I’ve been thinking about maths… high school maths.
The other day I wrote about my unschooling high schooler. I told you how my sixteen year old daughter Charlotte feels like she is drowning in maths. The exercises for each of the maths topics in her course are never-ending. They take a long time to complete. Which would be okay if it was interesting and relevant. But it’s not. So what’s the point? Because she really wants to learn maths?
I did say, “Charlotte definitely wants to do maths.”
I’m been thinking about those words and I’m no longer sure they are true. Oh yes, she voluntarily learns maths. She even chose how she wants to learn it. She asked me to give her a subscription to a particular online course. And I didn’t protest. Or even question her choice. It’s up to her what’s she learns. Though I admit I felt secretly relieved. I have to prove Charlotte is learning maths for homeschooling registration purposes. An online course provides lots of records. It’s very convenient. Yes, I want the words, “Charlotte definitely wants to do maths,” to be true.
So does she really want to learn any more maths? I think she’s got to saturation point. But being Charlotte, which means she has a good dose of Elvis stubbornness, she ploughs on regardless.
“Why don’t you leave maths for a while?” I suggest. Charlotte frowns. I can see she is worrying about ‘getting behind’. Oh how I hate those words. Getting behindwhat? Structured courses tend to teach our children that certain things have to be learnt in a certain order by a certain time. Otherwise you ‘get behind’. Yes, the weekly report doesn’t look too good when you ‘get behind’.
I don’t like the lessons Charlotte is learning from her maths course. And I’m not talking about numbers. While she is busy watching video lessons, filling in worksheets, being rewarded with certificates and waiting for weekly reports to arrive, her motivation to learn is driven by the words ‘getting behind.’ She is not learning because of interest or need. It’s not self-directed learning. In my eyes, it’s not real learning. I thought we’d left fulfilling other peoples expectations behind years ago. It seems we haven’t.
“It’s nearly the end of the year,” I say. “You’ve done enough maths for one year. Have a break.”
I’d like to see Charlotte step back from maths for a while. Allow time to rekindle her interest in the subject… or not. Do something else. Live life without the stress of having to keep up, hanging over her head. Because is it really necessary she studies maths right at this moment?
I considered looking for some everyday experiences that might teach Charlotte the maths she needs to know. And then I realised no everyday experience will teach her the kind of maths she is battling her way through. We don’t use higher maths in our regular lives. If we don’t use it, we don’t need it. So why do it?
Because maths is a logical subject. It helps with thinking. It is good for the brain. But then again, so are a lot of other things.
You never know when you might need maths. It can always be learnt when it’s needed. It’s never too late. And it will be learnt quicker and make more sense when there’s a reason for learning it.
Because the Board of Studies says maths must be learnt (or taught). I think this is a stumbling block for a lot of people. We do need to satisfy registration requirements. But then again, the Board of Studies are reluctant to register homeschooled students as year 11 and year 12 students. They prefer to classify them as year 10 extension. And to me, that says no higher maths is needed.
So I think Charlotte has done enough maths. For now. Maybe forever. We’ll see. I want to help her get back her sense of adventure, a desire to pursue learning purely for its own sake.
“Read a few books. Find a patch of sunshine and lie in it. Draw a dragon. Write a story. Watch a DVD. Run down the bush track. Catch a bus into town. Do nothing but think. Smile.”
Charlotte smiles.
Sometimes, without realising it, we can get re-entangled in the world’s expectations and ideals. It creeps up on us. Sometimes we need to stop, have a close look at our children, listen, and reassess. We need to help them reclaim their unschooling sense of adventure.
I suppose it depends on what area she wants to study as to how much maths she needs to know. I like the logic of math but not the long winded questions that can take forever to complete. I find even the younger girls get those already and "loathe" them. Because we aren't unschoolers and use a math curriculum I make sure we do a living math class once a week to try and ensure they aren't scared off the subject forever. I always listen to the needs of the kids as sometimes you do need to step away and regain some fun if things are going stale in the learning room, it even happens with hobbies that they may have been passionate about for years. You are wise sweet lady, to try and steer Charlotte away for a break.
BTW how's Imogen's foot/ankle?
Lisa,
You are quite right. Some areas of study require higher maths. I did a science degree and I needed maths. But Charlotte is looking more at the arts… creative arts or writing. I guess if she changes her mind, she can always return to the maths. I know there are some good preparation for uni maths courses available.
I love reading your living maths posts. Yes, you make maths come alive for your girls. Fun activities do prevent things becoming routine and boring. They make maths relevant too.
I've been thinking about a child's personality too. Charlotte is the type of person who will pursue something because she feels she has to. She's hard on herself. Maybe she just needed 'permission' to let go of something she took on.
Imogen's ankle is still healing. She's off the crutches but still wearing a support bandage. I keep forgetting about her injury and I walk much too fast for her! No ice skating for a while yet. You are so kind remembering Immy's ankle. Thank you for asking! How's your own injury? I hope there won't be any need for surgery.
OOOh….OooooH…OOOOH! Have you ever heard of "Life of Fred" Maths??? It is Maths in "Literary" Form. My eldest daughter, Cheyenne loved them from pre Algebra on up…now they have made elementary Maths as well.
This is from Amazon.com:
Life of Fred books provide a self teaching, self contained, comprehensive math program with answers included. The character Fred explains the need for math in everyday life.Life of Fred: Advanced Algebra covers: Ratio, Proportion amp Variation, Radicals, Logarithms, Graphing, Systems of Equations, Conics, Functions, Linear Programming, Partial Fractions, Math Induction, Sequences, Series, Matrices, Permutations amp Combinations.This book is to be used with Fred s Home Companion: Advanced Algebra study guide and answer key. Author: Stanley F. Schmidt Format: 318 pages, hardcover Grade: 10 Publisher: Polka Dot Publishing
Karla,
Thank you so much for taking the time to copy and paste all this info about Life of Fred. I appreciate it very much. I won't delete the comments because I'll be able to return and read them again. Also other people might find them interesting.
