Academic Systems Algebra Positioning Paper

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