Scholars Online Mathematics Course Sequence
Note: Mathematics class sessions use a browserbased open source text chat, audio and whiteboard package that does not require our students to purchase any additional software.
Scholars Online currently offers a fiveyear sequence of mathematics courses, beginning with the Discovering Mathematics Series — Discovering Algebra, Discovering Geometry and Discovering Advanced Algebra — which provides a comprehensive algebra and geometry curriculum. Advanced students who have already mastered algebra and geometry can work with our teachers on a similar PreCalculus and Calculus series authored by Paul Foerster. These courses meet the mathematics standards of both the NCTM and Washington State.
Our math teachers believe that learning happens by doing — by doing problems and by creating models, virtually or actually. Teachers incorporate the use of the TI84 calculator and The Geometer's Sketchpad, and Tinkerplots, requiring students to engage in handson exploration of many areas of mathematics. Students are challenged to go beyond the computational answer to a deeper conceptual understanding. Knowing that the answer is correct is not enough. Knowing that the answer is correct is important; knowing why it is correct is the key that enables students to construct their own core knowledge base and develop their own deep understanding. In pursuing understanding, the textbook is a flexible tool rather than scheduling taskmaster. Teachers may extend time spent in basic areas and selectively use enrichment materials from different parts of the text to ensure complete understanding, rather than pursuing rote completion of the assigned text.
Balancing comprehension and execution
For a number of decades, there have been strong disagreements about how to teach math. The Traditionalist and Modernist opponents in these “Math Wars” trade phrases like “drillandkill” and, “It doesn’t matter if the answer is right or wrong, if you understand what you’re doing”.
The “Traditionalist” school places a lot of value on specifics, on details, and on correctness, often using drills to achieve a certain fluency with the symbols.
The “Modernist” school places a lot of value on understanding, often trying to stimulate discovery on the part of the student, rather than mere duplication and rote memorization. “New math” can ask more, not less, of the students. This is also insufficient for some students, especially the more concrete thinkers.
We believe this is a false dichotomy, sensed, even if only unconsciously, by people on both sides of the “Math Wars”. The Traditionalists are not opposed to understanding and discovery, nor are the Modernists opposed to fluency and correctness. How can we reconcile the two approaches, and reap the individual benefits each can offer?
We can start by remembering that the final goal of education is learning, mastery on the part of the student, not teaching. We suggest that math learning proceeds in three steps:
 Imitation
 Illumination
 Inspiration
We can all hope for inspiration, but that can neither be scheduled nor taught.
The origins of mathematics are physical, sensory, and tangible: a shepherd has twenty sheep; if one is sold, then he has nineteen. A farmer in the time of the prophets has three ephahs of olive oil, and sells two, leaving one. These don’t change — and though the units for liquid measure might, the quantity of olive oil just doesn’t depend on how we measure it. The fundamental rules of algebra reflect the behavior, the invariant behavior, of physical things. For this reason, many parts of mathematics have an almost inevitable aspect to them. People say, “But of course!” when a mathematical concept is well expressed.
“Show me how to…” is a phrase every parent, most older siblings, friends, mentors, and teachers have heard. After being shown, the learner tries it independently. Sometimes the learner’s attempts work, sometimes they don’t. We learn “debugging skills” at an early age, in exploring the world around us, in trying to do things successfully.
Humans learn by doing, by “trying things out” — so a teacher has to “carve out” a period of time from everyday life when the student can focus on an activity and practice it. This is both classtime and homeworktime. Whether it’s playing the piano, playing football, or mathematics, proficiency requires practice, and learning requires repetition.
After doing a new activity a number of times, many people have an “Aha!” experience, as they figure out “what’s really going on here.” We can reasonably call that “Aha!” experience “illumination”. Once seen in the bright light of understanding, at least some things will never look the same again. This “Aha!” experience can lead to further exploration and to real discovery on the part of the learner — and whether or not that discovery is original or not, it’s a good thing, as the Modernists emphasize. Unfortunately, that doesn’t always happen. After all, it took many very intelligent people hundreds of years to figure out what should be taught in a oneyear math course.
But we’d like even more – more than rote learning, more even than understanding and application. We’d especially like a level of inspiration, an enthusiasm, that leads some students into becoming professional mathematicians. There’s only one way here: the learner must be at least a bit independent of the teacher, because the learner intends to surpass the teacher. Even the touchstone of inspired living, Jesus Christ Himself, said that His followers would do greater things than He Himself — changing the model for the relationship between teacher and student forever. And he did it by living it, by demonstrating it.
Echoing Jesus Christ, an effective mathematics teacher
 demonstrates,
 asks questions,
 requires practice from the student,
 guides, and
 corrects a student’s misunderstandings.
Computers and the internet are only a means. Behind any internet learning platform there must be an effective teacher who can provide the illumination and inspiration needed for the fullest expression of the good that God created in us.
Individual courses
If you would like to see a course not yet listed, please use the EMAIL US link below to contact Scholars Online Administration with your course request.
Students who were enrolled in courses from previous years will find the teacher, text, and course description information available from the student's unofficial transcript, which can be reached from the parent's Account Management Center, or from an alumni's own Account Management Center.

