Thursday, February 5, 2015

Following the Child...But What Am I Observing Exactly?

Maria Montessori said, "following the child." So I am trying to follow my children. Sometimes it feels like I am following along, sprinting at top speed, trying to keep a glimpse of the back of my son's jersey in my sights, all the while trying not to fall flat on my face over some other lesson I forgot to present first. Other times it feels like I am stuck in traffic at a stand-still staring at my child's back bumper on which is a sticker that reads, "WHAT? I'll move when I am good and ready." And still other times I feel like I am following my child down a crowded city street, with a thousand other attention-getters trying to get my attention, and then when I face forward to find this short little person again, I walk straight into a lamp post and think, "WOW, that didn't work."

Yeah, that third picture is where I am now. I saw an interest, presented what I thought was my best response to that interest, and now I'm thinking, maybe that wasn't the best response to that interest. I am wondering, "what AM I observing exactly, and how should I respond?"

In the last couple of weeks D has repeatedly expressed a lot of interest in number symbols and counting quantities. At first I wondered where in the world did he get this information. I had certainly not introduced this to him. TV? Books? T and S? Other family members? He started pointing out number symbols in books, on signs, in magazines, in stores, and in T and S's work. (At this very moment as I am writing this, he is looking at a book. He is ignoring all of the pictures and naming the page numbers. For numbers like 15, he says, "one-five.") He started counting trucks. He started counting fingers, pretzels, decimal fraction cubes, pieces of string cheese, rings, you name it. He saw the number rods WAY up high in a closet and told me, "Mama, I really, really, really want to do THAT work." We hadn't fully finished the red-rods (the prerequisite to the number rods and the entire math sequence) but I figured, well he's interested, let's try. This is about when I faced forward and got a forehead full of lamp post.

The number rods are identical in dimension to the red rods that we didn't finish. The number rods have 10cm bands of alternating red and blue color along their length. The red rods are, well, all red. The 10 cm number rod is all red. The 20 cm rod is 10 cm red and 10 cm blue. The 30 cm rod is 10 cm red then 10 cm blue, and then 10 cm red and so on...until we get to the 1 m rod which has ten bands of alternating color. 

The first number rods lesson is a naming lesson. We set up the rods on the rug, with the red left ends justified. The longest rod is at the top of the rug and the shortest rod is at the bottom of the progression. We count the rods using our hand to touch each alternating color. I'll say, "this is the rod of three" and point to the rod with three bands of color. Then I will touch my hand to each colored portion from left to right, and say, "one, two, three." Then I would ask D to do the same.

The aim of this material is to demonstrate quantity and to link this quantity with language. Ultimately the child will be able to select the rod of say, seven, without counting the sections first, but just by sight, then verify that it is the rod of seven by counting each color section, and then replace this rod in graded order. D is no where near this. 

He can figure out the rod of 1, 2, and 3, and sometimes 4. After this things get a little hazy. We count too fast and the rod of 6 becomes the rod of 9. Or we forget that 8 even exists. He always needs to count and cannot recognize any rod larger than three by sight. So, maybe his counting is rote counting and not real quantity counting? I don't know. I do know that we are missing the thrust of this lesson. 

BUT, he still loves number symbols. So after asking on the message boards, I introduced to the sandpaper numerals. He saw the sandpaper and we went right to our finger sensitizing station. Then we came back and we felt each number and named it. Usually you would add language using the three period lesson. (The first period is, "this is six." The second period is "please find six." The third period is "which is this?") D didn't need any period lesson. He already knew the names of the numbers. He did need to see me trace each number correctly. We called the lines and curves, "roads." D sat and did this work 4 times. He was amazed that THIS material was all for him. I think he also thought that the math shelves were for T and S only.

As you can see in the photos, he used both hands to trace the sandpaper numerals. Honestly, I couldn't tell which side was easier. We did sensitize the left hand first to trace with his left and then we sensitized his right hand and then felt the numerals using this hand next.
Here is D "cementing" the rods together. He likes all things heavy-construction-equipment.
So, I was advised, and I agree with this advice, that we hold off on the number rods for a bit. We'll revisit these again in a few months and at this later time progress into the math sequence. He loves the number symbols, so we'll continue tracing the sandpaper numbers. We will wait to actually DO something with the numbers until we revisit the number rods and start adding symbols to physical quantities.

