Wait, What? That's Not Math! Or: Using Algebra in Everyday Life Without Realizing It

Earlier today I was having a discussion about GMO’s on my Facebook wall, and it struck me: sure, we’re chatting about GMO’s.  We’re engaging in rhetoric.  But we’re also following the basic steps employed in algebra.  What does a conversation about GMO’s have to do with algebra?

GMO’s (Genetically Modified Organisms) invoke a complex array of social, technical, and legal topics, on which many people continue to disagree.  I had posted a link to another blog that looked at just one aspect of the anti-GMO movement— the impact of non-GMO labeling on breakfast cereals and nutrition— dissected, and refuted it, politely, but firmly.  One respondent complained that the linked blog (or perhaps my endorsement of it) failed to address additional issues such as Monsanto’s activities, monoculture, gene patents, and other ancillary issues.  In my response, I remarked that I believe the issue is so complex that only by breaking it down could we find the real problem and solve it.  If the main concern is gene patents as a practice, labeling foods as GMO does not address the real problem.  If the main concern is monoculture, only looking at Monsanto is probably not the answer.  If one is concerned about health issues related to Bt corn, labeling human insulin as a GMO product does nothing to enlighten the consumer.

It finally struck me that at the heart of the conversation, we are answering the perennial question . . . “Why do I have to learn algebra?”  What we are doing in this conversation is, essentially, exercising the logic of algebra.  As students dive deeper into mathematics, they learn to break the problem down, then solve for some variable, x.  One of the biggest challenges many students face is identifying what part of the problem is represented by that mysterious x.  With practice, students learn to structure a problem so that when everything else is pared away, they are left with x all alone, and what it represents on the other side.

The GMO debate is like this.  Smart people talk at cross-purposes to one another, not because one side is dim and the other is brilliant, or because one side has a complete grasp of all issues and a single answer for all and other lacks it.  It is because we have the conversations without first solving for x— what is it that we are trying to figure out?  

In his excellent blog post, Prof Keith Devlin points out that the very first algebra books did not even include any symbols at all beyond the ten needed to express digits; they described the logical development of problem solving.  Devlin describes the original algebra text by al-Khwarizmi, written in Baghdad around CE 820, and notes, “The focus was on how to think about problems, and had nothing to do with manipulating symbols. That is algebra. It is exactly the mental toolkit that … is crucially important and should be taught in schools.” (NB Devlin is referring to another work and noting where he and the author differ and agree on how algebra is currently taught in schools).

This process— breaking down the problem, identifying our terms, unraveling the logic of the argument at hand could be considered logic, rhetoric, or debate.  Or . . . you just might be exercising those algebraic muscles.

Devlin article 1: http://www.huffingtonpost.com/dr-keith-devlin/andrew-hacker-and-the-cas_b_9339554.html

Thanks for reading!

--Jen

You Might Be a Homeschooler If . . .

You Might Be a Homeschooler If…

…you catch yourself singing, “Amo, amas, amat, amamus, amati, amant!” in the shower to the tune of the Mexican Hat Dance.

…your kids are in school when it is snowing or insanely hot out, and school is called due to weather when it is exceptionally pleasant.

...your child has used a knife or shot a gun at school.

…your kids have no idea what grade they’re in.

…lab day is a day when you invite your friends over to dissect brains.

…you love taking those middle of the day appointments with your kids, as there is no waiting room wait and they aren’t missing school.

…your kids eat home-cooked meals for lunch some days, and make their own lunches (at lunch time) fresh for themselves on other days.

…your car breaks down, and you see it as a learning opportunity.

…your kid is lost in a subject, and the teacher says, “That’s okay.  We’ll back up and do it again until you understand it, before we have to move on.”

…you routinely get to the end of the textbook where the really interesting stuff is hidden.

…you have 50 answers to the question, “So how will they ever be socialized???” and only 2 or 3 of them are socially acceptable.

…during reading time, your kids are moving about the room acting out the book as you read.

…your kids have perfect attendance, because if they’re sick you simply don’t have school that day.  

…you can take your child on vacation any time of year, without either lying on an excuse note or pressuring the school to not prosecute you for truancy.

