Life of Fred: Logic
Learn logic in a day! That is, a day in the life of Fred. Here is a complete coverage of logic in a mere 176 pages. No ancillaries required. That's right. No separate teacher book, no test pack, no workbook needed. It's all right here - the whole "Kittens" caboodle. Fred, now six (and still a professor at Kittens U), is preparing to give a logic lecture. Ironically, and somewhat conveniently, Duck (first introduced in Life of Fred: Apples) pays Fred a visit and provides ample fodder for some of the first topics covered in the book. Duck, who always speaks in sentences that are false, helps to illustrate both logic sentence structure and the concept of every sentence being True or False. As always, Dr. Schmidt manages to both entertain and train. Along with the levity and random bits of eclectic knowledge provided in chapter 1, Dr. Schmidt gets right down to introducing us to both pure and applied logic and the language of logic (the use of symbols, modeling, and structures) - all in the first few pages of the book. From there, the course progresses through the topics of truth tables, connectives, the language of logic, inductive vs. deductive reasoning, logic fallacies (covered all in ONE conversation), and predicate logic. These first six chapters provide a complete high school logic course. Once logic as a second language is mastered, working through the remaining ten chapters is the equivalent of completing a college-level logic course. This part of the course is more heavily theoretical. It uses the structures and models learned in the first part of the course, progressing to proofs, introducing more complex structures and lemmas, and giving much thought to Gdel's Incompleteness Theorem. No prerequisites are required to begin this course, though I think it would help if your student had completed Algebra and Geometry before tackling it. While the math skills themselves are not needed, the ability to reason well and think logically (and somewhat mathematically) is. There are no exercises to complete, though there are 99 "puzzles" to solve. In addition to a very alert and thoughtful mind, familiarity with and understanding of symbolic language, proofs, combinations, set theory, and other topics typically covered in higher-level math would aid solutions. As far as teaching time, there is none. The course is totally self-instructional. Instruction is directed to the student/reader and all answers are included in the back of the book. Dr. Schmidt goes to great lengths as the book's narrator to make sure the student does not take the easy road and check the answers before first exercising his/her brain. He also already anticipates questions and objections the student might have, with many "reader" interjections, shown in distinctive font, at these points. One quibble I have with the book (and a caution to parents) is Dr. Schmidt's unnecessary incorporation of drugs (cocaine) and drinking used in one of the early examples in the book. I can guess the reason for this, but I wish he had considered another option". This course will appeal most to those who enjoy math, enjoy Fred, and enjoy a good story along with their study.
Do you think Logic is a dry, boring subject? It's not! Not when Fred teaches it. What other math book has a chapter titled "Stinky Logic?" This book doesn't have bothersome "problems" or strenuous "exercises." It has delightful "puzzles," instead. It has serious mathematical Logic, from the basics to advanced topics.
As usual, Fred has adventures. Duck comes back. Fred is pressured to buy life insurance for his wife (Fred isn't married). Fred "beeps" the nose of 128 lions.
Suitable as a high school text (first six chapters) or as a college text (all 16 chapters).
- Sentences in logic
- Inductive reasoning
- Seventeen logic fallacies
- Predicate logic
- Proofs in predicate logic
- Direct and indirect proofs
- Set theory as a predicate logic structure
- Axiom systems: consistent, complete, meaningful, independent, and recursive
- Arithmetic model
- Gdel numbering of symbols, sentences, and proofs
- Proof of the Diagonal Lemma
- Gdels Completeness theorem
- Gdels two Incompleteness theorems and their proofs
- Many puzzles and their complete solutions
Even before we had a description of this math program on our website or in our catalog, we had many, many inquiries about it (and a goodly number of sales). Is it the name? Is it the concept of a small, pointy-nosed 5-year old teaching Calculus at Kittens University? Is it the outrageous storyline? Or are people desperate for another approach to math? Although I was the one who reviewed and decided to carry this program, I was initially skeptical about its scope. After all, much of the text was given over to following the Life of Fred, with all the strange humor and unlikely scenarios that go along with it. In fact, that's part of the attraction for a student who really doesn't enjoy math (yes, I have one of those). So, could the course possibly have the content that a more traditional text (like Saxon) has? Moreover, what type of person would actually use this course, as entertaining and whimsical as it is (if you can think whimsy and Calculus in one thought). Well, after using Life of Fred for Beginning Algebra and reading through most of the Fractions book, I think I can answer some of these questions.
