This workshop was originally presented at the April 5th, 2014 SACC Conference in Windham, Maine.
Keynote Presentation only: math workshop14 (pdf final)
Math is fun and natural for our youngest learners. Math is more than just numbers. Today there are many quality picture books available that enrich the math concepts we should be exploring with the children in our programs. Come and be exposed to a variety of picture books that can be integrated into early childhood education math lessons.
This workshop will share books more appropriate for the preschool ages and activities that will extend and enrich the learning. You will leave with a book list and links to resources for activities shared.
Notes for workshop and Keynote presentation:
Is “more” a math concept?
It actually is a basic one needed for understanding algebraic operations and should be one of the earliest math concepts developed.
Not sure if a toddler understands “more”?
Think about how they ask for another item. Or if you put two separate piles of a favorite snack item in front of a toddler and ask them which pile they want, the majority of the time the larger pile will be chosen.
As ECE teachers we need to open up to the idea that math is naturally in our environment and part of our day. We need to include math terms/language/vocabulary as part of our general conversations with children. ie: Use more, less whenever dealing with groups of objects. It isn’t about waiting for a formal lesson. Young children are naturally curious, so taking advantage of every opportunity for learning is important and should be our intention. All these experiences will be solidified when a child is exposed to those formal lessons.
Does a child need fine motor practice? Then let’s use clipping clothespins or large paper clips to figure out the more or less. Or open an egg carton and starting at one end drop small items like bottle caps, or pom-poms into the egg cup sections. One pile per line. Which fills up more sections? As a group have children pull small objects (that will fit their closed hands) from a center pile. Open hands and compare. Who has more, less, same. Take it one step further and graph results.
Does a child need more challenge? Add in the concept of same/equal. Have a mystery box. Oatmeal containers with a sock attached to the open end works really easily for this. The teacher or another student can place objects inside. Reaching through the sock another child feels around and counts the objects – (age up) write the number down, pull a card with the number, or pile objects off to the side. The child compares to items visible to them – “Is it more, less, same?”
This is also a nice concept to use for activity tables/trays. Children are able to work independently. I would have blank tally sheets available where they would draw to depict the more/less problems they made up themselves. Have a bowl of small objects. Directions are to put some of the objects on either side of the bowl. Draw the objects from each side into the square on the sheet that represents each side. For those that can count – write the number symbol in the square. You now have a math problem that can be recreated by whoever reads the sheet.
math workshop14 (final) ~ Keynote Presentation
(page 1) The books pictured here probably represent what most of you would think of if asked to provide/find a math picture book. You’d be right – these are all math picture books and we need to be using them with our children on a regular basis. I also believe we need to pull math into books that are not just “in your face” about math.
(page 2) The best kind of lesson plan for a preschool is one that incorporates a number of different learning ideas into one activity. In the world of education jargon, this is considered “cross-curriculum” teaching. ex: students are asked to work on identifying leaves, but then create a collage of the dried leaves in the shape of a tree. They are working on both science and art domains.
Good lesson plans for preschoolers will incorporate an activity along with an educational standpoint. We all know with shorter attention spans, preschoolers respond better to lessons that involve participation on their part.
I love using books as part of lessons as they allow us to combine learning and activities across academic areas. We need to take advantage of books in our work with developing and reinforcing math skills with young children.
(page 3) My goal is to help children learn early that math is fun, with the hope this interest or love will continue through their school years. Today there is an incredible number of quality books that cover the range of math concepts we should be exposing young learners to. For future success, I believe all children need the basics of education, but even more they will need the ability to communicate, an imagination, a willingness to explore, and a sense of self.
- Without an imagination a child will struggle to learn. Imagination allows a child to think out of the box, problem solve, and be independent.
- A willingness to explore means they are not afraid of making mistakes or failing at new things. They will ask questions, not necessarily excepting what just is or has been. There will be a flexibility to how they work and handle events that occur.
- A sense of self is just that. They will understand their individual skills or strengths. They will accept their weaknesses and in doing so will find ways to work around them. They will develop that self confidence that will allow them to challenge themselves.
I think math lessons naturally supports all this. So let’s use something that we already share with children because they enjoy it – picture books. It’s also important to understand that it isn’t just “in your face” math books that can be used to support math instruction at all levels. We need to open up how we approach teaching math through picture books.
example: Chrysanthemum by Kevin Hawkes. A little mouse with a special name. This is a favorite story for young children and doesn’t talk at all about math or have any underlying math concepts. What it does have is interest for children around something special to all of them – their names.