…you can take your kids with you when one parent travels for work, because school on wheels is a thing.

…school happens at midnight because there is a cool comet on the way.  And the kids can sleep in a little the next morning and still make it to school on time.

…the math room is on the living room floor, the history room is on the sofa, the reading room is in a comfy chair, with cat assistance, and the science room is in the dining room or the basement.

…you send your kid to the store with money and a list, and think the parents who sit with their kids in cars at the bus stop are negligent (read with common sense.  Assumes said stop is not in a crime-infested area).

…pajama day happens more than once per year.

…you see the educational value in some time on Minecraft.

…your elementary kids watch “Ice Age 2” and point out all the references to the Iliad and the Odyssey.

…you have marched across the living room in “turtle formation,” holding your scutum over your kids’ heads.  Then you have marched back the other way in locked phalanx formation.

…you have ever mummified a chicken.

…you geek out over researching new lesson plans.

…you hold parent/teacher conferences with yourself continually.

…you go shopping or to the doctor, and it ends up being a guided tour.

…Longwood Gardens (or whatever your local arboretum may be) is one of your classrooms, sometimes for botany, sometimes for poetry, sometimes for math, and sometimes for art or gym.

…your kids get recess multiple times a day.  

…school start and end times, and school year start and end times are a bit fluid.

…you are a little nervous about having to be the college guidance counsellor during high school.

…you read endless debates about whether high school level work completed before the final four years of school should count on a transcript.

…you are not completely certain when your child’s graduation date will be, because you are never really sure what grade they’re in.  You have a plan, but plans change.

…if your kids have gone a whole week without complaining about homework.

…your kids have been asked if they have any friends.

…your kids never have to worry about who to sit with at lunch.

…you’ve been asked if you believe in evolution, and you know more about it than the question asker.

…you’ve ever gotten a sunburn while diagramming sentences.

…the cat helps with geometry.

…if reading and writing in Greek is not all Greek to you.

Thanks for reading!

--Jen

Mid-Year Slump

Ah, it is that time of year again.  As we get set to resume the formal part of our learning (homeschoolers are always learning, in or out of school, just like kids everywhere) we get set to face my least favorite annual tradition: the mid-year slump.

We have been schooling year-round, with sprinkled vacations, for five years.  For the first time this year, we'll take a longish summer break (though still shorter than the typical bricks and mortar school).  We are now at approximately the midpoint of the year, and the looming summer break has if anything enhanced the mid-year slump.

From the point of view of the kids, their annual subjects-- those that change yearly, such as history era, science focus, any new foreign languages or writing challenges-- are no longer brand new, shiny, and exciting.  Yet, in the bleak midwinter, summer vacation seems yet nowhere in sight.  Our freaky weather this year is exacerbating the situation.  Normally, it is cold, icy, slushy, and yucky outside in early January in the mid-Atlantic region.  Lately, it has been sunny, largely pleasant, mild weather with confused plants starting to bloom.  So instead of the feeling that studying is better than going out in the cold yuck, the weather feels as if summer is nearly here.  Buckling down to week 21 out of 42 seems out of sync.

From my point of view, the problem is entirely different.  This is the time of year when I start gathering resources, vetting books-- text and more casual volumes-- researching experiments and writing assignments, scouting web resources, and jotting down plans that will become syllabi in late spring or early summer.  In the process, I get thoroughly excited about what we are setting up to learn next year, so much that I develop a strong impulse to abandon our current studies and launch into next year's stuff NOW.  Right.now.

For example, I received a new telescope for Christmas; it was a complete surprise, but a wonderful one.  I have been burying myself in star charts, reading about azimuth, ascension, lunar cycles, composition of comets, light waves, radiation, and more.  I am just BURSTING to share this wonderful stuff with the kids, shoving aside the rest of the year of my home field of biology.  I can't really do that.  We have awesome stuff planned for the second half of the year, from ecology to evolution to comparing plant biology to human senses (thank you to the Coursera course from Tel Aviv University that I took around this time last year, "What A Plant Knows.")  It was an exciting part of their courses to plan, so now I have to fight the desire to give it all short shrift and hustle on into astronomy.