Algebra 1 • 2019 listing  for reference only • Grade 8 or above
 

Primary Instructor
 


Sections [Enrolled students will be notified if teacher schedules change between course posting at the time enrollment opens and the scheduled start of classes. Please see Tuition and Fees for refund policy.]
 
  Section 1 Instructor: James Caleb Dean
 Classes meet from September 3, 2019 to June 8, 2020
 Monday 7:00 AM to 8:00 AM ET • Wednesday 7:00 AM to 8:00 AM ET • Friday 7:00 AM to 8:00 AM ET
 Enrollment Policy: Full Session Only
 Tuition: $400.00



Website
 
 Please review more extensive materials at the teacher's Algebra 1 website.



Description
 
 Algebra I is the gateway course for college admissions. This course examines 1) the acquisition, analysis, and display of data (graphs and charts), 2) multiple representations of linear and quadratic relations, equations, inequalities, and functions, and 3) factoring and multiplying expressions. As time permits, we may examine 1) experimental and theoretical probability and 2) simple trigonometry.
Throughout, careful reasoning and real understanding are encouraged and prized.



Meetings
 
 This course meets 3 times per week for discussion and review of assigned homework.



Homework
 
 Homework assignments will be posted on a monthly calendar that will reflect the discussions and progress during our online time.



Prerequisites
 
 Prerequisite: Successful completion of PreAlgebra or an 8thgrade level arithmetic course.



Recommended background
 
 PreAlgebra course through Scholars Online or equivalent.



Textbooks and Materials
 

Discovering Algebra: An Investigative Approach (Edition: 2) Jerald Murdock, Ellen Kamischke, and Eric Kamischke
 


TINSpire Calculator
 
 This text is required. ISBN: ASIN: B004NBZAW0 Publisher's website: TINSpire Calculator Best sources: Scholars Online Bookstore or amazon.com or any office supply store Other information: There are several models of the TInspire; the standard model is fine for this class. This handheld device should last through college.



Geometry • 2019 listing  for reference only • Grade 9 or above
 

Primary Instructor
 


Sections [Enrolled students will be notified if teacher schedules change between course posting at the time enrollment opens and the scheduled start of classes. Please see Tuition and Fees for refund policy.]
 
  Section 1 Instructor: Art Mabbott
 Classes meet from September 3, 2019 to June 8, 2020
 Monday 11:00 AM to 12:00 PM ET • Wednesday 11:00 AM to 12:00 PM ET • Friday 11:00 AM to 12:00 PM ET
 Enrollment Policy: Full Session Only
 Tuition: $500.00



Website
 
 Please review more extensive materials at the teacher's Geometry website.



Description
 
 In this course, you will develop a logical system of thought. You will examine the properties of geometric shapes, and make conclusions about them using your logical system. This course covers most of Euclidean Geometry and some modern Geometry using traditional western tools of compass and straightedge and eastern tools of paper folding (origami) and modern tools (Geometer Sketchpad). Analytic Geometry is included to reinforce previously learned Algebra skills. The early part of the course has the students investigating geometric phenomena and collecting conjectures about what they see. Later on the students prove the conjectures they have collected. Topics may include: similar and congruent figures, angles, geometric proofs, conjectures, counter examples, ifthen statements, inductive and deductive reasoning, valid and invalid reasoning, postulates and proof, coordinate geometry, transformational geometry, transformation matrices, special right triangles.
Class sessions will take place using a virtual white board (WIZIQ). All class sessions are archived for review by the students or if the student is unable to attend for any reason. Students will need to register with WIZIQ prior to their first class session and will receive a secure invitation from the instructor to attend class sessions.
Homework will be assigned and discussed during the class time. Only quizzes and tests will be sent to each student (as well as their parents) as both .docx & .pdf documents and returned to the instructor for evaluation. Students will have an opportunity to correct all assessments to show mastery. It is the responsibility of the parents to supervise their student while completing each assessment. The evaluations will be returned to both the student and parent.



