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How Can Administrators Support Staff’s Understanding of Geometry?

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1 Mathematics Preschool Learning Foundations A Focus on the Geometry Strand.

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1 How Can Administrators Support Staff’s Understanding of Geometry?

2 Agenda The relationship between the NCTM Standards, the Preschool Learning Foundations and the DRDP-R The Research Exceptional Children--Division of Early Childhood Recommended Practices English Learner Strategies Taking It Back to the Classroom NCTM-Refers to National Council of Teachers of Mathematics.

3 Outcomes Become familiar with the mathematics foundations with an emphasis on the Geometry strand. Explain how the DRDP-R and the NCTM Standards relate to the mathematics foundations. Discover the research behind the practice. Explore strategies to make geometry come to life in the classroom. Plan for taking it back to your classroom. NCTM-Refers to National Council of Teachers of Mathematics.

4 Norms Start on time and end on time. Turn cell phones off.
Help the group stay on task. Listen to thoughts and ideas of others. Contribute your thoughts and ideas. Use this as a slide if you want and/or chart them.

5 Parking Lot Please write questions on post-its and place them on chart paper titled “Parking Lot.” Slide optional: Place a couple of parking lot papers in the room. Point out the FAQs in the folder and let participants know that there is time set aside during this session to read them more closely. Other questions they have may be posted in the Parking Lot. We will try to answer as many questions as possible. Any unanswered questions will be sent to CDD for answers.

6 Name That Shape Squares and circles, rectangles and triangles…but do you know the name of 3-D shapes? How many of the 3-D shapes on the next slide can your table identify? ICEBREAKER: 5-7 minutes. The purpose of this activity is intended to get table groups to introduce themselves and share knowledge. It also has a math focus and gets people thinking about math early in the presentation. Facilitator may want to share a personal experience with geometry and/or let the participants know they shouldn’t worry about getting them all right. There may be one or two shapes that you are unfamiliar with. Introduce yourselves and work in your table groups to see if you can come up with the answers.

7 sphere cone prism cylinder cube
Clicking will uncover the name of each shape in turn. Ask people what things in the world they know of that are like these shapes. For example: the earth is a sphere, dice are cubes, etc. cylinder cube pyramid cuboid

8 Mathematics Foundations
NCTM Topics Number and Operations Geometry Measurement Algebra Data Analysis & Probability Mathematics Foundations Number Sense Algebra and Functions (Classification & Patterning) Measurement Geometry Mathematical Reasoning The National Council of Teachers of Mathematics Standards (NCTM) was one of the documents that California reviewed and considered when developing the Preschool Learning Foundations. Share the NCTM Five Main Topics handout. Ask participants what they see on the handout. It includes the Desired Results, the ECERS, and the mathematics foundations. This is a snapshot of all the components in the CDD initatives and the NCTM Standards. When you click, lines will appear between corresponding categories and foundations. Although the categories are not exactly called the same thing, the intention or content is the same. The NCTM considers the most important strands to be Number and Operations and Geometry. The NCTM Standards are listed in a hierarchical order of importance. The foundations are NOT listed in a hierarchical order. Since California recognizes the importance of Geometry as well, it is the second math module we are rolling out this year. Some of you may have come to our Number Sense trainings in the fall. We did not have the final mathematics foundations at that time, but CDD wanted the ECE field to begin to focus on math content. We will be revisiting Number Sense next year and including the foundations in the Number Sense strand.

9 Peeking Inside the Mathematics Foundations
Walk through the handout - PLF document. This document also includes the other California CDD initiatives.

10 Ask participants to take out their publication and follow along with you.
Point out the icons on the spine of the cover. Identify what domain each icon represents. Point out the words Volume 1 on the cover. Explain that this volume contains the first four domains (the first four icons reading from the top of the page). Explain that Volume 2 will contain the next three domains (visual/performing arts, physical development, and health), and that Volume 3 will contain the last two domains (history/social science and science). Point out that the icons and their colors are used to identify domain sections inside of the book. We will look at the sections of the book on the next slide.

11 11 Purpose The purpose of the foundations is to promote understanding of preschool children’s learning and to guide instructional practice. READ and pause to give people time to think about this.

