A very interesting discussion occurred on the LivingMathForum regarding the role of parent self-education and the ability to inspire our children. This will written into an article form, but in the interest of time, I am posting the discussion thread as it unfolded on the list.
Thread on Parent self-education and inspiration, was Mathematical People
< I had not heard of this book before and find the snippet you have included intriguing. I've added it to my wishlist :-) Thanks! > (This was in response to a short review of Mathematical People, Profiles and Interviews )
Julie: You know, one thing I've noticed about myself. If I don't continue to find things to read and learn from that inspire me, I begin to get bored and begin to lose my ability to inspire my kids. Every time I'm learning something new, I recover or maintain my motivation and inspiration. That's why I shared this review - it was and is inspiring to me! I often find inspiration in revisiting books, DVDs or other materials I haven't read or seen in a while, I learn new things I didn't catch the first time around. When I am inspired by mathematical ideas, I am inspiring my kids.
This may be the reason why we see a lot of people posting about mixing up resources. The kids used Singapore for a while, and it was great, but after a time you find you have gotten a lot out of a resource and you seem to get diminishing returns. Switch to something else, and they have the benefit of variety and a different point of view, a different angle, on approaching math, which revives interest and momentum. We very well may find ourselves going back to Singapore later (we have, to the word problems at least), it isn't that Singapore was "good" and then "bad" - it was just a resource that had a productive, useful time and then we put it away for a while.
When I look at my productive years of self education over the past 10 years or so, this is what I have done. A mix of reading, audio/visual aids, classes, email exchanges, teaching (which is another way of learning for me) seems to give me a continued stream of inspiration that I can pass on to my kids. I recall how much I enjoyed college on a quarter system, vs. a semester, because we were moving on to another class after 12 weeks vs. 18, LOL. Right now I always have a DVD and audio series going, one for times I drive, the other when I clean or have a moment to relax.
My kids seem to thrive learning in a similar way, and mixing things up once in a while does not mean any one resource is less valuable than another. This past year we have used all of the following with my 4th/6th grade girls on a rotating basis:
Hands On Equations
Ed Zaccaro's problem solving books
The Man Who Counted (modeling each chapter's riddles and solutions) and a lot of other journaling through math reading
MEP (which I am learning to enjoy for a different perspective, especially the activities)
Sample standardized tests which, believe it or not, turned out to be a great springboard for a great mix of topics we bunny-pathed on, such as statistics, probability, geometry and algebra
Danica McKellar's books
Life of Fred
Zillio Mountain for math fact games
Tons of math readers such as String Straightedge and Shadow read on their own or together and more I'm sure I am not recalling off the top of my head.
It may seem like this is jumping around, but it's not - very often we're using several of these all in the same day, each complementing the other. Along with this has been a lot of learning without any text, just learning through life and having fun, and I've been able to use skills and tools I've gained over the years that now save me having to look up lesson plans or other resources for ideas on how to teach, I can teach or facilitate their learning spontaneously and effectively when they are ready and want to learn.
The more I know how to inspire and teach myself, the less I have to rely on teaching materials, and it may be that we stay with a resource longer for continuity in deeper studies. I've done this with my boys when we got to formal algebra. I'm doing this right now with my daughters learning Latin. As long as I'm staying well ahead and am motivated, they come right along with me, and we're using three different texts in a complimentary way (two for reading, one for understanding the grammar and to learn how to write in Latin), but that's all the mixing up we do for this subject, because it works.
I guess that was a tangent, but I wanted to somehow express how important OUR education as homeschooling parents is in modeling and inspiring our kids to learn math. If we are bored or uninspired, we certainly can't be very inspiring to our kids. Sometimes our children's enthusiasm in learning something new can carry us through learning times, but what about when they don't have enthusiasm or interest in learning? Or when stepping up to another level requires more hard work than before? Inspiration is what makes hard work fun! It's what I'm always looking for in our homeschooling, because it provides motivation and momentum that makes learning more efficient, effective and productive. And being a bit of an efficiency freak, this is important to me :o)
In our early homeschooling days, a lot of what I was learning was how to look at math differently through curricula such as Math U See, but once that learning curve was mastered, I needed to move on to other things to keep my motivation up. I wonder if others experience this same dynamic in their own homes? I know friends who do, I just haven't heard a whole lot lately on the list about what parents may be doing to be inspiring models of learning for their kids. Anyone up to sharing?
