Teaching mathematics part II - good teaching

In part I, I broke down Charlotte Mason's writings on the reasons for studying the subject of mathematics.  I also introduced a problem in our current educational system - that math is pretty much overinflated above the other subjects of study which not only does a disservice to our youth, but creates a disdainful attitude towards math and, I would argue, towards learning in general.

I will be honest and say that I'm not really familiar with the way math is taught in the early grades, but from what I saw by the time the kids came to me around the ages of 13 or 14 -- well, in the words of Miss Clavel*, something was not right.

(*From the Madeline books by Ludwig Bemelmans)

"...As for the value of Arithmetic in practical life, most of us have private reasons for agreeing with the eminent staff officer who tells us that, --

'I have never found any Mathematics except simple addition of the slightest use in a work-a-day life except in the Staff college examinations and as for mental gymnastics and accuracy of statement, I dispute the contention that Mathematics supply either better than any other study.'

We have most of us believed that a knowledge of the theory and practice of war depended a good deal upon Mathematics, so this statement by a distinguished soldier is worth considering.  In a word our point is that Mathematics are to be studied for their own sake and not as they make for general intelligence and grasp of mind.  But then how profoundly worthy are these subjects of study for their own sake, to say nothing of other great branches of knowledge to which they are ancillary!"  (Charlotte Mason, Volume 6, Towards a Philosophy of Education, p.232)

What the staff officer pointed out - this is what my students understood to be true and they used it as a crutch to complain about having to learn math.  We're never going to use this stuff in real life, they would claim.  But that's not the point, I would tell them.  I tried to call attention to the beauty and logical nature of mathematics, and how it weaved in and out of the other sciences, but by that point, the students just didn't care.  It was as if they were too far gone.  For the most part, though, we really can't blame the kids for this disrespect for mathematics (we can, though, for their lack of work ethic which, from my experience in the classroom, seems to be pretty profound - sorry, just had to throw that in there!).

So what's the problem?

It's interesting how CM makes such a case for mathematics requiring a good teacher from the beginning.

"There is no one subject in which good teaching effects more, as there is none in which slovenly teaching has more mischievous results..." (Home Education, p.254)

"The success of the scholars in what may be called disciplinary subjects, such as Mathematics and Grammar, depends largely on the power of the teacher, though the pupil's habit of attention is of use in these too." (Towards a Philosophy of Education, p.7)

This point of a good math teacher is brought up in the Eclectic Manual of Methods as well.

Math "is a subject in regard to which the young teacher is liable to make serious errors of judgment, both as to the method adopted and the manner of conducting recitations under that method." (p.105)

So why is it so important that mathematics have a good teacher?

"Mathematics depend upon the teacher rather than upon the text-book and few subjects are worse taught; chiefly because teachers have seldom time to give the inspiring ideas, what Coleridge calls, the 'Captain' ideas, which should quicken the imagination.  How living would Geometry become in the light of the discoveries of Euclid as he made them!" (Charlotte Mason, Towards a Philosophy of Education, p.232)

Oh how true this is!  We all know how the math that's taught in the U.S. today is "a mile wide and an inch deep."  There's no time.  No time to linger, contemplate, understand, revel in the beauty that is math.  It's all jam-it-down-your-throat-and-move-on-so-we-can-cover-the-material-before-the-big-test.  Lather, rinse, repeat.  Every year.  And because there's so much material to cover before the school year is over, math really cannot be taught properly - resulting in a lack of the necessary depth and deep understanding and reverence.

I know.  I've been there.  I tried many times to give my students time to discover and think deeply about the material.  But two things hindered that attempt:  1) I couldn't give the students the time they needed to delve into the material because we would eventually have to move on to the next topic (see above paragraph), and 2) The kids struggled, big time, because they were not used to thinking.  And there were probably two main causes for this.

First, it was obvious that they had never been given, in their earlier years, the time or the opportunity to think for themselves about mathematics.  And as a result, they were not solid foundationally, even in numbers.  And that's where it all starts - numbers!  It was AMAZING to observe how little number sense my students had, even my 8th grade Algebra students who were considered more gifted mathematically than my 9th grade Algebra students.  The majority of them could not do simple calculations in their head.

Second, there is an issue that is so common in schools today and presents big problems:  Every child moves on.  I taught at three different public schools, one of them being one of the largest and most prestigious public schools in our state, and no child was held back until they reached high school - 9th grade.  So for 9 years, even if a child failed a subject, he still moved on to the next grade!  How is a child supposed to learn Algebra when he doesn't even know the basics?  It's setting them up for frustration and failure.

So how is this remedied?  What are the steps that a good teacher should take to encourage deeper understanding and a more respectful attitude toward mathematics?