Similarly, my high school freshman will be a sophomore next year and taking the second half of world history.  I am going crazy trying to winnow down the list of possible literature to match up with the history course, knowing he can't read everything in one year, no matter how enthusiastic his mother is.  We can't start on the list now-- he's done a terrific job wrestling with the literature of the ancients and will now be starting medieval writings.  I, of course, want to read it all, revisiting old favorites and discovering writings I have never yet encountered.  (By the way, faithful readers-- if any of you have any favorites among non-western writers for next year (renn/early modern/modern) I'm all ears!  I'm also up for hearing about readable titles that illuminate international events from a non-USA perspective, to challenge ideas and perspectives for this rhetoric stage kiddo).

The kids have the job of getting back into the swing of things and focusing on the now, rather than the distant horizon of summer.  I have the task  of reminding myself why this stuff was so exciting last January, and to also stay in the now, focusing on the wonder before us today rather than what will be next year.  We'll get through this midyear slump, as we always do.

I have some great labs planned, to include some of the kids' buddies, running some DNA fingerprinting, visiting local streams, and more.  My freshman is looking forward to reading the Qu'ran and looking for common themes drawn from the surrounding literature, surviving Dante's Inferno, and beginning another semester of current events with a lively online group of teens as well as finishing up a course in symbolic logic.  My middle schooler is looking forward to shifting his history focus to medieval times for the second half of the year, doing more biology labs, and diving farther into algebra to find the fascinating problems.  I will somehow balance enjoying their discoveries, following through on all the exciting plans I made a year ago, with getting up in the night to go watch the skies and wondering about next year.

School Bus Time Approaches. I No Longer Feel the Same Way I Once Did.

Ah, that time of the year again . . . when I constantly bite my tongue when hearing other parents talk about not being able to wait until they can ship their kids back off to school.

I don't think it's as simple and clear as judging them as not missing their kids enough (I know many schooled parents who DO miss their kids during the day . . . and I also remember having that "can't wait for the schoolbus" feeling when my kids were in school, even though I did miss them).  I think there are multiple factors at play.

When you are accustomed to a routine-- get up, eat, meet the school bus on time, free time for the stay at home parent to do housework, errands, doc appointments, meet the schoolbus, afterschool activities, dinner, homework bed-- your life has a predictable feel to it that gets disrupted in the summer.  I think it is normal to feel antsy when your routine is disrupted, and to welcome that routine back, no matter the pitfalls.

Households with two working parents and young kids also face a dilemma in summer about how to ensure their kids are supervised properly, and that stress is relieved when school resumes.

Finally, in today's world, the notion of just letting your kids be bored sometimes instead of constantly entertained, in entertainments arranged by adults, is an odd one.  Many of today's parents feel pressured to make sure their kids are busy and productive.

I think when you are accustomed to having your kids cared for by someone else all day most days, you do start to think of taking that on for yourself as being harder than it actually is if doing so is just your normal routine.

But I admit I still feel sad when I hear it.  It comes across as sounding as if the parents really don't like their kids or spending time with them.  And I think the kids overhearing it can sometimes hear it that way too-- and kids overhear more than we usually realize.  I am happy now that I get to spend my days with my kids (over four years now, not to mention their pre-school days).  I am happy that our "routine" includes them being around, so it doesn't feel like a burden.  And I do think that parents who make spectacles of themselves at this first school bus pickup are pretty far gone-- that behavior sends a really bad message to the kids.

We are not better humans because we homeschool.  We are not superior to kids-in-school parents.  There are good and less-good parents in both camps.  But even knowing I once felt the same way, it's hard to hear parents celebrating handing their kids off to strangers, and that they don't know how to interact with their own children for more than a couple of days per week, or not trusting their kids to be okay if not being "organized" by someone.  It's just hard.  But I know it's complicated, and so I bite my tongue.  Then go hug my kids, and thank my lucky stars that homeschooling is an option for us.  It has definitely changed my outlook on life and family.

Thanks for reading!

Jen

20 Reasons to Love Homeschooling

This is a guest blog by my 14 YO, with an introduction and commentary from me.