This is one of the reasons I love Montessori theory so much. It is a living puzzle, literally. What am I seeing? Why am I seeing this? What biases do I have that affect what I am seeing? How can I look through my Montessori lenses and analyze what is going on? How should I respond to what is going on? All this pondering, puzzling and implementation is so interesting to me and these are some of the things that are enjoyable to me about this whole homeschooling experience.
D is doing his binomial cube again. (Another post about this is here.)
S got to do some more bells, and this time she actually graded the bells, three times. (Unlike last time. How did I get her to grade the bells correctly? I represented the lesson. I probably used more language than Maria Montessori would have, but in this case, I re-presented how to grade the bells and pointed out that I never touch the white bells unless I am playing up and then down the bells to check that ALL of them are in order. In this case re-presenting worked. Somehow I am not a firm believer that re-presenting a lesson to the child who is making errors really works to right that child's incorrect performance. Anyhow, believer or not, in this case, S was able to grade the bells very well after a second presentation.) 

You can see here our bells cabinet is a tad low for S. D is still kind of short, and this height was meant to accommodate his vertical challenges. I think I made this cabinet 19" high. All of the shelving (except our map cabinet) was made by moi. I used 1x12 pine (select pine without knots) for the shelves. They stand about 1" away from the wall because of our quarter-round. On top of this shelving unit only, I put two pieces of 5' length laminate flooring that click together. (I think the shelving unit is not as long. And with the middle support, I didn't install any stringers because this shelf wasn't going to be supporting much weight. The middle support doesn't extend to the floor.) This gave me just enough room for all the bells. I screwed the laminate down onto the shelving unit to make sure it wouldn't bump around. It is a little squishy but it works. I made the felt top to fit the bases of the bells and I think I "taped" it to the laminate flooring so it wouldn't slip around either. It looks a little wonky, but it works. Now, where am I going to put the tone bars?
A package arrived from Thailand!! It was filled with these cute mini vintage padlocks from this vendor on Etsy. I'd been wanting to get a small manipulative activity like this for D for a while now. All of these padlocks have keys not number combinations. He really, really loved this set.
Originally I had purchased these when D was doing all of his opening and closing work and I had thought that I'd hide some of the locks in some containers and the keys in other containers so he'd have to figure out which key went to what lock. Well he is done, or rather I am done, with the open/closed work, and the keys got mixed up anyway, so he still had to figure out which matched up in the end.
The Etsy vendor was super sweet, and very, very, prompt. I couldn't have asked for better customer service. She was even able to give me a deal on the lot. We were convo-ing back and forth and she seemed concerned that there were small pieces in this set and so this material might not be appropriate for small children. I assured her that the children would be under the constant supervision of an adult while working with these locks. And I know for a fact that D doesn't put stuff in his mouth other than food.
You can see how bitty this one is. T is holding it, but his hands are actually kind of big in real life.

This vendor has all sorts of vintage locks and the different shapes and sizes make this activity more interesting.
T is still practicing naming his cubes. (Repeat work, wonderful!) We will move on to calculating values next.
A little microscope and creative writing work...and interesting outfits that day.
This is what S saw through the microscope.
I've been working on several primary language materials lately, one of which is the 4 sets of cultural folders. This sets seems particularly daunting to me. I usually need whatever material to match the albums exactly and usually these materials aren't available for sale anywhere. The same goes for this material. So, that means I feel compelled to create this set and like I mentioned in the last post, I don't feel much like "creating" anything nowadays. So I am trying to break out of my mold a little and adapt a material that isn't what is in the album to be used with the lessons that are in the album. Trying is the vital word here. 

This collection of folders contains four sets. The first set should include general pictures that illustrate each continent like landscapes, animals, people, plants, etc. The second set should include pictures from each continent more related to people, cultures and fundamental human needs, like clothing, food, shelter, music, art, religion, etc. The third set should be more country specific and each folder should contain pictures about human life, particularly, the life of a typical child in that country. (This set should contain a variety of countries, but need not include every country. And the fourth set should be even more specific and each folder should contain images of a certain topic within a particular country, like architecture in Spain, or rugs in India, or traditional music in Thailand. All folders should contain cards with images on the front and short descriptions on the back side. The cards need to be coded so the guide can figure out which card goes where if any get rearranged. And each set should be stored in a folder, that has some kind of image, or marking, on the outside so the child knows in which set it belongs. WHEW. Just writing that makes me feel a bit dizzy.

So, the picture above, no they aren't cards. They are books. I looked at this project and I looked at my little D. I know that T and S would be interested in this work, and could work WITH D on this work, but really this work is for D. And only for D. So, what was I going to prepare for only one student? Goodness, this could get to be a slippery slope of laminate pretty fast. So I decided some books could sub in for a few of the card sets.

