a student completed individual reports, including a Section Progress Report and a topics, lessons, modules, and concepts. detailed Learner Progress Report. Each report can be With these reports instructors can: viewed, downloaded, or printed anytime, anywhere. • Monitor and analyze students’ progress quickly and accurately Section Progress Reports • Identify for each student patterns of activity that A Section Progress Report summarizes the achievement are problematic including attendance problems, of students through the course by providing information skipping of lesson modules, or ineffective use of on what lessons each student has completed, what instructional modules scores they have received for each lesson, the cumulative time each student has spent on all lessons • Provide students with insightful personalized support to date, as well as several student and class averages. • Identify groups of students with similar problems for small group instruction From this report, instructors can regularly: • Establish peer tutoring • Determine the overall pace of the class • Identify when to present mini-lectures to reinforce • Determine the overall achievement selected materials or post discussions for • Quickly identify individual students who may require collaboration assistance as indicated by poor performance in terms of pace, achievement, or time-on-task • Identify students who may be candidates for early completion • Identify content areas where groups of students may need additional help • Export student scores to gradebooks or spreadsheets While viewing the Section Progress Report, an instructor can click a student’s name to link directly to that student’s detailed Learner Progress Report. Section Progress Report (by assignment) Learner Progress Report Results: Success for Students, Faculty, and Campuses Faculty and students have achieved significant the following three examples demonstrate the success through the use of Academic Systems continued success of Mediated learning.* Algebra. Faculty consistently report that their Community college. A community college’s historical students are learning better and learning more. pass rate for its basic algebra course was 31 percent. student academic achievement. Data provided By the second term of Academic Systems Algebra, the by campuses using Academic Systems Algebra pass rate increased to 36 percent and in the third term show that faculty and students have improved pass to 42 percent—a 35 percent improvement over the rates an average of 5 to 15 percent over pass rates historical pass rate. in traditional courses. Many faculty have achieved Four-year urban university. A four-year urban pass rate improvements of more than 20 percent. In university experienced positive results in the first term. addition, campus data shows that retention rates Historically, the pass rate for basic algebra was 47 increased at more than 75 percent of campuses that percent, but in the first term of Academic Systems used Academic Systems Algebra. Academic Algebra, the pass rate was 70 percent. The second Systems Algebra has been successful in a wide term, the pass rate increased to 73 percent—a 55 variety of settings. Successful results are being percent improvement over the historical pass rate. realized on new and experienced campuses, in courses of varying section size, with instructors who are experienced with technology, and with those who are not, with students who are comfortable with instructional technology, and with those who have Mathematics Tools had little or no experience with it. Successful results Academic Systems Algebra’s lessons offer both have also been found in urban and non-urban areas, independent and guided use of a number of in community colleges and four-year colleges and mathematics and problem-solving tools. universities, with students who are taking the courses for the first time, and with those who have the grapher enables students to plot points and previously failed the course. to graph linear equations, linear equalities, quadratic functions, conics, and other relations. These are Faculty attribute the improved achievement to the represented both algebraically and geometrically, individualized, learner-centered environment created and students may choose from different algebraic by the Mediated Learning approach of Academic representations as they explore the connection Systems Algebra, which provides an effective and between algebra and geometry. The Grapher is supportive learning environment. integrated into relevant Explores and is available for independent use from the tools menu. Results continue to improve in the second and third terms: campuses that have used Academic the Journal is a tool that allows students to take Systems Algebra for several terms show even better notes online. The program prompts students to use results in the second and third terms. the Journal when they view a concept summary screen in Explain or Explore and when they record their observations of a guided exploration in Explore. Students may open their Journals at any time from the tools menu. the calculator is available at any time from the tools menu to help students perform arithmetic operations. Four-year state university. A