Re: Parent self-education and inspiration, was Mathematical People
I'm also that mom that you describe. If I'm not learning, motivated and excited, I won't know how to teach my girls. They are not in formal years of teaching, but I'm getting ready. I'm reading, and the more I get into things, the less I need textbooks.I'm a fan of mixing resources, with a CM spine of procedures (living books, narration, living math, Bible...) I add to that equation.
But for math I'm also learning to LOOK AT IT differently, to understand it and enjoy it, and that's transferring to the girls.
RE: [LivingMathForum] Parent self-education and inspiration, was Mathematical People
"This may be the reason why we see a lot of people posting about mixing up resources. The kids used Singapore for a while, and it was great, but after a time you find you have gotten a lot out of a resource and you seem to get diminishing returns. Switch to something else, and they have the benefit of variety and a different point of view, a different angle, on approaching math, which revives interest and momentum."
Well, Julie, this post sums up my educational approach - in a way that I could never have expressed. Thanks for the entire post - I loved it.
At this point, I have become a bit uncertain that this was the right path - (not to use one program continually) but honestly, I can't help myself. I have seen so many ideas about how to approach concepts that I just can't follow a sequence ( I have to pull in that great activity here and do those interesting problems there). That is also why it is hard to give opinions on programs - since I am really using them for ideas on how to approach concepts from different angles (not to follow a sequence lock-step).
2 years ago, I was really concerned when I started hoarding grammar resources! I hate grammar and I recall asking my husband if I really need to teach my kids grammar..
But, because of Latin studies, my interest in grammar was piqued and we had to pursue the best ways of defining adjectives or what have you. It became more of a research project, than following a curriculum.
Again, what had once been a dry and dreaded topic became a keen interest because we were inspired. We looked for the clearest and most comprehensive view of different parts of speech. This is cause for concern...I wondered if I could ever just "do xyz" I mean really, who needs to look at 3 grammar references to figure stuff out? I began to think that I can make anything complicated!
This process is just how I learn best - by immersing myself in topics of interest.
Life took some twists and turns and I had to be less involved in my kids education, but recently, I am getting back to the place of learning with my kids again.
And, of course, I see the impact it has on my kids - who enjoy the process of learning with people who are passionate about topics.
Thanks for the good thoughts and sharing the process of learning in your home.
I, too, find myself spending a lot of time researching, background reading, etc. The difficulty I find is that I can see the value in several different approaches to something and wonder which will really be "best" for my kids. Example: I totally love the rigor of "classical" homeschooling and following a sequence, but I also love the idea of "unschooling" and exploring the depths of things that interest. It's difficult to find the balance between these two great approaches and so I find myself trying to cobble things together in order to get rigor, thoroughness, depth and interest all at the same time! :-)
I also wonder, just whose education is this anyway? Naturally the children are learning, but I suspect that this may be more about MY education in the long run. I'm certainly learning many things I never learned at school. There are some things that I will use a pre-made curriculum for because I acknowledge that I am not a master of it--so I will defer to someone who is. But other things, I spend enormous amounts of time and energy on because I want to master it. And so I read, research, and generally immerse myself in certain subjects because I want MY education to be better. In the end, I hope that this will be inspiring to my kids.
Thank you Vicki, Audrey and Silvia, I love hearing back from others on this! Audrey, I just loved what you said here:
< I also wonder, just whose education is this anyway? Naturally the children are learning, but I suspect that this may be more about MY education in the long run. . . There are some things that I will use a pre-made curriculum for because I acknowledge that I am not a master of it--so I will defer to someone who is. But other things, I spend enormous amounts of time and energy on because I want to master it. And so I read, research, and generally immerse myself in certain subjects because I want MY education to be better. In the end, I hope that this will be inspiring to my kids. >
This is where I've found myself after, goodness, we're finishing 13 years of homeschooling. In the middle, it was a struggle, and I often felt unsure, but not any more.