These books are about clothing, music, homes, and farming. (I am waiting on other books from Amazon about food, celebrations, and the life of children in other countries.) You never really know what you are ordering when you order anything on-line and haven't seen it in person first, but these books turned out to be PERFECT!! Perfect for primary. They have large color photos, simple, simple text, and depict a HUGE variety of cultures and there are plenty of shots of children. The ONLY issue I have with these books is that they are super skinny and they are paperback. They will get lost in our shelves that is for sure. I am trying to figure out some kind of front-facing shelves like MBT has in her classroom which I think will make texts like these more accessible.
One of the food books we already received is this one! I am not sure about the romanized spelling on the front cover, (although literally phonetic in English, this isn't the Korean phonetic way it is typically spelled, it would be bibimbap) but the story is really cute. There is a nice rhythm to it too and a bit of rhyming for young listeners. The book is entirely in English, but when we read it we substitute the Koren words we know into the story. S, who can now read, said to me the other day, "mama, it doesn't say that. It doesn't say, dangun." (Dangun, or 당근, is the word in Korean for carrot.) Oh, and the recipe in the back of the book isn't really all that authentic, but it does take a unique angle and divvies up the steps into adult and child roles. Message me if you want a more authentic recipe.
More compound words for S. You can see that we started doing our inventive spelling again and didn't really pay attention to the chart spelling.
This is for your reference if you'd like to decipher what S "invented" above.
T plowed through decimal fraction multiplication with a unit multiplier and simple division. He thought both presentations were very fun and asked what came next, with a smile. I told him that I needed to study up and that we could do the next lesson the following day. 
One of the reasons I sometimes feel T doesn't need much follow-up work in these areas, or any follow-up work at all, is that he figures out how to do these lessons without a lesson. I introduced the symbols for 0.63 * 3 and turned to him to ask him a question but he had already decomposed the multiplicand and was telling me the numerical answer. I told him, that was great that he knew the answer and asked him to set up the problem on the board. He set up three "sets" of 0.63 with the cubes, (6 in the tenths column, and 3 in the hundredths column for each set) combined them, exchanged 10 tenths for 1 unit and called out the answer, 1.89. I didn't show him a thing.

You can probably see skittles up in the photo above. Those are for division. I think I didn't get a shot of the multiplication before we started the division.
Here we are dividing 4 by 3, so 4/3=. I set up 4 skittles, and T corrected me saying that the divisor was 3, so we needed 3 skittles. Oh, right. Then we took out 4 unit cubes to divide up among our 3 skittle foot soldiers. T distributed one unit to each skittle and came up with one extra which he exchanged for 10 tenths. He continued to distribute tenths to each soldier until he had one tenth left which he went to exchange for ten hundredths. At this point, T said to me, "Mama, this could take FOREVER!" I laughed because yes, this problem does go on forever. I asked him "why he thought the problem would go on forever, and he said because he always had one left over after distributing his 10 to the three skittles. I showed him how to write this problem on paper and that in our decimal the 3 has a line over the top to indicate it is a repeating decimal fraction. T did do more division follow-up work later on and now it is on to the next lesson!
We haven't done dictation in a while, but we did it the second half of the week. I am taking our early lists from the All About Spelling curriculum and going over new spelling rules in this way. (I got this idea from MBT, who incidentally uses AAS differently than I do. I was going to link to one of her blog posts about AAS, but she has too many, so just go over to her blog and search for "all about spelling" if you want to know more about how she does it.) I only purchased the teacher manuals because I wasn't going to use the manipulatives that come with the curriculum. I just wanted to know which spelling rules I never learned. This curriculum also includes short dictation phrases as well.

Anyway, we were doing dictation phrases and the kids thought that "quit it" was particularly hilarious as you can see here.
Hilarious. Sometimes school is hilarious.

So, I am posting again on a Thursday for some reason. I don't think I'll get to post tomorrow since I am baking two cakes and am putting together a Korean BBQ Taco Food Truck inspired birthday party. No butane torches or isomalt are involved with this cake, but I am aiming to make it a replica of our wedding cake which was 5 separated tiers of chocolate cake filled with espresso buttercream and frosted in vanilla buttercream. Yum. I'll eat a piece for you. :) Have a great weekend!


  1. Those books look great!!! Share the name of the series!

    And you don't have to eat a piece for me. You can just mail it to me - I'll take care of the eating portion ;)
    (as I finish up a second slice of Dairy Queen ice cream cake --- I usually make birthday cakes but this week was far too busy and their peanut butter cake at half-off and a $3-off coupon just had my name ALL over it)

    1. Yum. PB ice cream cake sounds awesome! I got the books from here:

      They are the Our Global Community series published by Heinemann. I have a new post planned that shows a tiny bit of the inside of the books. I really felt like I was shooting in the dark with these and I also felt like I came up with a bullseye.