1.  Take our time and let each child progress as fast as he is able.

"Bear in mind that, in the study of Arithmetic especially, one step must be mastered before another is attempted.  Progress is necessarily slow and the golden rule is, 'Make haste slowly.'" (Eclectic Manual of Methods, p.131)

"Mr. Sealey, who has done such excellent work on the teaching of junior school mathematics in Leicester, agrees that much depends on the skill of the teacher...He considers that 'assignment cards' made specially to suit the needs of each child should become the main-spring of mathematics at this stage...If the child is to succeed in becoming 'mathematically literate' the teacher must treat him as an individual.  Different minds do not learn new concepts always in the same way.  Each child takes his own unique path to knowledge.  It is important that each child should be allowed to work at his own pace.  Miss Mason wisely remarked that the tortoise should not be expected to keep pace with the hare."  (G.L. Davies, Knowledge of the Universe, PNEU article) 

Every child is different and learns at a different pace.  It shouldn't be about finishing x number of lessons by such and such date no matter what.  Of course we need to encourage and guide our students to understand concepts in as timely a manner as possible (which really goes back to developing good habits), but we also need to give them plenty of time to master each step before moving on.  Math builds and if previous material is not learned, then the student will struggle later on.

2.  Develop the concrete ideas of mathematics first.

CM and Ray's both understand the importance of beginning with the concrete, not the abstract.  In this way, the students are presented with concrete ideas that mean something to them.  And these ideas are so critical in keeping the children interested in the work and, as a result, teaching them to think.  (Emphases mine in the below quotes.)

"The little child cannot grasp abstract ideas.  It is true you can teach him to repeat, '2 and 2 are 4;' '2 from 4 leave 2;' '2 times 2 are 4;' and '4 divided by 2 equal 2.'  But without the proper preliminary work, these words cannot possibly convey any clear meaning to his mind.  This kind of instruction in a primary class is simply machine drilling on abstract numbers and words which convey no ideas, or at best a mere jumble of ideas to the child's mind.  It is one of the worst, and at the same time one of the most common, faults in the teaching of arithmetic, and it is one which is very apt to disgust pupils with the subject from the outset.  On the other hand, if the proper method of teaching is pursued, which may properly be called the object method, the children are taught to think; they will be interested at the very beginning, and they will be kept interested by this method until they are successfully carried to the point where the object method is no longer necessary, and their minds are ready to grasp the abstract, through careful preliminary drill on the concrete." (Eclectic Manual of Methods, p.107-108)

This is also what CM said - that children should not be presented with the abstract with the intention of applying the material to real situations, but should instead be presented with the real, concrete ideas, resulting in an ability to understand the abstract later on.

"But children should not be presented with the skeleton, but with the living forms which clothe it.  Besides, is it not an inverse method to familiarise the child's eye with patterns made by his compasses, or stitched upon his card, in the hope that the form will beget the idea?  For the novice, it is probably the rule that the idea must beget the form, and any suggestion of an idea from a form comes only to the initiated...The child, who has been allowed to think and not compelled to cram, hails the new study with delight when the due time for it arrives." (Home Education, p.263-264) 

"The fact is that children do not generalise, they gather particulars with amazing industry, but hold their impressions fluid, as it were; and we may not hurry them to formulate...The child whose approaches to Arithmetic are so many discoveries of the laws which regulate number will not divide fifteen pence among five people and give them each sixpense or ninepence; 'which is absurd' will convict him, and in time he will perceive that 'answers' are not purely arbitrary but are to be come at by a little boy's reason.  Mathematics are delightful to the mind of man which revels in the perception of law..." (Towards a Philosophy of Education, p.152) 

This is what a good math teacher does - he (or she) allows the individual student time to discover and manipulate the concrete ideas that can be built upon, guiding them along the way.  This will eventually lead to the understanding of the abstract, and in the process, gain an appreciation for the beauty and truth of mathematics; the logical and rational nature of it.

{On a side note, there is, I believe, another big issue at play:  I don't think every student needs all the upper level math that we currently make them learn, and CM would agree.

"But why should the tortoise keep pace with the hare and why should a boy's success in life depend upon drudgery in Mathematics?  That is the tendency at the present moment to close the Universities and consequently the Professions to boys and girls who, because they have little natural aptitude for mathematics, must acquire a mechanical knowledge by such heavy all-engrossing labour as must needs shut out such knowledge of the 'humanities' say, as is implied in the phrase 'a liberal education.'" (Towards a Philosophy of Education, p.232-233)

Not every student has an aptitude for math or will pursue a career requiring math, and because of this, one would think they wouldn't be required to master all this upper level math.  But they are.  And it puts way too much pressure on the student and may, as a result, cause them to neglect the other subjects that provide for a well-balanced education.  But this issue requires a different kind of remedy.}

So now I've discussed two steps toward pursuing mathematics as a delightful subject worthy to be studied.  Next time I'll discuss two more steps in reaching this goal.

Other posts in this series:
Part I - why study math?
Part II - good teaching <---- you are here
Part III - good teaching continued
Part IV - laying the foundation

Teaching mathematics part I - why study math?