I too find things in rigorous classical education and unschooling that I appreciate, and in the end, I haven't found these incompatible, as much as others might seem they are oxymorons! The classical rigor I began to apply to MY education. This does in fact inspire my kids.
One of the most amazing things to me are the conversations I have with my nearly 18 year old son now. In the beginning I thought our family's goal was to educate a kid on how to read, write and do arithmetic, learn history and science, master subjects. But that changed over the years. If our goal all along was to raise a kid who thinks for himself, who has a broad based education that he owns for himself to be able to process what the world sends his way through his developed filters, to have the tools he needs to make decisions in his life, and to have a healthy love of learning survive and thrive after graduating from high school, then our goals have been achieved. Life is the real test.
RE: [LivingMathForum] Re: Parent self-education and inspiration, was Mathematical People
>The classical rigor I began to apply to MY education.
Julie, I'm intrigued by this. I'd love to know more.
I've always loved learning new things, and am not even always conscious of how it affects my son. He sees me reading all the time, working on math problems just because I'm intrigued (Pythagorean triples right now), getting excited about things I'm learning online, playing with languages a bit (no rigorous study there, so far), and working on a book.
But I don't think I know what "classical rigor" means, really.
I don't worry much about his learning. I think around here it'll come pretty naturally.
I'm enjoying this thread.
There's a lot out there on classical education and a number of different views on how to apply it to your education, but I look at it from the standpoint of how they approached education. Here are some ideas I apply to my own education.
Studying original sources, rather than always relying on someone else's interpretation and filtering of an original source. I have found myself really surprised when I've read an original source, finding out that I really disagree with some mainstream ideas out there on how they were disseminated. The most recent example I had of this was in my government class, when I actually READ John Locke's Treatises on Government. The tiny snippets and predigested sound bites in a textbook can't even begin to convey why his work was so important and influential to the founders of our Constitution. None of the students in the class I was teaching had ever read an original source and found it hard going (these were 11th-12th graders). I often use resources like a Teaching Company lecture on the work I read to help provide context and understanding for me, for example while reading the Illiad, Odyssey and the Aneid. Pure classical approach would be to read these in the original language, but I don't think I'll ever learn Greek and my Latin isn't that far along yet!
While modern classical education has produced a plethora of curricula to support families wanting to apply it, classical education would rely far less on curriculum. For example, one learned grammar through the study of language, not as a separate subject. For advanced subjects a good text is of course desired, and for us I need some support to teach Latin since I am learning it just ahead of my kids. Euclid's Elements was the first known math textbook and was used for centuries. But using a text and teaching through it is way different than workbook style curricula.
I value mentors and seek them out for myself and for my children. This is a classical education idea. Many of my "mentors" are the teachers of my Teaching Company courses, but I've sought out good instructors at the community college for some classes, and we did hire a Latinist for about a year to get us kick-started with Latin. I value experiences my children have with other teachers.
Classical education tends to focus on language and math skills in elementary. Some models place a lot of emphasis on history as well, others wait until later elementary / middle school, really focusing on basics. Some models emphasize Latin and/or Greek as being an essential element, others don't. After reading a book called Climbing Parnassus by Tracy Lee Simmons, I felt there was a lot of value to including at least Latin, and hey, here in California Spanish is an important language to learn, and Latin sets you up for Spanish really well, given the grammar you learn and the vocabulary, Spanish is derived from Latin primarily. So this is why I began to invest in it, and the more I do, the more value I see in it. I did have to work hard to find ways to give my kids an inspiring experience, Latin like math wasn't exactly what most people would consider an exciting subject to learn in the past! But there are great resources out there, and yet, I wouldn't know how to use them if I didn't do the work of learning ahead so I can mentor along with using the resources.
With math, this has meant reviving my own understanding of where they are going with higher level math, and studying math within its original contexts, history. It's harder this way, but I understand it much better, and it makes me a much better math mentor to my children.
There's more to it, but I'm out of time for email today, LOL. That might spark some more discussion. I don't want to get into debates about classical methods, there is plenty of that on other lists! These are just some broad-based ideas I've found very applicable to my own education and which I am trickling down to my kids even within our relaxed homeschool environment.
What an uplifting, inspiring, and reassuring conversation. I'm going back to your posts and copying some of what you wrote to have it present.
