Math works

[lalaland42]

Does anyone have a resource where I can learn about early math works?

DD has been eavesdropping in on older students and I realized she has learned addition but she still can't write. She gets excited and wants to do addition at home, at school, and everywhere else but she is still young and seemingly doesn't have the motor skills to form numbers without tracing.

I have been using objects (stars and beans) to help teach her but I feel in the dark about how the Montessori method deals with math. I also don't want to push her but she keeps asking to work on it. I don't want to discourage something she has interest in, YK?

[freistms]

I found the early childhood learning board on the 4 real learning forums (http://4real.thenetsmith.com/) to be a great place to learn about Montessori. It is a catholic homeschooling website, but most of the people who regularly post on teh early childhood board are Montessori homeschooling. There is a ton of information about free resources and making your own manipulatives, as well as information on economical places to purchase good quality materials.

Also, Montessori for Everyone is a great resources for lesson information and do-it-yourself materials. http://www.montessoriforeveryone.com/

Not sure that is exactly what you are looking for.

[lalaland42]

Thanks a bunch.

Originally Posted by freistms

Not sure that is exactly what you are looking for.

Neither am I. I guess I am looking for a way to do what she is asking for at home without screwing up royally.

[MattBronsil]

Here is a Math Album to help you get started:
http://eiu.edu/~cfsjy/mts/_link.htm

Matt

[lalaland42]

Thanks Matt, I'll look at that too.

Just to explain what happened.

DD found some window clings in a math activity book I intended to give to her older cousin. They had numbers 1-10, written, represented by stars and numerals and a couple of addition signs and equals signs. A month before I picked her up from school and she said, "mommy 5 + 5 = 10" so when she wanted to play with the window clings I showed her how to add using the numerals and stars.

DD was so excited. Almost in a way I had never seen. She started asking to do addition every spare minute of the day. The next day she didn't want to go to school until I told her I would ask her teacher if she could do addition at school. Again, so excited. It was one of those times where you know you have an opening to teach her something.

When I picked DD up from school that day, she was really upset. Her teacher had given her a work where she had to add and then write the answer down. Since she can't form numbers (she is still working on tracing) she couldn't do the work. Then she said addition was too hard and that she didn't want to do it again.

I talked to her teacher this morning and told her how upset Sophie was that she couldn't do the work because she can't write the numbers. I know she is doing things a little out of order but I was hoping they had something that was purely representational.

DH and I met in math grad school and we are really surprised (but thrilled) that Sophie has such a draw to numbers. We don't want to push her but I don't want her to get discouraged because of a little thing like writing. We generally don't do purely academic things at home because I want her to have plenty of free play time (she just turned 3) but I was hoping if I could pick up something that was in her ability it would help.

I hope that clarifies things a little. Oh, and I've never taught anything below college algebra so I am not sure how to break it down into smaller bits. That is another reason I was looking for materials.

ETA: I was a college teacher for a while and it was just one of those moments I always loved having with my students. YK, where they are so open and willing to learn, they just need someone to present the stuff.

[MattBronsil]

I usually don't have 3 year olds that are too excited about addition, so that's great that she is excited. Well...let me change that. I have them excited about it with the red rods and figuring out quantities to 10. I then show them how to put them together with the ten rod and get teen numbers. It's great that she's interested in it in other ways, too. : :

My assumption is the teacher probably jumped a little too far ahead, which happens sometimes. That is shown by the fact that she had trouble with the writing part. Maybe numbers already written out where she can select the correct tile. I'm picturing a work having the following (I just assume she knows all numbers 0-19, for the sake of this example):

--Tiles from the hundred board, numbers 2-19.
--A sheet with various addition problems. The sum of all problems will be a number between 2-19, but no numbers will repeat.
--19 counters

Your daughter can do the addition problems with the counters then select the correct number and put it down on the paper in the right spot. She can still do the addition work, she can still get everything out of an addition work that she needs to help understand addition, and she doesn't have to worry about writing the numbers correctly.

The school might only have 1 set of the 100 board tiles, but there might be other tiles they can use.

Other works she might be interested in are the teen boards and the ten boards.

