Focus on Attributes!

posted by Dr. Bilge Cerezci

As she sits on the floor, a three-year old starts stacking blocks with various shapes and sizes. After some experimentation, she realizes that it is hard to build a tower if a block lays on its curvy side.


What does this 3-year-old discover about shapes?

From an early age, young children notice different shapes have different characteristics, even if they don’t know their names yet. They realize that some shapes have points while others have none. They also discover some shapes have flat sides while others don’t. Traditionally, we teach children the names of basic two-dimensional shapes: circle, square, triangle and rectangle and assume that being able to name these shapes indicates a higher level of geometrical understanding. Unfortunately, this can be any further from the truth. In reality, young children need your help to focus on attributes of shapes rather than overall appearance. For example, as you build a block tower together, encourage your child to pay attention to defining attributes of the each shape you are using. You might say, “I see you are stacking up the blocks that have flat sides. Look, all of its sides are flat. How is this one (i.e., cube) different that this one (i.e, half circle block)?” As you continue with the activity, encourage your child to use her fingers to trace and feel the shape. Give them a plenty of time to feel the shapes, count the sides and even ask them to find an item in your home to that resembles that shape.

As children manipulate various three-dimensional shapes, they will eventually build deeper understanding geometrical shapes such as flat faces of solid (three-dimensional) shapes are two-dimensional shapes.

There are many ways to encourage and help your child to learn about shapes. Here are some of the games you might play with your children at home:

* Drawing shapes in sand or foamshapes in shaving cream

* Walking around shapes drawn or taped on ground

shapes on the floor

* Making shapes with bodiesbodies making shapes

Shapes are all around us and it is easy to play games like these at home, outside and elsewhere. Most importantly, make sure to have fun while doing it.

The Early Math Experience Matters

posted by Dr. Bilge Cerezci

Traditionally, mathematics education has not been considered developmentally appropriate for young children (Battista, 1999). Math is abstract while young children are deemed to be concrete thinkers, and some cognitive developmental work done in the mid-twentieth century has been used to suggest that young children’s mathematical ideas develop on their own timetable, independent of environmental factors like teaching (Piaget, 1969). Over the past two decades, however, a growing body of literature has indicated that many mathematical competencies, such as sensitivity to set, size, pattern, and quantity are present very early in life (National Research Council [NRC], 2009). magnetic numbers plus symbolsYoung children have more mathematical knowledge, such as an understanding of number and spatial sense, than was previously believed. For example, research suggests that young children have a basic understanding of one-to-one correspondence even before they can count verbally (e.g., pointing to items in a collection and labeling each with a number) (Mix, 2001). Further, young children also enjoy exploring spatial positions and attributes of geometric shapes by building towers with blocks and cubes and by manipulating various materials, such as puzzles and two- and three-dimensional shapes (Clements, 1999; Clements & Sarama, 2008). They also demonstrate emerging awareness of measurement, when they begin to notice and verbalize similarities and differences in the size, height, weight and length of various objects and materials (Clements & Sarama, 2008). In addition, research also suggests that 3 and 4 years-old children engage in analytical thinking as they collect and sort materials by various attributes (e.g., color, size, and shape) and in algebraic thinking as they copy the patterns they observe in their surroundings and create their own patterns by using pattern blocks and other materials (Epstein, 2003; 2006). In fact, as research points out, most children enter school with a wealth of knowledge in early mathematics and cognitive skills that provide a strong foundation for mathematical learning (Clements & Sarama, 2009; Ginsburg, Lee, & Boyd, 2008; Mix, 2001).

There is also new evidence that achievement in early mathematics has a profound impact on later success. For example, Duncan and Magnuson (2009) examined the mathematics achievement of children who consistently exhibited persistent problems in understanding mathematics in elementary school and analyzed it in comparison to children who had stronger early math abilities. The results of the study revealed that 13% of the children with persistent problems are less likely to graduate from high school and 29% of them are less likely to attend college than those who had stronger early mathematics abilities. In other words, the initial differences in mathematics skills in early years may lead children to remain behind their more knowledgeable peers not only in primary grades but throughout their formal schooling (Geary, Hoard, & Hamson, 1999).

Studies also showed the predictive power of early math skills compared to other academic skills, such as reading. Lerkkanen, Rasku-Puttonen, Aunola and Nurmi (2005) investigated the relationship between mathematical performance and reading comprehension among 114 seven-year-old Finnish-speaking children during the first and second years of primary school. The results suggested that the level of mathematical knowledge children have before schooling is very important because these skills are predictive of their subsequent reading comprehension. In other words, early mathematics skills predict not only later achievement in mathematics but also later reading achievement. Similarly, Duncan and colleagues (2007) conducted a meta-analysis of 6 large-scale longitudinal data sets to examine the relationship between early learning and later school achievement. Of them, two were nationally representative of U.S. children, two were gathered from multi-site studies of U.S. children, and last two focused on children either from Great Britain or Canada. The researchers focused on the relationship between school-entry skills (i.e., reading achievement, math achievement, attention, internalizing behavior problems, social skills, and anti-social behavior) and later math and reading achievement while controlling for children’s preschool cognitive ability, behavior, and other important background characteristics such as, socioeconomic status, mother’s education, family structure and child health. Their meta-analysis revealed that only three of the six sets of school entry skills and behavior are predictive of school achievement: math, reading, and attention. Further, early math skills were consistently a stronger predictor of later achievement compared to reading and attention (Duncan, et. al., 2007). Consistent with the educational attainment analyses (Duncan & Magnuson, 2009), early math achievement was found as the most powerful predictor of later school achievement (Duncan, et. al., 2007).

