In early November, Erikson Early Math Team members made several presentations at NAEYC’s annual conference. In a three-hour session, instructors Rebeca Itzkowich and Mary Hynes-Berry had participants engaged in exploring Big Ideas about measurement as they used both direct and indirect measurements in order to figure out how long a piece of leather would need to be to make a lovely tree “bracelet.” They later turned their adding machine tape lengths into rulers with arbitrary units so they could determine not just which tree girth was bigger, but how much bigger it was.

As further proof that math is all around us, we were delighted to see that in December examples of “yarn bombing” or knitting cozies for trees showed up in Evanston! We’re sure there was all kinds of measuring involved.

There are any number of wonderful books that give children very concrete images to show how big creatures are and to make comparisons to their own size. Steve Jenkins’ Actual Size and Prehistoric Actual Size have been favorite choices in our past workshops on measurement. Find the author’s website here: http://www.stevejenkinsbooks.com

In last year’s Idea Book, Laura Miller reported how she and and her preschoolers from Prieto Academy explored linear measurement after studying polar animals. They wondered, “Are we taller or shorter than an Emperor Penguin?” They used the book Penguins! by Anne Schreiber to find out that the average height of an emperor penguin was about 44 inches tall.

They used measuring tape and large butcher paper to mark this height and, with the help of an overhead projector and a toy penguin, they created a shadow of a penguin. Students worked together to make the penguin shadow match the mark they made on the butcher paper. Children compared the height of the shadow to the mark on the butcher paper. Comments such as “We have to make it bigger,” “Not that big!” and “Move it over!” were made until the height of the shadow and the mark on the butcher paper were the same. The class traced the shadow of the penguin and then they were ready to compare their heights to that of the penguin. Comparison statements that the children used included, “I am the same size as the penguin,” and “I am a little bit taller.”

After this experience with direct comparison, Ms. Miller asked the students, “How else can we measure this penguin?” The first response from a student in the morning class was, “Books!” Discussion arose surrounding how they could use books to measure. There were a number of questions to consider:

• Should they lay the books flat or stand them up?
• Would they fall down?
• Are all books the same size?

Ms. Miller shares the conversation that ensued:

One student, Laura, suggested we could lay the books flat so they would balance better than if we stood them up. After realizing that not all books are the same size and it would take a lot of books to complete the task, Jonathan suggested we use blocks! “We can use blocks; they’re the same!” Jonathan said in reference to blocks being the same size. Children shared their ideas of what they thought would be the best blocks to use. It was decided that triangles would be too tricky and rectangular ones would work best. After stacking the blocks and counting how many long rectangle blocks (8) and how many square rectangle blocks (16) would equal the size of a penguin, one of our reading buddies pointed out that the number was doubled because it takes two square rectangles to make a long rectangle.

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Focus: Big Idea of Data Analysis

• The main purpose of collecting data is to answer questions when the answers are not immediately obvious.
• How data are gathered and organized depends on the question.

At the Early Math Project’s May learning lab, participants observed a fun project tradition. As has been true for four years, the authors of this year’s Idea Book were in the room for its unveiling and discussion. The Idea Book allows program participants to submit write-ups and photos of activities they used to make their math lessons more engaging and to put their own spin on the research lessons discussed in the learning labs. They are organized according to the five major content strands and printed in a spiraled book so that even though the program is over, these Big Ideas remain accessible and inspiring for years to come.

Since the May session addressed important ideas of geometry, the discussion of data analysis didn’t get much attention—in the workshop, that is. However, the Idea Book includes a variety of great ways to make surveys and analyzing data meaningful, engaging activities.

Heather Duncan did a particularly striking job of explaining how she and her kindergarteners at South Shore Elementary have made collecting data from surveys and discussing them a regular part of their classroom life.

Heather prefaced her description of their process by pointing out how important it is to take time to really explore the ideas and emphasize the children’s work and thinking. She typically does a process that stretches from three to five days and always ends up with a product everyone can see.

• Day One, they collected results of a survey, usually related to a topic they were already studying. For example, while studying the human body, Ms. Duncan had them compare each student’s height to a cut-out of an average kindergartener hung up in the class.
• Day Two, they synthesized the results. “We used the chart,” she wrote, “to count and determine totals for each designation (taller, shorter, same size) and whether any groups have more/less or the same amount as any others. We also compare totals from the a.m. class with the p.m. class and discuss any similarities or differences in results.”
• Day Three, they further discussed the results and talked about the best way to show them on a graph. In this case, they decided on a bar graph.
• Day Four, they used the resulting graphs to make some conclusions. She wrote, “Which group had more or the most? Which had less, the least, or the fewest? What do we know about the question or our class as the result of our survey?”

They turned the results into a poster, a bulletin board display, or part of a “trivia book” at the end of the school year. Ms. Duncan comments, “[The activity] has since become practice, because we have found it to be a very rich experience. It’s been invaluable using math in context to study things we care about and to answer questions generated from our own interests.”