12 The Foundations… are for all children, including children learning English and children with disabilities. They describe the knowledge and skills that young children typically exhibit: at around 48 and 60 months of age; as they complete their first or second year of preschool; with appropriate support; and when attending a high-quality preschool program. Read Slide

13 High-Quality Programs Include
environments and experiences that encourage active, playful exploration and experimentation purposeful teaching to help children gain knowledge and skills specific support for children learning English specific accommodations and adaptations for children with special needs

14 How is the mathematics domain organized?
A Guided Tour How is the mathematics domain organized?

15 The Sections Introduction The Foundations Bibliographic Notes Glossary
References and Source Material As you present each bullet, you can tell a little bit about the sections. Introduction: It is important to realize that the introduction contains valuable information about the domain, including underlying assumptions and the use the foundations with children with special needs and with English-language learners. Foundations: The foundations describe what children learn. Today we will focus on one strand of the mathematics foundations. Bibliographic notes: These contain the research related to each domain’s strands. Glossary of terms: These are terms that are defined in each domain to support the understanding of the content. References: This section includes research upon which the mathematics foundations are based. There is a summary list of the mathematics foundations in the Appendix.

16 Map of the Foundations Mathematics
Domain Strand Substrand Age Foundation Examples Foundation Distribute the handout version of this slide to participants. This slide illustrates the way the foundations are organized. This example is the Geometry strand. Use a laser pointer to draw participants’ eyes to each part of the page. Point out: The name of the domain (mathematics) The name of the strand at the top of the table (in this case, Geometry) The name of the sub-strand (Children identify and use a variety of shapes in their everyday environment). Note that substrands always end in “.0”. The two levels (at around 48 months and at around 60 months). Remind participants that the foundation describes typical behaviors at around 48 months and at around 60 months. The foundations (there are TWO foundations on this page, ONE for each age level) 1.1 for 48 months and 1.1 for 60 months; 1.2 for 48 months and 1.2 for 60 months. The examples (reminder that these are only a few of the ways that children may demonstrate the foundation)

17 Foundations Organization
Domain Age Strand Substrand Foundation Note to presenter: This slide contains the same information as the previous slide. It is not new information, it is just organized differently to accommodate different learning styles of participants. This is a summary slide. You might ask those who attended an input session if any of these terms are familiar to them. You might ask them to read the words aloud as they fly in from the side. You can ask them to find it on their map. Examples

18 Strand - Substrand Order
There is a developmental progression from three- to four-years-old within a substrand. The order in which the strands and substrands are presented is not meant to indicate a developmental progression. Bullet 1: Read slide and then say, for example, in the Geometry substrand on page 158, “Children begin to understand positions in space” at around 48 months, and “Children expand their understanding of positions in space” at around 60 months. Bullet 2: Read slide and then say, for example, there is no developmental progression from the Number Sense strand to the Algebra and Functions strand ( Mathematics). In the strand Number Sense, there is no developmental progression between substrand 1.0 at around 48 months “Children begin to understand numbers and quantities in their everyday environment”, and substrand 2.0 “Children begin to understand number relationships and operations in their everyday environment.”

19 Bibliographic Notes This is a transition slide.
We are going to look at this section of the mathematics foundations more in depth.

20 Ready for a Challenge? Can you complete this crossword puzzle?
Answers can be found in the Bibliographic Notes from pages This is an activity and the handout will be in their folder. Purpose: Participants engage in a brief activity to demonstrate how the research is tied directly to the foundations.

21 Answer Key You can show this slide and hand out the answers as well. Using a printed copy is optional.

22 Foundations and the DRDP-R
How the Foundations and the DRDP-R Work Together Transition slide…

23 Foundations and the DRDP-R
At about 48 and 60 months A guide and teaching tool DRDP-R Developmental continuum An assessment tool It is important that people understand that the foundations describe the knowledge and skills that all young children typically exhibit: at around 48 and 60 months of age; as they complete their first or second year of preschool; with appropriate support; and when attending a high-quality preschool program. The DRDP-R is the observational assessment tool.

24 Foundations and the DRDP-R
At around 48 months 1.0: Children begin to identify and use common shapes in their environment. At around 60 months 1.0: Children identify and use a variety of shapes in their everyday environment. DRDP-R Note that the foundations describe what children can do at two discrete points in time, at about 48 months and at about 60 months. On the other hand, the assessment tool, the DRDP-R, describes preschool children’s development on a continuum: not yet, exploring, developing, building and integrating as well as emerging, allowing teachers to pinpoint where along the entire continuum a child is at in their development.