Even though young children are natural mathematicians (NRC 2009) and capable of developing some complex mathematical ideas (e.g., addition) and strategies (e.g., sorting by multiple attributes to analyze data), it is also true that they do not become skilled in mathematics without adult guided rich and intentional interactions with those foundational math concepts. This month, we are going to focus on three of these foundational math concepts (e.g., number sense, sorting and geometry) and how you can provide your youngsters with rich and engaging math experiences that offer for opportunities and structures for the development of deeper math understandings.

Silly Putty Recipe Card

Baby Brains and Math- Chanting and Singing

Did you know that babies respond more to the “rhythm” of speech than the words themselves?  It is a natural impulse to speak to babies with a higher-pitched-than-normal voice, a sing-song lilting quality to the words, and a repetition that is particular to these interactions.  Throughout my career, I have had students and new parents ask me about speaking this way.  There are many people who don’t like it and feel like there is something wrong with it.  I have heard that this type of speech is discouraged by their families and even ridiculed, calling it “baby talk.”

It isn’t baby talk.  Baby talk is when you speak like a baby to other grown-ups, or older children.  The above-described speech was traditionally called “motherese” but is now called “infant-directed speech” or “parentese.”  Babies’ brains respond positively to this type of speech and their whole bodies respond to chanting and rhythm.  If you put an infant on your lap and bounce her to the rhythm of music or a chanted tune, the infant will nod her head, bounce her body up and down, and kick her legs and arms to the beat.

We can use this as a means of supporting mathematical concepts with infants.  Through repetitive chanting of songs, infants will begin to internalize number words and concepts.  If you sing “The Wheels on the Bus” with an infant in your lap, you can encourage the notion of “round and round” (spatial thinking) and “up and down” (more spatial thinking).  If you chant, “This Little Piggy” touching each of baby’s toes one at a time, singing,  “this little piggy went to market…” you will encourage “one-to-one correspondence.”

Geometry III

In addition to thinking about spatial reasoning, we also want children to learn basic spatial terms.  This is also true of mathematical terms in general, but the use of spatial terms throughout the day can help reinforce concepts of spatial reasoning without expressly doing so.

Throughout the day you probably do this without even thinking about it.  You say things like, “Put you coat inside your cubbie.” (Inside is a spatial reasoning term.) Or you might say, “The tissues are on top of the shelf.” (On top of is another spatial reasoning term.)  The reason that this is important is that we don’t want to say general things like “The tissues are there,” as the general nature of the statement doesn’t expressly support the learning of the these important terms.

I like playing “Hotter, Colder” with children.  You know the game.  It is when you have a child or children try to find something hidden in the room either in plain site or hidden away and you give them clues by saying, “Hotter” when they get closer and “Colder” when they get further away. Instead of using the words hotter and colder, you could use closer and farther, or nearer and farther.  This is will be one more way to incorporate spatial terms into your everyday activities.

Geometry II

Simple maps be one of the best ways we can introduce children to and reinforce basic concepts of spatial thinking.

Imagine drawing a simple map of your sand table.  On it, you indicate where certain small toys can be found (you have buried them there, previously).  Children (I would suggest one at a time) can go over to the table and using the map unearth the hidden objects.  Of course, children can simply dig around and find the objects, but if you design this activity specifically for the purpose of map use, the children will know that this is a game with a specific set of rules to follow.

You may have to help children under 4 orient the map so they can mentally imagine how the map lines up to the actual sand table.  This mental rotation of objects in space is a fundamental geometric skill.

This activity can be repeated using simple maps of areas all over your center, classroom, and outdoor spaces.  It works just like hide and seek except there is map, clues, and investigation involved.  If you create some good ones, go ahead and get them laminated and then they can be used and reused over and over again, with dry erase markers.



Geometry is so much more than learning the names of shapes for young children.  When we think of Geometry, we might harken back to that high school class where we had to memorize loads of formulas to determine circumference, area, diameters, and volume. This is NOT what we do with young children.

For young children, geometry is really housed in a larger concept that we call “spatial thinking.”  This includes mathematical skills such as categorizing shapes and objects, measurement, perspective, mental transformation of shapes (being able to turn a shape upside down), scaling, proportion,and location. This list is in no way complete, as there are many more ways that spatial thinking can be taught and learned in the early years.