four-year state university learning resource center, at home, or in the workplace. had historical pass rates of 68 percent in its basic The instructor manages the technology-mediated algebra course. With Academic Systems Algebra, instructional environment by establishing a detailed faculty increased the pass rate to 73 percent in the syllabus, delivering mini-lectures, monitoring student first term and to 88 percent in the second term—a 29 progress through PLE, and working one-on-one with percent improvement over the historical pass rate. students or small groups. Instructors are also available during office hours. Faculty report more effective instruction and learning environment. Faculty nationwide report that distance learning: an Interactive Internet course Academic Systems Algebra creates a better instruction and learning environment for themselves and their With Academic Systems Algebra, campuses can students whether on campus or online. Instructors deliver a multimedia-rich course over the Internet. who have made the transition to the Mediated Learning Faculty have many options available to design the approach report that their students are learning better course to match their own course objectives, syllabus, and learning more. Faculty say they are energized by and goals. Utilizing the flexible options for assignment using the new methods while students say they are structure, content availability, integration of faculty now understanding and enjoying mathematics. With created resources, and communication tools, faculty Academic Systems Algebra, faculty can provide a can offer their course to an online community of diverse population of students with a more learners with confidence. Via the Internet, instructors individualized learning experience. Students can can access extensive data about their distance learning access more learning resources, when they need them sections with specific detail about each student. and at the level they require, anytime, anywhere. Faculty With this data, instructors know where their students can better utilize scarce and valuable resources— are relative to the syllabus and can utilize the including their expertise and their time—and gain more communication tools to give specific, focused flexibility in the way they teach. assistance and support to students as needed, as well as foster an online community by utilizing collaborative * Please note that the results of specific campuses are threaded discussions. kept confidential. scheduled class Meetings Plus remote access As another alternative, many campuses combine Implementation Models scheduled classroom meetings with the flexibility of Academic Systems Algebra is being used successfully off-campus remote access to give students more time in a number of different implementation models, ranging to work in Academic Systems Algebra lessons. In this from full integration into scheduled classes to distance way, campuses can maximize scarce classroom learning. Some of the common implementation models resources, yet still have the benefit of face-to-face are described below. interaction between instructors and students. scheduled class Meetings On campus In this blended implementation, students attend One common implementation is using Academic a regularly scheduled class in a lab with their instructor Systems Algebra as the curriculum in regularly 1 to 3 hours per week. Students are also required to scheduled class meetings with an instructor for 3 to 6 spend additional hours each week working in the hours per week in an electronic classroom (lab). Each library, a learning resource center, at home, or at work. class meeting, students work on Academic Systems Algebra lessons at a workstation on the campus Faculty can access PLE to monitor student progress intranet. Students who need extra time can use and plan their curriculum from their office or home. open lab hours in the classroom, in the library, in a Support PLATO Learning Services builds educator capacity to • Access PLATO Learning’s online support knowledge promote increased student achievement through the base and valuable supplementary resources including use of PLATO Learning solutions. Our goal is to curriculum guides and teaching materials collaborate with educators, schools, and campuses to • Learn tips and tricks used successfully at thousands encourage continued learning, implement successful of installations worldwide programs, and achieve student success at all levels. The PLATO Learning Services team provides • Receive product enhancements and information about professional development, support services, and upcoming product updates—via the Product Update consulting services to help campuses make the most of Center—quickly and easily their investment in technology. continuous Improvement PlatO learning is dedicated to providing: Academic Systems Algebra is the result of a true collaboration between PLATO Learning and educators. • campuses with the confidence that their technology From the very beginning, the instructors and students implementation will run at optimal levels and meet using this program have been partners in our ongoing their needs; effort to continuously improve Academic Systems • Faculty with the capacity to