So the math teacher in me pulls from this:
- take apart the names into individual letters
- sort and group like letters together
- look for patterns in how letters group together
- charting each name to see which is longest/shortest
- how many have pairs of letters………
All this is math. All this is FUN for kids. All this is developing skills needed for success with higher level math. All this also combined math with other areas of a strong curriculum and is easily adapted to meet a vast range of abilities. All this is budget friendly – borrow the book through interlibrary loan, use letter manipulatives, use recycled scrap paper. All this is time friendly – pre-prep letters for children or have them write on shapes/chart/…..
(page 4) I recently took a college class on teaching math to young children. A section was about using books with math. The class broke the books into 3 kinds……….
I do not focus on that in the books I pull to use with the children. All I think about is how I can use the book. It doesn’t matter if the math is “in your face” or I have to help the children make the connection. I do not want math to be isolated. I want children to develop a love for math, understand it is fun, it can be played around with, it is naturally a part of our days.
Many of you are probably familiar with this hot series of books: Pete the Cat. (Read) …Groovy Buttons – easy to connect with math. What about …White Shoes? – where’s the math here – ideas? (Read) ((use colored squares passed out at beginning of workshop)) – language pattern and sequencing events
To find and include picture books into our math lessons we need to have knowledge of math concepts appropriate for the preschool age child. I use ELG Math Domains ((http://ccthemeslessons.edublogs.org/)) to be sure I’m taking advantage of all the math occurring in our daily activities and pulling books into that.
(page 5) For those of us who work with young children it’s natural for us to be talking shapes and counting. Math is so much more than that. In fact I start with Patterns. So much higher level math is built on patterns. Children love them. There are many to be found in their real environment. There are tons of hands-on activities that can be used to teach/reinforce/expand patterns with children across a range of ages. However, it is also probably not an area that we would think there are many picture books for. There we would be wrong.
(read) Press Here – pom-pom pattern activity
Bugs educreations (link also in Keynote)
(page 6) Preschool children can never get enough practice with counting, but so often there is no story line to counting books. It is important to look for those counting books that offer more – Mouse Count – Mice and snakes are always fun characters that hold the interest of young children. I love books that provide connections to our natural environment, expand our language base and are fun for me to read. Children’s author, Mem Fox stated in an interview Oct., 17, 2012 before keynoting the NAEYC’s Annual Conference, “Rhyme, rhythm, and repetition are incredibly important in books for small children. Repetition and rhythm probably even more than rhyme.”
Mouse Count provides that rhythm, repetition. Add in suspense (I love to whisper when the snake finds the sleeping mice) young children never tire of this story and the counting forwards and backwards, which leads into fun counting activities. (site link) This is a simple activity and not unlike others that we do throughout the years the children are with me. I believe repetition is important to learning many skills and developing a solid understanding of concepts. However, repetition of the same game can get boring.
(page 9) Subitizing has really come into play with the Common Core State Standards for Mathematics which stresses conceptual understanding and number sense over rote memorization of mathematical procedures and facts. In prepare children for success in elementary grades we need to stay aware of the changes in expectation for K, especially.
What do we need to be aware of when teaching math concepts to our youngest learners?
1. Number fact fluency is the number 1 reason kids start to fall behind in math.
2. Two main goals of Kindergarten math: learning how numbers correspond to quantity/ putting numbers together and taking them apart
3. Facts to 10 are based on an understanding of 5. Facts over 10 are based on understanding of 10. Because of this understanding ten-frame work will support this skill.
Children use counting and patterning abilities to develop conceptual subitizing. This more advanced ability to group and quantify sets quickly in turn supports their development of number sense and arithmetic abilities. The spatial arrangement of sets influences how difficult they are to subitize. Children usually find rectangular arrangements easiest, followed by linear, circular, and scrambled arrangements. For young children, however, neither of these arrangements is easier for any number of dots. Indeed, two-to four-year-olds show no differences among any arrangements of four or fewer items (Potter and Levy 1968). I believe it is because they are just learning to equate number value to objects.
(page 10) This story introduces children to the idea of “reasonable numbers.”
In Teaching Number Sense by Chris Confer, the concept of reasonable numbers (and the understanding of them) explains the concept is based on the real life experiences of the child. ex: A person might have one or two dogs, but not 20 or 30. Children may vary in their answers to questions such as – “The right number of earrings on an ear is….” Some things will have definite answers, while others will vary based on experiences. You want to guide children to understand reasonable numbers – it wouldn’t be reasonable for a person to have 30 earrings on an ear, but it might be reasonable to have 4.
We also need to know how the numbers relate that we are counting. What is the answer we are looking for. (prezi- 1+1=5)
(page 12/13) Shape and size open up lots of learning opportunities with young children. Most shape books are pretty straight forward.
I often find myself using misc. books when approaching the idea of size, comparison. Young children love monsters, giants, dinosaurs. It’s easy to read these books and then compare, measure from a giants view to a child’s view.
