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Teaching Method
Traditional
Teacher-centered curriculum commonly used in classrooms that may include a text, teacher manual, tests, etc.
Charlotte Mason
A methodology based on the work of a 19th century educator who maintained that children learn best from literature (Living Books), not textbooks.
Classical
A methodology based on the Latin Trivium (three stages of learning), including the grammar stage (memorization and facts), logic stage (critical thinking), and rhetoric stage (developing/defending ideas).
Unit Study
A thematic or topical approach centered around one topic that integrates multiple subject areas.
Montessori (Discovery)
A methodology based on the work of a 20th century educator that emphasizes student and sensory-driven discovery learning and real-life applications.
Other
Other methodologies
Religious Content
Secular
Contains content contrary to common Christian beliefs (i.e. evolution).
Neutral
Avoids religious or theoretical topics or presents multiple viewpoints without preference.
Christian/Religious
Faith-based or including instructional religious content.
Learning Modality
Auditory
Learns through listening, talking out loud or reading out loud.
Visual
Learns through seeing, prefers written instructions and visual materials.
Kinesthetic/Tactile (Hands-On)
Learns through moving, doing and touching.
Multi-Sensory
Curriculum that employ a variety of activities/components.
Presentation
Sequential
Curriculum progresses through well-defined learning objectives. Emphasizes mastery before moving to the next topic.
Spiral
Topics and concepts are repeated from level to level, adding more depth at each pass and connecting with review.
Conceptual/Topical
Focus is on the “why,” often with a unifying concept as well as specific skills; coverage may be broader.
Teacher Involvement
Low Teacher Involvement
Student-led materials; parent acts as a facilitator.
Medium Teacher Involvement
A mix of teacher-led time and independent student work.
High Teacher Involvement
Teacher-led lessons; may utilize discussions, hands-on activities and working together.
Additional Materials Required
No other materials needed
Everything you need is included.
Other Materials Required
There are additional required resources that are a separate purchase.
Other Materials Optional
There are additional resources mentioned or recommended but are not absolutely necessary.
Working with applied math, this book allows students to solve most
second-order differential equations; however, answers you get in numerical
analysis are only in numeric approximations. Calculus is recommended as a
prerequisite because students are learning how to integrate tons of functions.
Students write fairly simple computer programs in this course. Complete
solutions are included.
Publisher's Description of Life of Fred: Numerical Analysis
Solving every equation that is in the form f(x) = 0. Bisection method.
Solving f(x) = 5. Solve x to the x power equals 5. Solving f(x) =
g(x). Finding the value of
cos(cos(cos(cos(cos(cos(cos(cos(cos(cos(cos(cos(x)))))))))))). Secant
method. Newton method. Finding the polynomial to interpolate five
points. The Lagrange polynomial. Dealing with 900 points and no given
f(x). Splines. Piecewise polynomial approximations. Numerical
integration. Why Simpson's rule is true. Numerical differentiation.
Monte Carlo methods. First-order ordinary differential equations
starting with y' = g(x). Starting with y' = g(x, y). Euler's method.
Runge-Kutta method. Second-order differential equations. Second-order
boundary problems. Second-order initial value problems. Parabolic
partial differential equations. Elliptic partial differential
equations. Hyperbolic partial differential equations.
Life of Fred(LOF) is an unconventional series of math texts that seem accessible and friendly, especially for students who dislike traditional programs. According to Dr. Schmidt, the author, this series is designed to teach you the math you need to know without repetition, redundancy, and a multitude of problems to work. LOF follows the storyline of Fred's life while incorporating solid math concepts and skills. Motivated or independent students will appreciate this series, as well as gifted math students who might need a challenge. Written to the student and intended to be self-teaching, the author prefers that students use these with very little help from you, so they can learn to study and understand on their own. Even the solutions (found in the text) are addressed to the student. In fact, there's a lot of actual instruction in the solutions, which students should read after trying to solve problems on their own. Math in a story context can sometimes make more sense to students than stand-alone math concepts - especially if it's an entertaining story! Students do two books per year up through pre-algebra; beginning with algebra, one book per year.