Ella Frances Lynch Arithmetic

[Hunter]

I just read the first chapter on Arithmetic in the Eclectic Manual of Methods.  I think this text is in line with a lot of EFL.  For example it recommends that NO book be used in primary class.  Also the work is oral and not written with the use of objects.  They even specifically mention pebbles. 

 

This text mentions the object lesson.  I assume this just means teaching with objects or our modern word manipulatives.  They really make a point to say that children must be able to recognize the group as a whole without counting by ones. 

 

As I am contemplating a summer math block that is a Waldorf inspired quality of numbers main lesson book, I wonder if I should have my son draw pictures of these groups in his math journal.  Not only a group of three for instance like the clover, but all possible combinations and separations.  Perhaps there are some flashcards that work for this method until rapid accuracy is acheived.

 

Page 110 had me a bit worried because it says, "...once forms the habit of counting by ones in order to answer such a question as, "How many blocks in this group?" it will be almost impossible to correct his error. 

 

This is something I've had my son do.  We have not done a lot of formal lessons though so perhaps with drill and proper instruction we can overcome this. 

 

This text does do addition and subtration together and then later moves on to multiplication and division.  EFL goes from counting to skip counting, but is skip counting really the same as multiplication or could it just be another form of addition that can later be explained as multiplication? 

 

After this I got a bit confused with terms concrete digital numbers and abstract digital numbers.  Then they provide a good table for early algorithms.  This could be something that is put into the math journal even according to EFL.  My biggest issue with the children writing this table would be if there handwriting was neat and clear.  I would just continue this as oral drill if handwriting was not sucessful yet.

 

Don't worry about the "impossible to correct".  :001_tt2:  to that. The Eclectic curriculum was a for profit series, that was being threatened with loss of sales by series following Grube's and other methods. Publishers filling parents heads with worries of lifelong failure due to not using THEIR curriculum from day 1 predates the 21st century.  ;) Everything is fine. 

 

Copying tables is going to be SLOOOOOOW work for some children. But until they can do that, they won't be ready for copying from a textbook. Even when using a workbook, they will not be able to correctly complete a long division problem. Many a 6th grader does poorly on standardized tests because he wasn't explicitly taught basic math handwriting.

 

Seriously, this is where the slant comes in. If you are choosing to use slanted cursive, of which there are equal pros and cons, a little more time and patience and explicit instruction is going to be needed with math handwriting in K-4.

[Hunter]

I just realized today that I can scan Strayer-Upton with my new scanner. I bought a papercutter today. I actually have a partially cut apart copy of Strayer-Upton that I scanned a few pages from awhile back and decided that there was no way I could scan the whole book with the scanner I had. I think I'm good to go. Maybe Friday or this weekend.

[arliemaria]

Don't worry about the "impossible to correct".  :001_tt2:  to that. The Eclectic curriculum was a for profit series, that was being threatened with loss of sales by series following Grube's and other methods. Publishers filling parents heads with worries of lifelong failure due to not using THEIR curriculum from day 1 predates the 21st century.  ;) Everything is fine. 

 

Copying tables is going to be SLOOOOOOW work for some children. But until they can do that, they won't be ready for copying from a textbook. Even when using a workbook, they will not be able to correctly complete a long division problem. Many a 6th grader does poorly on standardized tests because he wasn't explicitly taught basic math handwriting.

 

Seriously, this is where the slant comes in. If you are choosing to use slanted cursive, of which there are equal pros and cons, a little more time and patience and explicit instruction is going to be needed with math handwriting in K-4.

 

I'm glad to hear I haven't ruined my child before we even had a proper go at schooling.  

 

I do not think we will attempt any copying of tables this year or probably even next year.  I will begin handwriting at some point during this year.  I still have not read enough or made a decision on handwriting, but would love to begin with cursive.  I just worry about the effort we will need to exert in the beginning.  This will most likely be slanted as that is what I learned and use myself.  I wonder if perhaps as I do our main lesson block I should skip the Roman Numerals and just use the slanted tally marks.  We can still learn the hand, arm, body forms for the Roman Numbers, but I don't think it is necessary to have him draw these in his notebook.  Plus the tally marks are a group which is what the Eclectic Manual of Methods really stresses the child needing to immediately identify.

[Hunter]

Another reason I like tally marks more than the Waldorf Roman numerals, is that Waldorf uses IIII for 4 and VIIII for 9, instead of the commonly used IV and IX.

[stm4him]

I am not sure I am in love with her method, but I LOVE her philosophies so far.  I am on the writing and drawing chapter now......

[Hunter]

I have been reading the chapters on home teaching and observation tonight.

 

I've been wrestling with whether to use the KJV for copywork, or a more modern version that uses the current fads in punctuation. I was impressed with the bit on pages 145 that talked about a student spending all day indoors studying spelling, grammar, and composition learning HOW to express himself, but having nothing to express. This gives me more confidence picking the KJV, despite the students not able to learn the most commonly used mechanics by copying it.

 

From page 145, "It is just possible that Lincoln and Edison and others became really great because they did not have the disadvantages of a modern education." I know that Lincoln, as I do, self-educated grammar and always felt like he was lacking in that area. He read and read and read books with atypical grammar and punctuation, making it harder to absorb one standard. Was more good that harm done for him? I have come to think so for myself, but have been having a harder time PLANNING that for students.