I'm about to begin homeschooling my oldest and, as I mentioned in my post on our curriculum choices for next year, it took me awhile to finally settle on a math curriculum, even though I have a math background and taught high school math in the public school system for five years.  However, figuring out what and how to teach a first grader is a little different!

After the request of a reader to write a little more about teaching mathematics and choosing a curriculum, I've been doing some research as well as some reflecting on my days as a teacher.  As a result, I have a few posts in the making on this subject - a short series.

And I just want to say that I'm so thankful for the request to write more about this topic because I have really enjoyed it and have learned quite a bit in the process!

Most of the research that I've been doing about mathematics comes from Charlotte Mason's writings, a Parent's Review article entitled Knowledge of the Universe by G.L. Davies, and The Eclectic Manual of Methods, which is the manual outlining the teaching methods of the Ray's Arithmetic books - the curriculum that I've chosen for our math studies.  So, part of what I've written about will include how the method of teaching mathematics in the Ray's Arithmetic books not only leads to a solid foundation in mathematics, but also lines up pretty well with what Charlotte Mason (CM) wrote about teaching math.

Let me say, though, that although I have chosen at this point to use Ray's Arithmetic as our primary math curriculum, I'm not saying that Ray's Arithmetic is the best, or the only, curriculum that 1) aligns with CM's methods, and 2) leads children to a solid foundation in mathematics.  I'm sure there are many wonderful math curriculums out there - I've heard many homeschooling moms attest to this fact.  I chose Ray's because I do believe it will lead children to that all-important solid foundation in mathematics AND I like how Ray's is a simple, no frills, straightforward way of teaching the subject.  I think the simplicity of the method allows for deeper understanding in the long run.

My hope is that, even if you use a different math curriculum, you will still glean something useful from this series.

Moving on!

Math is kind of my thing.  That probably sounds conceited, but of course I don't mean it to sound that way.  I've always loved math, I went to college and earned a math degree, and then went on to teach math in the public school system for a few years.  It comes fairly easily to me and I've always thought that it was a beautiful subject.  It's rational, logical - a subject to be revered.

But not everyone would agree with me.  I saw it first hand in the years that I taught 8th and 9th grade students Algebra I.  The attitude towards mathematics was pretty sorry.  The students did not want to do math.  They didn't like it.  They thought it was too hard and just didn't understand why they had to learn this, in their words, pointless subject.

It's a good question to ponder, though.  Why study mathematics?

First, Charlotte Mason (CM) has something interesting to say about why we should not study mathematics.  Something that I've never really thought about but makes perfect sense as I look back on my days as a math teacher.

"The question of Arithmetic and of Mathematics generally is one of great import to us as educators.  So long as the idea of 'faculties' obtained no doubt we were right to put all possible weight on a subject so well adapted to train the reasoning powers, but now we are assured that these powers do not wait upon our training.  They are there in any case; and if we keep a chief place in our curriculum for Arithmetic we must justify ourselves upon other grounds.  We take strong ground when we appeal to the beauty and truth of Mathematics..."  (Towards a Philosophy of Education, p.230-231) - emphases mine

She points out that the purpose of studying the subject of mathematics is not to develop reasoning skills in children - because they already have them!

"Perhaps we should...cease to put undue pressure upon studies which would be invaluable did the reasoning power of a child wait upon our training, but are on a different footing when we perceive that children come endowed to the full as much with reason as with love..."  (Towards a Philosophy of Education, p.151) - emphases mine

Children are born with the ability to reason, just like they're born with the ability to love.  It's something God put in us when he created us.  It's one of the things that makes us human - our intellect.  And as we grow, not only do we mature physically, but also mentally.

However, our society has put much more pressure on the teaching and learning of mathematics more than any other subject (besides language) because it is seen as a means of learning problem solving and reasoning skills.  And this is not conducive to what CM said about how "education should be a science of proportion, and any one subject that assumes undue importance does so at the expense of other subjects which a child's mind should deal with." (Towards a Philosophy of Education, p.231)

"'The mind feeds on ideas and therefore children should have a generous curriculum.'" (Towards a Philosophy of Education, p.111) 

So, why study math, beyond what we would consider practical to our daily lives?  It seems there are two main reasons.

1.  To sharpen reasoning skills.

There's a difference between sharpening a skill and developing a skill.  Developing really means to cause something to come about, but we already know that our reasoning skills are something God gave us when he made us.  So math doesn't develop our ability to reason, but helps to sharpen - strengthen, hone, improve - this ability.  And it also strengthens within us certain habits.

"The chief value of arithmetic, like that of the higher mathematics, lies in the training it affords the reasoning powers, and in the habits of insight, readiness, accuracy, intellectual truthfulness it engenders."  (Charlotte Mason, Home Education, p.254)

But this sharpening of our reasoning doesn't come just from the study of mathematics.