A friend of mine who also homeschools posted to Facebook a list of 20 reasons to love homeschooling (Read it here), generated her daughter (I am totally poaching her idea here).  I decided that it would actually be good to have my boys reflect on what makes homeschooling enjoyable for them, and below is my 14YO's list.  I agree with him on most of them-- though #11 cracks me up, as I doubt he ever had a "several hour long lecture" in public school.  That may be how he recalls it, though!  As with my friend, I post this with some concern it will make us sound like completely lax homeschoolers, which is not the case at all; this 14YO has finished algebra 2 already and is powering through geometry; is finishing up a 4-year world tour of history from which he remembers quite a bit, has read books on high school and college reading lists, etc etc etc.  Somehow, with all that, he still seems to have had no trouble coming up with 20 reasons to love homeschooling.  I will also note that he has excellent study habits overall, tending to stick with a task as long as necessary rather than giving up or getting distracted.

My favorites from his list are 2, 4, 9, 14, 16, 17, 18, and 20.  I think they nicely sum up some of my favorite things about homeschooling too, and I'm thrilled to see he appreciates these things.

I do think any of us might benefit from this exercise-- what is it that occupies most of our time?  A job, a new baby, a new vocation in training?  Sitting down to reflect and generate a list of 20 reasons to love why I do what I do would certainly boost my spirits; perhaps I should do it next!

So without further ado, here is DS14's (4 1/2 years of homeschooling) list:

1. Snack whenever
2. Actual challenge
3. Random days off
4. Cats
5. Sit anywhere for work
6. No work after school
7. Break anytime
8. Can do sports
9. Flexible
10. Can sleep in
11. No several-hour-long lectures
12. Can do essays right on the computer
13. Can take days off to play with friends
14. Independence
15. Can finish before 3:00 pm
16. Can learn stuff on my own
17. Not every day is the same
18. Can go to fun places on weekdays
19. I don't have to worry about bullies
20. I can ask for help whenever I need it.

Thanks for reading!

Jen

The Story of Science: A New Book Review

  Update: the book is shipping early!  If you have been waiting to order one, you can go for it!


    I have had the privilege of previewing Susan Wise Bauer's upcoming book, The Story of Science: From the Writings of Aristotle to the Big Bang Theory (Norton, release date May 11, 2015)
over the past several weeks. These have been a few weeks of sheer reading pleasure.  This volume belongs in any home library-- homeschooler, interested lay-reader of the sciences, informed voter, or any person who wants more context for today's media reports about new (or "new again") scientific discoveries regarding our health, the environment, and our world.
     The scope of this new book is vast, covering the development of the scientific method itself, as well as developments in scientific thought from ancient through modern times.  Other collections or books have attempted the same feat; what sets this effort apart, in addition to Bauer's clear, accessible writing style, is her reliance upon primary sources to tell most of the tale.
     Each chapter discusses an important leap in the progress of Western scientific thought, placing the writings of the featured character in the context of their time and place of life as well as of scientific inquiry.  Every chapter concludes with a list of recommendations on how to investigate the source material, including helpful commentary on clarity of translations, where to obtain a free copy when available, readability of versions of the text, inclusion of original artwork where relevant, and, where a reading of the entire selection might not be necessary to grasp the essential point, a guide to what to read from the source material.  To make life easier for the reader, Ms. Bauer has developed a website with hyperlinks to many of the source materials, not only from the well-known Plato's Timaeus, Aristotle's History of Animals, but the oft-neglected works of Bacon, Hooke, and Wegener.  Additionally, there are links to more modern authors such as Stephen Jay Gould,  Steven Weinberg, and James Gleick, and their writings which are aimed at more general audiences than technical journal articles.
    It is not necessary to read every primary source referenced in Bauer's walk through scientific history in order to get much out of the book.  I do recommend reading all of Bauer's chapters, as they reinforce the understanding that each discovery owes something to those that came before it-- whether the new direction in thinking builds on past understandings or overturns them.
     This book truly felt like the story of how and why we know what we know.  Dogma was developed, and sometimes refined, but many other times overturned entirely.  The process of science involves unending questioning of that which we sometimes take for granted, and the biggest leaps have come from those who had the courage to ask, "What if . . . what we know about this is wrong?"  This book causes the reader to both appreciate the scientific process and the ability to intelligently question that which we dogmatically hold true-- and to understand how the interfaces among science and society and human nature can sometimes cause confusion and conflict.
    Susan Wise Bauer's The Story of Science: From Aristotle to the Big Bang Theory has obvious applications for particularly rhetoric stage (high school age) homeschooled students of any type-- classical, unschooled, eclectic-- but interest in this work should not be limited to homeschooling families.  This is a book for all adults who are fascinated by the Great Conversation, that linking of minds that extends back to the ancients.  This is a book for anyone who is concerned about making sense out of how the scientists get and evaluate their ideas, whether they are talking about GMO's, global warming, allergies, or signs of life on Mars.  This is a book for anybody who would love to have an accessible, understandable guide to reading excerpts or works from some of the greatest scientific thinkers in Western scientific development, a guide that will place each work in context and point out the best places to read original sources.
    Of course books such as this leave me wanting more.  I'd love to see a second volume, addressing those who had to be left out of this one-- perhaps one addressing mathematics, or non-Western scientific development; the contributions of Indian and Arabic mathematicians are of great importance to our everyday lives, and many modern conveniences we enjoy today were developed not in the West, but in Asia or other parts of the world.  The story of how these discoveries arose, impacted, and became intertwined with those in this volume would make for a fascinating read as well.  In some respects, it might have to be a different book, as I'm not certain how complete the written records are of all of those achievements, whereas this book focuses on the writings of great scientists, but it would be fascinating nonetheless.
     Now I'm off to figure out where this book will fit into our homeschool's high school plans . . . if you decide to get a copy and read it for yourself, please leave your comments here!  I'm very interested in hearing whether others were as captured by this book as I was, and how you either plan to use it in your homeschool or in your life.