Thanks Julie for sharing that in conversations with your 18 yrs old son you went from thinking hs'ing was about teaching reading (that's what's crossing my mind with a 5 and a 3 yrs. old), to realizing true learning it's more to aid them to think by themselves and all that you expressed so well in a few words.
I also gravitate between the structure of a CM/Classical approach and unschooling, isn't that funny? I agree that it has to compliment somehow, at some deep level behind the apparent contradiction. I enjoyed the description of the rigor of a classic approach, great inspiration to guide our learning.
I was born in Madrid, and I studied Latin and Greek (but I'll have to relearn it with the girls). I believe that it helped me tremendously when I came to the States. In a year or two I acquired a decent oral ability in English, and now, apart from my accent, I'm very pleased to be able to read and write in English which has become a very cherished 'adopted' language.
In regards to education I want the girls to be disciplined, I see the value of reading books that are a challenge and not giving up until we acquire the needed frame of knowledge required to understand them. The discipline in math and Latin and Greek specially that the classic approach has, and to me the history from primary sources is a big incentive. I don't know American History, and I'm enjoying history again. This time I'm filling my not just gaps but black holes in the subject.
This is something small, but it's my experience of learning by myself. I taught myself photography, I don't consider myself a leading photographer (in part not because I'm bad, but I don't devote all the time others do. But I'm not excusing myself -a poor craftsman blames his tools? how is that saying?- I'm happy with what I've learned about photography and I'm making your own websites and blogs for free, for example, which I also learned alone. I also have learned some cooking -again not chef like, but decent for a family and pleasing for dh-, the art of living frugal, which I'm constantly perfecting, and I'm constantly reading and learning as a way of life. I'm not aspiring to fame or riches, I'm doing it from complete internal motivation, as a way of existing and to feel alive, as a means to inspire the girls and model self learning to them. What was that quote by Mortimer inspired by Shakespeare too that a life not examined is not worth living?
Back to the idea of learning, I miss college because of the interaction with others which is also needed to grow (but we have others in the groups at least), I wish I could study philosophy (my major) again, now I'd probably understand it :-) The problem was that we read too many books 'about the author' and too few original sources. We were too young to 'understand', so we tried to understand the interpreter. But after I read Mortimer Adler's "How to Read a Book", and SWB article on tackling the originals (Plato, Aristotle, Shakespeare...) my approach has changed. I haven't read Shakespeare in English and that's one of my goals. Euclides is in my list, and as you said, I don't think I'll get to read Homer in Greek or any classic in Latin, but Spanish is really close and I, at least, will be reading from original sources, translated but original.
I totally agree too that this is more OUR education. Not selfishly, but it's inevitable that the parent is the one who gets the most, Ruth Beechick says we who hs are those who end up educated. And our children hopefully learn to think and to love learning and if they teach their children, the cycle will repeat.
I thought it was just me and my constant love for uncovering what's behind the scenes (philosophy of education, history of education, history of math, principles, approaches...), but I see there are more parents in these circumstances. I've felt understood, and humbled too by all the amount of knowledge and learning you undertake with children and a life to live.
Finally I'd like to just add that my strongest motivator to learn Greek, Latin (I don't know if we could ever try with Hebrew) is to be able to read the Bible or some passages in those languages and have a deeper understanding of His Word as original as possible. I get a lot of the riches from reading the Reina Valera Spanish translation from the KJ times, its Spanish is a pleasure to read and it enriches my English and vice versa.
Silvia wrote: < In regards to education I want the girls to be disciplined, I see the value of reading books that are a challenge and not giving up until we acquire the needed frame of knowledge required to understand them. >
When my kids were young, I read aloud challenging books to them, a LOT, and we had challenging audiobooks on in the car when we went on trips or regular commutes somewhere. I still read aloud, and now my youngest 10 year old can go through the Old English version of Pilgrim's Progress with ease, only asking me what some of the most archaic words mean, and she enjoys the language. When they were young, they would read picture books and easy stuff on their own, but over time, they got to the point they could and would read more challenging literature on their own. The one thing I didn't do was push difficult reading on them until they were clearly ready, that would have been a big mistake (the mistake I made with math, in fact, and had to learn how to do damage control with my oldest :o).
