California Preschool Instructional Network (CPIN). 05/2013

California Preschool Instructional Network (CPIN). 05/2013
California Learning Foundations and Curriculum Framework Presents: Number Sense ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). 05/2013

Outcomes Participants will become aware of key concepts to be developed in the Number Sense strand of the Preschool Learning Foundations (PLF). Participants will become aware of key strategies in the Preschool Curriculum Framework (PCF) regarding Number Sense development.

Who is here today? Present Absent Who is Here Today?
INTENT: Participants interact with one another and think about math during a warm-up activity. OUTCOMES: Participants will observe a welcome activity that involves math and have the opportunity to connect that activity to math concepts. MATERIALS REQUIRED: Chart paper with “Who is Here Today?” T-chart, Character stick puppets, PPT notes, Handout 1: Who is Here Today Activity Plan TIME: 10 minutes PROCESS: Prior to the training put the math character stick puppets on the tables. Keep the puppets that ARE NOT present at the front (e.g., Negative Nelly).Welcome participants to the math training. Tell participants, “The first thing we are going to do is take attendance.” Draw participants attention to the “Who is Here Today?” T-chart. Tell participants, “I am going to call roll. If you can help me out by letting me know which characters are here for the math training today I would appreciate it.” Begin by modeling with co-trainer. Ask out loud, “Is Ms. Marvel Math here today?” Co-trainer says, “Oh yes, here she is,” and takes puppet to the T-chart. Continue asking who is here by reading down the character list, with all the characters being placed on the T-chart. Integrate the characters who are NOT present (these will be in the front with you. Debrief: Following completion of the list say, “Alright, let’s count how many characters are here today for the math training. How many aren’t here?” Have participants think about what other math questions could be asked. How might participants adjust this activity for their classroom? What do they like about it? Explain how this activity integrates a deeper level of math for calendar time and that it can be useful for all age levels. Refer to the Who is Here Today Activity Plan (Handout 1), provided by Lorraine Haas, for a specific example of how to do this in the classroom. SUMMARY: Participants will participate in activator activity.

Early Learning Development System
Briefly go over the 5 elements. Element 1: At the center of the system are the Learning and Development Foundations which describe the learning and development infants and toddlers typically demonstrate with appropriate support at around 8, 18 and 36 months. It also describes the learning and development for preschool children that is typically demonstrated with appropriate support at around 48 and 60 months of age. Having statewide foundations provides all teachers and programs with knowledge of the expectations and goals for children in California to use as they plan activities, the environment, and interactions. Element 2: Infant and Toddler and Prekindergarten Learning and Development Guidelines present information about how to provide high-quality early care and education, including recommendations for program policies and day-to-day practices that will improve program services. In addition, the Preschool English Learner Guide provides teachers with the knowledge and tools they seek to educate preschool English learners most effectively. Element 3: The first and second volumes of the Curriculum Frameworks. These publications are a resource for teachers to support setting up environments, selecting appropriate materials, supporting children’s self initiated play and learning, and planning and implementing teacher guided learning activities. The frameworks are not a curriculum. Element 4: The fourth component of the system is the Desired Results System. It is a continuous improvement system that is intended to improve program quality. The system consists of: the Desired Results Developmental Profile© which measures children’s progress towards the Desired Results, the Parent Survey which measures parents’ satisfaction with the program, the Environment Rating Scales which assesses the classroom environment, and the Program Self Evaluation which assesses program quality. Element 5: In California, numerous professional development opportunities are available to assist programs. These include the Program for Infant/Toddler Care (PITC), California Preschool Instructional Network (CPIN), California School- Age Consortium (CalSAC), Family Child Care at Its Best, the mentor programs, pre-service, the CDE/ECE Faculty Initiative Project, the Child Development Training Consortium and the Desired Results Training and Technical Assistance Project.

Two California Department of Education Resources
We will be using two CDD resources during this session. (Click to reveal Preschool Learning Foundations, Volume 1) This is the Preschool Learning Foundations, Volume 1 (PLF). The foundations describe how children develop, grow, and learn. The preschool foundations are for all children and reflect the diversity found in California. (Click to reveal Preschool Curriculum Framework, Volume 1) This is the Preschool Curriculum Framework, Volume 1 (PCF). This framework presents strategies and information to help teachers enrich learning and development opportunities for all of California’s preschool children.