First, Fred IS the unlikely mathematician in all of us. Despite his youth and other cards stacked against him (you'll have to read the books to understand this), Fred is amazingly successful as a math professor. Why? It's because he finds math so intriguing, entertaining, and downright USEFUL in everyday life (his life, the Life of Fred). Why, math is everywhere in the world of Fred - and no matter how things are going, he can always see the math in it.
Then, there's the psychology of Fred. You want to help the little guy. I mean, he's smart, but so innocent, kind, helpful, endearing - small, helpless, underweight (why, when he was erroneously inducted into the army, they had to use a little cup instead of a helmet for his uniform!). Clearly the underdog in many situations, Fred has ended up in the hospital in both books I've read - even though one injury was accidental. But I digress. You do get wrapped up in the Life of Fred. And because you're rooting for him and concerned about him, you kind of get taken up in the math that pervades his thoughts. No matter how tough the Life of Fred gets, he always has time to explain the finer points of math to those needy souls around him. Don't get me wrong, Fred has plenty of fun, too. He always makes the best of things and has some great student/friends at Kittens who also seem to need math in their everyday lives...
These are, indeed, the most unconventional full-program math texts I've ever seen. Maybe that's why students who dislike traditional programs are so drawn to LOF. The books just seem more accessible and - well, friendly. Maybe it's just the author's personality or particular gift, but students who are turned off by traditional math seem to find refreshment and even inspiration in LOF. Although you may have read some debate on whether the series is too lightweight for a basal program, my two cents is that it is not. The math is all here - and then some. What is missing is repetition, redundancy, and a multitude of problems to work. These books are like my favorite college math text. When I first saw it, I thought it was too slim for a whole-semester course. Ha! Every word in that book was loaded. The text was so cunningly and concisely written that you actually had to study every word because nothing was repeated. While LOF isn't quite that concise (it does have a complete storyline along with the math), Dr. Schmidt doesn't waste words or your time. Every problem is almost like a brainteaser - just a little out of your reach unless you truly grasp the concepts. It gives you a chance to figure things out for yourself. There's a whole lot of brain-stretching going on. Therefore, gifted math students are also drawn to these courses as they allow them to be challenged. Another good candidate for LOF is the remedial student who has already been through the course using another text. If it just didn't click, I would try this one. Finally, a motivated or independent student would also appreciate using the course. It's purposely addressed to the student and intended to be self-teaching. In fact, 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 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. In short, just about EVERY student could use this program. The only shortfall I have seen in the program is for students who really need a lot of constant repetition and reinforcement. In some sections there are just not enough problems, even using the Home Companion. I had this problem twice in Beginning Algebra as serious as it needs to be. I both made up some of my own problems and supplemented with problems from Saxon Algebra 1 and Algebra 2 (some of the material is actually more advanced than in that series). I have since run across several other supplemental products that I could have used as well.