Matt

[nkm1968]

you can also try showing her how to form the numbers (the easiest, 1, followed by 0, 7, 2,3,9, 6, 4, 5, 8) only one number at a time with a makeshift "sand tray" (ie, a 9X13 brownie pan filled with cornstrach) and an index card with the numeral to be presented. Show her how you darw "the number one" in the tray, let her look at it, shake, and guide HER finger to draw the number one, look at it, and see if she can copy the motion after you shake it again. DD2 was able to learn how to draw the symbols for the different numbers without tears using this method (we did one or two per day) and show the ability to remember the next day, as long as I kept the session short (3 minutes) and fun and positive. My experience has been the younger my kid, the shorter the session. After about a couple weeks, she had 0-9 down pat (but she was 3years 11months), it is probably different amount of time depending on the age, interest, fine motor skills of an individual kid. DD1 resisted this kind of work until age 7, then it took her more towards a couple of MONTHS to be able to write the numerals 0-9 so that they were accurate/neat. But the cool thing about her being in Montessori was, she got to do all kinds of math work with friends who would inevitably do the writing part, with the stamp game, the checkerboard, the test tube division, etc so that she still practiced the concepts before she was able to write the equations...I love Montessori!!

[Lillianna]

I second the suggestion to practice writing the numbers with her at home.

Also, the more she can observe you writing numbers the better.

My daughter and I started a telephone book for her when she was slightly older than your dd. She loved to call her grandmas, cousins and friends by looking up their numbers and dialing the phone was alot of number practice.

Many times the children at school get excited about advanced concepts by watching the older children do their lessons. The more they observe, the more solid will be their experience when the get to those lessons themselves.

[snowmom5]

I haven't read the other responses but we had a similar problem this past year (second year of preschool) - ds is relatively advanced in math but has fine motor problems (indeed he has an IEP for fine motor for K starting in August). His teacher and I brainstormed, and I said, well, there's the movable alphabet, how about movable numbers, and ultimately she ended up buying number stamps for him - there are the kind that are dotted and can be traced (which are not necessarily favored from a fine motor perspective, but it allowed him to do math work such as 4-digit addition). I have seen something like them at Lakeshore Learning I think - let me see - here they are http://www.lakeshorelearning.com/sea...41!-1459982118

I think it is important not to let fine motor problems get in the way of her interest and ability in math - I hope you find a solution!!

[Lillianna]

yes, snowmom, now that you mention it, I remember my trainer saying a child who could not yet write numbers could use the small number cards (gold beads) with the stamp game.

For a young child, I think, though, that it would be best to follow the progression with the number rods and cards and work up to gold beads and stamp game. Lalaland42, which lessons has your dd been presented? (Has she been through Group 1 and 2?) The reason being is that, in the math area, the lessons progress from very concrete representation of the quantity to more abstract representations. This is an important visual and conceptual experience for much of the later math work. The number rods are combined to create sums and the number cards represent the equation.

[snowmom5]

Lillianna - Well, I have a goofy story for you about math works, and please forgive me because I don't know all the names of the works or what they even are exactly.

DS is a visual-spatial (right-brained) learner with left-brain (sequential/auditory) weaknesses. One quality of visual spatial learners is that they tend to learn better when they learn the whole before the parts rather than learning step-by-step. Sometimes this means learning the more complex first. Some things ds got right away, like the number rods. I think he was 3 or barely 4; he turned 5 in Feb. He wasn't really even talking in the classroom (has a speech delay) when he did the number rods after eavesdropping on someone else's presentation, or so the story goes... But, this past year he was having trouble with some of the simpler works that deal with concepts that are part of the more complex work of the stamp game (I beg forgiveness again because I don't even really know what the stamp game is - dd tried to explain it to me once LOL but I forgot). I think his teacher mentioned the thousands beads as being a problem for him, I can't remember. Anyway, ultimately she did give him a presentation on the stamp game, and bam, he got it right away. Then he was able to go back and learn the simpler works that comprised it, because he could understand the context of the simpler works, he could see where they fit into the big picture. They made more sense to him. (now he can count to a thousand in his sleep lol.) This just happened some time last winter/spring.