An examination of the physical environment is one sure-fire way to get kids talking about geometry.  Using examples from the area around you and them, try to look for shapes, edges, lengths, and areas.

Copying shapes using manipulatives such as tangrams is another way to explore geometry.  We are going to look broadly at tangrams another day, but for now, take a look at these two sets of tangrams and consider how children can explore them.


The Best Baby Manipulatives- Soft Blocks

I really like soft blocks for infants and toddlers.  Often, these are designed so they fit directly into the small hands of the youngest children.  They can get them into their palms and then directly into their mouths for easy exploration.  The ones below are also made in a safe plastic, so they can be easily washed either by hand or in the dishwasher.

These can be piled up, lined up, knocked over, and thrown about.  They are created so that providers and parents can label them and encourage language, especially mathematical language.  Using words like “blocks” and “squares” encourages spatial thinking language.  Using color words encourages categorizing.  Using words like “more” and “less” and “1, 2, and 3” encourages number and quantity.  These blocks are a great infant manipulative.

Presto Pippo

This game by Selecta Spielzeug is called “Presto Pippo” and is great fun.

Presto PippoWe received this game as a birthday present when Noah was 3 and we played it for the next couple of years.  The premise is this…

Pippo, the waiter, needs to clear all of the dishes off of the tables.  Children take turns moving him around the restaurant piling the dirty dishes on his trays until they topple over.  The game requires patience and steady hands but is really about balancing the dishes equally so that they don’t topple.

Children use their fine motor skills to place the dishes on top of each other, but it is their spatial skills that are honed while playing.  They have to figure out that the larger dishes should go below the smaller dishes, that the round sides will not balance well and that the two sides need to be balanced equally.

This game is beautifully made; small wooden dishes come in a little drawstring bag.  The board is colorful and beautiful to look at.  Pippo himself is a little carved wooded figure with a large flat head that can be used to carry dishes as well.



Perfect Timing

This morning, I received this update from ExchangeEveryday. I guess we are all thinking about puzzles and spatial awareness.

Puzzling Results
March 11, 2013

You must first have a lot of patience to learn to have patience.
-Stanislaw J. Lec

Susan Levine, Ph.D., from the University of Chicago, offered these insights on spatial thinking in preschoolers on the LearnNow website:

“As studies mount that spatial thinking can actually be enhanced by specific activities at the pre-K level, what can we say about methods that actually work? Our latest published work homed in on the dynamics of puzzle play with children as they migrated from ages 2 to 4.5. We tracked 53 pairs of kids and their primary caregivers (mostly mothers), at multiple intervals for 90 minutes per visit, recording the encounters on video.

“One of the strongest take-home messages from our study is that richer engagement with puzzle play at 2 produced a stronger grasp of STEM-centric concepts at 4.5. Specifically, the children who showed the most engagement with puzzle play at 2 stayed on their trajectory throughout our study period. Moreover, the strong puzzlers, when tested at age 4.5, performed well above their age peers in one of the gold standard tests for spatial skills — the ability to mentally rotate an object.

“So what’s the link between puzzle and spatial? Mastering the placement of puzzle pieces inherently compels the mind — young or old — to recognize shapes and patterns in certain objects and then to imagine how they might fit into the larger whole. More often than not, the skilled players must rotate the piece in their minds to conceive of its place, and then must test their hypothesis by actually trying to place it where they believe it to belong.”

Incidental Math

It was months and months ago when I originally wrote about “Teachable Moments” and how to find them throughout the day.  I’ve been thinking a lot about how so much of the learning that happens in the early childhood world occurs in a happenstance way, rather than intentionally.  That does not mean that teachers of young children shouldn’t be intentional, they should.  But being ready when an opportunity presents itself is a strength of great teachers.

Math is all around us- we simply have to look for it.  Consider this scenario.

Johnny is playing at the sand table.  He is filling and dumping a small bucket of sand into a sand castle mold.  He presses the sand into the mold  and then flips it over and all of the sand spills out.  Bea, the teacher, comes over and begins playing beside him.  She too, fills a bucket with sand and then pours it out.  A few minutes into this parallel play, Bea asks Johnny about what he is doing.  He tells her that he is making sand castles. 

Bea sees an opportunity to use math vocabulary and spatial reasoning to discuss Johnny’s play with him.  She uses words like, “heavy and light” to describe the weight of the mold when it is full and when it is empty.  She talks about “turning over” the sand mold so that it is upside-down.  She asks if he prefers “a lot of sand” or “less sand” when filling the mold. She offers suggestions about how to make the sand stick together.  They fill the bucket with water at the sink and add water to the sand to experiment with making the sand stick.

This “incidental” math moment happens during free play.  Often, these opportunities occur and we miss them.  Keep your eyes open and look for a chance to deepen and extend a child’s play.  When seized, these moments are golden.