Thursday, February 12, 2015

Why, Why, Why, Why?

Week 7, Part 1 February 9, 2015

Lately, D has been annoying S with the "why" question. He follows her around and says, "why, why, why....?" She hates it, and pretty much ignores him after answering the first three why questions. Interestingly, he doesn't do this to T.

This week we started out a little slow, but somehow I still have a ton of pictures to share. Monday, we didn't do school because I had to do weekend stuff I hadn't done on the weekend. Tuesday, we had an afternoon appointment and needed to eat lunch early before going, so we only spent a few hours in the classroom that day. But Wednesday, we got in a solid run. Surprisingly, we ended up doing a lot of practical life works. None of these works were planned, but some of them came about after re-discovering some old works that had been packed away since last year before the move.
This first practical life activity wasn't one that was packed away. That silly cat got in again and made another mess in the garden. (I haven't planted anything yet, but I had just dug out the soil the cat pooped in last fall and replaced that.) I really felt like giving up this time. Each time I need to dig out and replace 9 cubic feet of soil it costs me near $50. This time we tried to make some of the deer netting sides permanent and make the other sides less permeable. Here the kids are hammering in staples.
D got his own D-sized hammer for his birthday?? last year (I can't remember when we got this) so this is what he uses to help Daddy around the house. (Usually he is helping mommy because it is mommy who does the fix-it projects around the house.)
Opening our mouth helps with hammering.

UPDATE: The new tighter netting system is holding so-far. There was recent evidence that the cat tried to get in, but wasn't able to get through the much smaller space. I fixed that "small" space problem. But this fight isn't over yet. I am adding some sound and water sensors, and perhaps a 24 hour shot-gun armed security service. Okay, kidding about the last part. But I'll be, I'd really, really like to be able to grow some Korean peppers in MY backyard.
In other practical life news, we were back at the padlocks with the keys again, and with cute toes.
D put a stamp on his "thank-you" letter to a friend who sent us a package of goodies. He drew a pumpkin on a farm all by himself. I think it took him three minutes to color it in but he did this very nicely without going outside the lines.

Somehow D knew where to put the stamp even though he hasn't sent many letters. T also sent a thank-you letter and DIDN'T know where to put the stamp until his younger sister, who sends enough letters to keep the postal service in business, corrected him.
This was a advanced practical life activity we had packed away last year. I found it in some bin and brought it out again. S wanted to start knitting again and so we sat for about an hour today knitting together. 

This will be a scarf/shawl for her favorite stuffed animal, Baby. 

I used to knit A LOT when the kids were babies and before I started homeschooling. It was something I felt was a cozy and productive thing to do during the winter months. 

My mom taught me to knit holding the working yarn in my left hand, which continental style. I am righty, but I have a VERY hard time knitting holding the working yarn in my right hand, which English style. I am thinking that handed-ness doesn't really matter in this case and I am just teaching S the way I know how to knit. (Consequently, I'd be terrible at Fair Isle knitting where you need to use both hands.) 

You can see in the photo above, I chose to use circular needles for this project. (They are size 8s which is a common size for beginners.) You can use straight needles for a simple first project like a scarf. Circular needles are usually used for things like hats or sweaters that turn out tubular. Here, we just turn the work when we get to the end of a row. You can probably also tell that we are working the very, very simple, knit-every-row, garter stitch. This is so that S can feel the rhythm and get the hang of what goes where. There is plenty of time to learn other stitches later.

The yarn in the shot above is acrylic. I generally don't like acrylic yarn. It can feel clammy and tends to pill a lot. However, the acrylic yarns can feel softer to the touch than 100% wool, and cashmere is a bit pricey for a first time project. One of the things I like about knitting is the feel of the yarn. That softness slipping through my fingers is a wonderful soothing feeling. So be sure to pick the "feel" of your first project with care. (My personal favorite places to get yarn are Purl Soho and Quince and Co. Somehow I always felt intimidated walking into a yarn store with real staff who knew tons more than I did, or ever would know, about fiber. Purl and Quince are actually real stores in NYC and Portland, ME respectively. I just have never been inside them. The pink sweater S is wearing in the next shot is made of Quince and Co. rosa rugosa Lark worsted weight and the pattern is one of my favorites and it is Tiny Tea Leaves by Madelinetosh...wow, I remembered that!)