 

EFL nature study goals make so much more sense to me than CM. Students are supposed to be training their senses, storing images for later comparisons, and acquiring useful vocabulary. Identification is not a primary goal.

 

Page 157, "...he who brings something to the book is the one who gets something out of it. This quote is in defense of early nature based science instead of early book based science.

 

This book is answering questions I have been wrestling with for awhile.

 

I'm hoping to type out the library list and provide links for each book.

[vaquitita]

EFL nature study goals make so much more sense to me than CM. Students are supposed to be training their senses, storing images for later comparisons, and acquiring useful vocabulary. Identification is not a primary goal.

 

Page 157, "...he who brings something to the book is the one who gets something out of it. This quote is in defense of early nature based science instead of early book based science.

I'm wondering why you think CM focused on identification as the primary goal of nature study? This is not my impression. The focus seems to be on training their observation skills and having real hands on experience with nature. I'm expressing that later one badly. But as an example, to have spent some time observing one bird- eating, it's nest, it's eggs, it's young, etc. so that then later when reading about some other bird, they have real life experiences to compare it too. Nature journaling, while yes it's nice to be able to identify and label somethig (or at least it is for us adults. Lol), the real beauty of drawing what you see is you have to really look at it, really observe.

 

That at least has been *my* impression of CM nature study. i am curious why you think differently? Maybe I always read into it what makes sense to me. Lol.

 

I'm going to get sucked into reading this book and further confusing myself. Lol. :willy_nilly:

[arliemaria]

So plans for first grade arithmetic (currently, and of course always subject to change):

 

We will first try to get our speech evaluation completed before June.  I am giving myself some time here because I will be having a new baby on Tuesday.  This is to check to see if his 13/14 counting stumble and phonics blends are related to speech delays.

 

Second project will be to begin a Waldorf inspired quality of numbers study.  I am not sure yet what type of notebook I want to use or if I want to actually use a notebook.  I think this might be easier without a notebook and just do it on artist quality paper that we could use to decorate our learning space.  Later if we want we can bind all the pages into a book.  

I will complete a page alongside him.  We will either watercolor the page or do a color wash with our beeswax crayons.  We will do a border design for each page too with the corresponding number.  I like the border designs in Efficiency Arithmetic:  Primary page 3.  https://play.google.com/books/reader?printsec=frontcover&output=reader&id=z-BEAAAAIAAJ&pg=GBS.PA3

 

We will do the slanted tally marks large and in the center of the page with drawings of groupings of that number around it as suggested in the African Waldorf Math book.    I think the first week we might be able to do 1-3, but probably beginning with four we will need to spend more time if we are to "instantly give the number of any group of objects not exceeding ten, at sight, and without counting."  I think I will make flashcards to help with this part of drill.  I will of course have him do these groupings with the objects as well.  Lots of manipulation.  If he would like I can even take pictures of his groupings to use for the flashcards.  

 

I think this will be enough work for the summer.  Any other suggestions if following EFL/Eclectic Manual of Methods for primary before beginning skip counting and abstract written tables of math facts?

[arliemaria]

Once we have learned many of the "groups" I might use these pages as review.  https://m.flickr.com/#/photos/taffeta/5814773615/

[stm4him]

I wish I knew how to teach them to identify things.  That is a goal I have given up on because I just never have been able to pull it off.  I am settling for the drawing of nature first from books and then from our own land and just spending lots of time out in it.  But I really wish we could name things.  I just don't have time to help make that a priority right now.

 

As for primary math....I think these border drawings and picture links are adorable and fun, but I wonder if they are necessary.  To me, most of those come so naturally without teaching them that it seems one could pick up with that at a little older age and fly through it rather than needing to spend a whole summer on it unless it was child-driven.  I don't mean to criticize at all.  I am just looking at it from the perspective of a mom of many who has to cut away anything that can be picked up more quickly and independently when they are older.  I am also wondering if it is a left-brained, right-brained thing.  My husband and I are both left-brained and our kids are too from what I can tell so far, but my oldest (from my first husband) is very right brained.  I am beginning to wonder if she would have benefited from all of these kinds of more pictorial activities.  For the others it seems unnecessary.  The pictures are cute and all that but programs like Singapore annoyed me with all the pictures.  The abacus is a little different to me in its usefulness because of the groupings (the Right Start one I mean), but most of all that primary number work seems like it would naturally be discovered by a child in the first 8 years anyway unless they had a severe learning issue.

 

As for grammar, I was one who naturally picked up on punctuation and capitalization from reading and my second child is like that, but I did not know it well enough to teach it to those (like my oldest) who don't pick up on it naturally and there are many times I second guess myself because I am basing things on how they look.  I really like to have the tools to explain things and the correct words.  I want to have the basic rules in my head through either memorization or checking of their Hake books over the years.  There are things I can explain in math, Greek, and Latin only because I have spent time checking their work and other things I know because we memorized them in Classical Conversations.  I want my children to have these things in their heads too either by repetition over many years in their workbooks or memorization.  If you have practiced using something or have something solidly memorized you can recognize in ANY book when it is following our current standards of grammar usage or not and explain the differences.  That is the difference between being able to put your natural grammar skills to use for others or not.....