Meetings
 
 This course meets 3 times per week for discussion and review of assigned homework.



Homework
 
 Homework assignments will be posted on a monthly calendar that will reflect the discussions and progress during our online time.



Prerequisites
 
 Prerequisite: Algebra I or an equivalent level of study.



Recommended background
 
 No special background required.



Instructor's Notes
 
 Mr. Mabbott expects his students to reach mastery of all skills learned. Therefore the students will be asked to rework all assessments until such time that they can demonstrate mastery at 100%. Oneonone support in addition to regular class meetings will provided as needed.



Textbooks and Materials
 

Discovering Geometry (Edition: 5) Michael Serra
 
 This text is required. ISBN: 1465255028 Publisher's website: Discovering Geometry Best sources: Scholars Online Bookstore Other information: ISBN 13: 9781465255051



Algebra 2 (Advanced Algebra) • 2019 listing  for reference only • Grade 10 or above
 

Primary Instructor
 


Sections [Enrolled students will be notified if teacher schedules change between course posting at the time enrollment opens and the scheduled start of classes. Please see Tuition and Fees for refund policy.]
 
  Section 1 Instructor: Art Mabbott
 Classes meet from September 3, 2019 to June 8, 2020
 Monday 1:00 PM to 2:00 PM ET • Wednesday 1:00 PM to 2:00 PM ET • Friday 1:00 PM to 2:00 PM ET
 Enrollment Policy: Full Session Only
 Tuition: $500.00



Website
 


Description
 
 As far as possible, students are allowed to investigate algebraic concepts and processes before being introduced to the formulas and symbolic representations. Topics for exploration will include: linear, quadratic, exponential, logarithmic, rational, and irrational functions. You will expand your understanding of the number system to include complex numbers, and you will develop an understanding of the concepts of elementary trigonometry, elementary probability, and sequences and series. You also will learn to model realworld problems using these concepts.
A graphing calculator will be required at this level and beyond.
Class sessions will take place using a virtual white board (WIZIQ). All class sessions are archived for review by the students or if the student is unable to attend for any reason. Students will need to register with WIZIQ prior to their first class session and will receive a secure invitation from the instructor to attend class sessions.
Homework will be assigned and discussed during the class time. Only quizzes and tests will be sent to each student (as well as their parents) as both .docx & .pdf documents and returned to the instructor for evaluation. Students will have an opportunity to correct all assessments to show mastery. It is the responsibility of the parents to supervise their student while completing each assessment. The evaluations will be returned to both the student and parent.



Meetings
 
 This course meets 3 times per week for discussion and review of assigned homework.



Homework
 
 Homework assignments will be posted on a monthly calendar that will reflect the discussions and progress during our online time.



Prerequisites
 


Recommended background
 


Instructor's Notes
 
 Mr. Mabbott expects his students to reach mastery of all skills learned. Therefore the students will be asked to rework all assessments until such time that they can demonstrate mastery at 100%. Oneonone support in addition to regular class meetings will provided as needed.



Textbooks and Materials
 

Discovering Advanced Algebra: An Investigative Approach
(Edition: 3) Jerald Murdock, Ellen Kamischke, and Eric Kamischke
 


The Geometer's Sketchpad  Student Edition (1yr license) (Edition: 5) Nick Jakiw
 


TINSPIRE (either Numeric or CAS) Texas Instruments
 
 This text is required. ISBN: Best sources: Scholars Online Bookstore



PreCalculus with Trigonometry • 2019 listing  for reference only • Grade 11 or above
 

Primary Instructor
 


Sections [Enrolled students will be notified if teacher schedules change between course posting at the time enrollment opens and the scheduled start of classes. Please see Tuition and Fees for refund policy.]
 
