Researcher for a day: What kinds of animals live in the Amazon?

posted by Lindsay Maldonado

By day, I’m a researcher at Shedd Aquarium. I study people though, not animals – but, at Shedd, there are also a lot of people who do study animals. Some of these people are conservation research scientists or aquarists, who use math, and science, to help them learn more about the animals in their care, or animals in the wild. No matter who, or what, your subjects are, collecting data helps researchers collect information (i.e., data) that can provide answers to important research questions. For example, I might want to know how many visitors learned something about how they can help animals after their visit; or a conservation researcher might want to know how many seahorses live in a certain area of the world. So, to get us started, let’s pretend we are research scientists. We have our clipboard loaded up with our data collection sheet, some pencils, and our observation eyes. Now we’re ready to start collecting data!

penguin survey

Data analysis is one of the big ideas of early mathematics and can serve as a foundation for introducing other big ideas like sets, number sense, and counting — and, what better place to apply these ideas than at the aquarium with real living animals.

We have some important research questions to answer, so let’s get back into scientist mode. Today we want to know how many different animals live in the River Channel – and, we’re going to answer this question by observing animals (i.e., gathering data) and documenting what we see (i.e., organizing and describing data). These are all important steps to data analysis! If we want to know what animals live in the River Channel, we first need to make some observations. What do you see? A variety of animals live in the River Channel. How many animals do you see? Can you count them? I see 8 animals.

how many animals

Like the Amazon River, this habitat shows the diversity of animals that live in the river. What kind of animals do you see? I see turtles, stingrays, and fish.

kinds of animalsWe can sort the animals in the River Channel in a number of ways. First, we can sort by the attribute: type of animal. There are fish, turtles, and stingrays. Let’s put these animals on our graph. Representing data, in this way, is an important part of data analysis and allows us to interpret the data we collected.

blank graph

Let’s revisit our research question. We want to know how many types of animals live in the Amazon River. Through observation, we saw that fish, turtles, and stingrays live in the Amazon River so there are three types of animals in the River Channel. But how many of each live there? Let’s use our graph to help us organize our data. How many fish do you see? How many turtles? How many stingrays?

animals on graph

In what other ways can you sort these animals? You can use any number of attributes to sort the animals in this picture. We used the attribute of type (turtles, stingrays, and fish) but you could also sort these animals by size or shape. Observing animals at an aquarium is full of math possibilities. You can use data collection and data representation as the foundation for exploring the big ideas of early math. Keep exploring data analysis in the classroom. Try more data activities here.

Let’s sort this out!

posted by Dr. Bilge Cerezci

sorting rocksAt all ages, children classify intuitively to make sense of their world that seems largely out of their control. By 2 weeks of age, infants distinguish between objects they suck and those they do not. By 2 years, toddlers form sets with objects that are similar. In preschool, children begin to sort objects according to a given attribute and form categories. Many parents have likely walked into a room to see their four-year old putting their blocks or other toys in piles based on color or type. So why sorting is important you may ask. By sorting the objects around them, children start using their analytical thinking skills that is the lifeblood of mathematics. Studies have even been shown that by comparing objects to one another and understanding the relationship between set of objects, children engage in transitive thinking: A blue block is bigger than a red block and smaller than a yellow block. So, blue blocks need to go into a medium-sized block pile. Practicing sorting skills also provide children with models for organizing things in the real world, such as putting toys into the right toys boxes or putting the socks in a sock drawer and underwear in the underwear drawer.

Sorting Ideas

Helping children recognize math in the real world and finding everyday math activities at home is a great way for parents to reinforce young children’s sorting skills. Here are some of the sorting ideas you can implement in our home:

* Collect real-life objects such as rocks, marker caps, marbles, and buttons. Ask your children to guess which objects will together and which items will not. Ask the children to sort them according to different attributes such as; color, texture, type and etc.

* When it’s clean up time, ask your child to sort toys by attributes. For example, ask your child “Can you pick up all the toys that are the same color as this?”

* Encourage your children to name groups of things or activities. For example, at the dinner table, talk about attributes. You might say “2 people at this table wear glasses, 4 don’t.” or “3 have curly hair, 3 have straight.”

