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

Using Children’s Literature to Reinforce Classification

posted by Dr. Jeanne White

When older children and adults perform chores such as doing laundry or putting away dishes, they may not even realize they are making decisions about how to classify objects into categories—washing the white clothes together and putting the plates together on a shelf.  Young children can begin to see how objects can be sorted into categories with the help of several children’s literature books.

Young children naturally sort objects by color.  Have a variety of books available that introduce colors and show objects of a particular color so children can make associations with the object and the color.  A fun book that can be used to explore colors is The Color Box (Dodds, 1992), in which a monkey named Alexander crawls into a box to discover a world where everything is black, then another where everything is white, then yellow, and so on until he ends up back in his world where there are objects of every different color.  Then provide groups of objects that can only be sorted by color such as Unifix cubes or square tiles.  Once children have sorted these objects by color, they can count the number of cubes or tiles in each group and compare them—which group has the most?  Are there more red cubes or more orange cubes? Then make several types of objects available for children to sort by color such as beads, tiles, cubes and blocks.unifix cubes scatteredunifix cubes and other shapes

After children have had several experiences sorting objects by color, they can begin to explore other attributes.  In the book, The Button Box (Reid, 1990), a boy visits his grandma and finds a box with hundreds of buttons inside.  He sorts them into categories such as buttons covered with cloth, sparkly buttons, metal buttons and buttons from uniforms.  He also lines them up based on size and color.  At the end of the story, the boy and his grandma close their eyes and each choose a button from the box.  Then they look at them and talk about all of the ways the two buttons are alike and the ways they are different.  Follow up the story with a game similar to the one in the story, by comparing two buttons or other toys that have similar attributes such as two dolls or two cars.

Another book that can be used for classification of objects is How Many Snails? A Counting Book (Giganti, 1988).  On each page there are illustrations of one type of object but they vary by size, color or design.  On the first page there are eight clouds for children to count.  Then there are more questions to answer, “How many clouds were big and fluffy?  How many clouds were big and fluffy and gray?”  Children can use their toys to count, sort and answer questions such as, “How many frogs?  How many frogs are yellow?  How many frogs are yellow with a green stripe?”  Incorporate science by introducing various types of insects and asking children to tell you how they can sort them—by putting all of the insects that are the same color together or by putting the insects with wings in a group. four frogs

When children sort and classify objects into groups, they are building a foundation for graphing and data collection.  grasshoppersThey can create unique ways of sorting objects into groups and once they know how to put objects into categories, they can help with all of those chores!

Using Children’s Literature to Reinforce Patterns

posted by Dr. Jeanne White

Young children naturally begin to create patterns with objects such as Unifix cubes or colored tiles, even if they do not realize what they’ve created is called a pattern. A child’s early knowledge of color or shape patterns can lead to later recognition of more complex patterns in large numbers and within the four operations.

A book that can be used to introduce young children to patterns in the environment is the book Math Counts: Pattern (Pluckrose, 1995).  The book contains photographs of patterns found in nature such as on leaves, flowers and insects.  The book also shows patterns found in familiar objects such as on a car tire, the sole of a shoe and wallpaper.  Encourage children to draw or photograph their own pattern discoveries such as on clothing, jewelry or furniture

.bracelets

jewelry boxAnother book that can be used to introduce patterns is Rooster’s Off to See the World (Carle, 1972).  In the story, one rooster decides to travel and meets two cats, three frogs, four turtles and lastly, five fish.  As he meets each set of animals, pictures of the animals are displayed in the upper corner of the right page.  Children can see the growing pattern of animals from one rooster up through five fish.  Eventually, all of the animals disappear, starting with the five fish.  The pictures of the animals appear in the upper corner of the left page and gradually disappear until only a picture of one rooster is there.  Children can see another pattern as the number of animals decreases from five down to one again.

Set up activities following this book such as displaying familiar object to create an AB pattern (using only two different elements in the pattern) for a child to continue.  Start with color patterns and say the colors aloud as you display each one, “Red, blue, red, blue.…”  After several examples of color patterns, use toys and say the name of the objects as you display each one, “plate, spoon, plate, spoon….”

patternspoonsOnce children have practiced recognizing and repeating patterns with cubes, blocks, toys and familiar objects, they can begin to listen for patterns in songs, stories and nursery rhymes.  A book that can be used as an example of a pattern set within a story structure is The Napping House (Wood, 1984).  It’s a rainy day and everyone is napping in the house, including a snoring granny.  But then the granny is joined by a dreaming child, followed by a dozing dog, then a snoozing cat, a slumbering mouse, and a wakeful flea.  Each of these nappers pile on the bed with granny one by one, and are introduced on each page, one by one, adding to the words from the previous page:  “And on that granny there is a child…and on that child there is a dog…and on that dog there is a cat….”

