Art of Problem Solving Volume 2: and Beyond Text & Solutions

SKU
016713
Grade 9-12
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.
Consumable
Consumable
Designed to be written in; not reusable.
Non-Consumable
Not designed to be written in; reusable.
Our Price
$49.00
Description
Publisher's Description of Art of Problem Solving Volume 2: and Beyond Text & Solutions

The Art of Problem Solving, Volume 2, is the classic problem solving textbook used by many successful high school math teams and enrichment programs and has been an important building block for students who, like the authors, performed well enough on the American Mathematics Contest series to qualify for the Math Olympiad Summer Program which trains students for the United States International Math Olympiad team.

Volume 2 is appropriate for students who have mastered the problem solving fundamentals presented in Volume 1 and are ready for a greater challenge. Although the Art of Problem Solving is widely used by students preparing for mathematics competitions, the book is not just a collection of tricks. The emphasis on learning and understanding methods rather than memorizing formulas enables students to solve large classes of problems beyond those presented in the book.

Speaking of problems, the Art of Problem Solving, Volume 2, contains over 500 examples and exercises culled from such contests as the Mandelbrot Competition, the AMC tests, and ARML. Full solutions (not just answers!) are available for all the problems in the solution manual. (Please note: The new 7th edition features a different look from previous editions, but has the same content.)



Category Description for Art Of Problem Solving
This is an outstanding math program for the math-gifted student. It is rigorous and oriented to the independent problem-solver. The Texts are student-directed, making them perfect for the independent learner or homeschooler. Based on the premise that students learn math best by solving problems – and preferably problems that they don’t already know how to solve - most sections begin by presenting problems and letting students intuit solutions before explaining ways to solve them.  Textual instruction, then, is given in the context of these problems, explaining how to best approach and solve them.  Throughout the text there are also special, blue-shaded boxes highlighting key concepts, important things to retain (like formulas), warnings for potential problem-solving pitfalls, side notes, and bogus solutions (these demonstrate misapplications). There are exercises at the end of most sections to see if the student can apply what’s been learned.  Review problems are found at the end of each chapter. The Solution Manuals contain complete solutions and explanations to all the exercises, review problems and challenge problems. It is best for students not to access these until they have made several attempts to solve the problems first. One motivating box in the text coaches, “If at first you don’t know how to solve a problem, don’t just stare at it. Experiment!” That pretty much sums up the philosophy of the course, encouraging children to become aggressive problem solvers. Students should start the introductory sequence with the Prealgebra book and continue through the series. If you are coming into this course from another curriculum, you will probably want to take a placement test to decide where to enter this program. The introduction and intermediate series together constitute a complete curriculum for outstanding math students in grades 6-12.

As with the Introductionbooks, the Art of Problem-Solving teaches approaches and methods for solving problems, usually in the context of example solutions, which are reinforced and expanded on by working through the exercises that follow. If you are familiar with the Introduction books, the general philosophy and presentation is basically the same. If you have not used them, PLEASE READ THE PRECEDING DESCRIPTION, as it also applies to this high-school level course. Because this course does not follow a traditional scope and sequence for algebra and geometry, you should consult the table of contents for each volume displayed at our website. Both volumes emphasize geometry, as the authors feel the subject is particularly neglected in most curricula. Think of these books as a banquet for the math-hungry. Students are urged to interact with the books, not just plod through them; to skip around and sample the various topics. If they have trouble digesting something, they should just skip over it and return later when they've had more practice solving problems. They are also encouraged to revisit "finished" topics in order to keep their understanding current.

Lesson text in the volumes is sparse and liberally punctuated with many, many examples. Example solutions are complete and provide the bulk of the instruction. Symbols appear in the margins to help students get the most out of the text. The eye symbol denotes especially important sections that should be read and re-read until understood. The threaded needle indicates difficult problems or concepts which may require additional help or explanation. A bomb highlights potential mistakes that the average math student makes, and helps your child to avoid them. Chapters are relatively short and are divided into smaller sections. This is not a lesson-by-lesson book. Students should work as far as they can in each chapter, depending on their own ease of understanding. Each chapter is followed by problems to solve, often culminated by a "Big Picture" interesting math vignette. Completely worked and explained solutions to the problems are in the meaty Solutions Manualwhich is requisite to the course.

< Did you know that logarithms were actually invented as a trick to do multiplication? They literally turn multiplication and division problems into addition and subtraction ones. Did you know that a formula like the quadratic formula exists for solving cubic equations? It's true and ingeniously simple. If any of this excites you (or more relevantly, your student), this is the course for you. Albert Einstein would have eaten this up as a youth.

Texts are self-study and strictly for the highly-motivated math student. When she finishes these, she will be ready for any college-level math course, to ace the SAT, and to compete in the Mandelbrot Competition. Not only that, but instead of just learning how to work specific math problems, your child will know math in a way that sets him apart from his peers, preparing him for excellence in science, engineering, math, or any other field that requires exceptional problem-solving ability.

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Product Format:Other
Brand:Art of Problem Solving
Grades:9-12
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