Domain Organization The Number Sense strand refers to concepts of numbers and their relationships. It includes the development of counting skills, the understanding of quantities, recognizing ordering relations (which has more, fewer, or less), part-whole relationships, and a basic understanding of “adding to“ and “taking away” operations. PCF, Vol.1, p. 239

Common Core NCTM Alignment
California Learning Foundations Number Sense Understanding Number Quantity Understanding Number Relationships and Operations Common Core Standards NCTM Focal Points for Prekindergarten Common Core NCTM Alignment The three resources above outline key elements of early Mathematics. Notice the similarities. Today we will focus on the California Learning Foundations; but closely related are the Common Core Standards and the NCTM Focal Points. For more information see the Handout 2: NCTM Focal Points for Prekindergarten.

Hearing From the Experts
“Children possess and build mathematical competencies from their first year and keep on learning mathematical ideas throughout their preschool years.” Clements, D.H. & Sarama, J. “Creative Pathways to Math,” Scholastic Early Childhood Today Journal, 2003. Push the Blue words “Dr Clements Says” to connect to a You-Tube Video: <iframe width="560" height="315" src=" frameborder="0" allowfullscreen></iframe> Dr Clements Says

Trends in International Mathematics and Science Study 2011
Forward Growth Compared with 1995, the U.S. average mathematics score at grade 4 was 23 score points higher in 2011. Compared with 2007, the U.S. average mathematics score at grade 4 was 12 score points higher in 2011. International Comparisons At grade 4, the United States was among the top 15 education systems in mathematics. At grade 8, the United States was among the top 24 education systems in mathematics. Chart Explaining 2011 Trends. Forward Growth: Compared with 1995, the U.S. average mathematics score at grade 4 was 23 score points higher in 2011 (541 v. 518). Compared with 2007, the U.S. average mathematics score at grade 4 was 12 score points higher in 2011 (541 v. 529). International Comparisons: At grade 4, the United States was among the top 15 education systems in mathematics (eight education systems had higher averages and six were not measurably different) and scored higher, on average, than 42 education systems. At grade 8, the United States was among the top 24 education systems in mathematics (11 education systems had higher averages and 12 were not measurably different) and scored higher, on average, than 32 education systems. NOTES: The 8 education systems with average mathematics scores above the U.S. score were Singapore, Korea, Hong Kong-CHN, Chinese Taipei-CHN, Japan, Northern Ireland-GBR, North Carolina-USA, and Belgium (Flemish)-BEL For a full report go to: Full Report

International Growth Over Time
Highlights: Unites States changed an average of 23 points in overall score Portugal changed an average of 90 points in overall score The Czech Republic changed an average of -30 points in overall score The change in average score is calculated by subtracting the 2007 or 1995 estimate from the 2011 estimate using unrounded numbers. Highlights: -Unites States changed an average of 23 points in overall score -Portugal changed an average of 90 points in overall score -The Czech Republic changed an average of negative 30 points in overall score Full Report

FRAMEWork Quote However, children’s intuitive sense of number does not imply that everything they need to learn about numbers and operations comes naturally. PCF p 241 Children enter preschool with an intuitive understanding of number and operations and with a natural curiosity and eagerness to learn about numbers. PCF, Vol.1, p. 241 ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). 05/2013

Foundations At 48 and 60 months After 1st or 2nd year of preschool
With appropriate support High-quality program ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). 05/2013

Map of the Foundations Handout 3: Foundation Map: The foundation map provides a snapshot of the foundation organization. Turn to page 159 of the PLF to following along. Handout 4: Foundation Chart: The foundation chart provides another way to take notes on the foundations. Throughout the day we will continually return to this chart to add ideas and compare between the month foundations. Activity: Plan Chart Note Taking INTENT: Participants become familiar with the math foundations. OUTCOMES: Participants will examine the foundation map and become aware of the terminology used. Participants will compare the age level progression within the math foundations. MATERIALS REQUIRED: Handout 3: Foundation Map, Handout 4: Foundation Chart, PPT notes, Preschool Learning Foundations (PLF) TIME: 10 minutes PROCESS: Show participants the foundation map on the PPT screen. Highlight each term of the foundations and invite participants to follow along in their book (PLF). Ask participants to look closely at the foundation map and compare the growth between 48 and 60 months. Participants take out Handout 4: Foundation Chart, and write down anything they notice as important, especially within the progression between months. Share that Handout 4 will be a document we return to frequently throughout the training. It can be used to take notes and keep ideas about the foundations. Provide three-five minutes of time to navigate the map and the foundations, and to take notes. Ask participants to share what they have noticed. SUMMARY: Participants become familiar with the Foundation Map and Foundation Chart.