Encourage young children to listen for patterns when you read stories or to look for patterns in photographs and illustrations in books, on posters and other media.  Recognizing patterns sets the foundation for algebraic thinking—analyzing patterns, relationships and change throughout the study of mathematics.

Using Children’s Literature to Reinforce Geometry

posted by Dr. Jeanne White

As young children are formally introduced to the names of shapes, they begin to notice these shapes in their surroundings.  They see their plate as a circle and their napkin as a square when they eat dinner.  They look at the windows and doors in a room and recognize them as rectangles.  Tana Hoban’s book Shapes, Shapes, Shapes (1986) uses photographs of familiar objects such as pots and pans, and scenes such as construction sites, to present various shapes. Children will find more shapes on each page as they look at the photos again and again, and as they learn to name more shapes such as trapezoids and ovals.

An activity that can follow the introduction of this book can be allowing children along with family members to take photos of shapes in their home, their neighborhood or school.  They can display and compare the photos and name the shapes in each other’s photo.a door

a bureau

a lamp

In addition to two-dimensional, flat shapes, young children should be introduced to three-dimensional, fat shapes.  Reading the book, Changes, Changes (Hutchins, 1987), can open a child’s mind to the endless possibilities of how to arrange 3D blocks to build structures.  In this wordless picture book, a wooden couple builds a house but it catches on fire, so they must build a fire engine, then a boat to deal with all of the water, and so on.  Encourage children to find 3D objects in their environment such as food containers that represent cubes, cylinders, and rectangular prisms.  They can build their own structure with these containers and name them as they build.a pic of food boxes

Once children are familiar with the names of shapes, they can expand their vocabulary to include attributes of shapes.  The book, If You Were a Triangle (Aboff, 2010), includes illustrations of triangles that are slices of watermelon, Yield signs, faces of pyramids, designs on wallpaper, and more.  The text repeats the phrase, “If you were a triangle…” and lists attributes such as “three sides,” or “three corners” and introduces the terms polygon and angle.  At the end of the book, specific triangles are shown—equilateral, right and isosceles—along with examples of these triangles put together to form a new, composite, shape such as a rectangle or rhombus.  Children can look for triangles in their environment as well as practice putting the triangle Pattern Blocks together to form new shapes.a pic of 2 shapes red and greana pic of 2 shapes blue and green

Another concept children learn in early geometry is relative position.  Young children are gradually exposed to words used to describe the position of an object or person relative to other objects or people such as above, below, beside, in front of, behind, and next to.  Young children are also starting to distinguish between their right and left and are learning to move, and count, forward and backward.  A book that is fun for children to use to learn these concepts is Bug Dance (Murphy, 2002).  The bugs in this book go to school together and in gym class they learn a dance that teaches them to take steps to the right and to the left, then hop forward and backward.  Young children can perform the dance as the book is being read over and over.

After children have practiced their dance moves they can practice the terms in the book, as well as other position words, to describe the position of Pattern Blocks.  For example, children might say: the square is below the hexagon; the triangle is on the right of the square; the trapezoid is on the left of the square; the triangle is next to the square. a pic of 4 shapes

There are many children’s books that are written to introduce shapes, however many use the word “diamond” instead of rhombus.  I try to avoid these books or let children know a diamond shape is called a rhombus when we are learning math.

Using Children’s Literature to Reinforce Counting and Cardinality

posted by Dr. Jeanne White

Young children love it when an adult sits down and reads a book to them, carefully studying the illustrations before the adult can turn the page.  Why not seize these opportunities as a way to introduce or reinforce mathematical concepts?  There are four reasons why I like to use children’s literature as a mathematical resource:

  1. Literature can offer examples of real-life problem solving.

When I read The 3 Little Pigs to a child, we discuss how many pigs there are and how each one has a way to solve the problem of how to prevent the wolf from blowing down their house.  Even though pigs can’t really talk or build a house, the young child begins to understand the idea of a problem and solution as well as the lesson that sometimes we have to go back and try a new solution.

  1. Children can discuss and demonstrate how characters use math.

In the book, Pete the Cat and His Four Groovy Buttons (Litwin, 2012), Pete the Cat sings a song about his four buttons.  But as he loses one button at a time, he alters his song to include three buttons, then two, then one.  Young children can see, and hear, how Pete the Cat uses math in his everyday life by counting the remaining buttons each time he loses one.

