Here is a bit of what we did the last two weeks in the classroom. For some reason our more recent lessons haven't been as photography friendly. Sometimes I need two hands and sometimes I just plain forget to snap one. So this is a sampling of what went on.
An introduction to the golden beads!! D is starting work with the golden beads. I kind of can't believe it. I've been looking at those early math materials on the shelves all year and wondering when we'd get to them. Well the time has come to get to them, and get to them he did.
In about two sittings he was able to independently identify which was the unit, the ten bar, the hundred square and the thousand cube. This first presentation introduces the child to the different number categories in a sensorial manner, "look at the unit, now feel the thousand cube. It feels much heavier and larger than the unit." Then we added language and named each object/category/quantity using the three period lesson. (A small note here: my albums recommend using glass beads only and note that plastic beads, whether strung or fused, don't have the heft and weight that the glass beads do to truly give the child the best sensorial impression. We have plastic beads from Montessori Outlet. For a second I thought about getting glass beads just for these first exercises. The only reason I didn't was because I wasn't going to be able to get my hands on them fast enough. D needed them NOW.) (Another note to those needing to move their classrooms half way across the country: don't wrap your golden beads in bubble wrap or plastic. Ours were in non-climate controlled storage for three months and this made the plastic stick to the beads in some places. The beads aren't overly sticky, but since I like things to be perfect, they aren't exactly perfect either.)
After D was able to name each quantity, we played a fetching game where I asked him to collect a certain number of a single category quantity. I'd say, "please bring 3-hundred squares." He'd go to a mat across the room to our "bank" and count out three hundred squares and bring them to our mat. Then he'd count the hundred squares once again to verify that he had indeed brought three, the right amount. D was able to do this fetching game easily thanks to the 1-10 numeration work he had just completed.
After this exercise, we will be working on identifying a quantity in a single category. (Like I would collect a group of three thousand cubes, present these to D, and ask him how much is on the mat.)
I've read that the typical child starts with the golden beads and then proceeds with the collective exercises that demonstrate all four operations (+ - * /.) In D's case he was so interested in counting EVERYTHING that I thought that we'd proceed with the teens and the tens work in parallel. These are the first exercises in the linear counting section of the Primary Math album. The direct aim of the teens exercises is to give the child a sensorial impression of the quantities of 11-19 and how they each relate to the quantity of 10. We will also introduce the traditional names of the quantities. These works will aid D in his quest to count to 100 "all-by-himself."
This material includes bead bars from 1 to 9, and (9) ten bars. We use a long narrow grey felt mat on top of our work rug to isolate space for our work. I first showed D how to set up the upside down pyramid of bead bars. The nine bead bar is placed at the top and the one bead bar is placed at the bottom.
I then realized that the children have already seen this configuration working with the red rods and the number rods. I also realized that we have been doing the snake game upside down. The black and white bead stair should also be orientated with the nine-bead bar on top and the one bead bar on the bottom. Oops. It amazes me to see these consistencies throughout the Montessori sequence. When you see something that is similar to something you've seen before, even if the new thing is a bit different, it always brings up a sense of comfort, confidence, and calm--ahhh, this seems familiar. What a brilliant way to guide learning and exploration.
So admittedly, we didn't get further than the upside down pyramid in our first presentation. He just wanted to count the bead bars, again and again and again. It was really neat to see that confirmation that we've hit this sensitive period right. Whew.
On a separate occasion, we again took out the golden ten bars and began forming the quantities 11-19. At the top is eleven: one golden ten bar on the left and a single red bead bar on the right. The iteration at the top of the shot is 12, then 13, and so forth. You can also see that D didn't feel the need to organize his bead bars into that upside down pyramid.
We set up the beads in this manner and then added language in a three period lesson. He knew many of the names already, but 13 was pretty difficult. We are still in between the second period and third period at this point.
In the next exercise the adult will name a number and the child will build it. After this, the adult will build a number and the child will name it. Then lastly the child will build the numbers in order.
Typically, this work comes between ages 4 and 5.5 years.
Still later on we brought out the teen boards. This equipment consists of two rectangular wooden boards, with six horizontal bars affixed to each of their faces equally spaced. The bars create a space for other wooden cards to be slid underneath them. The first board has 5 tens printed on it and the second board has 4 printed tens. The set also comes with 9 number cards with the numbers 1-9 printed on them. Finally, the entire set is housed in a wooden box. I think we got ours from Alison's Montessori. This is a very heavy work, and the boxes are almost too cumbersome and large for D to be able to carry them from the shelf to the rug.