The only reason I found this out is that I was having a long conversation with his teacher about visual-spatial learners, and I was trying to explain some things I had read about, in particular this whole/part learning, which sometimes includes complex before simple rather than step-by-step simple before complex. It seems backwards, doesn't it? (I laugh to myself that ds learns backwards.) I didn't even really understand the complex before simple angle until the teacher relayed the above story about the stamp game. She said something to the effect that part of her montessori training included allowing them to try a complex work even when they were struggling with the simple - not sure how she phrased it exactly. She's pretty fresh out of her training - this is the first class that is all hers - and I don't know if my other kids' teachers, who have a lot more years under their belts, would do this.

(also, if your dd happens to be more of a visual learner than a sequential learner, see e.g. http://www.visualspatial.org/ , I wouldn't want to feel married to a step-by-step progression of learning concepts - seeing the big picture first can make all the difference for some kids. Unfortunately, except for the above story about my ds and the stamp game, which probably lacks key details that I just don't know, I really don't know how this complex vs simple applies to montessori math, especially concrete vs. abstract)

just my two cents

[Lillianna]

Originally Posted by snowmom5

Lillianna - Well, I have a goofy story for you about math works, and please forgive me because I don't know all the names of the works or what they even are exactly.

DS is a visual-spatial (right-brained) learner with left-brain (sequential/auditory) weaknesses. One quality of visual spatial learners is that they tend to learn better when they learn the whole before the parts rather than learning step-by-step. Sometimes this means learning the more complex first. Some things ds got right away, like the number rods. I think he was 3 or barely 4; he turned 5 in Feb. He wasn't really even talking in the classroom (has a speech delay) when he did the number rods after eavesdropping on someone else's presentation, or so the story goes... But, this past year he was having trouble with some of the simpler works that deal with concepts that are part of the more complex work of the stamp game (I beg forgiveness again because I don't even really know what the stamp game is - dd tried to explain it to me once LOL but I forgot). I think his teacher mentioned the thousands beads as being a problem for him, I can't remember. Anyway, ultimately she did give him a presentation on the stamp game, and bam, he got it right away. Then he was able to go back and learn the simpler works that comprised it, because he could understand the context of the simpler works, he could see where they fit into the big picture. They made more sense to him. (now he can count to a thousand in his sleep lol.) This just happened some time last winter/spring.

The only reason I found this out is that I was having a long conversation with his teacher about visual-spatial learners, and I was trying to explain some things I had read about, in particular this whole/part learning, which sometimes includes complex before simple rather than step-by-step simple before complex. It seems backwards, doesn't it? (I laugh to myself that ds learns backwards.) I didn't even really understand the complex before simple angle until the teacher relayed the above story about the stamp game. She said something to the effect that part of her montessori training included allowing them to try a complex work even when they were struggling with the simple - not sure how she phrased it exactly. She's pretty fresh out of her training - this is the first class that is all hers - and I don't know if my other kids' teachers, who have a lot more years under their belts, would do this.

(also, if your dd happens to be more of a visual learner than a sequential learner, see e.g. http://www.visualspatial.org/ , I wouldn't want to feel married to a step-by-step progression of learning concepts - seeing the big picture first can make all the difference for some kids. Unfortunately, except for the above story about my ds and the stamp game, which probably lacks key details that I just don't know, I really don't know how this complex vs simple applies to montessori math, especially concrete vs. abstract)

just my two cents

Theoretically, the Montessori progression actually starts with activities that present the "big picture" first and are extremely visual (concrete representation of concept) and then get more simple (ie. more abstract). The gold beads are a more complex activity than the stamp game is. I agree that many times the concepts are solidified as the child moves through the next challenge. As a matter of fact, the key concepts are repeated in many of the different materials in order to offer repetition in new and interesting ways. For example, the four different practice charts for addition each serve the same purpose but offer a new way to practice the math facts.
I'm not trying to say that children should be "married to a step by step progression of learning" in the sense that they should be held back if not perfect at each lesson. The lessons should still proceed. But the progression is important specifically because it goes from seeing the big picture first towards repetition with specific aspects of the concept. I speculate that this work with the big picture (gold beads) is why snowmom's son is able to do the stamp game at this time.