Academic Systems Algebra Positioning Paper

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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




                                                                                    
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