(page 13) Here is another genre of common books that are great fun for math work- our folktales. Use Goldilocks and the Three Bears, The Three Little Pigs, and The Three Billy Goats Gruff to learn about the number 3. After reading several times, compare and contrast the 3 books.
- Taste porridge (oatmeal). Predict if would like first, then graph if like or not.
There are also now many more reversal stories: Somebody and the Three Blairs is a reversal of the Goldilocks story.
- Use manipulatives for story retelling with Big, Medium, Small
- Use playdough to create bowls
- Use blocks to make beds
- Sequencing events
(page 15) Charting is fun, but Venn Diagrams can be so much more fun. They also can take and bump up the learning. With charts we usually make it and then ask the questions. I have found Venn Diagrams to take information and visually show comparisons. It allows children to compare multiple items, characters, books, results and visually see their knowledge. Children need that visual/concrete information point. Venn Diagrams seem difficult, but they are really easy and totally adaptable. That said it is not a starting off point – charts and graphs come first.
If you are doing an author study try doing a Venn Diagram of the books. We had compared If You Give A Mouse A Cookie, etc. books.
A favorite Venn Diagram ended up looking like a flower after we figured out how everything overlapped.
(page 16) Give a Mouse a Cookie
- Mouse cookie graph: http://ericabohrer.blogspot.com/2012/10/mouse-cookie-graphtivity-laura-numeroff.html
- Could do a baking project with recipe reading – numeral awareness, fractions, measuring
- Tasting party
- Make the graph from the tasting – classroom/master graph that children copy so have one to take home.
With the cat and cupcake could do as a felt board with different colored sprinkles for the cupcake – develop understanding of number sentences for addition and even subtraction, or just 1 to 1 counting.
- venn diagram
Books and resources:
There are many books appropriate for use when working on developing math concepts with young children. Here are ones I have used with my group. I have divided them as I usually use them, but know some overlap or are appropriate for multiple concepts. (* own, others borrow from the library)
*Press Here ~ Henre’ Tullet
Pattern Bugs ~ Trudy Harris – patterns to be found on pages visual and auditory
*Brown Bear, Brown Bear What Do You See? ~ Bill Martin, Jr.
*The Dress I’ll Wear to the Party ~ Shirley Neitzel
*The Very Busy Spider ~ Eric Carle – repetitive text
Dots, Spots, Speckles and Stripes ~ Tana Hoban – wordless photograph of patterns found in feathers, flowers, animals and people
*Jump, Frog, Jump! ~ Robert Kalan – cumulative tale, pattern in Jump, Frog, Jump! refrain
*Chicka Chicka Boom Boom ~ Lois Ehlert – pattern in the rhythmic chant/language
*Silly Sally ~ Audrey Wood – repetitive language pattern, cumulative
*Who Took the Cookies from the Cookie Jar? ~ Bonnie Lass & Philemon Sturges
*Good Night Gorilla ~ Peggy Pathmann
*Caps for Sale ~ Esphyr Slobodkina
*Pete the Cat I Love My White Shoes ~ Eric Litwin – language pattern
*Ten Black Dots ~ Donald Crew – counting
Eggs and Legs ~ Michael Dahl – counting by twos
*100 Hungry Ants ~ Elinor J. Pinczes – regrouping 100
Fish Eyes ~ Lois Ehlert
*Counting on Calico Cat ~ Phyllis Limbacher Tildes
Ten Apples Up on Top ~ Theo Lesig
*The Right Number of Elphants ~ Jeff Sheppard – reverse counting
* So Many Bunnies: a bedtime abc and counting book ~ Rick Walton – count to 26
*Ten Terrible Dinosaurs ~ Paul Stickland
*Gray Rabbit’s 1,2,3 ~ Alan Baker
*One, Two, Three, Oops! ~ Michael Coleman – figuring out how to count things that move
*Turtle Splash! ~ Cathryn Falwell
Build a Snowman 1,2,3! ~ Megan E. Bryant
On the Launch Pad ~ Michael Dahl
Tally O’Malley ~ Stuart Murphy – how to tally items/graphing
*Rooster’s Off to See the World ~ Eric Carle
*Frog Counts to Ten ~ John Liebler – number symbols, counting order
I Spy (Little Numbers)
*Alligator in the Elevator ~ Rick Charette – ordinal