"...Our business is to provide abundant material upon which this supreme {reasoning} power should work; and that whatever development occurs comes with practice in congenial fields of thought."  (Charlotte Mason, Towards a Philosophy of Education, p.151)

So we must first realize that math is not the means to the building up of our reasoning skills and our ability to think and problem solve.  Those things come from taking part of an intellectual feast from many different subjects.  The study of math is important, but it's just one piece of the puzzle.

2.  To develop an appreciation for and a reverence of the beauty and truth of mathematics as one of the natural laws of the universe.

Let me continue the very first CM quote from above (again, emphases mine).

"We take strong ground when we appeal to the beauty and truth of Mathematics; that, as Ruskin points out, two and two make four and cannot conceivably make five, is an inevitable law.  It is a great thing to be brought into the presence of a law, of a whole system of laws, that exist without our concurrence, -- that two straight lines cannot enclose a space is a fact which we can perceive, state, and act upon but cannot in any wise alter, should give to children the sense of limitation which is wholesome for all of us, and inspire that sursum corda which we should hear in all natural law."  (Towards a Philosophy of Education, p.230-231)

And another quote.

"In a word our point is that Mathematics are to be studied for their own sake and not as they make for general intelligence and grasp of mind."  (Towards a Philosophy of Education, p.232) 

Mathematics is to be studied for the same reasons we study any other science - for its beauty and truth.  But the problem in schools today is, it seems, a problem that's been around for awhile.

"Arithmetic, Mathematics, are exceedingly easy to examine upon and so long as education is regulated by examinations so long shall we have teaching, directed not to awaken a sense of awe in contemplating a self-existing science, but rather to secure exactness and ingenuity in the treatment of problems." (Charlotte Mason, Towards a Philosophy of Education, p.231)

Could I just bold that whole quote?  Read it again, please.  Seriously.

Whoa.  How true is this today?  Our current educational system is what?  REGULATED BY EXAMINATIONS.  There's way too much emphasis placed on excelling in mathematics (and, again, language), that we just glaze over the wondrous nature of it.  Instead, we push and push and cram and cram the material down the kids' throats, in an attempt to get them to pass the test, and in turn, we create disdainful attitudes toward the subject amongst our students.  The kids are not inspired with "that sursum corda which we should hear in all natural law."  There is no "sense of awe in contemplating a self-existing science."  There is no respect for the subject as what it is.  And on top of that, the other subjects that are worthy of studying and altogether provide a feast of ideas upon which to grow are pushed to the side with the belief that they are not as important.

I've seen it in action and it doesn't seem to be going away anytime soon.  What a disservice we are doing to our youth.

So, mathematics is to be studied because it's worthy to be studied.  It not only sharpens our reasoning skills and strengthens within us useful habits, but it is a natural law of the universe; a self-existing science.  However, we must not neglect the other subjects that make for a well-rounded education.

Other posts in this series:
Part I - why study math? <---- you are here
Part II - good teaching
Part III - good teaching continued
Part IV - laying the foundation

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First grade scheduling

I recently shared our first grade curriculum plans and now we'll talk about scheduling!  We haven't begun year one yet, so I can't tell you how the following schedule is working.  These are my plans for the year, including a schedule of what and when we'll read the AO readings and a daily schedule/routine for getting all the work done.

First, the schedule of readings.  I've only done this for term one so far.

At first, I wanted to schedule certain readings for certain days.  For example, Our Island Story would be read on Mondays, Paddle to the Sea on Tuesdays, etc.  But.  I remembered that I am one who, if we miss say, the scheduled reading for Monday, would probably get a little irritated and it would throw my whole week off!

Thankfully, I came across the idea of looping.  Instead of assigning certain readings to certain days, I put the readings in the order that I would like for us to read them, and we'll just go down the list during our reading times each day.  So, my books are in the following order:

Our Island Story
Aesop for Children
Paddle to the Sea
The Blue Fairy Book
50 Famous Stories Retold
Just So Stories
Burgess Bird Book
Parables of Nature
Herriot's Treasury for Children
D'Aulaire books
(I'll discuss the Shakespeare readings below.)

I wanted to mix up the readings a bit so that 1) the history readings are spread out (this will probably be more helpful when there's more of a mix of World and American history in the coming years), and 2) we're not reading books from the same category all at once, like all of the literature readings at the end of the week, for example.

I am planning to have at least two times set aside throughout our days in which to do our readings.  At the beginning of the week, during our first AO reading time, we'll read from the first book, Our Island Story.  Then, barring no scheduling havocs, we'll read from Aesop for Children in the next time slot.  If we happen to miss Aesop, we'll pick it up the next time we read, even if it's the next day, and we'll just keep going from there.  This way everything stays in order.  We have to make it through the whole list before starting at the top again.

Here's my document for checking off the readings (here is a link to the pdf file):

Each week we'll just work our way down the list, marking off as we go.  I'll keep this handy throughout the term, maybe on a clipboard or something.

This grid came from the AO year one 36-week schedule page.  I downloaded the word document, then copied and pasted the rows for term one into a new document.  I rearranged the rows so that the books are in the order that I want to read them.