  1. The text can provide common language and context for problem solving situations.

When I would read the book, The Doorbell Rang (Hutchins, 1986), to my primary students, we used little chocolate chip “cookies” cut out of brown tagboard and small paper plates to act out the story.  On the first page, Mom makes 12 cookies for Victoria and Sam to share.  This provides an opportunity for children to talk about how to distribute the 12 cookies on the two plates and then how to make sure the same number of cookies is on each plate.  Throughout the story, more children come to the house to share the 12 cookies, which are continuously distributed evenly among the growing number of children.

  1. Children can apply mathematical concepts with literature.

In the 12 years I have been teaching math methods for the pre-service teachers at Elmhurst College, the teacher candidates are always amazed at the number of children’s literature books used to teach mathematical concepts, from PreK through eighth grade.  I have also conducted workshops for preschool and kindergarten teachers, as well as for families of young children, who are also surprised at how easy it is to use literature to teach and reinforce mathematical concepts including counting, patterns, geometry and sorting.

Using Children’s Literature for Counting and Cardinality

red dots in a row

Young children learn to count to ten with meaning—they should not only be able to rote count from 1 to 10 but be able to count up to ten objects.  Adults and older children can become role models for counting and demonstrate the concept of cardinality, the awareness that the last number said is the total amount. When first introducing the concept of counting, use a book with the same objects on each page such as Ten Black Dots (Crews, 1986).  As you read each page and model how to count the number of black dots on each page, the child only has to pay attention to quantity since each object is the same size, color and shape.  Then practice counting up to ten circle counters so the child is only paying attention to the quantity.red dots in groups of 5

 

Once children are able to count objects that are the same size, color and shape, read a book such as Math Fables (Tang, 2004), in which animals are shown in different configurations along with a rhyming fable, from one spider up to ten beavers.  This book can be read to children again when they are ready to break down numbers and group them into more manageable and familiar amounts.

colored frogs

 

An activity that can follow this book can be counting familiar objects such as toys or food.  Allow the child to touch each object while counting, whether counting illustrations in the book or toys on a table.  The child should also be able to repeat the total number of objects.  For example, “One, two, three.  Three frogs.”

yellow dots

 

Once children can count up to ten objects, they can begin to learn the complements of ten (one and nine, two and eight, etc.) with the book Ten Flashing Fireflies (Sturges, 1995).  In this book, two children are outside collecting fireflies in a jar.  First there is one firefly in their jar and nine fireflies in the night sky.  Then they catch another firefly and two can be seen in the jar and eight in the night sky.  After repeated readings of this book, try playing a game in which some “fireflies” are in the jar and some are in the sky.  Show the number of fireflies in the sky and have children figure out how many are in the jar.  They can have ten counters of their own to help them figure out the math problem.

 

I hope you have as much fun as I do, reading children’s literature and creating related math activities to introduce and reinforce these counting and cardinality concepts.

Where’s The Math?

Math is a natural way of thinking and making sense of the world. Mathematical situations arise every day. You have to be ready to notice the math all around us and to engage children in doing and talking about math. Attribute is a mathematical idea that arises very early. Attributes are properties or qualities that allow us to describe & classify the world around us. We perceive attributes of the world around us through our senses. Attributes can be used to group. Attributes can be described with increasing precision.

What might you see or hear if children are thinking mathematically about attribute? They might be matching objects, describing objects or sorting objects. They might be paying attention to color or shape or size or texture.  If you notice children noticing and using attributes, you might ask them: Why do these go together? Why do these not go together?

When adults are comfortable talking about math, children will share ideas without prompting. Here’s an example from a preschool classroom:

Chris & Tracy approach their teacher with excitement: “Look, our shoes are the same so they are a group! There are 4 shoes, 1, 2, 3, 4 … It is a group of shoes with holes”

crocs

Teacher: “I see you have a group of 4 shoes with holes. My shoes have little holes on the strap where I buckle the shoes. Can my shoes be part of your group?”

Chris & Tracy: “No, teacher, you have to have big holes all over to be in our group”

Teacher: “I see … you have made a group of shoes with big holes all over. Does anyone else have shoes that belong to your group?”

In a kindergarten classroom, a child runs up to the teacher and says, “A triangle equals a square!” Some teachers might say, “What do you mean? Triangles have 3 sides, and squares have 4. They’re not the same.” However, this mathematically sensitive teacher says, “What do you mean?” The child answers, “Come see!” The child leads the teacher over to the block area, where there are a lot of unit blocks for the children to play with. (Do blocks give you an idea of what the child might be thinking?) This is what the child showed the teacher:

blocks

Two square blocks can be put together to make the same shape as one longer rectangle block.

Two long triangle blocks can also be put together to make the same size rectangle shape.