[Hunter]

I'm sick today and will have to wait till tomorrow to respond to most of this.

 

Arliemarie, google "number bonds".

 

This youtube video is pretty good. The method for teaching number bonds can also be used with numbers other than 10.

https://www.youtube.com/watch?v=sHhrm0S8f0Q

 

Google "playing cards math". This page and videos will get you started.

http://www.crewtonramoneshouseofmath.com/math-with-playing-cards.html

 

http://www.esc16.net/users/0020/FACES/2013%20FACES/Handouts/Reid%20and%20Stott%20Problem%20Solving%20Math%20Card%20Games.pdf

[Hunter]

I haven't done much with dice, but here are few games

http://www.curriculumsupport.education.nsw.gov.au/primary/mathematics/assets/pdf/moreactivities/dice.pdf

 

Domino video

[arliemaria]

I wish I knew how to teach them to identify things.  That is a goal I have given up on because I just never have been able to pull it off.  I am settling for the drawing of nature first from books and then from our own land and just spending lots of time out in it.  But I really wish we could name things.  I just don't have time to help make that a priority right now.

 

As for primary math....I think these border drawings and picture links are adorable and fun, but I wonder if they are necessary.  To me, most of those come so naturally without teaching them that it seems one could pick up with that at a little older age and fly through it rather than needing to spend a whole summer on it unless it was child-driven.  I don't mean to criticize at all.  I am just looking at it from the perspective of a mom of many who has to cut away anything that can be picked up more quickly and independently when they are older.  I am also wondering if it is a left-brained, right-brained thing.  My husband and I are both left-brained and our kids are too from what I can tell so far, but my oldest (from my first husband) is very right brained.  I am beginning to wonder if she would have benefited from all of these kinds of more pictorial activities.  For the others it seems unnecessary.  The pictures are cute and all that but programs like Singapore annoyed me with all the pictures.  The abacus is a little different to me in its usefulness because of the groupings (the Right Start one I mean), but most of all that primary number work seems like it would naturally be discovered by a child in the first 8 years anyway unless they had a severe learning issue.

 

As for grammar, I was one who naturally picked up on punctuation and capitalization from reading and my second child is like that, but I did not know it well enough to teach it to those (like my oldest) who don't pick up on it naturally and there are many times I second guess myself because I am basing things on how they look.  I really like to have the tools to explain things and the correct words.  I want to have the basic rules in my head through either memorization or checking of their Hake books over the years.  There are things I can explain in math, Greek, and Latin only because I have spent time checking their work and other things I know because we memorized them in Classical Conversations.  I want my children to have these things in their heads too either by repetition over many years in their workbooks or memorization.  If you have practiced using something or have something solidly memorized you can recognize in ANY book when it is following our current standards of grammar usage or not and explain the differences.  That is the difference between being able to put your natural grammar skills to use for others or not.....

 

I think the only thing to do with identifying things is just show the image over and over until they can see that it is five, etc.  Perhaps this is ignorance, but I assume much of it is just familiarity and repetition.  It may also be a goal I give up on, but this is my first real go at it so I might as well try.  We will definitely continue our family nature diary and spending LOTS of time outdoors.  We have 16 acres so most days in nice weather we are outside most of the day.  I have been sick (cholestasis of pregnancy, possible preeclampsia/HELLP) so I have not been outside much the last few months, but we did recently paint forsythia.  We talked about the flowers because they have four petals nearly in the shape of a cross.  This along with dogwood, etc. could be on our IIII (4) page.  

 

I doubt much of this is necessary and like EFL says page 101-102, " It has been demonstrated that we have to work for a year to teach a six-year-old child what he could learn by his own efforts in a single month when he is eight years of age.  The child at ten is just as far in advance and fully as good a student of arithmetic if he commences his study at eight rather than at six."

 

I want to offer activities that I do along with him instead of just a workbook.  I want him to have fond memories of doing math with me.  My mother died young leaving my sister at age 6.  I think that is part of my motivation.  I homeschool for many reasons, but one is time.  I want time with my children.  I want them to have as many beautiful memories of us together as possible.  Please truly know I do not take anything on a forum as criticism.  We have an IKEA abacus, but honestly don't know how to use it much.  I have thought about trying to find a used copy of Right Start, but don't really want to spend much money.  I know the Right Start abacus is two colored and wondered if I should disassemble my abacus and make is so that each row is two colors of five beads or even repaint the beads to match.  Thoughts/Ideas?

 

As far as grammar for me, I have not even really began to explore what I need to learn myself before I teach it.  It is on the list though.  I just want to make sure I have my math plan complete with action tasks so I don't have to constantly rethink what my next step is.  Once I get this down, I'd love to discuss what EFL and others say about grammar.  Possibly another thread for another chapter of Educating the Child at Home?