use technology to Algebra. To facilitate faculty involvement in the increase productivity and enhance instruction; and continuous improvement process we convene periodic • students with the excitement of learning and the forums where instructors share experiences and offer desire for personal growth. suggestions for improvement, and utilize easy-to-use software feedback forms for reporting issues or PLATO Learning Services provides educators, schools, making suggestions. and campuses with the tools and resources necessary to operate successful implementations of PLATO Learning solutions. PLATO Learning collaborates with you to reach the ultimate goal—student success. technical support PLATO Learning provides technical assistance through PLATO® Support Services which allows campuses to: • Operate smoothly and with maximum uptime through support services and updates • Obtain help 24 hours a day, seven days a week, 365 days a year through a comprehensive support web site (http://support.plato.com) • Receive quick answers to inquiries from a Technical Service Representative via e-mail or over the phone Appendices Appendix I—Academic Systems Algebra: Content and Applications A campus can customize its mathematics courses using any of the lessons available in the Academic Systems Algebra series. Three typical courses are described below. Prealgebra real-World applications The course features four students who use Approximately 70 hours of instruction for basic mathematics at school, at home, and in the workplace. mathematics and prealgebra courses in two- and four- These settings supply many opportunities to illustrate year colleges. Provides comprehensive coverage of all the mathematics via applications. Examples are standard topics, including an introduction to algebraic included from business, shopping, cooking, medicine, expressions and equations. Includes additional material sports, media, computers, and transportation. supporting mathematics explorations, applications of mathematics to real-world problems, writing and Integrated Mathematics tools observation activities, and collaborative learning projects. and special Features Tools are featured on practice screens where students topics covered are presented with different levels of problems. Based • Whole Numbers upon their responses, students receive additional • Proportional Reasoning I problems at a higher level or receive more problems at • Fractions the same level to help them move on to the next level • Decimals of problems. Four students offer multiple types of • Proportional Reasoning II assistance to address varied learning styles. • Ration and Proportion • Percent Elementary Algebra • Signed Numbers Approximately 70 hours of instruction for elementary • Geometry algebra courses in two- and four-year colleges. • Interpreting Data Provides comprehensive coverage of all standard • Units of Measurement topics, plus additional material supporting mathematics • Graphs explorations, applications of mathematics to real-world • Introduction to Statistics problems, writing and observation activities, and • The Real Numbers collaborative learning projects. • Solving Linear Equations and Inequalities topics covered • Essentials I: Preparing for Algebra explorations • The Real Numbers In each lesson, students can use mathematics to pursue one or more investigations. Some investigations • Solving Linear Equations and Inequalities require students to gather data in their classroom or • Introduction to Graphing community, then analyze and present the data. Other • Graphing Linear Equations and Inequalities investigations ask students to explore mathematical • Solving Linear Systems relationships. • Exponents and Polynomials • Factoring • Rational Expressions • Rational Exponents and Radicals explorations • A daycare center manager determines the best use of • Identify greatest common factors and least common volunteers by solving a system of linear inequalities multiples by finding prime factors • A biologist uses radicals in her study of factors that • Explore properties of real numbers affect fish populations • Use a graphing tool to analyze slopes, lines, and • A farmer uses rational exponents and radicals to linear equations describe his experiments with different crops to obtain the maximum yield from his land • Compare different forms of linear equations and their graphs • A student volunteer who handles surveys and mailings for a nonprofit center uses radical expressions in • Analyze graphs of linear equations his work • Use a graphing tool to find solutions of systems of • A student uses ratios to calculate the cost of a certain two linear equations number of items • Use a graphing tool to find solutions of systems of • A photographer uses rational expressions to describe two linear inequalities his camera settings • Explore multiplication and division of polynomials • The student determines the amount of fencing needed • Use a tool to find the greatest common factor of to enclose an area of a park two polynomials • Runners find changes in elevation during a race by • Factor a difference of two squares, perfect square adding and subtracting signed numbers trinomials, and sums and differences of two cubes • A young man