The boards are placed on the vertical felt narrow rug, end to end. We place the card numbers on the right hand side stacked in the correct order with the 1 on the top. I took the first card with the "1" on it and slid it into the top slot over the first zero to create "11." I also said, "this is eleven." After this, D took the stack of cards, and slide them into the remaining slots over each zero from top to bottom and said, "twelve, thirteen, fourteen, fifteen, sixteen, seventeen, eighteen, nineteen." When I asked him to "show me fourteen" he wasn't sure quite which one it was. I think he had just remembered the numbers in sequence and could recite them in order only.
In a later lesson another day, he was able to "show me [x number.] which is the second period of the three period lesson.
During a still later lesson he was able to tell me "what is this" and name the printed number I indicated. He can also complete the first exercise when the adult asks the child to build the printed teens numbers randomly. I'll say, "please make 14." He'll pick up the 4 card and place it in the fourth slot and say, "14."
There are two more exercises where the adult builds a number and the child identifies it by name and then when the child builds the numbers in order before we start pairing the bead quantities with the printed numbers on the boards. But at this point, I think he has done both of those other tasks by accident without formal introduction and he is ready to start pairing beads and numbers symbols which is the third and last stage of the Teens Lessons.
D also got started with the Tens lessons. In the shot above he is comparing (10) ten bead bars to a wooden hundred square to make sure they are equivalent. (This exercise isn't part of the formal lesson.) In this presentation there is a box of 45 golden ten-bead bars in a wooden box, and a long narrow felt mat which we place on top of a work rug.
In this presentation, we unroll the narrow grey felt mat (from Alisons Montessori) vertically and we start forming quantities at the top. I placed 1 ten-bead bar orientated vertically at the top of the mat and said, "this is ten." Then underneath I placed 2 ten-bead bars side-by-side orientated vertically and said, "this is two tens. We also call this twenty." Then I repeated the process with thirty. We continued with the three period lesson naming ten, twenty and thirty, which he was able to do easily. Afterward, he wanted to see all of the remaining quantities to 90 laid out and wanted to know what they were called. There are no further exercises for this first tens sensorial experience besides a three period lesson to learn all of the names of the quantities. The direct aim of this lesson is to help the child learn the traditional names for the tens 10-90 and to associate the name with the symbol. This lesson usually is presented between 4 years and 5.5 years of age.
After the tens beads are presented and the child can name the quantities, or in this case, when the child asks to see the "next work" we move on to the tens beads and boards. This work includes two tens boards similar to the teens boards in design and style, except they are printed with the numbers 10-50 and 60-90. We continue to use the box of 45 golden ten-bead bars and the long narrow felt mat. The prerequisite lesson is the tens bead work.
In this presentation, we set up the boards end to end, with the board printed with the numbers 10-50 on the top. I placed one golden ten bead bar next to the symbol 10 and said, this is ten. Then I placed two golden ten bead bars next to the symbol 20 and said, this is 20. And then we continued in a similar manner through 90. I don't remember if D took over counting out the ten bars and naming the quantities or not. He was interested in the number cards that came with this set, and the fact that the font on the number cards was slightly different than what was printed on the boards.
Then he wanted to write all the numbers on small index card pieces and stick them on the cards and the boards with double-sided tape.
The direct aim of this lesson is to help the child learn the traditional names for the tens 10-90 and to help the child learn that two tens is 20 and so forth. In addition, this work will help the child associate the name of the number with the number symbol. The child usually gets to this work between 4 and 5.5 years of age. The work that comes after this is the Tens Stage 3: Beads and Boards 11-99 lesson when the child will learn how to create all numbers from 11 to 99 and this is traditionally when we use the number cards D decided to recreate.
Anyway, back to numbers. Here D is using both the sandpaper numbers and the teens beads to create quantities and then write their number names. He was very very very proud of this work and he was super focused through it all. He is in his sensitive period for these numbers RIGHT NOW and it is really cool to see. I just keep reminding myself to "BACK OFF" and just let him explore what he needs to explore in the way HE needs to explore it. This isn't a formal lesson, or even an extension of a lesson. D made up this exercise. But something inside him just NEEDED to do THIS: write down numbers. He is using the correct pencil grip, the Montessori materials he feels he needs, and is doing constructive independent work. What more could I ask for.
Afterward, D really did seem calmed, refreshed and ready to move on. After a period of intense work D is always more interested in other materials and works in the classroom. I am still amazed to see first-hand the phenomena that Maria Montessori first witnessed.
Oh, we are working, working, working on learning our letter symbols. Though we squarely hit D's sensitive period for numbers, I seriously missed his sensitive period for sandpaper letters. He no longer wants to feel the sandpaper letters, so now I am trying other tactics to get him to practice forming his letter symbols and help along his muscle memory.