[arliemaria]

Here's a good article for you, stm2him.  Teaching all K-6 math in approximately 20 hours.  http://www.besthomeschooling.org/articles/math_david_albert.html

[arliemaria]

So last night as I wanted to find out more about early arithmetic instruction found this article on Ambleside Online:  http://www.amblesideonline.org/PR/PR07p008FirstStageArith.shtml This is an article not by Charlotte Mason, but by the late Rev. R. H. Quick.  I found it to be very compatible with EFL.  He talks about how we have to teach conceptions of numbers gradually.  That we must "settle firmly in the child's mind the facts about numbers up to ten; and make these facts thoroughly familiar."  He mentions Grube and the German thought of spending an entire year on numbers to 10 with a second year on numbers to 100.  They do not have the child write any notations at all.  He also advocates for the child to learn to recognize their numbers without counting.  He gives a short example of how to teach groups and units within a group.  

 

I was happy to see two alternatives to our current counting (eleven, twelve, thirteen, etc.).  He uses 10, 2 and 10, 3 and 10, &c., &c. His other way was onety-one, onety-two.  These might be helpful strategies to use with my son as he is having trouble saying thirteen and fourteen.

[stm4him]

The second article I have not read yet, but I will be interested to see if he explains why it can't be learned just as easily in an unhurried environment naturally by the child without needing to be taught explicitly.  

 

The first article is very interesting.  I once read a blog post from a TJED Mom who allowed her children (who were at least middle school if not older) to not do anything and though they did eventually begin to read and write more and more on their own, at least one of them did not decide to touch math until he was 16 (if I am remembering correctly.)  All of a sudden he decided he was interested and went through an incredible amount of math in a very short time with focused, motivated study on his own.  It was really interesting and gave me hope that if my daughter ever did decide that she wanted to reach higher levels in math she could probably buckle down and knock out a whole level in a short time.  

 

The article made me wonder if it would be "safe" to leave a child until 6th grade and then have them go through the Strayer-Upton series in three years, finishing by the end of 8th grade ready for Algebra (or even before then if you skip parts of the third book).  But the key would still be whether they were motivated or not.  Who can know if or when their child will be motivated?  Also, in some states it probably isn't even an option.  Here it isn't mandated, but they are tested every year in math after age 7.  I do not have to turn the test in but it would be a little scary if it were ever asked to be seen by an official.

 

This January I bought CLE's remedial math books and worked on them with my oldest two because I was convinced that they could understand some concepts that they had not yet reached in their Saxon books.  I was right and they were able to learn some new, harder concepts in these books (and understand what they were doing at least in terms of algorithms, maybe not 100% understanding but that is hard to tell) but when we went back to our books and they weren't practicing those things they forgot how to do them and when we recently hit division (short division with a remainder) with my 10 year old he was almost in tears about learning it even though we had covered it in January and he had been able to do it then (though it was a bit of a struggle then too).  This is a boy who is an incredible reader and speaker so it is not a reading comprehension issue.  I think it is a dislike for math and a lack of inner motivation to learn it.  Most of the time he does fine, but I know he could learn a lot faster if he were motivated.  This also happened in grammar.  We spent a year and a half intensely studying grammar at our co-op and at home.  He did really well and learned a lot.  The second year he was at the top of his class in understanding the concepts and knowing the answers, etc.  But after spending a few months not doing it he began to forget.  So for me it isn't necessarily how fast someone can learn something, but whether they will retain it long term and I am not convinced that someone will retain something they learned over a short period of time UNLESS they are actively putting those concepts to use immediately and consistently.  The kind of grammar I was teaching him (parts of speech and diagramming) were not being used right away because he was not at the point in his Greek and Latin lessons where complex grammar concepts were being put to use.  He did develop a love for grammar and in that environment he was motivated to learn it, but I gave him Hake Grammar because I want him to continue working on it for as long as it takes to retain it long term.  He is also learning mechanics and spelling and vocabulary in that program so it is hitting language arts from a variety of angles and I believe it is worth his time to keep working on the mastery of the English language in a systematic way.

 

My oldest daughter has always struggled with math and language arts.  She did not become a fluent reader until she was 8.  Imagine 4 1/2 years of sounding out words (for both of us).  At 13, she is just now becoming a voracious reader and because of that I have seen her spelling improve naturally.  My second child was a voracious reader at 8 and so he has been a natural speller.  That makes me wonder if all the toiling over spelling I have done has been unnecessary and that once they can read well and choose to do it A LOT they will naturally begin to spell.  Hake addresses some spelling concepts and they work daily on either copywork or dictation plus a journal entry (which I check daily for errors in spelling and grammar) and so part of me thinks that just focusing on getting them reading a whole lot and the spelling practice that they will get in 4th grade and up is enough without the burden of lots of spelling practice in younger years.  I DO prefer using spelling to TEACH blending because it just makes more sense to me.  But I also know that knowing the spelling rules and phonograms has made me a MUCH better teacher of reading.  I was always a natural speller but knowing the WHYs of spelling have been valuable to me.  So for that reason I still think spelling should be taught explicitly and I think it is easier to find time for that when a child is young vs. when they are already studying several subjects.  In fact, I think after a child can write in cursive it is the best use of their time to study phonics and spelling until they are well on their way with reading and then they can focus on basic math concepts (much of which they will have already figured out by that time) and move into studying a math text on their own with daily corrections done alongside Mom (and reteaching concepts as necessary.)  But for me this is also a matter of practicality.  If I have two older students I must meet with daily to look over their work and have my finger on the pulse of their learning (as well as gaining a second education through the review of math and grammar material and the new learning of Greek and Latin) I need to streamline what I do with my younger ones.  So right now I know that it is best to focus on phonics with my 6 year old, spelling with my 8 year old, and cursive and blending with my 5 year old.  That doesn't mean that I don't do any other subjects with them, but that is my FOCUS.  