A few notes:

~ I moved around a couple of the readings:  "Prince Darling" and "Toads and Diamonds" from The Blue Fairy Book, and "Only One Woof" from Herriot's Treasury.  You can see at the bottom of my table where they were originally.  I moved them in order to keep a maximum of 8 readings per week (the two Aesop readings per week count as one since they're short).

~ For Paddle to the Sea I'm going to use Charlotte Mason Help's (CMH) schedule of this book which means reading Paddle in term one, then reading two chapters of Charlotte Mason's Elementary Geography per week in terms two and three.  That's why Paddle is different from the original AO schedule.

~ AO only has half of the Burgess Bird Book scheduled for the whole year; one chapter every other week.  I've heard so many people talk about how the book is so wonderful and just flows if you read it from beginning to end that I've decided we'll read one chapter each week with a plan to finish the whole thing (which will take longer than 36 weeks - we may begin it a few weeks early and finish it a few weeks late).

~ See the Shakespeare row at the bottom with the asterisks?  I plan to begin a "morning" time routine (I hope to keep you updated with our morning time plans throughout the year) consisting of Bible and poetry readings, memory work, possibly Spanish, and a read-aloud or two.  On the weeks that Shakespeare is scheduled, I'm planning to read that as the read-aloud during morning time.  Addy (4) won't be required to sit in during this, but I would love for her to.  It seems that most families read Shakespeare together, so I think this would be a nice way to do that.

~ I mentioned in my first grade plans post that I'm not planning to read Trial and Triumph this year, so that's why it's missing.

Still with me?  I hope!

Now on to the daily schedule!

At first I made a schedule with the actual times that I wanted to do everything throughout the day.  So for example, morning time would be from 8:30 to 9:00, math from 9:00 to 9:15, writing from 9:15 to 9:30, then a break for 20 minutes, etc, etc.

But.

Like I said earlier, if I did this kind of schedule and we got behind, then I may or may not get a little irritated and it would throw the whole day off!

Instead, I'm going with a routine rather than a schedule.  Things are in order, but it's not so particular that we have a certain time of the day for each subject.

Here is the weekly schedule checklist I made for term one:

I'll print this off each week so that I can check off each item and make any notes that are needed.  I may keep this on a clipboard with the readings schedule from above.

A few notes:

~ Notice how I did not assign the actual days of the week:  Monday, Tuesday, etc.  I put day 1, day 2, and so forth, so that if we miss Monday because of sickness or something, then Tuesday turns into day 1.

~ The first block for each day is morning time, which will probably be during or right after breakfast.  Bible is first because I definitely want Addy involved for that, but after that she is free to go if she wants.

~ I put the subjects in the order in which I would like them to be accomplished during the day.  So once we're done with morning time, we'll probably break for morning chores, then come back and Izzy will start with math.  Writing practice is next, followed by one of our AO readings from above, then reading instruction, then the second AO reading.  If we have to take breaks, we have to take breaks.  Of course, I would love to get this all done together, maybe with a short break or two, and be done before lunch.  But, if we only get math, writing, and one reading in before lunch, so be it.  Sometime after lunch we'll continue with reading instruction, then the second reading.  And then she'll get to recorder practice at some point during the day!

~ You'll also notice that next to each subject is a number in parenthesis, for example Math (15).  That's the estimated amount of time that will be spent on that particular subject.  CM was an advocate for short lessons, and I agree with that, so we will be staying close to those numbers.

~ Bible:  AO has certain Bible selections to be read each week, but I am doing something different.  I'm going to be using the selections at Penny Gardner's website, with two days of Old Testament readings and two days of New Testament readings, then a chapter from Wisdom and the Millers on Fridays (I mean, day 5!).  We'll probably just go down the list on her website, but only keep the readings to around 10 minutes per day.

~ I plan to "do school" four days per week with the fifth day being a day of enrichment.  We'll still have a morning time, but instead of all the academic-y stuff, this is when we'll do our art and music studies, drawing lessons, handicrafts, and nature studies...aka the fun stuff :)  I'm not planning for us to do everything listed every Friday.  I mentioned in my previous post about how I plan to rotate these subjects.  We'll see how it goes.  And I hope to keep you updated!

Whoo!  That's my plan and I'm *hopefully* sticking to it!  Have you made your schedule for the upcoming year?  If so, I'd love to hear about it!  Maybe I'll glean some good ideas :)

First grade curriculum plans

I've been planning and researching and organizing these past few months in preparation for our first year of official homeschooling.  Izzy (6) will begin first grade sometime this year and I finally feel like I'm getting a grip on the whats and hows of what I will teach her.