Therefore, one of the squares takes up the same space as one of the triangles. In other words, they are worth the same, or, as the child says, they are “equal.”

This child was thinking hard about both the attributes of these shapes and the relationships between them. One might even say that the child was doing algebra, because they were using equivalences:

2S = R   and   2T = R           Therefore, 2S = 2T               Therefore, S = T

In both of these scenarios, the teachers are building the children’s understanding of foundational mathematical ideas and their confidence in using math to make sense of their world.

I hope that you will be open to the joy of finding math any time, anywhere with the children in your life!

What Are They Thinking?

posted by Lisa Ginet

It is hard to know what is going on in anyone’s brain. Even when asked to explain ourselves, we cannot always express our ideas clearly. Young children, who are still developing both their communication and reasoning abilities, have an especially hard time explain their own thinking in words or “showing their work” when they are solving problems. Why does it matter to understand what children are thinking about? It helps us to respond to them in ways that nurture competence and confidence.

So, how do we figure out what’s happening in children’s minds? We need to watch what they are doing and listen to what they are saying for clues, then interact with them intentionally. Here is an example from a preschool classroom:

From nearby the teacher has been watching Jenny and Samantha work with the materials at the sorting station.

two-children

 

 

 

 

 

materials

 

 

 

 

 

 

The teacher has noticed the children taking the straight items from the collection without talking and putting them on the black paper. The teacher also noticed that Samantha takes each item and rolls it with her hand before she places it on the paper. After the paper is almost full with items, the teacher decides to approach the children.

Teacher: Tell me about your group.

Jenny: Son Palitos (These are sticks)

Samantha: Uh… no..no

Teacher: Samantha you don’t seem to agree with Jenny. What is your group then?

Samantha: A group that rolls

Teacher: Are you saying that what makes this a group is that all the things in it roll?

Samantha: yes, see (Samantha shows how different items in her group roll)

Teacher: Could this be part of your group? (The teacher offers a circular wooden object)

Samantha: (Samantha takes the wooden objects and tests if it rolls) Well, it kind of rolls.

(Samantha then adds the object to her paper)

Teacher: What should we call the group then?

Jenny: Cosas que ruedan (things that roll)

Teacher: I can see why you are naming your group: “things that roll.” There are sticks, pens, brushes, markers, pencils, straws and round pieces of wood but they all roll.

This teacher is drawing from a repertoire of intentional responses that help to surface children’s thinking:

  • Stop & Look – Take the time to observe what a child is doing. Try to figure out what the child’s ideas or goals are.
  • Say what you see – Use precise, descriptive language to describe what you notice. Provide labels to actions or structures that are mathematical.
  • Re-voice what you hear – Use precise, descriptive language to echo and expand on what a child says.
  • Check with the child – Always ask child to confirm your understanding of their ideas and intentions.
  • Wait – Allow child the time to react or respond to an adult prompt
  • Use comments / questions to invite / provoke children’s thinking

We will never be able to be inside children’s brains, but we can closely attend to their actions and words, and then intentionally respond in ways that draw out their ideas. The more we understand about what children are thinking, the easier it will be to help them love, understand and use math.

 

Math is fun? Really it is.

posted by Lisa Ginet

“Let’s do math!” I often say at the start of a workshop. This may lead to some panicked looks or trips to the bathroom. If I say, “no pencils or calculators involved,” then a few people will laugh, and most will look more willing to try what I suggest …

math-workshop

What are these people doing? The Counting Calisthenics! If you need a break from the computer, you can do it, too! Stand up and count while you move:

Touch toes – “1”

Touch knees – “2”

Touch hips – “3”

Touch shoulders – “4”

Throw hands up – “5!”

Continue counting while repeating movements

(toes, 6; knees, 7; hips, 8; shoulders, 9; hands up, 10 …)

Keep going until you want to stop.

After you sit back down, consider this question: If you kept doing the toes, knees, hips, shoulders, hands up counting calisthenics, what movement would you be doing at “456”?

It would be quite exhausting to actually keep doing the counting calisthenics all the way to 456, but I expect that, if you think about it a little, you will be able to figure out that you would be touching our toes at “456.” You probably noticed that your hands were up in the air every 5th number, and then the cycle started again. So, your hands would be up in the air for “455” and back at your toes at “456.”  You are using what you know about the structure of our base-10 number system and the pattern of the calisthenics movements to arrive at an answer. You are doing math!