25 Geometry It’s more than shapes!

26 Geometry - It’s More Than Shapes
Locations, Directions, and Spatial Orientation Visualization and Spatial Reasoning Transformation and Symmetry Source: NTCM Showcasing Mathematics for the Young Child pages 56-57 1st bullet: Shapes refers to identifying shapes, naming shapes, building shapes. IMPORTANT NOTE: Children learn about shapes during the preschool years, and their concepts of shapes stabilize as early as age six (Clements 1999). 2nd bullet: Preschoolers explore space and learn about the properties and relationships of objects in their environments. How many of you have created or seen children create maps of the classroom or outside areas? This is what we are talking about. 3rd bullet: Spatial reasoning and visualization involves creating mental images of geometric objects, examining the objects mentally, and transforming them. We will do some activities related to this concept later in our presentation. (This is in the feely box game and the showing-the-picture and having-them-draw-it activity.) 4th bullet: Transformation and symmetry can be seen when children build with geometric shapes. They slide, rotate and flip shapes to determine whether they match (Clements 2004). Children use transformation when they solve puzzles that require them to build a shape from smaller shapes.

27 California Preschool Learning Foundations
“Geometry is the study of space and shape (Clements, 1999). Geometry and spatial reasoning offer a way to describe, interpret, and imagine the world.” Source: Preschool Learning Foundations, Bibliographic Notes, page 164 Today our focus is on Geometry.

28 Geometry Research Clements, D. H., Sarama, J., & DiBiase, A.-M. (Eds.). (2003). Engaging Young Children in Mathematics: Standards for Pre-school and Kindergarten Mathematics Education. Mahwah, N.J.: Lawrence Erlbaum Associates. The following information is based on a presentation by Dr. Doug Clements at a CPIN meeting in May 2007. Talk a little bit about the work Dr. Clements has done with CPIN in the past 2 years if you want. Show the book and give a brief explanation of the book and the work you have done with the book. Maybe share some of the highlights you enjoyed reading about.

29 Young Children and Shape: Two Studies
Hundreds of children, 3 to 6 years old First study used same tasks as used in previous research with older students This information comes from a study done by Dr. Doug Clements and Dr. Sarama with 100’s of children. In this study 3-6 year olds were given a task to identify shapes. This was the same task given to year olds. The intent of the study was to compare 3-6 year olds to older children. The task may not look developmentally appropriate because it was a pencil and paper task. However they had to replicate the study by having all children do exactly the same task. Dr. Clements recognizes that this is not the kind of task you would do in a classroom with young children.

30 Circles Correctness 92% - 4 year olds 96% - 5 year olds
Few youngest chose ellipse and curved shape Described as “round” Thus, easily recognized but difficult to describe Matched shapes to visual prototype Children were asked to find all the circles. In the preschool version there were no numbers in the shapes, on the assessor’s version there were numbers. It was known that children can identify one shape correctly. For example, if I had a bowl and showed it to a child, the child would say it is a circle. When the child is given lots of shapes it is harder to find all the circles. These children were from Buffalo, New York who came from lower socio-economic background. 92% represents the average correctness for 4 year olds, 96% for 5 year olds and 99% for 6 year olds. For the younger children, this was prior to school instruction. Some of the errors included missing the little circles, or identifying example 11 as a circle. (Laser point to #11 if you can.)

31 Squares Only slightly less accurate in identifying squares: 82%, 86%, and 91% Youngest lower on nonsquare rhombi but not on “tilted squares” Minority reasoned about properties, but was relationship between such responses and correct selections The scores were a little lower for squares. Some of the responses included: Children did not include #3 as a square. They would say it is a rhombus or a diamond. The older children would say #5 is a diamond when it is really a square turned on its side.

32 Triangles Task Lower, but not low: about 60%
Property responses present, but only 18% Inverse-U pattern: 5’s more likely than 4’s or 6’s accept both non-standard triangles and those with curved sides Triangles were lower. For example, #5 looked like a triangle even though it has squished sides.

33 Rectangles Slightly more than 50%
4’s were more likely to accept the squares All accepted “long” quads w/ pair of parallel sides #3, 6, 10, and 14 Properties less frequently Rectangles even lower. #6 isn’t a rectangle. Children would say it was and that it is just on its side.

34 Compare to Elementary—Rectangles
These are the results of the preschool age compared to the elementary age study identifying shapes. What strikes us about this graphic is that the gap is low between the ages, but the gap is higher when you look at socio-economic status. It is basically a flat graph. Now let’s look at triangles. CLICK to NEXT SLIDE.

35 Compare to Elem.—Triangles
This tells us something about what children know when they come to school. Children know a lot about naming shapes, but the interesting thing is that naming shapes should not be what children are doing in 6th grade. This graph says that we are not doing much to teach children more than naming shapes as they move through the grades.