Regarding discipline, if you are following CM then you are probably reading that keeping formal lessons really short is key. You want them to want to learn. I got to where in the early elementary years I didn't have scheduled formal lessons. I took every opportunity that presented itself, and we did lots of "studying" at bedtime reading sessions, in the car, or impromptu sessions.
Discipline at these ages focused on family contributions with chores, and music lessons, both of which were areas they could understand why discipline is needed, what the end goal is. With music, it was especially helpful when we could be a part of groups that provided additional motivation and relevance to the discipline of practice. When they are very young, trying to teach academic discipline is more difficult and can create damaged attitudes because they cannot possibly begin to see why discipline is necessary in academics, *especially* in a homeschooling environment. In school, at least everyone else is doing it, and deadlines and assignments make some sense in that the teacher has to keep the whole class on track together. In a homeschool environment, none of this is the case, so schedules, goals and deadlines don't make a lot of sense until they develop the maturity to begin to see why these skills need to be developed.
I have always sought out classes for my kids like an art history class they took for several years, where the class was wonderful for them, and a certain amount of in between class work was necessary for them to be able to participate in the class itself. This fostered discipline in that there was a clear reason to do the work in between, and the motivation was the fact they *wanted* to be in the class. As adults, this is what we do - if we want something for ourselves, we will do some things we might not otherwise do if we consider the end goal worth the effort. We don't go through motions having no idea why we are doing them, except in situations where we've hired say, a violin teacher or martial arts instructor to teach us, or we take a class, and we defer to their expertise without always knowing why. But we still know our end goal, to play violin well, or to become a black belt, to master a difficult subject we want to master, etc.
< Back to the idea of learning, I miss college because of the interaction with others which is also needed to grow (but we have others in the groups at least), I wish I could study philosophy (my major) again, now I'd probably understand it :-) The problem was that we read too many books 'about the author' and too few original sources. We were too young to 'understand', so we tried to understand the interpreter. >
Oh boy do I understand this! I was on the fence between an English major or business (pretty funny huh) after high school, and I eventually chose the more practical business major with an emphasis in accounting and finance. But I took a number of literature classes, and now that I find myself reading classics, I look back and realize all that I missed in those readings. We had to read so much in such a short time, much of it excerpts, which didn't allow one time to understand any context. It would have been much better to cover less ground, but more deeply. One of the few highly memorable experiences I have from high school was reading The Scarlet Letter over an entire semester in my junior year with a great teacher (one of the few whose name I can remember!) taking the time to thoroughly understand the work. I had no idea until that time how much could be communicated through literature like this. I am glad seeing my 9th grader go through the Odyssey over an entire semester with a group. Our society does seem to go more for quantity over quality though.
I loved college when I went back in my mid 20's after taking a few years off to figure out what I wanted to do. And I've learned that taking a community college class once or twice a year now has been great both for continuing my education and satisfying my desire to be in this environment again. Plus the deadlines make sure I complete a course, home study with a family can definitely get put aside very easily! I always do my homework though to get a good teacher, now that I'm going to classes just for myself, to learn, vs. satisfying credit requirements, I don't want to waste my time.
< Ruth Beechick says we who hs are those who end up educated. And our children hopefully learn to think and to love learning and if they teach their children, the cycle will repeat. >
Freakonomics is an interesting book that challenges some assumptions and beliefs we have about things that may be taken for granted. One idea that I walked away with is that who we are has far more influence on our children than what we do. The author gives the example of someone who learns that kids who go to college were exposed to lots of books when they were younger. But simply stocking one's home with books won't do it. The fact those kids grew up with books in their homes reflected the fact their parents were educated and valued books themselves. Who the parents are matters more than what they do. So, if you have a desire for your child to be educated, you need to be educated yourself. On the flip side, if we are educated, learning all the time, we can relax that even with all the mistakes we might make, our kids will turn out all right, because of who we are.
Yes, a great topic to discuss, thanks Silvia!