While you are doing these activities, use words such as “same,” “different,” “math,” “group,” “collection” and “set” as they apply and encourage your child them to use when they are describing their groups and comparing the groups they have created to one another. You may also ask your children questions such as, “Can you figure out what goes together?” “Can you sort these a different way?” “Why do these go together?” “Why do these not go together?” These kinds of open-ended questions will allow you to better understand your child thinking and push your child to be more precise in explaining their mathematical thinking processes.

Different children, different decisions

Children at different development stages are equipped with different mathematical abilities. A younger child will likely require less categories (sorting by two attributes) while an older child often can handle three, four or more. What you use for sorting also depends upon the age and ability of the child, as well as their interests. Some materials may be more challenging to sort for younger children (e.g., visually ambiguous materials) while others too simple and even boring for an older child (e.g., colored unifix cubes). Using real-life objects and situations to provide sorting experiences is always beneficial for all-around learning for all age groups. The bottom line is to know your child’s abilities, interests and to meet them where they are at, so you can just give them the right amount of challenge without underwhelming or overwhelming them.

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.

Number Sense: Make it Real!

numbers opaqueposted by Dr. Bilge Cerezci

Young children are motivated to explore mathematical concepts they encounter in their everyday interactions with the world. Through these interactions, they develop a range of informal understanding of numbers including ideas of more or less and one-to-one correspondence. For example, a child as young as two knows if she gets more or less crackers than her friend next to her. She also exhibits her basic understanding of one-to-one correspondence when she insists on getting a cookie because her brother had one and she had none. Such intuitive understandings of number sense may help lay the groundwork for later understandings of numerical equivalence and operations, such as addition and subtraction. While serving as important building blocks, such understanding does not necessarily help young children explicitly examine and interpret their experiences in mathematical forms. So, how do we help young children make connections from these informal knowledge around numbers to a deeper, more concrete understanding of numbers?

Helping children recognize math in the real world and finding everyday math activities at home is a great way for parents to reinforce young children’s developing number sense. For example, when you are setting your table for breakfast, ask your child to join you. You can ask them how many plates do you need to set the table or whether you have enough eggs for everyone or not. While they are taking the plates from the cabinet, encourage them to count. When young children practice counting, they’re also learning one-to-one correspondence. A child that understands one-to-one correspondence knows that 4 plates equals 4 or that 5 eggs equals 5. To help them practice this concept, give your children large groups of objects to count. For example, you are making a strawberry cake for dessert and you only need 10 strawberries. You may ask your child to help you figure out whether you have enough strawberries or not. As they are practicing this skill, children may count some of the strawberries twice and/or skip counting some of them. Therefore, it is important to closely observe your child as she is counting. When she is double-counting some of the strawberries, does she realize what she has done? Does she self-correct? In such instances, resist the temptation of correcting them. Instead, ask her to double-check her answer and give them enough time to check their work and self-correct their mistakes. If she is struggling, provide them with some strategies she can use(e.g., moving strawberries to a different pile as she counts).

Taking this kind of approach not only allows children to see math as fun, but also helps them see numbers as useful tools that they can use to make sense of the world around them. While doing these kinds of activities, the most important thing you can do is to help your child see math is something that makes sense and it is practical and enjoyable. This will help your youngsters to build a strong understanding of math and develop a love of learning math that will last a lifetime.

square blocks

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

Math Morning Meeting

posted by Stephanie Forsman

Each morning, my class has a Morning Meeting that consists of a Morning Message, a Greeting, a Share, and an activity. It is a great way to start the day, reinforces our sense of community, and sets the expectations and goals for the day.  These meetings last anywhere from 15 to 30 minutes. While I cover many topics during these meetings, my favorite topic is math. I love a Math Morning Meeting!

I have an interactive Morning Message (a message written on chart paper with an area for the kids’ responses) that the children work on during morning arrival and then later talk about during Morning Meeting.  Anything from identifying and giving the monetary value of coins to measuring various line segments with a ruler using both inches and centimeters, we try to either reinforce what we are working on in math or cover a topic that isn’t heavily hit upon in our curriculum. For example, when working on multiplication facts, I will put up problems that are related and share a pattern.

