Many of our DREME TE resources can be used to support students’ understanding of the ways in which we are born to pay attention to the math in the world. This resource provides information on how this attention leads to surprisingly sophisticated interactions between infants and toddlers and their environment and caregivers.

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Ideas for Engaging Students around Select Resources

In this resource, we highlight ways in which the DREME TE resources can be used to support students’ understanding of the ways in which we are born to pay attention to the math in the world. We also provide information on how this attention leads to surprisingly sophisticated interactions between infants and toddlers and their environment and caregivers.

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Resources about very early math development

** Counting on Counting**: This resource reviews research on young children’s numerical perception and thinking through the eyes of Alyssa and her caregivers. We begin with two-day old Alyssa’s ability to notice the difference between cards with two dots and three dots. We follow Alyssa into her toddler classroom, where at age two, Alyssa knows that when three balls are hidden in a bag and only two are taken out, that one ball still remains in the bag.

** Counting on Operations**: This resource reviews research on young children’s intuitive ideas about operating on number. Six-month-old Luci has expectations about how many toys should be on a small stage when they are added or taken away when initially hidden behind a screen. When the answer isn’t what she expected (two toys plus one toy doesn’t equal two toys!) she looks longer as if to say, “Nope, that wasn’t what I expected!”

** Objects and our Place Among Them:** This resource reviews research on young children’s spatial abilities. Infants’ ability to track parents’ movements and preference for face-like patterns provides early evidence of spatial awareness. Four-month-olds can distinguish the difference between a picture where dots are above a line and one where dots are below a line, and one where dots are to the left and one where dots are to the left. Through Monique’s experiences in her toddler class we hear her use of positional words and her ability to accurately retrieve toys from where she hid them.

** Pattern Paths to Algebra:** This resource reviews research on young children’s pattern and algebraic thinking. Infants can perceive and prefer auditory patterns that were heard in the womb (mother’s voice and heartbeat and the cadence of the book Cat in the Hat). Much of human learning happens through discerning patterns in our environments. Infants and toddlers push bowls off of highchairs repeatedly to make sure that the same result happens consistently (an interesting noise!) or add “ed” to words to indicate past tense (think “runned” here) because “ed” occurs at the end of so many words they’ve heard.

** Measuring Up:** This resource reviews research on young children’s measurement abilities. We follow Carlos, who at four months notices the difference between a set of increasing in size squares and a set of decreasing in size squares when shown one at a time on a screen. At age two, he uses measurement words (big, tiny) to describe dogs at the highly engaging dog run at the park.

**Life is a Sort of Data Gathering Activity**: This resource reviews research on young children’s use of data throughout their young lives. Newborns prefer their mother’s voice over other females’, use the “s” sound to indicate plurals, even when it doesn’t work quite right (mouses, sheeps). Toddlers, through their experiences with shapes and shape sorters, learn which hole will accommodate which shape.

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Teachers are Capable: Ways to support infants and toddlers in the classroom

**Environment – Provide opportunities where children are…**

- in a mathematically rich environment (manipulatives, sets of objects, blocks, puzzles)
- engaged in mathematical conversations (quantity comparison, how do you know [this is a square]?)
- provided with meaningful mathematics activities (follow their interests)
- exposed to modeling of mathematical thinking (I wonder how many [more train track pieces we need to make an oval]?)

**Activities**

- Counting fingers/toes/eyes/ears/feet
- Fingerplays (Open Shut Them, Five Little Ducks, Ants Go Marching, Five Little Speckled Frogs)
- Hide and go seek
- Books (Very Hungry Caterpillar, Hippos Go Berserk)
- Puzzles
- Real life story problems (
*Hmmm, there are two of us but Jaime wants to play too. How many plates should we put on the table?)* - Fair-sharing (
*We have 4 cars, how can you divide them up so that you each have the same number?)* - Comparisons (Which pumpkin do you think is heavier?)
- Different ways to group objects (vehicles – type, color, size
*This bike has two wheels! But this trike has three!*)

**Mathematical Language**

- Counting
*How many**baskets have you made??*

- Operations
*If you add***more**water what do you think will happen?

- Measurement
*Isn’t that a***big**dog? Look! A**little**dog!*Which***one**is**heavier**?

- Spatial Relations
*This looks like a***circle**, do you see any other**circles**?*Look***up****high**, now look**down low**.

- Patterns and Algebra
- Look at that caterpillar, it’s
**striped**! Look,**black yellow white, black yellow white**!

- Look at that caterpillar, it’s
- Data
*Can you put the***red**cars in this bucket and the**yellow**cars in this other bucket?

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Other DREME TE Resources

**Engaging with Video that Highlights Very Young Children's Thinking about Number**

: Ben at age three shows off his counting abilities.*Ben Learns How to Count*: Dr. Ginsburg talks about children’s interest in counting and how we can get an insider’s view of their numerical thinking through conversations and interactions.*Herb Ginsburg Talks about Counting*

**Understanding the Mathematical Development of Infants and Toddlers**

Toddlers can subitize very small quantities and discern that two sets of objects differ in quantity at certain ratios (2:1 and 3:2 for example).*The Mathematics of Counting:*Very young children engage in fair-sharing activities during play, dividing toys among playmates and caregivers and put pairs of duplo animals on each toy train. These activities set the stage for later*Beginning with Multiplication and Division:*engagement in problem-solving that involves multiplication and division skills.Infants and toddlers have considerable knowledge about operations, beginning with more and less (“You got more cookies!”)*What Children Know and Need to Learn about Operations:*: Infants and toddlers use estimations of size, shape and distance to inform their movements (reaching for toys, pulling up on a couch and taking sliding steps along its edge).*The Mathematics of Geometry and Spatial Relations*: More development on infants’ and toddler’s abilities to differentiate between shapes and ability to navigate the world with relative ease.*What Children Know and Need to Learn about Shape and Space*: Infants and toddlers can sometimes seem obsessed with more and less (“I’m bigger than you!” “You got more than me!”) commonly noticing these differences across their home and classroom environments. We can take advantage of this interest to support young children’s burgeoning measurement skills.*The Mathematics of Measurement*: Children sort objects in their environments from a very young age (food they like and food they don’t like, for example!). This data gathering (pushing the green objects to the side of their plate) serves as the foundation for problem-solving skills.*The Mathematics of Data*: A vignette in which teachers think about whether the “right” word is the goal.*Children’s Words Measure Up*: Babies’ environments are filled with patterns from heartbeats, to fabrics, to the songs their caregivers sing.*What Children Know and Need to Learn about Patterns and Algebraic Thinking*: Questions to ask young children that engage them in thinking about patterns and a sampling of activities that support our understanding of their thinking.*Formal Assessment: Spotting Patterns*

**Examples of Picture Books for Birth through Toddlerhood Children**

(Bear Counts, The Very Hungry Caterpillar, Hippos Go Beserk)*Using Picture Books: Counting*(Ten Red Apples, Quack and Count)*Using Picture Books: Addition and Subtraction*(Mouse Shapes, Round is a Tortilla, Up, Down, and Around)**Using Picture Books: Spatial Relations**(Mr. Noisy’s Book of Patterns, Pattern Fish)*Using Picture Books: Patterns*(Inch by Inch, Just a Little Bit)*Using Picture Books: Measurement*