Tana Hoban and Ann Morris are both gifted children’s book authors who combine minimal text with wonderful photos that beg to be pored over again and again. Many of them are organized around ideas that call for mathematizing. For example, just the cover of Hoban’s Shapes, Shapes, Shapes or Cones, Cylinders, and Spheres will make it easy to engage children in wondering what regular geometric shapes they can spy in the classroom or on a walk around the school. Be sure the children record their findings by drawing or making tally marks so that they have data to analyze when they get back to the classroom. As you guide a discussion into asking what shape seems to be the most common, be sure to include the all-important follow-up: Why? Why do you think that is so? Why do you think you found many more rectangles than triangles?

In the same way, Ann Morris’s Shoes, Shoes, Shoes and Bread, Bread, Bread can jumpstart a survey of the different kinds of shoes the children are wearing or the kind of bread they like, as well as encourage some serious thinking about good ways to categorize them. Make sure you have them show the results. Once again, the best thinking comes as the children and teacher converse together about what questions they have and how they see the data making sense.

The 2011-12 school year brings big changes for Erikson’s Early Math Project and its work with teachers. Not to worry—the project will continue to serve Chicago-area prekindergarten and kindergarten teachers and schools. What’s changing then? The project is expanding and changing its design and implementation to create a more intensive, long-term impact for teachers in the program.

The final moments of the project in its current form highlighted the number of sturdy ideas built and maintained by teachers over the last four years. At the April learning lab for first-year participants, teachers explored the Big Ideas of geometry, from location and direction to spatial reasoning to attributes of shapes. For second-year seminar participants, their May workshop centered on assessing classroom lessons. Watching an in-class lesson resulted in a lively discussion about the presentation of the lesson and why it matters.

“The project changed the way I used manipulatives and books and resources to benefit the kids that was truly meaningful in their minds,” said Jennifer Meath, a second-year seminar participant from Smyser Elementary. “It put math on the forefront of my thinking in many ways.”

The next four years will see a different model for Early Math programming through Erikson. Rather than one- and two-year programs with teachers throughout the Chicago Public School system, the focus will be on eight schools for four years, working with all the prekindergarten through 3rd grade teachers in those schools. The gradual empowerment of teachers over time to take a greater role in their own learning of mathematics is similar but more extensive than the previous model. This is in direct response to recommendations from teachers in past years, as well as a desire for a more intensive program by the instructors.

“Each year you’re going to learn more,” second-year participant Eileen Goedert of Crown Elementary said. “I wish I had the ability to do just another year because it has really increased my kids’ ability to do math.”

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Ms. Ocasio had two primary goals. In the large group setting, she wanted to see if the children could sort a collection of household objects by the attributes of type of object and size. In the small group setting, Ms. Ocasio wanted to analyze the children’s ability to follow directions and identify the objects in English. It is important to help dual language learners understand math language in both their home language and in English. She hoped that the small group setting would give the children the opportunity to express themselves more freely as they think about expressing math vocabulary in English.

“I want to allow different groups of children to work together,” Ms. Ocasio said. “[I want to] mix the group of children that normally do not play together – boy, girl, English-dominant, Spanish-dominant, more expressive with less expressive.”

Two things Ms. Ocasio would add for future uses of the activity would be encouraging the children to sort sets by a third attribute and including the materials in the dramatic play area for further exploration.

Whether a child’s home language is English, Spanish, or Swahili, wordless books are a great tool for supporting the child (and her family) in developing mathematical thinking and language. Because it is the illustrations that carry the story, the child and the adult who read along are literally constructing the meaning. In last month’s newsletter we saw how rich language around number comes from Anno’s Counting Book. Equally rich conversations that count can come from exploring Eric Carle’s 1, 2, 3 to the Zoo, which also represents each number with visuals, numerals, and number words.

Both Anno and Carle have always had a strong mathematical strain in many of their picture books, which rely on the illustrations as much or much more than on the text. In Anno’s Journey, children and adults can talk out the voyage in time and space that takes place as we turn from one page to the next.

Two other wordless books that can get children using positional, sequential, and other words as they tell the story are Tomie dePaola’s Pancakes for Breakfast and an old but still available book by Mercer Mayer, A Boy, a Dog and a Frog. Changes, Changes by Pat Hutchins adds yet another twist. A single set of building blocks gets reconfigured as a block man and his wife build a house, use pieces from it to create a fire engine to stop the fire that destroys it, and then move off. They use a boat to get to a new land where they once again build their house. We’ve seen gifted block builders literally reconstruct the story page by page with their own set of blocks.

Some other stories that get told through pictures and with very minimal text can be used to develop and support the positional language that is so important to dual language learners (DLL). The Early Math Project has been using Rosie’s Walk by Pat Hutchins for years. In addition, Have You Seen My Duckling by Nancy Tafuri is a kind of “eye spy” game that will get children explaining exactly where the ducklings are hiding in the background of the picture.