3 x 3 =

3 x 6 =

3 x 12 =

3 x 24 =

I have a problem for each of the children and one that I use as an example.

For Morning Meeting, we sit in a circle and begin with a Greeting. In keeping with our Math topic of the day, we play Match Card Greeting. I give each child a card on which I’ve written part of an equation. For example, one child gets a card that says “3 x 6”; and another student gets one that says “= 18.” The children move around trying to find the match for their card. When the children find their match, they greet each other. A simple “Hello” or “Good morning” is fine. I always keep a big stack of Index cards on hand for games such as this and this greeting can be adapted and/ or modified for almost any concept; addition, subtraction, shape recognition.

After the Greeting and the children are settled back into a circle, we do a Share. Share can be anything. Topic driven, partner share, a prearranged share in which one student shares something they’ve experienced or an object brought in from home.  During a Math Morning Meeting and when we are working on a specific skill, I will announce a topic for an around-the-circle sharing. Since we are working with multiples of “3”, I will refer back to the Morning Message and ask the children what they notice. “I am definitely seeing a pattern with not only the answers but the problems. Who else is noticing what I am noticing?” The children take a minute to think and then I will start to entertain answers. The children get so excited to share what they notice and there are usually so many extensions and directions I can go based on their observations, that I usually have to jot down notes and table some of their observations for another time.

Since we are working on multiples of “3”, we will play an adapted game of “Ruof” called, “eerht” which ends up sounding like “earth.”  Three spelled backwards. The children stand in a circle for this game. The children count off and on every multiple of “3”, they say “eerht”  1, 2, eerht, 4, 5, eerht… If the they say the multiple of three or make some other mistake, they sit down and the count off starts again.  I play this game for every multiple up to 12 and have even played this game using square and prime numbers. The children love it and challenge themselves to see how high they can count.

After the activity, the children sit back down and we end our Morning Meeting with a heads up about what we’ll be working on during math that day, pretty obvious given our Morning Meeting work and ask if there are any questions, comments or concerns.

Math Mornings Meeting are so beneficial and bring so much enthusiasm to the math that is happening in your classrooms. By 9:15 am, we’ve already had a good 20 minutes of math, the children had fun practicing their math facts, and their minds are warmed up and thinking about math for the rest of the day. I highly recommend the book, Doing Math in Morning Meeting, 150 Quick Activities That Connect to Your Curriculum by Andy Dousis, Margaret Wilson, Roxann Kriete. The book contains math-themed ideas for all four Morning Meeting components: greeting, group activity, sharing, and morning message. Have fun!

Click here to see the link to the book below.



Baby Brains and Math- People and Number

Did you know that infants as young as 6 months old, have a rudimentary understanding of number? When babies hear two voices they will look for two people and when they hear three voices they will look for three people.  This was discovered in a study that presented infants with pictures of two and three people.  When the infants heard two voices, they looked at the picture with two people on it and when the infants heard three voices, they looked at the picture with three people on it.

Fascinating!  We have always believed that human beings are hard-wired for language from birth and before.  Perhaps, we need to rethink our ideas about baby brains and math.


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.”

Baby Brains and Math- The Concept of More

When our first child was born, my husband was studying special education at the University of Illinois-Chicago.  He became very interested in using sign language to communicate with non-verbal students so he began studying it.  When Noah came along, Larry was convinced that we could communicate better with him if we gave him “language” before he could produce oral language.

One of the first mathematical concepts that infants begin exploring is the concept of “more.”  That was the first sign language Noah learned.  He learned how to say “more,” ask for “more,” and respond to “more.”  This simple sign became his first way of communicating with us, confidently expressing his needs.  This concept of “more”is one of the basic foundations of quantity.

Simply bring your thumbs up to the other four fingers and tap both hands together while saying or asking, “more.”  You will be amazed how quickly an infant will learn to mimic the movements (if not exactly, fairly close) and then use the language appropriately.

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.