We at the Early Math Collaborative want to encourage you, and all adults who spend time with young children, to build new math ideas and new math associations by engaging in fun and meaningful math activities. Why? If adults are going to engage children in doing real math and constructing authentic mathematical understanding, then the adults need to exercise their own “math muscles.” Because many adults have bad memories of math in school, they often avoid doing math with children. It can be hard to engage adults in exploring foundational math if they don’t feel good about math and don’t think they can do math. Just as learning math facts from flashcards is not an effective way for children to become fluent and flexible problem solvers, blindly following activity directions will not help adults understand the math in the activities or respond effectively to children’s comments and questions.

“Counting Calisthenics” is just one of our Adult Learning Activities. While they involve basic math concepts, Adult Learning Activities are not children’s math that we are asking adults to do; nor are they activities to repeat with young children. We have designed these activities so that they:

  • pose a puzzle or problem;
  • are interesting enough to capture and retain adult attention;
  • are easy to implement;
  • may have more than one solution or route to solution;
  • clearly focus thinking on foundational mathematical idea(s).

We hope that having fun doing math will help convince you that the world is not divided into those who are good at math and those who aren’t. We can all be doers of math, and we can build the same confidence and excitement in the children in our lives.

 

 

What is Math?

posted by Lisa Ginet

When you hear or see the word “math,” what do you think of? Your high school algebra class? Balancing your checkbook? A geeky engineer with pocket protectors? When you add “early childhood” to “math,” what do you think of then? A little one learning to say, “1, 2, 3, 4, 5, 6, 7, 8, 9, 10”? A bright poster with a circle, triangle and rectangle neatly labeled? All of these are common ideas about what math is and how math starts, but none of them are what I mean when I say “foundational math.” Before I tell you what I do mean, I want you to try something.

Look at this image:
shapes-pictureConsider this question:

Which of the figures are the same?

Often when I ask this, a person says, “They are all different from each other.” Another says, “They are all the same; they are all shapes.” Both of these answers make sense, but I often ask people to keep looking to see if anyone can come up with another answer. Usually, people then generate these six answers:

  • top two shapes are both orange
  • bottom two shapes are both green
  • left two shapes are both striped
  • right two shapes are both solid
  • top left and bottom right are both circles
  • top right and bottom left are both triangles

In fact, although none of the two shapes are identical to each other, any two of them are “the same” in some way. Figuring this out involves logical thinking about the attributes of the shapes.

This shape activity demonstrates one definition of mathematics – a logical way of thinking that allows for increasing precision. We can use math to make sense of the world. We can use math to solve problems. To use math in these ways, though, we cannot just memorize facts. We must build our own understanding, so that we can think flexibly in different situations. Without a strong foundation, a tall building would not stand for long. Likewise, without a strong foundation in mathematical concepts, children can struggle to understand the more complex mathematical thinking they need later in life.

At the Early Math Collaborative, we have developed a set of 26 “Big Ideas” – key mathematical concepts that lay the foundation for life-long mathematical learning and thinking. While these concepts can be explored at any early age, they are powerful enough that children can and should engage with them for years to come. As you engaged in the shape activity earlier, you were using two of the Big Ideas:

  • Attributes can be used to sort collections into sets.
  • The same collection can be sorted in different ways.

Most likely, you were not thinking about these ideas consciously; rather, you were looking at the shapes and thinking about them. You were using math to make sense of the puzzle I posed and to come up with a solution. This type of math may not match your prior notion of math as quickly-recalled facts and properly executed procedures. You may need to set aside some of those notions in order to develop a deep understanding of foundational math that will help you have fun doing math with children.

 

Introducing the Guest Blogger for the Month of December and January – Lisa Ginet

The holidays are nearly upon us and for that reason, our guest blogger’s posts will appear over the course of the next two months as we send out 2016 and welcome in 2017.

lisa-img_0368-500x500

Let’s welcome Lisa Ginet to the Math at Home blogoverse.  Lisa comes to us from the Early Math Collaborative at the Erikson Institute where she has been an integral member for many years.  Her expertise comes from years in the early childhood classroom, and as an adjunct faculty member in Chicago.

Since 2009, Lisa Ginet has been a member of Erikson’s Early Math Collaborative, which is transforming the understanding, teaching and learning of early mathematics from the ground up. Before that, Lisa spent more than a quarter century as an educator in various roles: classroom teacher, child care provider, parent educator, home visitor, teacher trainer, and adjunct instructor. She has worked in diverse settings, from child care centers and elementary and middle schools to community colleges and private universities.

 

During her time working with Erikson’s Early Math Collaborative, Lisa has thought a lot about the essence of foundational math, engaging adults in enjoying and doing math, bringing to life children’s mathematical thinking, and authentic mathematical environments in early childhood classrooms. Lisa will reflect on the lessons she has learned and what they mean for those of us who want to help children love, understand and use math.