36 What Children See Ring the triangle
Here is a sample of a second grade workbook page from 20 years ago. The direction was to ring the triangles. The hanger is circled as the example. It is not a triangle because it has a hook. The musical triangle is not a triangle because it is open at the top. The sailboat is a pentagon. If you circled just the sails it would be correct. This worksheet doesn’t differentiate between 2-D and 3-D shapes. IMPORTANT TO STRESS THAT WE ARE NOT ADVOCATING WORKSHEETS IN PRESCHOOL. THE INTENT OF THIS SLIDE AND THE NEXT SLIDE IS THAT ELEMENTARY SCHOOL MATHEMATICS AND PUBLISHERS ARE AT TIMES INACCURATE.

37 What Children See More recent, but not more mathematically precise
Here is a more recent worksheet and it is a bit better but… The ball is not a circle. It is a sphere. On paper it looks like a circle except for the way they illustrated it. If you flattened a ball it would not make a circle. Again the musical triangle has an opening…a triangle is closed at the corners. It is important to get children to think precisely. We are not saying they will get into trouble if they say a musical triangle is a triangle. However we want to use precise language when we are talking about shapes. For example, a slice of pizza is not a triangle…it is a section of a circle. It has 2 straight sides and one curved side and when you put it together with other slices it makes a circle. IMPORTANT TO STRESS THAT WE ARE NOT ADVOCATING WORKSHEETS IN PRESCHOOL. THE INTENT OF THIS SLIDE AND THE NEXT SLIDE IS THAT ELEMENTARY SCHOOL MATHEMATICS AND PUBLISHERS ARE AT TIMES INACCURATE. It is important that we DO NO HARM! We must be more precise.

38 Geometry Must Move Beyond “Basic” Shape Naming to:
Parts & Properties Shape attributes Include analysis and description Mental images and transformations Composing and decomposing We have to do naming right. We must be precise in our own language. We have to provide experiences that help children create mental images and transformation with shapes. All of math is about composing and decomposing, in Number Sense it is adding and subtracting, etc. Geometry uses shapes to create things in art, architecture, math, and science.

39 Learning Trajectory for Shapes
Shape Matcher Shape Prototype Recognizer Shape Recognizer Side Recognizer Angle Recognizer Shape Class Identifier If you remember learning trajectories for counting, these are a similar idea. Learning trajectories are like a developmental continuum for learning about shapes. REFER TO CLEMENTS LEARNING TRAJECTORY HANDOUT. 1. It is what it sounds like; matching basic shapes with the same size and orientation. Then, there is a second level which matching same basic shapes with a different size. Third level within this category is matching shapes with different orientation. 2. Child recognizes and names protoypical circle, square, and typical triangle. Recognizes unusual shapes. Child names some things as a rectangle when they are really a parallelogram. (SUGGEST YOU DRAW A PARALLELOGRAM ON CHART PAPER OR WHITE BOARD.) 3. Child recognizes some non-prototypical squares and triangles and may recognize some rectangles, but usually not a rhombi (diamond). 4. Recognizes more different shapes: rectangle sizes, shapes, and orientation of rectangles. Identifies sides as distinct geometric objects. Matches angles concretely. Recognizes hexagons and trapezoids. Names most common shapes and knows fancy shapes including rhombi. Recognizes angles as separate geometric objects. This level is beyond preschool.

40 With an elbow partner, take a moment to compare the learning trajectory for shapes with Measure 24 on the DRDP-R. How do they compare?

41 Geometry and Spatial Sense
Remind the group that you spoke about spatial sense earlier when you talked about geometry being more than shapes. Ask them to get a piece of paper and that you are going to show them a picture for 2 seconds and they will draw what they see.

42 Geometry Snapshots Ready…?
When you are in slide show mode only the words will appear You have to click to get the graphic. Show this slide for 2 seconds. Draw what you see? Ask them what they drew? Some people will say they saw 3 triangles, or an envelope, or 1 large triangle and 2 small triangles. Tell audience that it is important to only show it for 2 seconds and then show it a second time. This is an activity that would be done with kindergarten and first grade. The intent is getting children to talk about what they see. Did they see it as line drawings or shapes within the line drawings. This gets children thinking. It forces us as adults to see it differently. It forces us to reprocess information. Prepare them for next slide by asking them to get out a few pattern blocks. Geometry Snapshots Ready…?