Thanks for reading!

Jen

PS This page contains affiliate links below-- if you click through to buy the book from Amazon (See link at the bottom of the page), you'll help fund my writing of this blog.  To buy the book without providing anything to me, simply to go Amazon.com and type the title or author into the search box.  I was sent a pre-publication copy of the book to review by Norton, but not provided any actual compensation for writing this review; the opinions expressed here are strictly my own.

Know When to Fold'Em

Ever have that wonderful feeling that you just found THE ultimate curriculum that will be so completely perfect for your kiddos, will not only facilitate learning the subject material you have targeted to learn this year, but also build up bonus material of life skills or something else on the side?  This pile or box or set of plans just has you quivering with anticipation to get started . . . you are SO excited to unleash the excitement for learning that you know will happen when you merge these materials with your teaching skills and your kids . . . and . . . WHAM!!!

That was the sound of everything hitting a brick wall when the completely over the top perfect, exciting plans you have are a complete, total, abysmal, cataclysmic failure.

Ever have that happen?

We have.  The vast majority of what we try works pretty well for us.  But when we swing and miss, we go big.  So what then?  Start over.  Either look back at something else that worked or start from scratch.

This year we experienced that brick wall in a big way.  Although I still feel it is a terrific program -- for families that are not ours-- our brick wall this year was Exploration Education physics.  I was terrifically excited about it from the time I saw it in in a friend's hands.  I KNEW it was exactly what I was looking for in physics-- experiment based, mathematical, kid-directed, and it had two levels for my two kids, standard and advanced, that could still work together very nicely, without needing "tweaking" to make them work together; the more advanced mathematical pages were just left out of the standard book, so younger could watch or assist with older's additional labs without being responsible for the extra data recording and analysis.  What more could a homeschool Mom ask for?  Right?  Wrong, in our case (I still think it's a worthy program, for what it's worth, and know another family who is doing really well with it-- this post is NOT a ding against EE itself).

As an added bonus for us, I liked how the instructions for building projects were written directly to the kids; I really felt one of my DS's could gain some self-confidence from learning he could follow the instructions to put together the projects without me helicoptering over him and make these cool motorized race cars, gliders, sail boats, and more that are involved in this super cool kit.