We do the sand tray a bunch and we also go through a lot of shaving cream. He loves writing letters in shaving cream in the shower. I'd love it too if they came up with an unscented shaving cream.
Typically the child would have focused on learning the sandpaper letters in one quick 3 week period. After finishing the sound to symbol association they would quickly move on to using the moveable alphabet to begin creating words, then phrases, then sentences, and then stories. The moveable alphabet allows the child to communicate his/her thoughts without having to have the motor coordination to hand write. At this point the child has had thorough aural training and can segment most any word. With the knowledge of which letter symbol goes with which sound, they can then spell most any word and therefore begin to communicate that which they desire to share. On average this stage begins somewhere between 4 to 4.5 years of age.
After much work with the moveable alphabet the child is ready to begin drawing these letter symbols by hand. After prerequisite work with the geometry cabinet, the tactile materials, the leaf cabinet, and sandpaper letters the child will begin work with the metal insets. I've mentioned these before as well as D's seeming disinterest. So, he is focusing more on the mazes to help develop mastery of the hand in using a writing instrument including, pencil pressure, keeping within an outline, and control of movement. The metal inset work typically begins close to 3.5 years of age.
The sand tray is also introduced as a work to develop handwriting. This is a shallow tray filled with sand in which the child can trace symbols. After some control has been achieved with the metal inset work, this work helps to further develop coordination and control of movement.
After the sand tray comes the chalkboards. There are a few different types of chalkboards. The one D is using here has no lines. Typically, the child would sensitize the fingers, select a letter symbol, trace it, give the sound and then would write the letter on the board with a piece of chalk and say its sound. This material again works to refine the child's hand coordination and control of movement. Successive chalk boards introduce lines that help the child form and space their letter symbols accordingly.
Now, I must also add to this very abbreviated list of handwriting preparation D did not follow this sequence. We were in transition during his sensitive periods and all of our belongings were in a storage crate or three. But since we missed these sensitive periods, we are picking up the pieces and trying to build a foundation of skills that will help serve him and patch up any gaps. I am not quite sure how much of what to do and when to do it, but I am trying to let him lead, and am listening to him tell me what he needs and when he needs it. I am also returning to some of the books I've read in the past that explain a bit about what to do with children who haven't had the needs of certain sensitive periods met to figure out how we should better proceed.
D is interested in words, and how to express himself, and even in reading what others have written. So I am hoping that he will catch himself up and master the skills he needs to be able to express himself as he desires.
Here D is working with the chalkboards and in this case, creating something a little outside the scope of letter symbols.
I made this sand tray from a few pieces of balsa wood (to cover the handle holes) and a tray I found at Jo-Ann Fabrics.
Wow, that was a lot about D's primary work. I guess I had a lot to say because neither of the other children did this at home.
S found our Zoology nomenclature materials (from Montessori R&D) on the shelves and decided to explore them a bit. I was thrilled that she just decided to look through these materials on her own accord. I did give her some suggestions about where to find more information about a few of the questions she had about the content in these booklets. True to form she was most interested in the worm-like classes of invertebrates. Yuck. Here she is looking up the bones of amphibians in one of our bone books. (Sorry, I just don't remember which book.)
Then she got out our Animalium book and started looking for pictures of worm-like animals. She then decided to make a booklet of her worm drawings. A wonderful, if a bit icky, independent project if I do say so.
S also seems to like grammar just like T. It must be the Montessori lessons because I sure as anything did NOT like grammar when I was in school trying to learn it.
Here I have her the first verb lesson. I actually took this lesson from the Cultivating Dharma album. You can read more about this lesson here.Here S is working through the first verb lesson in the KotU album. First we talked briefly about the black pyramid that it represents the old, stable, noun. Then I introduced the grammar symbol that depicts the verb. A red ball is spherical, it can move easily, and it is red like the hot sun. Just like the sun gives energy to the earth, the verb gives energy or movement to the sentence. S seemed to like this idea.
In this work, we introduced a new grammar box for the verb. S selected the first filler box that contained sentence cards and word cards. She chose a first sentence card and read both sentences out loud. Then she formed the first sentence with the word cards and then chose the alternate verb word card. Then she acted out the command. In this case she spoke a word and then whispered a word. Then she placed the appropriate word cards in the appropriate grammar box compartments.