43 Snapshots with Pattern Blocks Ready…?
Let’s try this…The second clip brings the graphic up. To make graphic disappear after 2 seconds push the back button. Show briefly. Ask, “What did you see?” Now build it with the pattern blocks. This activity is down with a teacher and small group of children. The pattern block design is on the rug or table with a towel over it. The towel is pulled back for 2 seconds. Give children 2 peeks. Some will say a clown blowing a bubble or a fish, or a person at a party blowing a horn. This is important because again, children are building imagery just like in the previous activity. Use more than pattern blocks, as often children refer to them by color since hexagons are always yellow in pattern block. So instead of saying “hexagon”, they say “the yellow one.” Snapshots with Pattern Blocks Ready…?

44 Learning Trajectory for Composing Geometric Shapes
Pre-composer Picture maker Shape composer Substitution composer NOTE TO TRAINERS: The trajectory handout is used again here. The information you want them to look at is in the right column. Remind the participants that a learning trajectory is like a developmental continuum. Pre-composer--Manipulate shapes as individuals, but unable to combine them to compose larger shapes Picture maker-- Puts several shapes together to make one part of a picture. Uses “pick and discard” strategy. Shape composer-- Combines to make new shapes with anticipation. Choose shapes using angles as well as side length. Intentionality “I know what it is!” Substitution composer-- Finds different ways to fill a frame emphasizing substitution relationships.

45 DRDP-R Measure 24: Shapes Developmental Levels
When we look at the DRDP-R Measure 24 we see that the Building and Integrating Levels are included in the Composing section of this presentation. The learning trajectories match up with this idea of composing and decomposing.

46 Books Shape Flip Book! The Greedy Triangle Mirror books
The Shape of Things Dot and Line (What other books do you know about?) Ask the group for their suggestions for additional books they have used for geometry concepts.

47 Shape Set Activity Designed based on research and wisdom of expert practice Consistency: Pattern blocks, tangrams Diversity: Circles and sections, different rectangles and triangles, other shapes This activity comes from: Clements, D. H., & Sarama, J. (2007). Building Blocks-SRA Real Math, Grade PreK. Columbus, OH: SRA/McGraw-Hill. If you have these blocks let participants take them out of the bag and play with them. There is a handout with all the shape names that you can place on the table with the bag of shapes. The upper right section are what you would find in a set of pattern blocks. Hold them up as you name them, (triangle, rhombus, diamond, square, hexagon, trapezoid). These shape sets include more than what you see in pattern block sets which are important to have in the classroom. Pattern blocks are always the same color and same size which makes them great for patterning. Point to the shapes in the upper left section of the slide. These are tanagram shapes which may be familiar to you. These Shape Sets are made of foam so they are quiet. Each shape comes in yellow and blue and different sizes. Children need to experience these other shapes as well and children learn that shapes come in different sizes and orientations. In the classroom you would introduce these block a few shapes at a time. Not the entire bag. Clements, D. H., & Sarama, J. (2007). Building Blocks-SRA Real Math, Grade PreK. Columbus, OH: SRA/McGraw-Hill.

48 Geometry in the Classroom

49 Let’s Play Use the materials on your table and the direction card to play the game. You have 20 minutes to play the game and to identify what foundations the game addresses and what kind of documentation you might gather to demonstrate children’s growth and development. Share your game with the group. Purpose: The intention of this activity is to help participants see what it looks like in the classroom and connect research to practice. After the EL & Special Ed part of this presentation, participants will be asked to adapt the game for children with disabilities and create strategies for EL students as well. Ask participants to pull the Geometry Games Worksheet from their folder to use in this activity. Click to next slide which shows the handout. IT IS STRONGLY RECOMMENDED THAT THIS WORKSHEET IS DONE AS A CHARTING ACTIVITY.

50 Let’s Play Ask participants to also complete the prompt indicating what foundation(s) this activity addresses and what documentation of growth and development they might be able to gather to document children’s growth on specific DRDP-R measures. Participants DO NOT complete the Children with Disabilities section or the EL Learner section.

51 Council for Exceptional Children Division of Early Childhood (DEC) Recommended Practices
Explain who the Council for Exceptional Children is and what they do. The following slides come from a book called DEC Recommended Practices. Click to next slide - the book cover is in the slide. Ask participants to refer to their handout.

52 Division of Early Childhood
Practices are individualized for each child based on: child’s current behavior and abilities across relevant domains instead of the child’s diagnostic classification the demands, expectations, and requirements of the child’s current environment team planning that incorporates the input of family and various providers staff knowledge of validated strategies including prompting and fading procedures to ensure acquisition of skills IEP consideration and/or requirements DEC Recommended Practices, 2005 This information comes from DEC Recommended Practices which was published in 2005. Have copy available to hold up or put on display. Adults design environments to promote children’s safety, active engagement, learning, participation, and membership in the group. Adults use ongoing data to individualize and adapt practices to meet each child’s changing needs. Adults use systematic procedures within and across environments, activities, and routines to promote children’s learning and participation. Also, consider ramifications of the diagnosis and plan accordingly.