 

Ok, I know this has been about a lot more than just math but I am thinking a lot again about the role motivation and maturity plays in learning in all subjects and how my time is best spent with my students.  I am considering the role dictation could play and learning without textbooks, but I keep coming back to the belief that retention is extremely important to me and that can often only be achieved with study over a long period of time and then application immediately following.  I also have to consider that I studied ballet for 7 years, piano for 10 years, and cello for 6 years and I remember very little of any of it because I wasn't motivated to practice and persevere enough and when I stopped lessons my knowledge of those dropped completely.  I did write several songs on the piano but did not have the ability to write them down because I didn't know enough theory and so now they are lost forever.  I only remember how to read basic rhythm and the notes on the treble clef even though cello uses base clef.  So admittedly it was more my lack of motivation to keep and continually use that information that allowed me to lose all of that study and it didn't matter how long I had been working on it.  Hmmmmm.....

 

One last comment about that article.  I noticed that he was estimating that one could learn all of K-12 math in 8 weeks (30 hours per week).  But that would require (most likely) that someone was available for that many hours for 8 weeks and in a large family that would never happen.  So even though I suppose it could be done, it isn't LIKELY to be done.  It is comforting, nonetheless and I am glad you shared that......I am going to search for that blog post I talked about.....

[stm4him]

And again, I just want to say, Hunter, thank you SO much for posting that book.  I have finished it now and it is absolutely one of my favorite books EVER.  The methods were interesting but not the crux of the book for me.  The philosophies and convictions were extremely timely for me and just encouraging and soothing in so many ways.  I know I will read it and quote it many times in my life.  

[stm4him]

Ok, either there is another blog post where she goes into more depth than this or my memory was very fuzzy, but nonetheless it is kind of seeing the motivation thing in practice with older students and math.  Here is the one I can find.  If I find another later I will post it.

 

http://shop.freedomeducators.com/they-arent-doing-anything/

 

Also, my 5 year old begs me to learn to read sometimes.  Between last night and today we covered 5 lessons in HTT writing (which I am also using for blending) and she wants me to work with her first every day.  She may change her mind when it becomes harder, but for now it is neat to see the motivation thing in practice with a young child.  

[arliemaria]

One last comment about that article.  I noticed that he was estimating that one could learn all of K-12 math in 8 weeks (30 hours per week).  But that would require (most likely) that someone was available for that many hours for 8 weeks and in a large family that would never happen.  So even though I suppose it could be done, it isn't LIKELY to be done.  It is comforting, nonetheless and I am glad you shared that......I am going to search for that blog post I talked about.....

 

If it was a highly motivated older child/young adult learning this I am sure they could search out the resources to do this even on their own.  With the modern advantage of sites like Khan Academy and software like Teaching Textbooks this is not a difficult task.  Or if using vintage texts like the man in the article used with his mixed aged class the concepts build on one another so they don't need a lot of assistance. (My assumption.)  I believe the article's teacher taught a thorough K-6 math, but my grandfather and many other men and women before us had only an 8th grade or less education and were successful.  My mother's father who was a bright man had to quit school because his family could not afford paper and shoes.  I can't imagine that.  I have tried many times to fathom what poverty that must be, but I know I can always get paper or shoes.  I am sure some of it had to do with just availablity in deep Appalachia.  Sorry to ramble.

 

More food for thought: 

 

 

This is an excellent TED talk about why math instruction above middle school level is unnecessary.  Maybe we should be investing much of our time truly teaching the basics and then turning over their this part of their education to the student to own for themselves.  If they want to continue they are free to, but whether it is necessary the jury is still out.

[stm4him]

I think this video is really interesting and warrants its own separate thread (it's that good).  BUT I also think that the reverse could be said.  That if all the math you need is the material in K-6 (or maybe 8), then math could be be delayed until they were older and their brains were a little more developed so that the Mr. Johnson story never happened.  I also think that it would be wise to go from a solid understanding of arithmetic to a study of finances and accounting rather than Algebra since that is what many of us wish we had been taught (and still struggle with as adults unless we have studied it out ourselves.)  I admit to requiring the high school math I plan to require to make it possible for them to go to college should they decide to do so.  But is that legitimate?  I don't know.  Couldn't they decide as adults to go to college at any time and still get there one way or another?  I knew an elderly woman in college when I went.  And I have a grandmother who only went through 8th grade math and is probably better at math than I am and I went through Trig and Math Analysis (plus college math).  

 

I will say that in another thread I started about math people were saying that in many trades you need some Trig.....and I would never have guessed that....