If you are just getting into knitting, check out Ravelry. It is a wonderful community of knitters and there are tons and tons and tons of very cool patterns for every level and every interest. 

S is a true beginner and finding the right hold is the biggest obstacle at this stage. When we knit, literally together, I hold the working yarn and control the gauge. She holds the needles and works the needles, under, through to the back, around, down and out, slip off. Once she gets the hand of how the needles "click" (I use bamboo needles, but if they were aluminum, they'd "click") then I'll introduce handling the working yarn tension. 

I think you may be seeing more of S's knitting on the blog in the future. Funny how she feels the urge to learn to knit once we relocate to one of the hottest states in the country.
Speaking of fiber...S also got it in her to do a little bit of embroidery. At fist it was going to be a bit of sewing practice, but very quickly, this project turned down the embroidery road. I also did a bit of embroidery when the kids were babies and there was nap time and before I ever had a thought about homeschooling. Mine ended up looking okay, but no where near professional. Good hand embroidery is just absolutely amazing. It is like art really. But you need to practice for years to come anywhere near this level of skill.

S is working with plastic canvas mesh. With her consultation I drew a pattern on the front with a black sharpie marker. Then she got to stitching using at tapestry needle and the same yarn she is wearing, coincidentally. (Sorry, I can't tell you what gauge the mesh is, or if it comes in different sizes, and I can't tell you the size of the tapestry needle. I just don't remember.)

She ended up naturally doing a running stitch: up through one side and down through the same side. Generally for outlining we'd use a back stitch or a stem stitch, but we are beginning so a running stitch is just fine. Then she began filling her cat outline with white yarn making this an official embroidery work. I think I was about S's age when I did my first embroidery work.

For all things awesome and fantastic about hand embroidery go to Mary Corbet's Needle and Thread blog. This is an AWESOME site. She was embroidering this for a church the last time I was doing a lot of embroidery.

Writing all this is reminding me that I should look up the historical origins of embroidery for S so that she can find out about the people who have been working this craft for centuries.

Okay, this looks a little like a pink dog.What would be the different between a dog and a cat outline? Do we need to add whiskers after we've filled our outline?
You can see a tiny bit of her fill here. 
D, got a new sound object box at the store. He thought this box looked like a treasure chest. Yes, there are way too many objects in his sound object box. We are working on transitioning our focus from beginning sounds to ending sounds. 

He knows virtually all his beginning sounds. (I say virtually because he gets these beginning sounds right about 99% of the time. On rare occasion he misses something, so we aren't perfect.) So, everything in this box, he automatically sorts into piles of beginning sounds. I didn't tell him to do this, he just decided to do this. For this work, D thinks the more objects the merrier. Then we explore A FEW of the ending sounds at a time. He is getting much better at segmenting those ending sounds. 
It will take us a while, but after we shuffle through all the ending sounds, we'll move on to middle sounds and then the sandpaper letters, finally introducing letter symbols. We are following the Dwyer approach to language and this primary work is preparation for writing and reading.
Sometimes we organize our sound objects by category and not by sound.
Other times we pretend we are a BMX race course.
S is really going with the compound words. Here she is making her own little booklet of compound words. 
This one was "custard donut." Don't know where she got this one. She doesn't like custard anything.
This was our super, super simple book binding method: a bunch of hole punches and a bit of yarn to sew it all together. We get our "b's" and "d's" mixed up a bit.
T pulled out the checkerboard Wednesday when I had thought we had packed this one in. As far as I can tell, there is no writing with this work. Maybe this is one of the reasons T likes doing this work. 

Here he set up the problem 9999*8496=. T is doing the second and final checkerboard exercise using his multiplication facts. He is also exchanging as he goes along. He multiplied 9 units by 8,000. He would have put a seven bar in the top row in the first blue box (from the right) and a two bar in the top row in the first green box (again from the right.) In this case, the two bar in the green box would signify 2,000 and the 7 in the blue box would signify 70,000, and together they illustrate that 9*8,000 is 72,000. Then he multiplied 90, or 9-tens, by 8,000. He would have put a seven bar in the top row red box (first from the right) and a two bar in the top row blue box (first from the right) to signify 720,000. In the shot above he already exchanged out the seven bead bar and the two bead bar from the blue box, and made this a nine bead bar in the blue box. 