The reality turned out differently.  I'll spare you the ugly details, but let's just say when you have a kid who has never been interested in building, don't buy him a physics program predicated on building the experiment components required for conducting the experiments.  It is one thing to set up the experiment; it is another thing to have to build the car or glider or boat first before you can experiment with it.  This is NOT the time to convince a kid he can learn to love building.  For a kid who LOVES building already, this will be a great experience.  For a kid who has never loved building . . . not so much.  Physics time was turning into, "OH, I think I have a headache, Mom, sorry, can't seem to concentrate today!" time.  Not cool.

When homeschooling, we all eventually face this dilemma-- usually more than once.  In many cases, it is wise to teach your kid to buck up.  We all have to do things that are not inherently fun, but have to be done anyway, and it's a bit of a disservice to teach kids that they can abandon necessary work just because they "don't wanna."  Young kids work can generally be crafted to be pleasant by an observant homeschooling parent, but as they enter the upper logic stage and rhetoric stage years (7th--12th grades for non-classical folks) it is time to start training them to do things even when they don't feel like it if you haven't yet.  You don't feel like writing this paper/doing this math assignment/finishing this project/cleaning the litterbox?  Do it anyway.  Life is like that, and you will find it hard to hold down a job or pass in college if you only do the things that appeal to you, kid.  However, in this case, the situation had a different feel.  When I looked at the situation, I felt that my biggest objective for the kids-- learning about physics-- was being impeded by road blocks in the learning plan that had nothing to do with physics.  I had to decide:  what was more important this year?  Physics, or learning to glue balsa wood together?  Different families could really have gone different ways on that for a 12 and 10 year old.  There is value in learning to use your hands and create stuff, and follow directions successfully.  I, however, chose the physics.  I did not want to leave the kids with a bad taste in their mouths regarding science.

So how, three months into our "year" do we reinvent the wheel?  We looked to last year's successful year of biology.  I sat down with a set of physics books that I like for their clarity of organization (Prentice Hall Science Explorer) a science encyclopedia, and the Creek Edge Press task cards, and I prioritized a list of concepts and mathematical relationships I wanted the kids to get over the remainder of our year.

Our first week looked like this: 

Monday:  Go research inclined planes and wedges.  For each one, draw me a diagram in your science notebook, and label all the parts.  Tell me what you find out about effort and force.

Tuesday: (stack of books on science and physics supplied, at various levels of intensity)  Read more about simple machines, focusing on inclined planes and wedges.  Make a list of things they are used for in everyday life.  Where do you see them around the house?  In living things?  Have you found mathematical relationships that describe what they do?

Wednesday:  Lab day.  We did a whole slew of labs revolving around inclined planes (wedges were harder).  We also worked on DS10's K'Nex roller coaster kit.  They explored the effects of mass on things going down inclined planes as well.  Not really related, but they also started watching a mini-series on the origins of the universe at their request (NOVA).  We kept data on white boards, and found averages and medians of different runs.

Thursday: Go research different classes of levers.  Label them, including the fulcrum, effort, and force.

Friday:  Read more about levers.  Show me where you find different levers being used around you, and what class each lever is.  Have you discovered anywhere that describes the mathematics of levers?  What do levers do for you in terms of force and effort?

DS12 also started reading a high school or college level text on physics-- reading is his preferred mode of learning.  I'm no longer forcing him to learn in a mode that is completely against his grain.  Everyone is happier, and learning a lot more physics.

I'm feeling a big difference too.  I no longer dread telling the kids it's time for physics, which really ought to be a ton of fun-- it really is, as one of our books is titled, "Physics with Toys!"  And Snap Circuits.  And a chance to learn stuff on your own and go on treasure hunts.  And drop stuff, bang stuff, stretch stuff, throw stuff . . . 

Most of all, I just have a feeling that we made the right call by chucking EE, which was not working for us at all.  Sometimes you tell the kids to buck up and get it done.  But other times, it is just the right call to quit what isn't working, ask yourself what your priorities are, and find a way to head towards your actual priorities and stop doing what isn't working.  Because . . . 

You gotta know when to fold'em.  Know when to walk away.  Know when to run . . .