 

And I will have to think through how this lines up with Art Robinson's ideas that science isn't really profitable until you have gone all the way through Calculus and can do real math.  So if you never get through higher math maybe you never get to science.  Does that matter?  I don't know since I don't enjoy science.  And there are those in classical ed. who talk about the beauty of math that can't fully be seen until one has gone all the way through Calculus.  Does that matter?  I am thinking about this today....

[Hunter]

 BUT I also think that the reverse could be said.  That if all the math you need is the material in K-6 (or maybe 8), then math could be be delayed until they were older and their brains were a little more developed so that the Mr. Johnson story never happened.  

 

I will say that in another thread I started about math people were saying that in many trades you need some Trig.....and I would never have guessed that....

 

And I will have to think through how this lines up with Art Robinson's ideas that science isn't really profitable until you have gone all the way through Calculus and can do real math.  So if you never get through higher math maybe you never get to science.  Does that matter? 

 

For GENERAL students, I think we need to delay math, then compact the higher math topics to the ones actually used like BASIC equations and BASIC trig, include more business math, and teach high school science as suggested in Science Matters.

http://www.amazon.com/Science-Matters-Achieving-Scientific-Literacy/dp/0307454584

[Hunter]

So last night as I wanted to find out more about early arithmetic instruction found this article on Ambleside Online:  http://www.amblesideonline.org/PR/PR07p008FirstStageArith.shtml This is an article not by Charlotte Mason, but by the late Rev. R. H. Quick.  I found it to be very compatible with EFL.  He talks about how we have to teach conceptions of numbers gradually.  That we must "settle firmly in the child's mind the facts about numbers up to ten; and make these facts thoroughly familiar."  He mentions Grube and the German thought of spending an entire year on numbers to 10 with a second year on numbers to 100.  They do not have the child write any notations at all.  He also advocates for the child to learn to recognize their numbers without counting.  He gives a short example of how to teach groups and units within a group.  

 

I was happy to see two alternatives to our current counting (eleven, twelve, thirteen, etc.).  He uses 10, 2 and 10, 3 and 10, &c., &c. His other way was onety-one, onety-two.  These might be helpful strategies to use with my son as he is having trouble saying thirteen and fourteen.

 

This guy is British, right? I think many of these vintage texts don't use coins more often as manipulatives, because the authors are not using base 10 money. Also coins were worth more back then and couldn't afford to be lost.

 

Pennies, nickels and dimes are awesome manipulatives. Fake dollar bills can be printed.

 

It's hard to spend too much time playing with coins and playing cards in the early years.

 

As for adding Waldorf art, mentioned yesterday, it depends on the family. If they were going to do art anyway that day, then 2 hours spent decorating the math paper is just as good as a different art project. But yes, too much art can get in the way of math teaching.

 

As for compacting increasing lack of retention, that can happen. But reducing a child's time to work and play and sleep and read and make art and observe can make a child less able to learn and retain than compacting. Running and knitting heals and develops brains. Work teaches character and problem solving, as well as providing body movements that heal and develop brains. Art and nature study increases mental health. Mammals NEED to play for so many reasons I cannot list them. Now they are saying lack of sunlight causes vision problems. Lack of retention is the least of our problems, especially when we are talking about topics that people don't use that much or at all.

[Hunter]

Back to trig. I like that Strayer-Upton includes a little trig after a little equations in the last book. Some older algebra 1 books used to include a chapter of trig at the end.

 

Delaying all trig to only after formal geometric proofs and algebra 2 makes no sense to me. 

[arliemaria]

For GENERAL students, I think we need to delay math, then compact the higher math topics to the ones actually used like BASIC equations and BASIC trig, include more business math, and teach high school science as suggested in Science Matters.

http://www.amazon.com/Science-Matters-Achieving-Scientific-Literacy/dp/0307454584

 

Could you elaborate on delayed math instruction?  I feel like spending months on the numbers to 10 is delayed compared to many who are doing addition/subtraction, etc.

[Hunter]

Could you elaborate on delayed math instruction?  I feel like spending months on the numbers to 10 is delayed compared to many who are doing addition/subtraction, etc.

 

Delayed differs for different children. But taking your time on the things we have been talking about. Not doing Saxon 54 for 3rd grade!!!!!!

[stm4him]

I wouldn't do Saxon 5/4 normally for a 3rd grader, but my particular 8 year old is quite capable and loves math and numbers.  If any of my children would want to go all the way through calculus it would be him.  He is close to mastering everything a child can learn in math in K-3 programs so I don't see the point of doing nothing new with him for a year.  But I think that I would not give him a full lesson.  I would give him half and see how long that took and if that took too long I would give him 1/3 of a lesson.  Thirty minutes is plenty.  I doubt I will do that with any of my other children unless they show the same aptitude and love of math....

[Hunter]

Gifted is different. But Saxon 54 is now being used as a 3rd grade classroom text by many schools, and i don't think that is developmentally appropriate for the masses.

[arliemaria]

Hunter, do you have any recommendations on how you would schedule the Prang Primary Course alongside my math instruction?  Should I wait until after I complete the number study to 10 or do this concurrently with the schedule provided in the text or another schedule altogether?  Any advice appreciated.  

[Hunter]

I would probably be doing it alongside, but that would depend on what else I was using for other subjects, and the child's reactions and readiness.