After she had completed all of the sentence cards, we explored word order a little further. I told her that "speak a word" and "whisper a word" are called permutations. Then we rearranged the sentence to read "a word" and I asked her "can you do what it says?" She replied, "no." Then I arranged the cards to read "a word whisper" and asked if she could do what it said. She said "no," and then immediately rearranged the cards into the order that made grammatical sense: whisper a word. We repeated this with another pair of sentences to further explore word order and how order affects meaning. These exercises help the child become aware of the construction of our language and that generally the verb can be found in a central location within the sentence, and that it will rarely appear at the end.
Finally, I showed her the verb energy chart where we see that the verb shines on the noun family (the noun, adjective, and article) and gives energy to the noun family. Generally the verb gives the noun energy, movement, and action.
After this, S will continue to work through the other verb grammar filler boxes that explore other aspects of the verb.
T challenged himself to work through the rest of the grammar boxes by the end of the summer. (He was in part challenged by Kal-El who just finished all of the grammar boxes.) He received all of the initial presentations in the 2013-14 school year. Here he is working on adverbs and I think he wrote down his own definition of what an adverb is in his work journal afterward.
We have started the Stories of the World. You can go here to read a bit more about it, or Google MBT's blog for "SotW" and read her descriptions of this curriculum from a Montessori homeschooling perspective.
After reading the first chapter about what history is about, T decided to create his own personal timeline. I think that this particular work is in the KotU history album as its own separate presentation. So, even if you don't have or do the SotW curriculum it is in the albums nonetheless.D spent three days taking apart and putting together the puzzle map of the US. (He spent three days doing this one time.) He has already done the prerequisite map of the world (the continents map) and the puzzle map of North America. With 49 pieces (Hawaii isn't a separate piece) this puzzle is a bit more difficult. But over three days, with the help of the blank control map, D was able to put all the states back in their places. The direct aim of this work is to aid the child in refining their sense of visual discrimination of shape and to indirectly prepare them for geography.
I think he asked me the names of most of the states. He certainly knows his home state! That piece went in first.
S and T have been working on geometry a bit though here it looks like fractions. Here we are working on adding and subtracting angles and this lesson is the KotU geometry album.
First I introduced this concept verbally. I said something along the lines of, "what if we put two red fraction circles in the Montessori protractor and see what they measure as a combined pair? Oh, each of these two quarter pieces here measure 90 degrees and together they measure 180 degrees. I wonder if you could find another pair to combine."
Afterward, I introduced how to write this expression on paper. "Let's add 1/3 and 1/5." We measured each individual angle separately and then we wrote each measurement down: 120° + 72° =. Then we measured the two angles together and found that they were 192° and we wrote this down as well.
Then S tried adding more than two angles together.
And then T and S started subtracting angles pretty much by accidental exploration. Oh, we can add them together, or we can take one away from another and get something else entirely.
Then T was playing around with the fraction circles and came up with this and the idea to build a board game.
They even made a dodecahedron die to go along with the game.
After these adding and subtracting angles lessons using the Montessori protractor we will move on to using a regular protractor, drawing angles, and measuring them as well as learning new terminology like bisect and amplitude. Still after this, we move on to learning about lines.
One afternoon I just took S aside for a little one on one time. She loved the attention and the easy quick focused lessons, and I loved that we didn't get interrupted and that we got some special time together.
We started off with a little bit of the large bead frame and naming quantities. Then we pushed on to some more elementary early numeration math lessons. This lesson is part of the commutative and distributive laws of multiplication lesson. I thought I had written about this lesson before, but either I didn't or I can't find it now. So, this is the commutative property of multiplication. We used a box of bead bars (in this case for the decanomial from Montessori Outlet) our cut out signs (which are HUGE and they are from Alisons), and grey and white number tiles from the checkerboard (ours are from Montessori Outlet.)
In this problem above, S set up 7*8 and 8*7. Then we laid out 8 white seven bars below the first equation and 7 brown eight bars below the second equation. S counted them up (she is still working on those math facts) and found that both equations equal 56. Then she placed 5 ten bars and a 6 bead bar below each equation to indicate their total product. She found that both equations equaled the same thing.
S continued to explore using the same commutative property principle. She said that this work was really fun. The child should continue to explore combinations on their own and then they can draw them on graph paper to continue the work. After the child can create equations fluently, we introduce the "commutative property" terminology. The next topic we will explore is the distributive law.
This lesson is in the early numeration sequence in the elementary math album. S will be officially entering 2nd grade so she could be considered a year behind on the math. I am not particularly concerned because she proceeds easily when it is a subject she enjoys, and I've found that her sensitive periods come pretty consistently about 6 months behind the Montessori average. She has the same sensitive periods as Montessori suggests but just not at the same average age.
Whew! So that is a bit of what we've been doing in the classroom. What have you been learning this summer?