  Section 1 Instructor: Art Mabbott
 Classes meet from September 3, 2019 to June 8, 2020
 Monday 3:00 PM to 4:00 PM ET • Wednesday 3:00 PM to 4:00 PM ET • Friday 3:00 PM to 4:00 PM ET
 Enrollment Policy: Full Session Only
 Tuition: $500.00



Website
 


Description
 
 PreCalculus, is the bridge course to Calculus. We will integrate rigorous real world mathematical scenarios with technology  Calculator and Dynamic Software. We will cement the concept that variables really vary. Beyond the traditional topics, we will be able to study concepts such as harmonic analysis of complex wave patterns and logistic functions for restricted populations growth. We will examine problems from multiple perspectives  graphical, tabular, functional, and situational. And we will revisit one of our tools from Geometry to assist us in our analysis of complex functions.
Class sessions will take place using a virtual white board (WIZIQ). All class sessions are archived for review by the students or if the student is unable to attend for any reason. Students will need to register with WIZIQ prior to their first class session and will receive a secure invitation from the instructor to attend class sessions.
Homework will be assigned and discussed during the class time. Only quizzes and tests will be sent to each student (as well as their parents) as both .docx & .pdf documents and returned to the instructor for evaluation. Students will have an opportunity to correct all assessments to show mastery. It is the responsibility of the parents to supervise their student while completing each assessment. The evaluations will be returned to both the student and parent.



Meetings
 
 This course meets 3 times per week for discussion and review of assigned homework.



Homework
 
 Homework assignments will be posted on a monthly calendar that will reflect the discussions and progress during our online time.



Prerequisites
 
 Algebra I, Geometry, and Advanced Algebra



Recommended background
 
 No special background required.



Instructor's Notes
 
 Mr. Mabbott expects his students to reach mastery of all skills learned. Therefore the students will be asked to rework all assessments until such time that they can demonstrate mastery at 100%. Oneonone support in addition to regular class meetings will provided as needed.



Textbooks and Materials
 

Calculus • 2019 listing  for reference only • Grade 12 or above
 

Primary Instructor
 


Sections [Enrolled students will be notified if teacher schedules change between course posting at the time enrollment opens and the scheduled start of classes. Please see Tuition and Fees for refund policy.]
 
  Section 1 Instructor: Fred Williams
 Classes meet from September 3, 2019 to June 8, 2020
 Monday 11:00 AM to 11:55 AM ET • Wednesday 11:00 AM to 11:55 AM ET • Friday 11:00 AM to 11:55 AM ET
 Enrollment Policy: Full Session Only
 Tuition: $650.00



Website
 
 Please review more extensive materials at the teacher's Calculus website.



Description
 
 The topics for this course include Limits, Derivatives, and Integrals (both Definite and Indefinite). We will explore tools and techniques for applying these concepts, such as the Derivatives of Products and Quotients, and the Chain Rule. We will also form connections with the physical world, both for understanding and also for application. We'll use computers and apps where appropriate.
This course uses an unusual format, using two phases. First, we go through Calculus Made Simple in 8 weeks for a fast overview of the subject. Second, we then turn to APEX Calculus for a deeper and more rigorous view.



Meetings
 
 This course meets 3 times per week for discussion and review of assigned homework.



Homework
 
 Students should allow at least 6 hours a week for homework. Calculus is a "contact sport", with new and different ways of thinking about the world  and it takes practice to become fluent in those new ways of thinking. Critical thinking  especially problemsolving  is also important, and we will practice that too. So students will need to allocate sufficient time for interaction with the material.



Prerequisites
 
 Students should be comfortable at the precalculus level (including courses such as Algebra I/II, Geometry, and Trigonometry). A placement test may be required depending on previous work.



Recommended background
 
 Precalculus (including Algebra I/II, Geometry, and Trigonometry) equivalent to Scholars Online courses.



Instructor's Notes
 
 Class meets three times a week for problem solving and any required presentation of material.



Textbooks and Materials
 

APEX Calculus (Edition: 4) Gregory Hartman, Troy Siemers, Brian Heinold, Dimplekumar Chalishajar
 
 This text is required. ISBN: 1719219591 Publisher's website: APEX Calculus Best sources: Scholars Online Bookstore for hardcopy. Hardcopy is in 3 volumes, but we will not use volume 3. The PDF when used with Adobe Acrobat Reader provides interactive 3D color graphics. ISBN is for volume 1. Other information: http://www.apexcalculus.com/ has the book in PDF form FREELY DOWNLOADABLE and is recommended.



Calculus Made Easy (Edition: 2) Sylvanus P. Thompson
 
 This text is required. ISBN: Publisher's website: Calculus Made Easy Best sources: Project Gutenberg download (free)


To enroll in any of the courses listed above, log into your Scholars Online Account Management Center using the login link at the bottom of any page and select the member you wish to enroll. If you do not have an account, you may create one using the Becoming a Member link under Enrollment in the Navigation bar at the top of this page.
Scholars Online was accredited by AdvancED and the Northwest Accreditation Commission from 20092016 and was accepted March 2018 with Candidate Status as a member of MSACESS.