I can feel your excitement about these books. Personal recommendation means a lot! I do like the sound of this maths course. I had a quick look at the website and can see there are appropriate books Charlotte could use. I might buy one and see if she is tempted to give maths another go the Fred way! I'll let you know how we get on.
Thank you so much!
Here is another blurb from Amazon.com:
My daughter Louisa used to hate math. Then we discovered The Life of Fred and now she LOVES math! At first, I was highly suspicious as I listened to Louisa laugh through her math lessons and totally enjoy doing them. I was stunned to watch her go straight for math when she started her homeschool work each morning. I picked up the book and read an outlandish story about a miniature boy named Fred and all his adventures. I was impressed to say the least! How could a girl who hates math actually be enjoying? I contacted Stan Schmidt, the author of the Life of Fred, and a retired college math professor of 28 years whose self-proclaimed mission is to help kids love math. I asked him, "How do I know a student who does Life of Fred will retain it?," to which he replied, "How much of your school algebra did you retain?" Ouch! If you have a creative child who is languishing on traditional math programs, you'll love Life of Fred! Beware: This is not a traditional math book. This is a child-directed course. The student reads the adventure story, does the math problems that occur as a natural part of the story, and checks their answers (the solutions are right there for the looking.) And learns to love math in the process! (Compare to Saxon at $50-70) Contents: Points and Lines, Angles, Triangles, Parallel Lines, Perpendicular Lines, Quadrilaterals, Area, Geometry Theories, Similar Triangles, Symbolic Logic, Right Triangles, Circles, Constructions, Non-Euclidean Geometry, Solid Geometry, Geometry in 4D, Coordinate Geometry, and Modern Geometry. Hardcover, 542 pages.
Here is a blurb ( I will have to divide it up as it is long) from Rainbow Resources:
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 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 and Decimals and Percents 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 http://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?
Sue…Please feel free to delete any of my replies…those last blurbs could make their own book! But, it was the most comprehensive review I could find…and I didn't want you to have to search for it!
No problem, Sue, it was fun! Really, for literary loving people, this is the Math course to try. The story is very amusing, and it is amazing how Fred connects SO MANY THINGS to math! It really helps the reader realize and connect with all the math in real life…
We also like Life of Fred! I have found they work very well for kids who have an intuitive grasp of math and like to figure things out for themselves. I have found them to be not as good a fit for kids who need more explanation – at least, they don't work alone for those kids. If I go through the book with them and help explain and show other ways of doing things, they really enjoy them. Although, Karla, have you done algebra? We loved fractions, decimals, and pre-algebra and then found the algebra book structured in a way that was too difficult for us. Did it change more with the higher books? Thanks!
Wendy…We began with the Algebra books…But my daughter had already gone through Saxon…We did Life of Fred Algebra over the summer, really, I just left it all to her and I would hear her laughing and she would share some of the story with me, I don't think that she found the format too difficult, she just liked the style much better. She did Geometry and the higher Algebra book as well…sorry, not much help with your question.
Yes! I love this post and you are so right, even though we have willingly become radicals (in other's eyes) we still find ourselves at times trying to conform to the very things we wanted to avoid.
I have an intense dislike of maths, I think this is particularly due to my high school teachers. I never thought I would use maths in my daily life. Then I started sewing and designing. My husband uses maths constantly in his technical drawing designs. But, we use it on our terms to suit our purposes. We don't know all the math theories and don't need to. It's funny too, when you use maths in a way that benefits your creative work, it's not boring, it's useful.
Kelly,
"we still find ourselves at times trying to conform to the very things we wanted to avoid"… It's disconcerting to suddenly realise that's what we're doing!
Teachers can make such a difference. They can bring a subject alive or kill interest in it completely. I suppose maths courses can do the same.
Your husband's drawings fascinate me. I am continually amazed how he keeps coming up with new designs which are all so complex and appealing. They are going to look great on T shirts. It must be wonderful sharing your creative works with each other. You talk the same language!
"I thought we'd left fulfilling other peoples expectations behind years ago. It seems we haven’t." I know that feeling! Some times it is a hidden fact, when I want my child to learn certain things for peoples expectations, some times I reveal it. Doing things for peoples expectations is like a virus you can't get rid of so easily.
Bernice,
Oh I love your last sentence! That describes the situation perfectly. I thought I had everything all worked out perfectly. It was only after I wrote the post about my unschooling high schooler I realised I was ignoring something I didn't want to know about.
I must come and visit your blog and read your latest posts. I've been writing and writing and writing…. I'm longing for some free time to browse blogs but I am enjoying the NaNoWriMo challenge very much. I hope all is well with you!
We have been having a very similar experience in one of Mxyl's college courses. All of a sudden he is working "for the grade" and memorizing just for the test!! He got an art history teacher who wants regurgitation of facts and is a severe grader (that's wrong: that art was done in 1330 BC, not 1350 BC!) It's pretty disheartening, especially because this is his area of interest. His (very strong) drive for excellence is turning into excellence in grades, not subject matter.
Wendy,
It seems that many homeschoolers get to the point where they have to jump through the hoops in order to get where they want to go. It's all part of a very imperfect system. I have seen my uni students doing things they think totally useless and a waste of time just because they want to pass a unit. I'm sorry to hear about Mxyl's art experience. You'd hope that a good art history teacher would share his passion for art and inspire a love for the subject, rather than bring everything down to the boring level of regurgitating facts. When our kids learn totally at home, it's so much easier!