Life of Fred is a series of 12 courses. Two of these are Fractions and Decimals & Percents. The author recommends waiting to start these until your child is old enough to work on his/her own (about 5th grade). Each of these courses should take less than a quarter of a year to complete. The new LOF Pre-Algebra 1 with Biology is formatted like the previous books, with BRIDGES rather than CITIES. It would fit in a teaching sequence between Fractions and Decimals & Percents and Beginning Algebra. You can get a good idea of what is taught in the course and the proportion of biology to algebra by checking out the table of contents on our website. Literally a "dream come true", Fred is every bit as entertaining while teaching biology as he is when teaching math! While this course will not replace high school biology, it will replace much of the biology instruction in a general science course. Pre-Algebra 2 with Economics completes the pre-algebra instruction, this time delving into topics such as interest rates, competition, opportunity costs, supply and demand. Following the same format as the Fractions, Decimals & Percents and Pre-Algebra 1 and 2, Dr. Schmidt has released Pre-Algebra 0 with Physics (formerly Elementary Physics). This book fits nicely into the Life of Fred sequence between Decimals & Percents and Pre-Algebra 1. Dr. Schmidt feels that too much time is lost before presenting physics in high school and this book is designed as an introduction to fill that gap. Algebra and Advanced Algebra should each take a little more than half a year. While Geometry takes place during one day in the Life of Fred (a Thursday after his sixth birthday), it is definitely a full year course. Trigonometry can be completed in half of a year and Calculus (although covering two full years of calculus) will take one year. According to Mr. Schmidt, after this progression "you will be ready to declare as a math major at a university at the upper division level and take third-year (junior-level) mathematics courses". For even more Life of Fred, there is also a Statistics course which "has much more material than is normally covered in a beginning university statistics course". It's been years since my required course as a business major at a university - I may just take this one myself. Partly to test the author's assertion and partly because life is full of decisions and, as the author says, "Success in life is 90% making the right decisions in the first place" (the other 10% is carrying them out). Also new is Linear Algebra (as serious as it needs to be). Scanning through the book, it looks a lot like an upper-level course called Finite Math that I took in college. It covers: solving systems of equations with one solution (includes Gauss-Jordan elimination, Gaussian elimination), many solutions, and no solution (includes data fitting); matrices; vector spaces; inner product spaces (including Fourier series and Gram-Schmidt orthogonalization process); linear transformations; and systems of equations into the future (including eigenvalues, stochastic matrices, Markov chains, Fibonacci numbers) It is described by Dr. Schmidt as a math course required by most colleges for math majors and should be taught after Calculus As far as progression, Dr. Schmidt has placed it at the very end of his other courses, after Statistics. Like other upper-level courses, this one has "Your Turn to Play" sections separating textual chunks. Each chapter ends with six CITIES. There is a separate answer key for answers not included in the text.
Organization and format of the books is similar; of course, they all have a captivating storyline centering on Fred Gauss, a very young university math professor. The author, Stanley F. Schmidt, Ph.D., is a witty guy, a good storyteller, and he also loves math. Unlike many programs, the text is not written at a 6th grade level. If anything, the text is imbued with a little "extra" knowledge in different areas - especially vocabulary. Dr. Schmidt also appears to be a Christian man. Although his books aren't preachy and in places tend toward gritty realism, you will find a strong plug for goodness here, along with a main character who says his prayers every night. Fractions, Decimals and Percents, and the Pre-Algebra books are structured a little differently than the upper-level books. Chapters in these are short (as are the books), ending with a Your Turn to Play problem set, followed by complete solutions with explanation. Generally, after every five chapters, there's a BRIDGE taking you from the culmination of the preceding chapters to the new material. Actually, there are five BRIDGES - your student has five tries to make it across the BRIDGE. These contain a ten-question review of everything learned to that point. Mr. Schmidt recommends that students get at least nine out of ten right to move on. Answers to these are in the back of the book. The final BRIDGE has 15 questions (20 in Decimals) and, again, five tries to pass. This gives a student ample opportunity to go back, study the material, and try again without feeling like they've failed. It is built-in remediation, rather than just failing and still going on (isn't this also the way we train our children? If they don't get it right, they need to correct and do it again). Starting in Beginning Algebra, chapters are longer. For courses with the Home Companion available (Advanced Algebra and Trigonometry), this book breaks the chapters into bite-sized lessons. Natural breaks occur when the student