Friday, October 7, 2016

Teaching Twos - Math

teaching toddlers math
Please remember that this is child-led learning through play and movement. No drills, worksheets, etc. I'm going to present them in a series of subjects:

If you haven't read my Early Math post, it has some excellent sources for why math introduction is as important if not MORE IMPORTANT than early language learning. We think nothing of talking to our babes in the womb and speaking to them from birth, but we often view any other form of early teaching as harmful. This simply isn't true. 

Learning through play and movement, observations in life, and experiences are how children learn in a developmentally appropriate manner. Of course they shouldn't be expected to do worksheets and drills. Those aren't even developmentally appropriate for a 2nd grader, though school systems choose to often teach them in this manner. 

Early math introduction has far-reaching benefits for children, and many cross-over aspects into reading and other subjects.

There is no expectation on the part of the child here. The expectation is on me to provide the teaching, the exposure to the concepts. The child either embraces it, ignores it, masters it, manipulates it, or just stores bits of it away for later. Often much later. But the point is that the information is there for them when they want or need it and more of it is retained, earlier, due to the exposure through casual, fun opportunities.

Rote Counting

This is what people often view as math learning. Number order and number recognition. This is such a blip on the radar of math learning, though. 

Rote counting is done daily here with our 0-10 chant. They love it. Rote counting is done more for introduction of number vocabulary, patterning/sequencing, and the concept of consistency, rather than getting them to be able to count, at this age. 

Since we begin in infancy with numeracy introduction, the 2's know their number names. Can they count? Not really. They have numbers they like and usually put them in numerical order. Mr. R likes "1,2,5!" Mr. H likes "1,3,4!" Usually they can pop up with the next number in a sequence, and they recognize some numbers. We say things like, "One, two, threeeee, GO!" to help with beginning counting. They are often observed counting in play.

One-to-one Correspondence

From birth we teach one-to-one correspondence. This is SO important for math and reading. We spend a little time on rote counting, but we spend a LOT of time counting THINGS. Numbers by themselves have little meaning, it is numbers as representations of quantities that have meaning, and that concept is as vital as the concept that words have meaning. We count things as least a dozen times a day: animals on a page, cups on the table, rocks in a bucket, balls we pick up, grapes on a plate, etc.

teaching toddlers math

Shapes & Geometry
We work on identification of: circle, square, triangle, heart, star, crescent, with diamond, rectangle and oval added in as needed. Shapes are not something we actively work on, but casually discuss in environmental and book experiences. Just like colors, they seem to just pick them up. 

Even more casually, I introduce 3D shape vocabulary, keeping in mind that they are TWO. The moon is a circle. They lack the abstract thinking to interpret it as a sphere, so for now, it is a circle or a crescent.

More actively, we work with shapes. Often this is not a shape learning activity, but a geometric manipulation activity and/or logic/reasoning activity. For instance, at 2 years and 3 months, the three in the picture below, all born within days of one another, are able to do tanagrams, shape sorters, shape puzzles, Wedgits, etc. that work with shapes, but work with much more than just learning shape identification. Even puzzles are working on perspective, movement across a plane, translation, rotation, etc.

teaching toddlers math

We also actively work with coordinate geometry terminology: up/down, back/forward, in/out, etc. I call this positional work. We do this as physial activities, casual observations, and purposeful book work. such as, "What is BELOW the bird?"


If I ask the 2's to get one or two of something, they can do that. We are working on more/less, a lot, big/small high/low and various other quantification concepts. 

Much of this type of learning is done in the sandbox and water table and playing with loose parts. Filling, pouring, dumping into a bigger or smaller container, trying to fit items into other items, all teaching proportion, volume, weight, length, height, concepts.

Even jumping off of things, stepping between pavers, reaching up for items, all teach measurement and proportion concepts.

Logic & Reasoning

Logic and reasoning are in play throughout the day. When I ask, "Is that okay?" I can see their young minds running through the reasoning. "Do you need to spend some time in time out?" "No." "Then what do you need to do?" Off they go making a better choice. Much of their logic and reasoning comes through playing with loose parts. We have a ton of stuff in our outdoor play area/classroom that they can use as they will. They often come up with uses for items that I never would have or could have thought up. Much of logic and reasoning comes from simply enabling them to experience a vast amount of different situations and the outcomes of their decisions pertaining to those situations.

teaching toddlers logic and reasoning

Patterning & Patterns

At 2, pattern learning is continued from infancy as a physical and musical activity. We are currently working on "Pat-pat-clap, pat-pat-clap, 1-1-2, 1-1-2, pat-pat-clap, I Love You, 1-1-2, 1-1-2."

Last month it was "Jump-down, jump-down, jump-down, spin around. [repeat]" They would jump up then squat down, and turn around after three rounds of that.

There are patterns sprinkled throughout our play and routine. "1-2-3 GO!" is even a pattern. The order we put out beds, is a pattern. 

teaching toddlers geometry math


They have their counting bears to color group as an acitivity center choice.
We also do this in pick-up, "Put all the cars away. Now, put all the baby doll stuff away." It may not seem like a mathematical activity, but it is purposefully intended to be such. They begin early on seeing that like goes with like and making inferences about grouping. This is also a science aspect - characterization, identification of traits.

teaching toddlers colors logic and reasoning

Beginning Computation

This is casual through observation. "Oh, look, you have three, 1-2-3, and he has three, 1-2-3. TOGETHER you have 1-2-3-4-5-6!" "He has one, can you give him another one so that he has two?" "You have one car and one more car, so you have two cars. one and one more is 1-2."