Since he can do this math in his head, he ends up having fewer bead bars rolling around in the next step. (Typically a less experienced child would place 8 nine-bead bars in the top green box, blue box, red box, and so on. When you slide the bead bars down in the next step, it can turn out that there are a lot of bead bars to count from each partial product and this can get "messy" and complicated.)
Here T slid down all the bead bars, careful to keep each hierarchy and category separate and organized. That two bead bar from the top right-most green box represents thousands. You can see in the shot above, that two bead bar landed in the 1,000 box at the bottom of the board.
T added up the quantities in each category and made his exchanges to ensure that there is only one bead bar in each category box. For example, if there ends up being a 21,000 T would put a one bead bar in the thousands box and a two bead bar in the ten thousands box.
Here you can see Ts final answer was the same as his "checked" answer on the calculator.
D helped out a bit organizing the grey number cards.

I thought I had another multiplication checkerboard post on the blog that explains more, but it seems like I don't. We must have been doing this work before I started writing in my blog posts.  
Here is S's Baby face down on the first addition finger chart. I don't remember T doing these. If I remember correctly, when we started homeschooling in the fall of 2013, I thought that T had already done these in primary. I was also following a different set of manuals at the time which indicated he was already past this. Now that I know more about the gaps he has, I don't think he ever got to do these memorization charts. 

S is getting to these a bit later than I would have liked, but again, I only found my album "fit" about a year ago, so I wasn't prepared to prepare her for these. This is the beginning of the memorization of math facts sequence. (A bit of help here please? I am going ahead with this memorization of facts WHILE continuing other threads. I don't know if I should have finished all other primary math threads before embarking upon the memorization sequence. S is part way through the bead chains, part way through the stamp game, and we are "reviewing" naming large quantities. She is now 7, but should I still wait to start this thread? Incidentally, she found this work really fun.)
This finger chart has addends in both blue across the top and in red down the left side. S selects a problem from the box. She reads the problem and writes it down on her piece of squared paper. (I think this is 1/4" graph paper I downloaded for free from somewhere.) Then she uses her right index finger to find the first addend across the top and her left index finger to find the second addend down the left side. Then she traces down with her right hand and across with her left until her fingers meet at the correct sum. She writes this sum down and says the entire equation again. 

S really liked this work.

To keep track of which problems S has completed, she puts done ones in this small container labeled "done." This container lives in the addition problems box, though I am not sure that this box will actually hold all of the done equations.
Then D decided to annoy S again by playing a game of rough footsies under the table. She wasn't impressed.
D is working to finish up the knobbed cylinders sequence. Here he is taking the cylinders out of the block and replacing them blindfolded. You can read more about this work here. In the photo above he is blindfolded and removing the cylinders.
Here T is helping D with his owl blindfold.
Here S is helping D with his blindfold while laughing hysterically.

You can see that he holds the cylinders completely differently when he is blindfolded. He typically uses only one hand with a well positioned pincer grasp to place each knobbed cylinder. Here he is using his fingers on his placing hand to find the right hole.

D still really likes "feeling" things with his feet, still.

All of my kids love, the "I don't know if you can" ploy. They are all out to prove me wrong. This is D's "I CAN do it Mama!" face.

D also decided to do a little color tabs box 2, in his own way.
T used to sit this way when he was younger too.
D said he was sad that he "ran-out" of train tracks.
S started the next geometry lesson on congruency, similarity, and equivalence with the constructive triangles. We started with the triangle box. Next we will progress through the other constructive triangle boxes continuing to explore congruency, similarity and equivalence. (The other boxes are hexagonal and rectangular.)

You can read more about our prior lessons on equivalence and congruency and similarity here and here.