encounters a Your Turn to Play (series of problems with completely-worked solutions following), but the Companions also provide sets of problems for each lesson in between. There are 108 lessons as laid out in the Fred's Home Companion Beginning Algebra study guide, but many of these are short; most students would combine some of them. By comparison, Saxon has 120 lessons, but this does not include testing whereas LOF's lesson count does. At the end of each chapter there are six CITIES (which all have names so you can assign a student to do Palmetto and Radcliffe for homework). Actually, I'm not sure why they have names - but, as with BRIDGEs, these determine whether to move forward. They have some review material from previous chapters, but are largely chapter recaps. They take roughly 20-30 minutes to complete and, again, give your student a chance to test, review, and test again (or you might work the first two cities together, assign the next two, and use the final two as tests). The first two CITIES have all answers provided; the next two have only odd answers shown; the last two have none. All answers not in the text are in the Home Companion or Answer Key. The back of each upper-level book (except Calculus) has an A.R.T. section (All Reorganized Together) containing definitions, formulae, theorems postulates - all the stuff you'd like summarized in one handy place together for easy reference. The Life of Fred actually begins in the Calculus as serious as it needs to be book (in which Fred is born), the first written (in 2001). Unlike the other volumes, it has all the Your Turn to Play questions and answers in the back and a Further Ado section containing even more rigorous material for you to include at your discretion. Possibly because this volume was originally written for college students, the material is edgier in this first book (Fred's dad drinks, his family is somewhat dysfunctional, and there are other allusions to drugs, alcohol and "hanky panky"). You may wish to skim ahead of your student and "edit" anything unsatisfactory.
So far, I'm giving a thumbs up to this unique (and slightly eccentric) math program. It has made math more palatable (and interesting) for my daughter. It has some unusual and novel approaches to problem solving (like a simple, foolproof method for factoring trinomials where the squared term has a coefficient > 1 instead of the guess and check approach employed in other books). It incorporates critical thinking and a discovery approach to math by its very nature. It integrates the value of learning in other curricular areas. It teaches math in the context of real life - okay, real life uses for math in a kind of surreal life. And, who wouldn't like a math book that begins, "Hi! This is going to be fun," then follows through on that promise? Visit www.stanleyschmidt.com for other Raves from Readers or to find out more about the content of the books - or even to contact the author directly. (You can even read some of Mr. Schmidt's 8:30 prayers). I'm not sure how Dr. Schmidt can include his home phone number on his website and encourage people to email and phone him with questions, but I have read several testimonies to his responsiveness. For a full scope and sequence, visit our website and take a peek at the table of contents for each level.
As a teacher, I have obviously enjoyed this course. But my daughter, Janine, has never had the innate appreciation for math that I do. Let's ask her what she thought (or thinks - we still have 14 lessons to go!). Here are her comments on Life of Fred Beginning Algebra as serious as it needs to be:
"I love Life of Fred because of, well, Fred! But also because this is the most creative math course I've ever seen. When I first looked at the math course, the thing that made me excited (besides the story) was not seeing millions of problems. Just a few, thought-provoking and even funny ones. In the lesson book, you'll only have one small page, then you can be done. The Cities don't even have that many problems. But they are all worth your time and un-repetitive, and most inspire a challenge or are a little puzzle. Mom didn't think it would be a full-fledged math course. But the more we've worked through it, I've seen that it's quite a bit harder and requires more thinking. No wonder it's been put on some "gifted" lists. Moving along... .the writing is HILARIOUS! It's almost like Stanley Schmidt and I have the same sense of humor sometimes. I've read Fractions and most of Begininng Algebra and enjoyed both immensely. It's a ridiculous, bizarre little series, which makes me love it all the more! My brother likes it so much he showed it to his college friends... and of course they all laughed. The characters are amazing, and the illustrations (especially of Fred) are priceless. Stanley even has a little fun subtly (and not so subtly) teasing movies, doctors, math books and a whole myriad of things, and he has never failed at amusing me. Math was my most hated subject. And while I can't say that I had a complete turnaround and wake up every morning saying "YAY! I get to do math today! Wheeeeee!" I can say that Life of Fred has taken all the dullness out, keeps me captivated, and injected a lot of fun. I'd call it an art piece, if a math book can be an art piece. An amazing, amazing series, even more so considering we're talking about a math course."
Well, there you have it - from teacher and student. Who says math can't be entertaining?
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.