53 Division of Early Childhood
Physical space and materials are structured and adapted to promote engagement, play, interaction, and learning by attending to children’s preferences, interests, using novelty, responsive toys, providing adequate amounts of materials and using defined spaces. DEC Recommended Practices, 2005 The important point is that we want to provide opportunities for children to access the preschool curriculum. So we must consider the physical space and the materials and make whatever adaptations are needed to create this access.

54 Preschool Learning Foundations and Children with Disabilities
Where in the Geometry strand can you find information about children with disabilities? What does it say about children with disabilities? Give participants 5 minutes to look through the geometry strand and see if they can find the footnote that is related to this question. Have them discuss what it says in the footnotes. The footnote is on page 157. Chart their responses. The next slide is a wrap up slide and you can compare their responses to the slide in case they missed anything. Tell them that this footnote appears throughout the math foundations. So, the information in the footnotes is important.

55 Geometry Foundations and Children with Disabilities
Children may need: assistance to manipulate objects adaptive materials that are easy to grasp to demonstrate knowledge in alternative ways without directly manipulating objects clearly defined work space materials that are easily distinguishable by touch Preschool Learning Foundations, page 157 This is a wrap up slide to the Special Ed information. People should have shared most of these ideas from the footnote. No need to spend a lot of time if the group found them and shared with the large group. Tell them you will give them an opportunity to put this information into practice by revisiting their game worksheet.

56 Revisit The Name Game What adaptations might you try to make your game more accessible to children with special needs? Record your ideas in the space provided. Purpose: To connect DEC and special education information to the games, but also to inform participants that there is information in the foundations that addresses children with disabilities. Ask them to also look at the handout and the section that says “Supporting All Learners.” There are additional strategies there that may be helpful when the revisit their game. Ask them to get their worksheet out and revisit the game to make suggestions for adaptations. RECORD THEIR IDEAS ON CHART PAPER THAT YOU HAVE ADDED TO THE ORIGINAL CHART. Consider what it said in the footnotes of the foundations in the Geometry strand. Once they have begun this work go back to the previous slide. Walk around and see how they are doing. Give people 10 minutes to do this. Do a Carousel Walk or ask a few people to share their strategies after they complete the EL section of the chart.

57 Preschool English Learners
Transition slide.

58 Walk and Talk Misconception: Math is about numbers, therefore, understanding the language of instruction isn’t so crucial. Reality: Math is abstract in nature and requires specific vocabulary to talk about it! The purpose of this activity is to connect EL Guide information to foundations, as well as other resource materials to the games. Partner into groups of two or three. Walk around for five minutes discussing how this reality impacts mathematical achievement of English-language learners. Facilitator—add the following if not brought out by participants: Exposure alone is not enough: -informal through play -formal through explicit guidance to take them to the next level -connect what they are doing -with thinking in a mathematical way (ultimately for success in school math later in K) Ask the child “Why? How do you know?” The child’s thinking will be revealed in what he/she says. Example: colored bears -a pile on the table, not necessarily a math activity -language comes in -need labels (single words), vocabulary, and formulas (meaningful chunks or phrases) such as “more than – not enough” to play in a mathematical way -for a pattern prompt: What would you put next? (2 red bears, 2 yellow bears, 2 red…)

59 Through using language creatively and interactively, children develop the thinking necessary to communicate mathematically to solve real problems with their everyday experience. Link to page 4 from English Learner Guide page 40 “Language development and learning are promoted when preschool teachers and children creatively use language.” Example: How much glue? Quantity and estimation You know how fun that traditional white sticky Elmer’s glue can be for all ages. Know of a teacher that made up a jingle – using language creatively, telling the children “just a touch, not too much” “un poquito, pegadito.” Rhyme the ending chunk, great for phonemic awareness, and fun to say.

60 Scaffolding as a Strategy
When children are given opportunities to build on their existing knowledge base, words in their new language are more easily mastered because they are linked to familiar concepts.

61 Minor Adjustments Check for understanding.
It is more than eye contact. Use of primary language, use of icon, use of actual object. Use follow-up questions. Create situations where the child can be successful. Mand Modeling-asking open-ended questions that give the student a chance to describe the situation, content, or context. Reinforce the child’s attempts to communicate.