Using the triangles in the first box, S found congruent pairs, similar pairs, and lots of equivalent pairs. S chose to trace, cut out, and glue on her triangles to make a collage of her equivalent figures from the triangle box.
S looked up the mathematical symbol we use for equivalent in her working notebook...
...and added this to her collage poster.
T recently started, and now pretty much has finished, the geometric multiplication work. Here we are working a multiplication problem with a two digit multiplier. You can see our problem at the top left part of the paper. You can also see two lines T has drawn. The horizontal line will represent the multiplicand, or the 5,472 and the vertical line will represent the multiplier, or the 92.
For our first partial product, we multiply 2 units taking 2 times. We follow along the multiplicand horizontal 2 squares and then follow up the multiplier vertical 2 squares and to create a square. Then we multiply 70 taken 2 times. We follow the multiplicand horizontal 7 squares and then follow the multiplier vertical 2 squares and then create a rectangle. We follow only 7 squares along the horizontal because 70 is really 7 tens, and we will designate category quantity to each square later in our problem.
Then T multiplied everything in the multiplicand by 90 and followed each vertical up 9 squares.
Next we color each rectangle and square to designate their category. Units * units is units and this is green. Tens * units is tens and this is blue. Hundreds * units is hundreds and this is red. Ten * tens is hundreds and this is red, and so on.
Then T wrote in each square his actual multiplication equation and partial product. In that first green square, he wrote 2*2=4.
Here you can see his partial products a bit better. At this step we really focus on the zeros. For example, thousands contain three zeros and ten thousands contain 4 zeros.
This is why the presentation says to shade in your squares lightly because you can't see the equations otherwise.
Then we write down all of our partial products from each of the rectangles at the top of the page and sum up to find our final product. In the end, we read the entire equation, and T likes to check his work using the calculator.

T knows what he is doing here. He just looses the details at times, like which category gets how many zeros, or how to right justify his partial products to align all the categories.

There is one extension activity for this lesson and then we move on to category multiplication. This work comes after the checkerboard work and is preparation for later squaring and square roots and category multiplication.

And that is all for the first part of the week. We are in the classroom for another two full days, so I expect to be back with another update soon. (Every time I type that something happens and that next post gets delayed. So scratch that. I'll get to posting the next time whenever the next time is.) :)

12 comments:

  1. Just because you asked ;) The memorization sequence for a 7 year old, looks very different from a typical primary age child - so go with what works for YOUR children. And definitely at this age, other math needs to be happening too. At primary (in AMI), the memorization
    boards come after working with the golden beads a LOT, then the snake games and multiplication bead bars and multiplication/division bead boards. :)


    I also wanted to share a point re: Dwyer --- Dwyer's method is the AMI method. Maria Montessori started it; AMI promulgated it; Dwyer summarized and published it in a booklet that (apparently!) was never meant to be used by homeschoolers or teachers as an actual outline. But it was that good, that people DO use it ;) However, I just want to clarify that the "method" is Montessori/AMI ;)

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    1. Seriously,I should just consult you, first. :)

      S is 7, but just turned 7. Wait you know this. ;) Anyway, she has had a number of developmental delays over the years but it has been a long time since we needed any therapy. She is very, very resistant to trying new things, unless they are artsy. I have been having trouble discerning whether or not she has just tipped into the elementary second plane, or is still keeping a toe in the first plane of development. I would think by 7 that the child is squarely in the second plane, but the fact that she loves, the addition charts, and doesn't mind small repetitive manipulatives makes me think that many primary aimed lesson will still "work" for her.

      Is it more that we should treat this like a remedial math situation because of her current age and the fact that she has so much elementary math ahead of her to accomplish before age, 9, or 12 or whatever age? I don't have a real preference either way, I am just hoping to set us up for some smoother sailing in the future and not create gaps and road-pot holes that will make our future work super frustrating. You don't want to see S frustrated. It isn't pretty.

      Would a remedial math sequence just look a little more swift than the primary sequence, still introducing the same materials in the same order, but not lingering in any one area unless there is a need or want to expressed by the child? In addition, we would be continuing in other areas of the elementary curriculum such as geometry to keep the child progressing forward?

      S did the golden bead collective exercises last year. She recently finished subtraction stamp game, and is mostly through stamp game dynamic multiplication. She did the addition snake game last year, and has had an introduction to the dot game, but we didn't linger there and she hasn't picked it up since. She is on pause with the skip counting until we shore up naming numbers and reading quantities. Today we went over the difference between 4-tens, 40, and 40-tens with the golden beads. She thought this was pretty silly when she saw how different 40-tens was compared to 40. But, just before she had called 40, 40 tens.