 

I don't mean that I would schedule both math and Prang every day! I just mean that I'd be playing with both these subjects at the same time, as it seemed right, and when reporting to an authority, I would list Prang form work as "geometry" or "math".

[arliemaria]

I am pretty certain that I am going to do the quality of numbers to 12.  Once we are finished with our numbers to 12 I want to start a bit of clock math and make this color wheel clock:  http://tinyrottenpeanuts.com/color-wheel-for-kids/

[Hunter]

Pretty clock idea. If someone is doing Spalding handwriting, notice that the primary colors are at 2:00 and 10:00.

[arliemaria]

I was wondering what you all thought of Harvey Bluedorn's article about delaying formal arithmetic until 10.

 

 http://www.triviumpursuit.com/articles/research_on_teaching_math.htm

[ElizaG]

I was just looking up a different math related topic, and found out about cyphering books.  These were sort of like copybooks, containing arithmetic rules (learned from someone else's handwritten book, not from a teacher's chalkboard lesson) and the "good copies" of sample problems worked out by the student.  The books were written in ink, with decorations and calligraphy used in the headers, and would be kept for reference.  They were common in the United States from the 1600s to the mid-1800s, but started to disappear when textbooks became more popular.  

 

Because of the need for good penmanship, students wouldn't be expected to do this type of work until age 10 or older.  Many of the examples found in archives are from 15 and 16 year olds.   It seems as if they often made the whole book in a year or so.

 

There are a couple of recent scholarly books on this subject by Nerida F. Ellerton and Ken Clements.  They're very expensive, but you can read the samples, and maybe some people will have access to library copies.  (I'll have a chance to read them myself, but will have to wait, which is okay since I have no free time right now anyway!)

 

Rewriting the History of School Mathematics in North America 1607-1861

Abraham Lincoln's Cyphering Book and Ten Other Extraordinary Cyphering Books

 

Searching for "cyphering books" also turns up many other interesting articles and photographs.

 

So both Hunter and EFL are on very solid historical ground, when they emphasize the importance of writing in math pedagogy. 

[ElizaG]

Just adding this link to an article about the Australian husband and wife who wrote the two books about "cyphering books."

 

-----

“Unless you are aware of your past, you’re going to repeat the failures of your past,†Clements told STATEside. “Unfortunately, in mathematics education, that’s happened far too often. You’re just seeing the same things being recycled. So what we’re trying to do is make people aware of patterns which have emerged—patterns which suggest strongly, ‘This is where you should be going.’â€

-----

 

If even 1% of the effort put into developing new teaching methods were diverted to this sort of basic historical research and pattern-finding, I think we'd be immeasurably better off.

[arliemaria]

I am thinking a lot more about ELF Arithmetic.  We have used a plethora of resources and I think our next math session I might try this:

 

http://barefootvoyage.blogspot.com/2013/06/math-and-write-stuff-charlotte-mason.html

[Hunter]

I was just looking up a different math related topic, and found out about cyphering books. These were sort of like copybooks, containing arithmetic rules (learned from someone else's handwritten book, not from a teacher's chalkboard lesson) and the "good copies" of sample problems worked out by the student. The books were written in ink, with decorations and calligraphy used in the headers, and would be kept for reference. They were common in the United States from the 1600s to the mid-1800s, but started to disappear when textbooks became more popular.

 

Because of the need for good penmanship, students wouldn't be expected to do this type of work until age 10 or older. Many of the examples found in archives are from 15 and 16 year olds. It seems as if they often made the whole book in a year or so.

 

There are a couple of recent scholarly books on this subject by Nerida F. Ellerton and Ken Clements. They're very expensive, but you can read the samples, and maybe some people will have access to library copies. (I'll have a chance to read them myself, but will have to wait, which is okay since I have no free time right now anyway!)

 

Rewriting the History of School Mathematics in North America 1607-1861

Abraham Lincoln's Cyphering Book and Ten Other Extraordinary Cyphering Books

 

Searching for "cyphering books" also turns up many other interesting articles and photographs.

 

So both Hunter and EFL are on very solid historical ground, when they emphasize the importance of writing in math pedagogy.

I don't think I saw this when it was first posted. The books look interesting, but the prices are inexcusable.

[arliemaria]

Wanted to update now that the "official" school year is nearing the end.  EFL math is now what I recommend to folks IRL when they ask me what I think about X math program.  Ladybug's confidence has grown so much and the work EFL presents is so effective that's its rather mind boggling to me that it has not been "discovered" till now.  This settles all the debates about old vs. new and is perfect for the mom who wants her kids to have "old fashioned arithmetic" but understand math from a conceptual basis like all the highly rated modern programs out there.  And best of all, its cheap!

 

We did end up using a set of base ten blocks, easier to keep organized than pebbles :lol:  and I deviated from EFL's plan and followed a suggestion in Ushinskiy of covering counting by 10s before starting written work per EFL.  She's been keeping a notebook for the past month, the work really is done independently and she really does "make up" her own lessons :svengo: .  I honestly didn't believe that part about it when we started.  When she's done with this notebook (it's very thin), I'm going to have her go back and rework everything both for neatness and mastery.