Julie, this is such a beautiful response and a PRESENT. It made my day. I'll take some of your writings and quote you in my blog. I'll always give you credit and link to your livingmath.net site, which I DO ALL THE TIME since I found it :-)
Your insight about how children who are homeschooled from birth won't get the academic discipline right from the start, but how we can teach it through music or when they participate in classes outside the home is very true. I have no proof of it, but it's something I can "sense". The world of deadlines, projects, tests, and the such, it's what the 'school world' is about (some of what it's about, to be fair), and when you learn at home the dynamics are different. We need to have this present so it won't hinder their development. But as you say, we shouldn't worry because we are blessed with such a vast spectrum of alternatives for them at any point that those skills will be learned, those things will be covered.
It's very reassuring to read about your daughter, how she was able to do that 'hard core' reading, I specially appreciate your comment that you never push her above her ability. You don't want to kill that love for learning, neglecting it is the other extreme, but you can be guilty of the first practice just as easy, specially if you are an overachiever type of mom (-guilty :-)
And yes, we live in a society that thinks that more is better. I also wish we could have studied far less things in depth. The process of studying something from different angles, with different views and details teaches you the important thing, the process, comparing, contrasting, analyzing, defending, rebuking... and once you posses those abilities you apply them to any other corpus of information, while accumulating information as if that was all the learning to be done takes you to the same place you started. I also had one of those teachers in high school, he was the one who motivated us to study Lord of the Flies. It was my philosophy teacher, you guess why then I study philosophy? He treated us youngsters as persons, and ALL of us would live up to his expectations.
Learning is contagious. When I'm interested in something and share it with my children, they see by example what it is to put time into learning something and working toward understanding a new idea, or developing a new skill. I'm a pretty good pianist, and teach my own children, but I'm trying to improve my violin skills with my son. They aren't much impressed when I rip into Chopin on the piano (maybe because I need more time to practice), but they do hear me practicing violin, because I practice with him almost daily.
I want to learn how children learn ... from the ground up. That's why I chose to home school. It's the most challenging thing I've ever done.
I got my doctorate in physics before my first child was born, and at that time, I thought I knew something. I taught physics at a university, and my students thought I did a good job of helping them learn. It was fun. It was a vacation from being Mom. Then I had twins, and left teaching because I couldn't do it well without leaving my children to someone else. I want to be the one who has the fun of raising them. I also stopped being inspiring to just about anyone. (Every now and then my 11-yo daughter says I inspire her, and I want to record it and have it to play back in the years to come!)
Turns out that what I learned in grad school was how to find resources and formulate questions. (Not like I need any questions of my own - I could go on forever just answering my kids'!)
Now I'm doing a husband-supported post-doc in elementary and secondary education, with my children (and a few friends) as my experimental group. It's important to me to keep my goals of learning in mind, and to find other adults who wonder about the same things. I learned of this Living Math group via a friend who recommended it after I shared a paper on Math education with her.
I read conversations here, and every now and then have time to participate. I also attend or Skype into (when I can) a graduate research group that reads papers on education, particularly those related to physics. The overlap is interesting, as the NYTimes Opinionator series on math came up in both groups.
I have on my "to read" shelf a pair of books by Alison Gopnik, a UC Berkeley psychologist that we read an excerpt from in the physics group: The Scientist in the Crib: What Early Learning Tells Us About the Mind and The Philosophical Baby: What Children's Minds Tell Us About Truth, Love, and the Meaning of Life
The intriguing idea we read from The Scientist in the Crib is that each person has an innate desire to learn, and satisfaction from learning, that is no less strong than our sensual urges. This is not so different from what Danica McKellar said in about learning math. "It's sexy to be smart." (Thank you for the pointer to her books, by the way.)
If we can tap into the exciting part of learning ourselves, our children can't help but notice and learn from our modeling. The challenge for me is to teach them in a way that is different from how I learned and keep the excitement alive. I forget about the details that have to go into new learning, and get too excited, and go too fast trying to get to "the good part". I have to learn to savor each new discovery for itself.
I remember when my daughter and her cousin (both under 2) didn't want to leave the embedded pebbles at the entrance to the Monterey Bay Aquarium because they were focused on the moment and didn't know what they might be missing. I'm trying to learn to focus more on the moment and learn from watching my students learn. We have time to get to the big stuff, but thelittle discoveries create a path for learning.
My time's up. Thank you for sharing part of your path.