determines how to best allocate money • Graph equations to examine direct variation, ratio, between two accounts by solving a system of linear and proportion equations • A bank officer uses a formula containing polynomials real-World applications to help a customer obtain an automobile loan • Students encounter real numbers in their daily lives • A family uses ratios and proportions to solve problems • Carpenters use fractions to build bookshelves related to a home business • A daycare provider solves a linear inequality to • The student learns how to express the relationship determine profit margins between the number of pages in a script and the length of a movie by writing a linear equation • A health care worker plots tuberculosis data to help identify trends • The student uses exponential notation to describe the difference in magnitude of earthquakes • A meteorologist uses linear equations to predict future levels of atmospheric CO2 • A baseball fan graphs linear inequalities to compare the number of hits made in a game with the number of hits he predicted • A businesswoman chooses the most profitable form of payment by solving a system of linear equations Intermediate Algebra • Find real solutions of nonlinear equations using a graphing tool Approximately 70 hours of instruction for intermediate • Use a graphing tool to find real solutions of systems algebra courses in two- and four-year colleges. of two or more nonlinear equations Provides comprehensive coverage of all standard topics, plus additional material supporting mathematics • Solve nonlinear inequalities by graphing their explorations, applications of mathematics to real-world corresponding functions problems, writing and observation activities, and collaborative learning projects. real-World applications • A biologist uses radicals in her study of factors that topics covered affect fish populations • Essentials II—A Review of the Essentials of Algebra • A farmer uses rational exponents and radicals to • Introduction to Graphing describe his experiments with different crops to obtain • Graphing Linear Equations and Inequalities the maximum yield from his land • Solving Linear Systems • A student volunteer who handles surveys and mailings • Rational Expressions for a nonprofit center uses radical expressions in • Rational Exponents and Radicals his work • Quadratic Equations • A newspaper reporter uses logarithms to investigate • Functions and Graphing topics ranging from truth in advertising to facts • The Exponential and Logarithmic Functions concerning a toxic waste spill • More Nonlinear Equations and Inequalities • An engineer uses complex numbers to design components for an audio system explorations • An artist designs pieces of stained glass with the • Use a graphing tool to analyze slopes, lines, and help of linear and quadratic functions linear equations • A businesswoman evaluates whether a store’s offer to • Examine different forms of linear equations and sell her hand-painted jackets makes sense financially their graphs using systems of nonlinear equations • Analyze graphs of linear inequalities • A market research team of a small company uses nonlinear inequalities to make decisions about the • Find solutions of systems of two linear equations sales potential of a new product using a graphing tool • A health care worker plots tuberculosis data to help • Use a graphing tool to find solutions of systems of identify trends two linear inequalities • A meteorologist uses linear equations to predict future • Graph equations to examine direct variation, ratio, levels of atmospheric CO2 and proportion • A baseball fan graphs linear inequalities to compare • Explore completing the square, the solutions of a the number of hits made in a game with the number quadratic equation, and the discriminant of hits he predicted • Explore relationships between functions and their • A businesswoman chooses the most profitable form graphs of payment by solving a linear system of equations • Use graphs to explore operations on functions and • A daycare center manager solves a system of linear inverses of functions inequalities to determine the best use of volunteer hours • Use a graphing tool to graph logarithmic functions and to examine their properties 0 • Medical center personnel use logarithms in various • A family uses ratios and proportions to solve problems aspects of their jobs related to a home business • Automobile salesmen use functions to choose a • The student learns how to describe the path of a ball marketing plan using a quadratic equation • The student learns how to express the relationship • A woman determines the rate of compound interest between the number of pages in a script and the needed to reach a particular monetary goal by solving length of a movie by writing a linear equation a quadratic equation • A young man determines how to best allocate money • The students describe population growth using between two accounts by solving a system of linear exponential functions equations • A group of architectural students use logarithms to • A photographer uses rational expressions to describe design a medical center his camera settings • A group of student entrepreneurs make decisions • A student uses ratios