First Day of Winter ~ Denise Fleming – ordinal numbers
*The Twelve Days of Christmas ~ Jan Brett
Can You Count to a Google? ~ – large numbers, infinity
*How Much Is A Million? ~ David M. Schwartz
*teddy bears 1 to 10 ~ Susanna Gretz
*1,2,3 To The Zoo: a counting book ~ Eric Carle – counting, wordless except for Number symbols
*Can you imagine…..? a Counting book ~ Beau Gardner – numeral/representation/ word
*Who’s Counting ~ Nancy Tafuri
*The Icky Bug Counting Book ~ Jerry Pallotta – non-fiction
*Feast for 10 ~ Cathryn Falwell
*One Potato: A Counting Book of Potato Prints ~ Diana Pomeroy
ADDITION / SUBTRACTION:
*Mouse Count ~ Ellen Stoll Walsh – addition/substraction
*Five Little Monkeys Sitting in a Tree/Jumping on the Bed ~ Eileen Christelow – subtraction
Each Orange Had 8 Slices ~ Giganti/Crew – thinking creatively about numbers and multiplication
The Doorbell Rang ~ Pat Hutchins – divide it up
*A Remainder of One ~ Elinor J. Pinczes – working with 25, regrouping, division
Domino Addition ~ Lynette Long – addition, counting
*Five Little Pumpkins ~ Ben Mantle
*Puppies in the Snow ~ James Young
*Pete the Cat and His Four Groovy Buttons ~ Eric Litwin – subtraction
1 + 1 = 5 and Other Unlikely Additions ~ David LaRochelle
Ten Sly Piranhas ~ Victoria Chess – counting in reverse story
NUMBER / FACT FAMILIES:
Quack and Count ~ Keith Baker – configurations for 7
*Mouse Shapes ~ Ellen Stoll Walsh
Perfect Square ~ Michael Hall
*The Shape of Things ~ Dayle Ann Dobbs
*Red Bear’s Fun with Shapes ~ Bodel Rikys
*If You Look Around You ~ Fulvio Testa – 3D shapes
*Lines ~ Philip Yenawine – Museum of Modern Art NY, vocab of artists, lines
*Shape Capers ~ Cathryn Falwell
*Shape Space ~ Cathryn Falwell
I’m the Biggest Thing in the Ocean ~ Kevin Sherry – comparison, size
A Pig is Big ~ Florian – bigger, smaller
Little Snowman Stan ~ Guido Van Genechten – Venn Diagram 2 snowman
*Biggest, Strongest, Fastest ~ Steve Jenkins
*Town Mouse Country Mouse ~ Jan Brett
*If You Give a Mouse a Cookie ~ Laura Joffe Numeroff
*Somebody and the Three Blairs ~ Marilyn Tolhurst
The Three Billy Goats Gruff ~
Measuring Penny ~ Loreen Leedy – measurement
The Tallest Snowman ~ Marcie Aboff
How Many Seeds in a Pumpkin? ~ Margaret McNamara – estimation
Balancing Act ~ Ellen Stoll Walsh – equality/inequality
Equal Shmequal ~ Virginia Kroll
*The Little Mouse, the Red Ripe Strawberry and the Big Hungry Bear ~ Don Wood – fraction
*Thunder Cake ~ Patricia Polacco – recipe for cake at book end (counting = time)
Give Me Half! ~ Stuart J. Murphy
Cluck O’Clock ~ Kes Gray
A Second is a Hiccup ~ Hazel Hutchings – a second is …time it takes to kiss your mom, turn around….second/minute/hours/day/week/month
The Clock Struck One ~ Trudy Harris – takeoff of Hickory, Dickory Dock with a cat chasing a mouse throughout the day on a farm
*The Wild Christmas Reindeer ~ Jan Brett
*The Very Hungry Caterpillar ~ Eric Carle – calendar and counting
*Cookie’s Week ~ Cindy Ward
Misc. Math Concepts:
*Seven Blind Mice ~ Ed Young – problem solving, comparing, ordinal numbers
*Paddington’s Opposites ~ Michael Bond – opposites
If You Give A Mouse A Cookie ~ Laura Joffe Numeroff – good author study where this series of books develops predictions, cause/effect, sequencing, idea of time
Pinterest Boards – Debbie @Country Fun Child Care
1, 2, 3….Math thru Picture Books: http://www.pinterest.com/countryfun/1-2-3-math-thru-picture-books/
Misc. Concepts: http://www.pinterest.com/countryfun/1-2-3-math-concepts/
Addition to Division: http://www.pinterest.com/countryfun/1-2-3-addition-to-division/
Google Drive Math Folder: https://drive.google.com/folderview?id=0B4YcgLTBqEheZFhzaEJFT2ltLTQ&usp=sharing
Count to 10 match cards – http://inspirationlaboratories.com/wp-content/uploads/2013/08/10-Black-Dots.pdf
Non-standard measuring – http://fairydustteaching.com/2011/03/jack-and-beanstalk-math-ideas/
My Favorite dice template site – so much varety: http://timvandevall.com/printable-paper-dice-template/
free printables: making equations / number line / 100 grid / coin sheet / : http://www.mamajenn.com/MamaJenn/MathPrintables.html