62 PRINCIPLE 1 The education of English learners is enhanced when preschool programs and families form meaningful partnerships. PRINCIPLE 2 Children benefit when their teachers understand cultural differences in language use and incorporate them into the daily routine. From Preschool English Learners - A Resource Guide, CDE Press 2007 Reference the English Learner Guide. Have it on display so you can hold it up. Survey participants for those who have attended an English Learner Guide training. There are 10 Principles referred to in the EL Guide. We will focus on 4 today. Volunteers read aloud to whole group. If you have an EL Guide Training coming up in your region, announce date and place. Let them know they can purchase the EL guide along with companion DVD from CDE Press. Provide a brochure for ordering information.

63 PRINCIPLE 4 Language development and learning are promoted when preschool teachers and children creatively and interactively use language. PRINCIPLE 6 Continued use and development of the child’s home language will benefit the child as he or she acquires English. From Preschool English Learners- A Resource Guide, CDE Press 2007 -Volunteers read aloud. Make the “talking” and “thinking” connection.

64 Mathematical Vocabulary
Determine the proficiency levels of each English- language learner in the classroom. Identify key vocabulary words and phrases to introduce and use in your lesson with English-language learners. -Proficiency is dynamic and can improve at different rates for different children. Not all ELLs are the same. (Briefly refer to handout in folders on stages of language acquisition. Taken from Chapter 5, page 46 of English Learner Guide) Model the stages using the example of a child requesting more juice. - Home language: “Quiero mas jugo!” -Observational /listening: child may appear to be passive or shy, but in reality is working very hard on comprehension. -Telegraphic/formulaic speech: “Want juice!” (fewest amount of words to get meaning across) -Fluid language use: “Can I have some juice please?” In a different context, the child may exhibit behaviors from a different stage (affective filter). Identify … You will have an opportunity to do this shortly.

65 Nine strategies for working with English-language learners
Refer to Mathematics in the Early Years. Have it on display so you can hold it up. Review the article in Chapter 23 by Laurie Weaver and Catherine Gaines, What to Do When They Don’t Speak English. The next specific nine (9) strategies are taken from this article. Adapted from Mathematics in the Early Years, edited by Juanita Copley, 1999.

66 Strategies 1, 2, 3 Modify language. Use manipulatives.
Use modeling and gestures. The following information comes from pages in the book Math in the Early Years. Modify language (use concise language, precise pronunciation, avoid idioms and slang, shorter sentences, emphasize concrete vocabulary). Keep it cognitively demanding. Use manipulatives (everyday objects, visuals, examples of what is being talked about, compatible with natural/intuitive learning). Use modeling and gestures (act out what you say, what you expect them to do). Demonstrate, first without scaffolds. (Tira el dado, cuenta los puntitos, cuantos son: w/scaffolds.)

67 Strategies 4, 5, 6 4. Use oral descriptors.
5. Respect the observation and listening time. 6. Match questions to the child’s proficiency level in English. 4. Use oral descriptors. Narrate what is happening. Example: (page 200 in the book-read from text) putting on a shirt, language parent uses. Describe completely—the parent uses “shirt, sleeve, arm, other arm, etc.” rather than “hurry up and get dressed.” 5. Respect the observation and listening time. In the book it is referred to as the silent period, but we no longer use that terminology. -Allow children to listen and choose when they are ready to speak. -Scaffold with peer interpreting. -Tell the EL child directly. Note: Receptive ability is greater than expressive. -Even in home language, they are thinking and talking about the concept. Match questions to the child’s proficiency level in English -observational, elicit actions Example: point to, show me, make, put, do… -eliciting higher-level thinking 6. Match questions to the child’s proficiency level in English—if the child is not yet speaking to you in English, elicit actions from them that demonstrate their understanding of the math concept, rather than expecting him/her to speak. Ex: point to, show me, make, put, do… Don’t avoid eliciting higher level thinking tasks. If you want to ask them why they did something one way or how they know, ask them and then tell them to tell their peer and this is what we want.