      So, what I am saying, and of course I can't hold you to a diagnosis since you can't observe her personally (though I wish you could) is that we should continue pushing through the stamp game multiplication and division, quickly review naming and reading numbers to move ahead and continue with the memorization sequence as long as she is interested. (She is moving through addition pretty fast, though I know from MBT's blog that it is the other operations that take years.) After she finishes stamp game, we should move forward with the LBF and more elementary lessons? Would you agree with this plan, without seeing the student? or am I applying my Montessori theory about planes of development incorrectly? Oh, following the child makes me feel like I am feeling my way through a dark forest blindfolded. Thank goodness there is a guide like you out there like a lighted lamp post. (We are reading the Lion the Witch and the Wardrobe...for the weird lamp post reference.) Thank you!!

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    2. And yes, yes, yes, the Dwyer method is a summary of the AMI method!! Oh, assuming others know things certainly get us into trouble sometimes.

      I would ask though, in the albums, phonograms are introduced "separately" from the other single letter sounds. From what I recall, the Dwyer summary suggests all 40+ sounds to be learned at the same time and that the double sandpaper letters be introduced at the same time as the single sand paper letters. Is this a distinction that I am making up in my head?

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    3. The descriptions are separate album pages, but the phonograms one should say to start them when about half the individuals are known; then working back and forth between individuals and phonograms (so if looking at 3 new ones in a day, it would be 2 individuals and a phonogram; or 1 individual and 1 phonogram) - so that all of them end about the same time.

      So it is not a distinction you made up ;) They are indeed listed separately, so many people think they are given at two different times ;)

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    4. Thank you for this!! Makes sense!! I feel like I am finally understanding some key underpinnings here that are so often misunderstood.

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  2. Abbie - the full remedial section focuses on the keys needed from primary that work with an elementary mind. They tend to be in short blips throughout the day, while other work in math and other subjects continues forward.

    A lot of the primary work is built in to the elementary work; so some familiarity is great, but whatever she missed, she will pick up in a different way in elementary.

    If she is happy with what you all are doing, it's fine; but if at any point it becomes tedious or annoying, then going with shorter blips several times a day would be better. It might be worth just flipping through the remedial section to see - you might see that she needs some of the shorter blips; and you might be assured that you are on the right path already ;)


    We LOVE NARNIA ;)

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  3. I read through the remedial section in the elementary album. Thank you for this reminder, I had before, but re-read it again to be sure. So, what I am gathering is that I should be looking out for tedious, or manipulatives being annoying, and if this does happen to start presenting in a non-primary lesson way, and instead introduce the keys in short spurts. If she is fine with going as she is, then great. The only consideration about the latter is time, and we should be continuing to progress forward to get to the elementary math (following the child of course.)

    The kids seem to love Narnia, or this book at any rate, too. They never want me to stop reading. Even when I'm half asleep.

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  4. I thought that you want children to do manipulatives in the first 3 years of elementary anyway. Well, want is a strong word, more like they still need it deelopmentally. In our public charter school, first graders start with the stamp game. It doesn't sound remedial. Also, isn't it true that some schools don't accept kids into elementary till 7? I thought the first plane of development can go up to 7.

    Is there a different way to present between elementary and primary when it comes to math? I had thought that with elementary you're just not as concerned with movement and exactness because that is soemthing they develop in primary. Is there something else I missed?

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    1. guavarama -- from what I know, and this is only my personal experience and we didn't go to a public charter school for Montessori, is that children in the second plane of development will begin to move away from small manipulative materials and repetitive work; the type of work that draws the keen interest of children in the first development. While it is true that children in lower elementary do use many materials that include manipulatives, counting individual beads, or individual stamps, and handling blocks and cylinders are not interesting to the second plane child any more. Their minds are now geared toward the why, the how does this happen, and the abstract concepts beyond what is physically in front of them. Again, this is just my interpretation of what I have read, and it is not necessarilly pure Montessori theory.

      As for starting elementary, our private Montessori school offered classes from 2yo-toddler classes through upper elementary - ending at age 12. The matriculation age for the lower elementary first years was 6 years of age by Sept 30th. Our school followed public school convention as well as Montessori theory regarding the second plane of development. I don't know how other schools do it, this, again was just our experience in northern Virginia.