It may be a little early to post curriculum plans, but I have decided to begin Izzy's first grade year around July (only two months away!!) because we have baby girl #3 due in September.  I would like to get at least a month or two in before our whole schedule/routine is thrown off due to a newborn.  Also, because of said newborn, I have a lot of "bucket list" items that I would like to complete in the next few months:  decluttering, yard sale, general baby prep, etc, and I don't want my homeschool plans to be put on the backburner.  I'm just not a fly-by-the-seat-of-your-pants kind of gal and I need a plan!  Plus, I tend to procrastinate and I just don't want to keep putting this off.

Anyway.

We're relying pretty heavily on Charlotte Mason's (CM) educational methods:  living books instead of textbooks to teach different subject areas, copywork in the place of spelling and grammar, narration instead of worksheets, and short lessons, just to name a few things.

So, here we go!

Booklist

I've decided to rely on Ambleside Online (AO) as our spine curriculum.  Here is the link to their year one (aka first grade) booklist for each subject - history, literature, poetry, science, geography, etc.  I plan to use all of these books with one exception:  Trial and Triumph.  I do think we'll read it at some point but I'm just not sure I want to read it yet.  I'm thinking of waiting another year or two when Addy (4) will be a little older and we can read the book together as a family, maybe on Sunday evenings or something.

Writing

I plan to have Izzy do no more than 10 minutes of writing each day (CM is an advocate of short lessons).  She can write fairly well, but I still plan to start with her mastering the correct way to form each letter (for example, making sure she writes an "o" counterclockwise and not clockwise which she has a tendency to do).  After we go through the alphabet, I'll have her begin copying words and short sentences from the above readings.

Reading Instruction

We'll do 15 to 20 minutes of reading instruction each day.  At this point, she already knows the sounds each letter makes and we've done quite a bit of word-building using CM methods.  You can find a breakdown of those methods here.  She has learned pretty well how to sound out words.  My plan is to use the McGuffey readers, beginning with the primer, to continue with both phonics and learning to read by sight.

The McGuffey readers are in the public domain, so they can be found for free online.  Here is a link to the primer.  Also, the Eclectic Manual of Methods is invaluable for learning how to teach reading using the McGuffey readers (and for teaching math with Ray's Arithmetic which I'll mention below).

Math

I've had a difficult time choosing a math spine, which seems silly because I have a math degree and I taught math in the public school system for five years.  However, there's a big difference between teaching 9th grade algebra and figuring out what and how to teach first grade math.

After much consideration, I've decided to use Ray's Arithmetic.  I like it because 1) it is that classical, tried-and-true method of teaching arithmetic, focusing on mental math and really understanding numbers, and 2) it's free!  You can find the Ray's New Primary Arithmetic book here.

Actually, the book isn't even used for the first year, unless the child masters the concepts quicker than anticipated (which I wouldn't be surprised if this will be the case with Izzy; she's pretty sharp when it comes to math...she must get that from her mother HA).  Like I mentioned above, the Eclectic Manual of Methods is a must for learning to teach math using Ray's Arithmetic.  AND the Ray's Arithmetic Yahoo group is also invaluable.  It has the whole plan for the first year.

I also plan to add in some living math books (great sites with lists of books here and here) and math-y games here and there.  My math pinterest page isn't much, but there are a few good games that I've pinned, so feel free to look!  We'll probably spend 10-15 minutes on math each day.

Foreign Language

I've decided on Spanish as our foreign language.  I really wanted to do French, but I'm much more familiar with Spanish, having taken it in high school and college, and it's just more practical living in the southern U.S.

At this age my goal is to introduce the language to the kiddos and have them learn some common phrases and vocabulary.  I'm thinking we'll shoot for about 10 minutes per day.

I'm not buying a Spanish curriculum at this point.  I searched around the AO forums and found a couple of sites on the internet that provide free resources for teaching Spanish to children.  One of them is the Salsa Videos, and here are some Salsa Teacher Support Materials and the support materials for teaching grades k-2 with the videos which I think will be necessary to implement this program.  I actually don't plan to use the videos at this point, but I'll definitely use the support materials because they contain a great deal of vocabulary and common phrases.

Someone on the forums also mentioned Spanishtown, which may prove useful as well.  I would also like to incorporate some illustrated children's Spanish literature (gotta search the library) and Spanish children's songs which I'm sure I can find on youtube.

Memory Work

I'm taking the suggestions at Charlotte Mason Help (CMH - scroll down to the Recitations section) for this area.  Izzy will learn and recite one Psalm, one passage of scripture, and one poem, as well as two hymns and two folk songs, per 12-week term.  I plan to set aside around 10 minutes each day for memory work/recitation.  I don't have my official selections yet (I'm not that organized at this point!), but when I do, I'll share them.

Picture Study

I'm again taking the suggestions from CMH for picture/artist study.  AO has a rotation of artists and prints to study each year, but I think it's important to expose young children to art that will capture their particular interests, developing an appreciation for fine art.  So, I'm going to be choosing different prints to study, rather than the ones listed on the AO website.  I'll choose one artist each term and we'll study six paintings by that artist - one every two weeks.  I haven't made my selections yet (see above), but again I'll share them when I do.