Not enough attention is paid to the early introduction of math vocabulary and concepts. Not just my opinion, finer minds than mine are saying this. Children learn many of these through their play, and we can scaffold that learning to a higher level through purposeful teaching. We can also provide them with a much broader base of concepts and vocabulary through casual observations of their activities.

I think I do a pretty good job at this. 

Wednesday, October 5, 2016

Teaching Twos - Language

teaching toddlers language

I had an interview recently and was explaining how I teach. She asked, with what I perceived as a large amount of derision, "What can you teach a TWO YEAR OLD?"

Yep, SHE was about to be schooled. 

Please remember that this is child-led learning through play and movement. No drills, worksheets, etc. I'm going to present them in a series of subjects:

Vocabulary, vocabulary, vocabulary
2-year-olds pick up about 10 new words a day, when provided with 10 new words a day. Each child has different words that s/he will be drawn to, so I need to expose them to many more than that. The favorite word for them all yesterday was flamingo. Since it is estimated that an average person only uses 700 unique words on any given day, and a child has a vocabulary of 14,000 words at age 6, it can be implied that only through targeted efforts at vocabulary introduction does this happen. The main source for this is READING. Each book introduces a child to another person's vocabulary and voice. Given that there is a DIRECT correlation between time spent reading and future grades and adult success, reading is the key aspect of teaching 2-year-olds language.

Parroting/mimicking/repeating of words is key to rapid vocabulary acquisition. We work on this from birth. A newborn will stick its tongue out if it sees someone do it. That's how it starts. We start with parroting of movements, move on to parroting of sounds/babbles, and on to words. A child that will parrot words will pick up twice as much vocabulary in half the time as a child that doesn't.

To expand vocabulary, we will work with our monthly/weekly preschool themes to prep vocabulary they will need for those in the following years.

Sentence structure
The little ones are 2 years and 2 months old now. This week we have been working on pronouns. Previously they all used their names and said things like, "John do it." "Daddy truck." "Mommy go." Now they are speaking at up to five word sentences, and have thrown out a couple of pronouns. So it's time. So instead of me saying, "No, that's Randy's truck. Give back." I'm saying, "No, that's his. Give him his truck back." In just a week the use of pronouns by the 2's has greatly increased. This is a conscious directional shift in how I speak to them, with a specific goal in mind. A few weeks ago they were not ready for this shift, now they are. 

In parts of the world where eye contact is discouraged, enunciation is much better and mastered earlier than here in the west. [Just read this, but can't find source.] For us westerners, it is rude to not have eye contact when speaking, however when the eyes are on eyes, the mouth movements are missed. I purposefully teach the children to look at my mouth when learning new words. I say the word in a specific tone that keys them to parrot me, and put my finger to my chin to indicate them to watch my mouth. 

I will have them parrot a few times, until improvement is made, or they look away, indicating end of interest. I always end with a, "Good job!" and high five.

Enunciation is key to being understood, so the sooner we get good enunciation of the words they know, the quicker we get better communication and fewer tantrums from communication frustration.

While many would consider the ABC song language acquisition, I do not. For me, it is mathematical sequence. It teaches order and the concept of consistency. The language component is simply the vocabulary introduction of the letter names.

ABC recognition means little to me. It doesn't matter to reading if a child knows an "A" is an "A", it matters that they know that "A" says "aaa." Most of my former 2-year-olds knew their phonics for both upper and lower case by 3, and learned the letter names by 4. This meant that they were often reading some at 3/early 4, without knowing their letter names.

We learn phonics through acquisition first of sounds. Not just letters and their partner sounds, but also digraphs and blends. We'll spend a week focusing on the CH sound for instance with casual references to the letters shown. We start at 2 to make clear the concept that letters make sounds. At 3 we work on sounds making words, and by 4 we move to words make sentences, make paragraphs, make stories, etc.

We also work on phonics through reading of alphabet books. I emphasize the phonics element, since the letter name is usually the focus of the book. It's easy with books like Dr. Seuss's ABC.

While reading, we work on many of the pre-reading skills
- Left to right convention
- Recognition of print as meaningful words
- One-to-one correspondence of words 
- Repetitive readings to encourage comprehension, sequencing, filling in

When we do reading, it is ALWAYS interactive. The children get to play out the story in some way. In Goodnight Moon they pop balloons, meow like kittens and do a lot of other movements and sounds. For any book that has a repetitive phrase, like Pete the Cat, then they say that phrase whenever I pause and look at them. If you haven't done this type of interactive reading, it's easiest to start with books meant to be interactive, like From Head to Toe by Eric Carle. However, any book can be made interactive. 

The one way we do letter name recognition is the first letter of their names. Since I put it on their work, and they have their names on their cubbies, I make a point of introducing the first letter of their names at 2 years old. 

Observational skills
A huge part of comprehension is paying attention to and remembering details. When we read, I always ask them to find different little elements within the pictures. With repetition, they become use to looking more closely, paying attention longer, remembering elements, connecting the story to the picture, and gaining a clearer understanding of the content. What this leads into is greater comprehension once they start reading, and a better ability to visualize the story once the pictures are removed in chapter books.

This is not done just in fine work like a picture book, this is a skill that we focus on at a large scale as well. The 2's will point out the moon, a pear in the tree, a spider web over the garden, an ant on a tree, etc. They are more observant through practice, and while the goal is to be better readers, having attention to detail and a broad visual perspective have many excellent advantages.

Language acquisition begins in the womb. So many pieces of the language puzzle are in place, ready to go, when a child hits 2. Twisting and turning the pieces until they make sense, go together, and create a beautiful picture of meaning, is a large part of the skill set learning for twos.