to calculate the cost of a certain affecting their small business using polynomial, number of items radical, and other nonlinear equations Appendix II—Detailed Scope and Sequence: Academic Systems Algebra Course Series topic lessons concepts Whole Numbers F1.1 Whole Numbers I Adding and Subtracting Multiplying and Dividing Rounding and Divisibility F1.2 Whole Numbers II Exponential Notation Order of Operations Proportional Reasoning I F2.1 Fractions I Equivalent Fractions Multiplying and Dividing F2.2 Fractions II Common Denominators Adding and Subtracting F2.3 Decimals I Notation Converting F2.4 Decimals II Adding and Subtracting Multiplying and Dividing Proportional Reasoning II F3.1 Ratio and Proportion Ratios Proportions F3.2 Percent Definition Converting Solving Percent Problems topic lessons concepts Signed Numbers F4.1 Signed Numbers I Adding Subtracting F4.2 Signed Numbers II Multiplying and Dividing Combining Operations Geometry F5.1 Geometry I Geometric Figures F5.2 Geometry II Perimeter and Area Surface Area and Volume F5.3 Geometry III Triangles and Parallelograms Similar Polygons Interpreting Data F6.1 Units of Measurement US/English Units F6.2 Interpreting Graphs Data and Graphs F6.3 Introduction to Statistics Statistical Measures Preparing for Algebra EI.A Fractions Multiplying and Dividing Adding and Subtracting EI.B Signed Numbers Adding and Subtracting Multiplying and Dividing The Real Numbers 1.0 The School of Pythagoras 1.1 The Real Numbers Number Line and Notation 1.2 Factoring and Fractions The GCF and LCM Fractions 1.3 Arithmetic of Numbers Operations of Numbers Solving Linear Equations and Inequalities 2.0 Old Number Trick 2.1 Algebraic Expressions Simplifying Expressions 2.2 Solving Linear Equations Solving Equations I Solving Equations II 2.3 Problem Solving Number and Age Geometry 2.4 Linear Inequalities Solving Inequalities Introduction to Graphing 3.0 Story of Descartes 3.1 Introduction to Graphing Plotting Points Rise and Run The Distance Formula topic lessons concepts Graphing Linear Equations and Inequalities 4.0 The Classroom 4.1 Graphing Equations Graphing Lines I Graphing Lines II Slope of a Line 4.2 The Equation of a Line Finding the Equation I Finding the Equation II 4.3 Graphing Inequalities Linear Inequalities Solving Linear Systems 5.0 The Great Train Rescue 5.1 Solving Linear Systems Solution by Graphing Solution by Algebra 5.2 Problem Solving Using Linear Systems 5.3 Systems of Inequalities Solving Linear Systems Exponents and Polynomials 6.0 King of Persia 6.1 Exponents Properties of Exponents 6.2 Polynomial Operations I Adding and Subtracting Multiplying and Dividing 6.3 Polynomial Operations II Multiplying Binomials Multiplying and Dividing Factoring 7.0 The Factor Gallery 7.1 Factoring Polynomials I Greatest Common Factor Grouping 7.2 Factoring Polynomials II Trinomials I Trinomials II 7.3 Factoring by Patterns Recognizing Patterns Rational Expressions 8.0 The Golden Ratio 8.1 Rational Expressions I Multiplying and Dividing Adding and Subtracting 8.2 Rational Expressions II Negative Exponents Multiplying and Dividing Adding and Subtracting 8.3 Equations with Fractions Solving Equations 8.4 Problem Solving Rational Expressions topic lessons concepts Essentials of Algebra EII.A Real Numbers and Exponents Real Numbers and Notation Integer Exponents EII.B Polynomials Polynomial Operations Factoring Polynomials EII.C Equations and Inequalities Linear Equations and Inequalities EII.D Rational Expressions Rational Expressions Rational Equations EII.E Graphing Lines Graphing Lines Finding Equations EII.F Absolute Value Solving Equations Solving Inequalities Rational Exponents and Radicals 9.0 Fishing for Roots 9.1 Roots and Radicals Square Roots and Cube Roots Radical Expressions 9.2 Rational Exponents Roots and Exponents Simplifying Radicals Operations on Radicals Quadratic Equations 10.0 Formula Machines 10.1 Quadratic Equations I Solving by Factoring Solving by Square Roots 10.2 Quadratic Equations II Completing the Square The Quadratic Formula 10.3 Complex Numbers Complex Number System Functions and Graphing 11.0 Office Functions 11.1 Functions Functions and Graphs Linear Functions Quadratic Functions 11.2 The Algebra of Functions The Algebra of Functions Inverse Functions The Exponential and Logarithmic Functions 12.0 Earthshaking Logs 12.1 Exponential Functions The Exponential Function 12.2 Logs and Their Properties The Logarithmic Function Logarithmic Properties 12.3 Applications of Logs Natural and Common Logs Solving Equations topic lessons concepts More Nonlinear Equations and Inequalities 13.0 The Learinnon Experiment 13.1 Nonlinear Equations Solving Equations Radical Equations 13.2 Nonlinear Systems Solving Systems 13.3 Inequalities Quadratic Inequalities Rational Inequalities Academic Systems® Developmental Education Solutions 800.44.PLATO or www.plato.com/ASalgebra.aspx Copyright © 2007 PLATO Learning, Inc. All rights reserved. PLATO® and Academic Systems® are registered trademarks of PLATO Learning, Inc. Straight Curve and PLATO Learning are trademarks of PLATO Learning, Inc. PLATO, Inc. is a PLATO Learning, Inc. company. Printed in the U.S.A. Part #00206074 PM164A 4/07

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