 

Stuff EFL doesn't cover, but easy to cover via real life: measurements, clock, money.  EFL says to play store every once in a while, haven't done that, I just take her with me when I go grocery shopping, we cook and have a garden for the measurements.  Clock got learned very naturally by following a schedule.

 

Hope this helps someone!

 

I am glad to see your follow-up.  I have been thinking about doing these lessons for so long.  We have been working through many different maths and it seems to be working really well.  I do think these would be great simple lessons to do.  Currently we've been doing a mini-curriculum (Professor Pig's Magic Math), but I think I might go re-read my notes on EFL arithmetic and see if I can't commit to doing it for our summer math.  Did you buy or make a DIY notebook for this work?  We are working on memorizing Longfellow's The Castle-Builder, currently.  This is, of course, EFL inspired via Hunter. 

Edited April 29, 2016 by arliemaria

[TX Pilgrim]

I am reading this thread with much interest.  I just found it and look forward to reading the full text recommended in the begining.  Someone asked at one point about a book that would help the parent think about how to teach the numbers through 20.  There is a vintage math program that does just that.  It is oral and uses pictures that look like dominoes to help explain concepts.  Just an interesting addition.  It also teaches ALL operations as you learn the number.  There is some slate work at the bottom but that could easily be adjusted to meet the needs of your child. 

 

Again, I know that her whole point is to not use a text book but if as the parent you are interested in examples of how to teach the concepts around each number this might be helpful. 

 

Thanks for finding this great older book. I can't wait to read more about poetry memorization too! 

 

 

[Soror]

Wanted to pop in and say that we've been using EFL's lessons almost exclusively for 3 months now with my 7 year old and I'm loving it.  The only extras we do are learning to write the numbers (in a grid notebook - once a week), the clock and calendar (daily life) and some occasional activities (finish the pattern type stuff) from Russian math.  I've completely dropped the C-Rods (though I'm saving them for the other kids just in case).  Ladybug's strength is not math so she's going much slower than EFL suggests it should take (doing it in two languages also slows her down), but what she's mastered is really learned and this is all in about 10 minutes a day.  For motivation, I told her that we're doing this so that at the end of the year I would drop her off at the store and let her pick up some groceries all on her own while I wait in the car outside.  She's super excited about that and does her work diligently even though it's not as fun as CRods and Miquon.

I appreciated your update. I read the chapter today on arithmetic and quite enjoyed it. Honestly I found it more clear and easy to understand than the Kitchen Table Math books I had bought for the same purpose. I believe I will start my 6yo with these lessons. I like that there is a clear progression and she can go at her own pace, I like that it cuts out a bunch of the extra stuff. We've started skip counting in Horizons so I foresee that going fairly well. Anyway, I'm excited to try it out :)

[ElizaG]

ltlmrs, thanks for the updates.  I had to laugh -- we once went to an open house at a local private school, where the principal was bragging about how hard the teachers worked to teach the calendar to the pre-K class.   They just kept hammering it in each day during circle time.   He was really proud of how it gave his school an edge over the others.   

 

There's an article on the folly of that approach here:  "Calendar Time for Young Children:  Good Intentions Gone Awry" (PDF) 

 

Their suggestions are probably unnecessary for a homeschooling family who often have conversations about time, and have a calendar on the wall, but I did like the idea of the guessing games.  :001_smile:

[arliemaria]

I am reading this thread with much interest.  I just found it and look forward to reading the full text recommended in the begining.  Someone asked at one point about a book that would help the parent think about how to teach the numbers through 20.  There is a vintage math program that does just that.  It is oral and uses pictures that look like dominoes to help explain concepts.  Just an interesting addition.  It also teaches ALL operations as you learn the number.  There is some slate work at the bottom but that could easily be adjusted to meet the needs of your child. 

 

Again, I know that her whole point is to not use a text book but if as the parent you are interested in examples of how to teach the concepts around each number this might be helpful. 

 

Thanks for finding this great older book. I can't wait to read more about poetry memorization too! 

 

I am looking at this book along with some of the other vintage math texts I peruse often.  I am planning on starting a math notebook soon.  I might have my son add the slate work to his notebook after he has solved it with manipulatives, etc.  I have debated teaching all operations for a while, but even my singapore math 1B we are in has multiplication.  So I should bite the bullet and teach it.

 

What else would you recommend to include in a primary math notebook?  I know in EFL she recommends starting the notebook when they can count by 2s, 3s, 4s, and perhaps 5s.  My son can count by 2s and 5s.  Would it hurt to go ahead and write those out in his notebook?

[arliemaria]

Have any of you discussed other topics of EFL instruction?  I just read her spelling chapter.  I would love to discuss this.  Perhaps a new thread?

Edited May 7, 2016 by arliemaria

[beka87]

I'm enjoying learning about EFL and her methods.  I've read a good bit of both BL and ECatH.  I also read the three linked articles in the very first thread.  I'm still having trouble picturing a day in life, so to speak, especially in Arithmetic.  Any chance one of you ladies using her methods could walk me through a lesson (or a whole day, over on thread number 2)?  Thank you!

[Jenn in CA]

I haven't read the whole thread, but does anyone else think EFL reminds you a LOT of Charlotte Mason? I'd be interested if anyone's compared the two.