Hymn/Folk Song/Composer Study

And yet again, CMH for this one.  At this point I'm not going to use AO's song and composer rotations.  I like how CMH introduces the young'uns to the orchestra, the ballet, and the opera, so we'll plan on that.  And I'll be choosing the hymns and folks songs at least for this year.

I plan to do the picture, hymn, folk song, and composer studies on Fridays, rotating each week.  I'll play the composer selection at different times throughout the week, and I plan to include the hymns and folk songs during memory work, too, rotating them on different days.

Drawing/Painting

Not quite sure about the painting part yet - CM advocates learning the dry-brush technique and I've played around with it, but I'm just not comfortable yet to teach it to a 6 year old.  So we'll plan to start with just plain ole' drawing lessons using the book Drawing With Children.  I should probably read this book soon...it's on my summer bucket list ;)

I would also love to incorporate some drawing drills that go along with this book which can be found here.  I'm wondering if we could do these during our morning time.

Nature Study

We'll plan to go on a nature walk once per week and keep a nature journal, recording and drawing birds, plants, and animals/insects.

We'll most likely take the journaling part kind of slow - maybe every other week or so in the beginning to get our feet wet.  We'll probably start this in the next few weeks.  As a result, I'll probably supplement a little with some nature/science books.  At this point I'm thinking of reading some of the Among the People series, probably during morning time.

Handicrafts

Oh boy.  Here's where I'm kind of at a loss at this point.  I know I want to teach the girls to sew, but first I need to learn!  Of course, I could just learn right along with them...

Anyway, I would love to teach them all kinds of things, but again, we're going to take it slow and go with something I'm familiar with.  (Plus I'll have a newborn, so...you know.)  We'll most likely spend the first term working on some cooking and baking skills (now that's what I know), and I'm thinking of doing some card making as well.

I know CM had her students working on the drawing/painting, nature study, and handicrafts every week, but I'm thinking of doing a Friday rotation, kind of like what Brandy explained on her blog, just so that we can get acclimated to all this new stuff.

Music Instruction

I haven't thought a whole lot about this area, but I would love to have the girls learn to play the piano.  I'll probably use CMH's suggestion of how to teach children to play the piano, starting with the use of a recorder.  I know this will need to be something done consistently, so I'm shooting for about 15 minutes, 4 or 5 days per week.

Whoo!!  Is that everything??  I hope so!  Sometime in the near future I'll share my plans as far as a schedule/routine for getting all this done.

Have you started planning your next homeschool year?

{Joyful Things} - books, birds, and beautiful weather

I know I already have a post entitled "Joyful Things" but I would like to continue this theme every now and then with a post highlighting the things we've been enjoying as of late...the joyful things; the things to be thankful for, which are usually the small things in life.

This morning I actually went back and reread the above post because...I needed to.  Yesterday was rough and I know we all have rough days and have a difficult time getting our mind back on the right track.  Sometimes we just need a reminder :)

So here are some things we've been enjoying.

I've already been enjoying the beginning of yard sale season.  I love yard sales!!!!  You just never know what you're going to find (that you probably don't need, HA).  I visited my parents last weekend and there was a huge yard sale at the local fairgrounds.  What did I come home with?  That's right....books!  Mostly children's books and at 25 cents apiece, I'm thinking I did pretty good.  Here's some of what I got:

A bunch of old Thornton Burgess books!

Lots of good picture books.

Some history picture books.

A few readers for Izzy.

Plus, this cool bird book.  It's got some lovely pictures...

Speaking of birds, Izzy and I went for a walk the other evening.  It was so nice because she held my hand the whole time (I had been out of town the previous weekend, so I think she missed me :) ) and we just walked and talked and looked at stuff - she's normally so go-go-go! and half a street ahead of us when we go for walks.

At one point we stopped to watch a pileated woodpecker (of course, I didn't bring my camera).  He was flying around and at one point flew to the ground and stood there about 10 feet away from us.  It was really neat!  Then we saw some birds on the street and I told her that I see them all the time in the trees next door, but I didn't know what they were.  We got home and she brought this book over to me and showed me what they were!  Mourning doves.

It was just so cool because I've been thinking about nature study which we'll begin in the next few months as we start our first homeschool year.  Like I said, Izzy is just a busy-body (we sometimes call her Busy-Izzy), never seeming to be that interested in just stopping and looking at things.  This gave me hope!

Some more nature things...

Izzy found a robin's nest in our peach tree a week or so ago with three eggs in it.  We've been checking on it each day, watching the mama bird guard her eggs.  Unfortunately, this morning I noticed only one egg was in the nest - the other two had fallen out and broken :(  It must have been the wind - the nest is on a pretty low swaying branch.

See the nest above Addy's head?

One day after it rained, we saw a big, beautiful rainbow.

Our first rose bloomed!

And a few more will be on their way soon.

Some of our veggies are coming up.