68 Strategies 7, 8, 9 Incorporate the child’s first language.
Consider cultural issues. 9. Connect with parents and math in the home. 7. Show that you value their home language – okay to use it, learn simple greetings, count to 5 – fun! Enlist help of fluent speakers (Link to page 6 from English Learner Guide, page 43 “Continued use and development of the child’s home language will benefit the child as he or she acquires English.”) Regardless of the program goals, home language is important for the child’s development. -anchor, link, promotes optimal learning (Research base supports this: Cummins ’96, Burnham-Massey, Pina ’90, Ramirez ’90 and others) 8. Be careful of making assumptions. -think EL child doesn’t understand, yet simply unfamiliar, eventually do learn Consider how familiar they are with this and help them by scaffolding. Ex: fork and spoon not necessarily common in young immigrant families Ex: methods of counting – differences in finger order -incorporate multicultural literature -invite family members in (Link to page 2 from English Learner Guide, page 28 “Children benefit when their teachers understand cultural differences in language use and incorporate them into the daily routine.”) Connect with parents and math in the home. -a lot of math happening in the home. Help parents become aware of how they can talk with their child to encourage math thinking. -provide vocabulary links to L1 w/classroom -post it, at sign in, newsletter (Link to paragraph 1 of English Learner Guide, Chapter 2, page “The education of English Learners is enhanced when preschool programs and families form meaningful partnerships.”) Note: Participants might need to address the notion of “confusion” when the child hears the information in two languages. Explain Cummins common underlying proficiency principle. Parents might ask this. They need support and education to understand about the developing bilingual child.

69 One More Time Revisit the Name Game
How might you adapt your game for English-language learners? Record your ideas in the space provided. The purpose of this activity is to use the knowledge from the previous set of slides to consider what needs to be done to support EL learners. Ask them to use their Supporting All Learners handout to help complete this and the ppt slides previously shown. CHART responses giving them about 10 minutes to do this. When done either have them share out their strategies or do a Carousel Walk to complete this activity. You can also ask the group if some of the EL strategies that you just shared would be good strategies for children with disabilities…what about for typically developing children?

70 Q & A

71 CDE Web site At the Web address, the underlined Preschool Learning Foundations link takes you to the publication. There you will have easy access to the chapters and sections within the 192 page publication. The Appendix, on pages , provides a summary list of the foundations. Frequently Asked Questions (FAQ) are posted on the website. Questions can be sent to Read the first bullet. Web handout On page in the Appendix, you will find a summary list of the foundations, excluding the examples and other material. Hold one up to show how small it is. Remind them that the preschool foundation’s address on the previous page is also on the CDE Web site. Many questions were asked during the extensive public review process. CDE has developed a set of Frequently Asked Questions to provide the answers to those questions. The Frequently Asked Questions (FAQ) document is a living document. Over time, new questions will be added and existing responses may be clarified as needed.

72 The entire document is online at the California Department of Education Web site. You can look at a specific section or download the entire document. This slide shows the way the web page is designed. The Appendix contains a summary list of the foundations, excluding the examples and other material. The foundations are also available for purchase through CDE press.

73 To Purchase The Preschool Learning Foundations publication is available for purchase from the CDE Press for $19.95. Ordering information can be found at the CDE Web site or by calling Remind participants that there is a handout in their folder with ordering information.

74 Bringing it Back to the Classroom
Share information from today’s session. Include the research and the importance of Geometry. Provide some of the resources shared today and give teachers time to read and discuss the information. Host a math make and take workshop providing all the materials and time needed for teachers to make games. Focus on making small changes guided by a consistent, coherent, grand vision. Allow teachers to learn and reflect on new approaches, implement them, and discuss. Provide teachers with high-quality mathematics references and classroom materials.

75 Action Plan Talk to your elbow partner to create an
action plan for supporting your staff and their professional development. Tell them they are going to talk to elbow partner to discuss this and use the action plan handout in their packet. But before you start…I would like you to consider these things…NEXT SLIDE.

76 Topics for Discussion How does this fit with our current experience and knowledge? What are the barriers to implementation? What more do we need (geometry materials, model strategies)? What are realistic expectations for Geometry content for providers? Are there special considerations for English-learners? How does this information impact children’s IEP goals? Read through and leave up during their conversation.

77 Thank you for coming Put your CPIN information here.
Announce next event.

78 Evaluation Please complete your evaluation.
Put your specific procedure here.

79 Optional Slides These should not be included in the ppt notes! Doug has given permission to show them but not to print them out.

80 For those still skeptical…

81 Is Mathematizing Appropriate?
Preschool math is not recent phenomenon. Historical pattern of appropriate, interesting mathematics from Froebel, to Montessori to today’s research.

82 Geometry in the World Pat H.’s preschool was studying bees.
Children noticed the hexagon. T: Why do you think they chose? C1: It popped in their heads. C2: They found one under a tree. Let’s see some of the others… Geometry in the World

83 There are several of these slides that show up when you are in slide show mode.

84 St. Jerome, Divinci Geometry in the World

85 Geometry in the World

86 Geometry in the World

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