      Could totally mail you a piece of cake esp. this time of year! My college roommate used to get her mom in Hawaii to over-night her Chinese fried rice and other stir-fry dishes to her in Maine! I am pretty sure at this time of year, the buttercream would be pretty frozen when it got to you! :)

  2. I can SO relate to your confusion over indication of readiness for math! My 3yr3mo son is counting *everything*, talks about numbers all the time, is beginning to recognize number symbols and chooses counting books over anything else. But, he hasn't done all the a Red Rod work and can only do 1-3 on the Number Rods. If I give him the 4 rod, he says "one, two, three, six, this is 6!"

    And thank you for the links to the culture books on amazon!! I'm with you, creating culture folders from scratch for a single child is way too daunting of an undertaking. I will be copying you and buying these books this week. And reading here for anymore ideas I can steal!

    1. :) I find it fascinating to "follow-the-child." Everyone manifests readiness in different ways and at different times.

      I am with you on the preparing for a single child. When I have my elementary hat on, I am thinking "for-three-children." Everything is for three. Even with the later primary materials, I am still preparing for two. It feels so weird to dwell in the early primary realm and realize that I will only have one going through this sequence. :) I am constantly going between not wanting to short-change the little guy to weighing my time and the cost of laminate to turn out the perfect product. Do let me know if YOU have any short-cuts or work-arounds.

      As for the books, I wasn't sure these would work, and am still not completely positive I've made the right decision here. My aim is to yes read the books, but to also discuss the photos we see, and use these as a launching pad for other exploration. I'll be sure to post "how" we are continuing to use these in the future.

      And for those who haven't read this post about continent folders, it is perhaps be best description of this material out there... you Jessica.

  3. I have some wise experienced things to say.

    1. I don't remember what it was like to have a child at this stage. I did it twice and have already blotted it out. You guys who are still in the trenches or have done this a hundred times instead of twice know more than I do about it. I've forgotten.

    But, I'll tell you what I do remember...

    2. Just because someone wants to stick their feet in the water it doesn't mean they want to go swimming.

    3. Just because someone doesn't want to go swimming, doesn't mean you shouldn't let them stick their feet in the water.

    4. Don't throw someone who only knows how to dip their feet in the water into the deep end of the pool and expect them to swim. They might, but they probably won't like swimming much afterward.

    5. Me Too happened to be ready for the number rods shortly before his third birthday:

    6. Kal-El had just turned four or was about to turn four when he started number rods. I probably waited too long with him because it was my first time.

    7. Me Too had trouble "not being sloppy" (like you describe D) when he started number rods so we used a frog. In fact, one of the pictures in the header on my blog shows the frog hopping from one segment to the next on the number rods. Here is a post about it: He was three in June and that post is from September.

    8. There are a bunch of math materials that are considered "group one" : number rods, sandpaper numbers, spindle boxes, cards/counters, and memory games. I wouldn't touch group two (namely collective exercises) with a ten foot pole until all of group one is super solid. That can take some time. They need to be able to recognize a collection of objects as a number, recognize a single item like a number rod as a number, recognize the symbol for the number, and be able to sequence the numbers confidently before moving on. I feel like the first three of those goals can be worked on concurrently. It won't hurt to hold off. Then, if you still have the sloppy counting problem try the frog. If you don't want to introduce a frog make sure you insist on "touch before talk." He must touch the next segment before he can say the next number.

    And that's all I remember.

    1. Anyway, my point with all the swimming is that you observed something real but he may only be wanting to get his feet wet. The wetter his feet get, the more comfortable he'll be when he swims.

    2. Thanks for the wise words about swimming. As someone who swims only when necessary, Jessica talking about swimming, and you talking about swimming is making me feel like I am swimming, when it isn't necessary for me to be swimming, and that it should be D who is getting ready to swim. Jeepers.

      Ahh, I need to start reading your blog archives again. You keep mentioning stuff that I haven't read yet! I am reading from the beginning.

  4. Ok so I was totally thinking that you should just cut the cultural books up. Use the pictures for your folders that way you could divide them up by continent. :) Then the paperback thing wouldn't even matter :). Ok, I gotta go to bed now after catching up on reading all these new posts and not posting anything of my

    1. Ahh, cut up books!! I don't know if I could. It is like making a mess with goldfish. I'd have to color copy or scan the other side of each page so I don't miss out on the image on the reverse side....