      As for the stamp game and elementary, my AMI albums include this lesson in the primary math sequence. My elementary albums begin with the wooden hierarchical materials and the large bead frame.

      I am unsure what you mean by your last comment. If you want to elaborate a bit I'd be glad to respond. What I think you are reaching to touch upon is the difference between primary presentations, elementary presentations, and the specific remedial math presentations I wrote about here in the comments section. At the primary level, we do present with the understanding that children are in the 1st plane of development and that receive information and respond to new experiences in the ways Maria Montessori describes in her books. At the elementary level, we present assuming that children are in the 2nd plane of development and our presentations are delivered differently, because these children receive information and respond to new experiences in ways different than children in the 1st plane. The remedial math lessons I was referring to, are a group of lessons a child may need if they are entering a Montessori classroom without a primary Montessori experience, or an experience that is incomplete. Since elementary children are in their 2nd plane of development, we present primary math skills to the children in a different manner than we would present the same skills to a primary aged child in their 1st plane of development. So, children who need primary presentations, but are of elementary age, get those presentations but they are presented differently to accommodate a different plane of development.

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    2. Abbie - you are spot-on! The only thing I would add is that the stamp game IS used in elementary, but for "group division" which is different from its use in primary.

      With that said, if the material is present, children coming into an elementary Montessori classroom with primary experience can certainly get it out and use it as they know from primary.

      Children can transition into the second plane anywhere from 5 3/4 until 6 1/2 (developmental delays can slow that down further, but generally a child who is typically developing in most ways will be moving into the second plane in portions ---- meaning they be ready for history presentations but still need some primary-style presentation in math - just one exampe).

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    3. Yes Abbie, that is what it is. But they still need manipulatives. It's just not used for repetition necessarily but as a tool as they gradually move towards abstraction. I would think the indirect goal of the manipulatives are now no longer to fulfill the child's need to develop their gross motor and fine motor skills.

      I always thought Montessori ELE was 6 years old too. But my friend goes to a school that Tim Sheldon is affiliated with and I was told they wouldn't accept kids till they are closer to 7. And then I read somewhere that Montessori's primary work is up to 7 somewhere.....

      Yes I was saying exactly what you're saying in regards to remedial work. I was pointing out my understanding is that the presentation itself is a bit more inexact in terms of movement and order. And maybe orally more "interesting" since that's what appeals to ele kids. But other than that, I didn't think there was much difference no?

      Maybe I was just responding to the word remedial (which is in my album as well). Given what I've been told as to what happens in public Montessori schools, I always though it's very age appropriate (rather than a child is behind) to use the stamp game for all the beginning math operations work, until the child decides they don't really need it. Also I'm reading in different books that more manipulatives as long as you can is really good for kids, because you see relations in numbers and in math in a much different way than manipulating numbers on paper....

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    4. My albums say that children who come into a Montessori elementary classroom should have completed all work with the stamp game, collective golden bead exercises, and the math facts memorization sequence (snake game, addition/subtraction boards, finger charts, and the like.) These lessons are not covered in the elementary math sequence, and these materials aren't in a traditional elementary classroom. These lessons and the materials used in these lessons were designed for the 1st plane child. This is why lessons in these areas for a 2nd plane child are considered remedial. And getting a 2nd plane child to work with these manipulative materials in the same manner as a 1st plane child isn't going to happen.

      For this reason, children who haven't gotten the full Primary sequence, and who need these remedial skills, receive these lessons in a way different than the 1st plane child would receive them. In a remedial situation, the guide would work with a 2nd plane child in short 1-5 minute blips to present, work with, and practice these lessons, several different times, through out the work cycle period. We follow the child, as always, and linger until the child has gained proficiency, but not necessarily mastery of said skill. The guide would also continue with other cosmic education lessons designed for the 2nd plane of development as well.

      At the 1st plane of development, the lesson would "look" very different.

      Additionally, at the second plane of development, manipulatives "look" different. There aren't lengths of beads to count out, or tens of stamps to gather up to exchange. No longer does the child count out 10 golden beads, a single red bead, in the blue tens square, represents one ten.The manipulatives at the elementary level are designed to represent abstract meaning and are used as a bridge to mathematical abstraction. Manipulatives at the primary level are designed to illustrate concrete physical quantity and thus their use is different.

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