Corn

Green beans and a zucchini plant on the left

We planted a lot more, but that's all that has come up so far.

We live close to the White River and spent some time there a couple of weeks ago.  It's a fun place to go during the summer (nature study site!).  The girls love to throw rocks and wade around.  Of course, it was too cold to get in.  We'll wait a few weeks.

Izzy's a climber.

So at one point, I turned around and Izzy was praying out loud.  {heart melting}

We've been enjoying the beautiful weather, spending lots of time outside.  Izzy got a new bike for her birthday.  Maybe we can work on getting the training wheels off this summer!

 Izzy likes to hang out in the peach tree every now and then.

Walking the dogs.

It's been fun watching Izzy play tball.  It's fun to watch her and Jared practice at home.

That's all for now!  What have you been enjoying lately?

Important blog change!

I have decided to change my domain from www.angelawilhite.com back to my original domain when I first started this blog:  wilhiteslivinglife.blogspot.com.

So for those who are subscribed to my blog, please resubscribe in the next day or two!  I will be changing the domain sometime today.  

Sorry for the inconvenience!

Education - what am I really after?

As we approach our first official homeschool year I've been doing a lot of reflecting about this mighty task we've decided to undertake.  Homeschooling I know is not for the faint of heart.  It will not be a cake walk, but I do have faith that it will be one of the most rewarding things I'll ever do in my life.

Part of these thoughts are an attempt for me to, when times are tough and burnout is on the cusp, look back on and remind myself of why I've made this decision to educate my children at home.  I don't want to forget the big picture, the ultimate purpose of this venture, what I'm really striving for.

So what am I striving for?  What is the ultimate purpose?  When it comes down to it I don't think the purpose underneath it all is to provide my children with a good education.  That's not really it - to make my kids smart...whatever that means :)

Don't get me wrong - the building up of the intellect is an important part of life.  It's not something to be taken lightly because that's part of what makes us human - our God-given ability to learn and grow our minds and reason and think.  So providing a solid education is important, just not the most important.

What else makes us human?  God expects us to grow, but not just grow our intellect.  He expects us to be transformed.  We were made in His image - our children were made in His image - and we have the God-given ability to reflect His nature, to grow into Him and His likeness.

To do that we must grow; flourish; mature - more than our intellect but our whole, spiritual selves.  And one of these days our children will grow up and leave our homes and it will be up to them to seek the righteousness of God and allow Him to transform them.  But right now, God has given us, the parents, that responsibility.

Right now (well, at least in my case) our children are too young to learn to seek and listen and obey God.  They're too young to really understand.  I mean, think about how long it takes us to scratch the surface of understanding!  It's a lifelong journey.

And it starts with us - the parents.  God has given us the responsibility - the privilege - of raising up our children in the way they should go so that they never depart from it.

My task, my ultimate purpose in educating my children and raising them up, is to teach them to pursue wisdom, to pursue truth, to pursue beauty in this beautiful world that God has given us.  To become virtuous beings.  To seek the kingdom of God and His righteousness, with faith, knowing that He will give us everything we need.  To help guide these precious beings into ones who will seek the Lord and love Him with all their mind, body, and soul.  (I must remember, though, that God is ultimately in charge of the results.)

And you know what?  I'm convinced that a government-run education program is not interested in those things.  They are not interested in our children pursuing wisdom, truth, beauty.  They are not interested in our children become virtuous.  They are not interested in producing adults who seek God and His kingdom and righteousness.  They are not interested in molding and teaching these children to love the Lord.  That's not what they're after.

I'm not saying that these things can't be taught to our children without homeschooling - although I will venture to say that I think the world in general would be a better place if more and more parents did decide to homeschool their children and for the right reasons.  But I understand that not everyone can and/or will homeschool.  Everyone has a right to make their own decisions and I am not meaning to imply that I'm doing it the right way and everyone else isn't.

Just because I've chosen to homeschool doesn't mean I'm better than anyone else or that my children will turn out better than a public schooled kid.  There are plenty of Godly men and women in this world who went to public school.  But I do think we all need to remember what it's really all about. And, I do think our decision to homeschool will make it easier to teach our children how to navigate this life with God at their center.  Honestly.  Because my children won't be spending more than half of their days in a building ran by the government, getting an education dictated by said government, who, as I mentioned, does not care about what I'm really after.

They will be at home, with me, with their siblings, with so much time and opportunity to love each other and learn with each other and grow with each other.  They will be at home with their family, the unit that should have the most influence on their well-being.  Yes, I may sound idealistic, but there has to be some idealism.  Otherwise, what's the point?

Like I said, it won't be easy.  Nothing truly worthwhile is.  But this is my task, my calling, my privilege, as a Christian parent - to give my all in raising up my children.  To teach them what's truly important through loving and serving them, and through the beauty in the world - which includes good books and mathematics and science and history and art and music.

"Train up a child in the way he should go,
And when he is old he will not depart from it."
Proverbs 22:6