Curriculum Framework Guiding Principles Research Highlights Routines, environments, and materials Vignettes Interactions and Strategies Topics in the PCF include guiding principles (in particular, the vital role of the family in early learning and development); the diversity of young children in California; and the ongoing cycle of observing, documenting, assessing, planning, and implementing curriculum. The framework takes an integrated approach to early learning and describes how curriculum planning considers the connections between different domains as children engage in teacher-guided learning activities. PCF, Vol. 2, Message from the State Superintendent, p. v Examples of each are listed on the following pages: Guiding Principles: PCF, Vol. 1, p. 233 Research Highlights: PCF, Vol. 1, p. 251 Routines, Environments, and Materials: PCF, Vol. 1, p. 237 Vignettes: PCF, Vol. 1, p. 243 Interactions and Strategies: PCF, Vol. 1, p. 244 ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). 05/2013

Guiding Principle Two Guiding Principles: Support English learners in developing mathematical knowledge as they concurrently acquire English. PCF, Vol.1, p. 235 Teachers should be aware of the challenges faced by children who are English learners and apply specific instructional strategies to help children learning English acquire mathematical concepts and skills. To provide children who are English learners with comprehensible information, they should simplify the terms they use, make extensive use of manipulatives, illustrate the meaning of words by acting and modeling whenever possible, and encourage children to use terms in their home language. PCF, Vol.1, p. 235 Dual Language Teacher Strategy INTENT: Participants apply teacher strategies for dual-language learners to Math development. OUTCOMES: Participants will consider the specific needs of dual-language learners through the lens of mathematical development. Participants will become familiar with teacher strategy resources, and will use them to guide their thinking. MATERIALS REQUIRED: Handout 4: Foundation Chart, Handout 5: Teacher Support Strategies, PPT notes, Preschool Learning Foundations (PLF), Preschool English Learners Resource Guide (PEL) - As a reference TIME: 10 minutes PROCESS: Read quote on PPT slide. Invite participants to consider how that might be enacted within their programs (currently or in the future). Share discussion points: “Teachers should be aware of the challenges faced by children who are English learners and apply specific instructional strategies to help children learning English acquire mathematical concepts and skills. To provide children who are English learners with comprehensible information, they should simplify the terms they use, make extensive use of manipulatives, illustrate the meaning of words by acting and modeling whenever possible, and encourage children to use terms in their home language.” PCF, Vol.1, p. 235 Ask participants how they address these unique needs on a daily basis with regard to math. Guide participants to Handout 5: Teacher Support Strategies. Share that this is a resource we will be returning to throughout the day. Describe the organization of the handout with regard to acquisition stages and strategies. With support of the EL lead, provide one example of a strategy that is beneficial for supporting overall math development in the classroom, and discuss which stage of acquisition it might best support. Allow time for participants to talk at tables and take notes. SUMMARY: Participants become familiar with the Teacher Support Strategies handout and begin thinking about dual-language development with regard to math in the preschool classroom. Support English learners in developing mathematical knowledge as they concurrently acquire English. PCF, Vol. 1, p. 235 ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). 05/2013

Build on preschool children’s natural interest in mathematics and their intuitive and informal mathematical knowledge. PCF, Vol. 1, p. 234 Guiding Principle This slide is an example of a Guiding Principle. Young children are mathematically competent, motivated, and naturally interested in exploring mathematical ideas and concepts. Teachers should recognize children’s early mathematical competence and build on children’s disposition to use mathematics as a way to make sense of their world. PCF, Vol.1, p. 234 How might you use technology to build on children’s natural interests? ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). 05/2013

Mathematic Domain Framework Strategies
Developmentally appropriate Reflective and intentional Individually and culturally meaningful Inclusive Developmentally appropriate Reflective and intentional Individually and culturally meaningful Inclusive Teachers address ideas and concepts that children can grasp at their developmental level and then progressively build on what children already know and understand. This approach applies to all children, including children with various abilities, disabilities, or other special needs (such as delays in language, cognition, or physical ability). PCF, Vol. 2, p. 227 The following is an example idea for creating an inclusive environment: Some children may need assistance in holding a book or turning the pages either through assistive technology or with the help of an adult or peer. For example, a book can be mounted so that a child need not hold it, and sturdy tabs can be placed on a book’s pages make them easier to turn. PCF, Vol, 1, p. 106 ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). 05/2013

Individualization of learning includes all children. PCF, Vol. 1, p. 5
There are approximately 45,000 children with identified disabilities in the CDE preschool system. This number does not include children at risk of a disability or developmental challenges. Children with disabilities represent the diversity of California’s entire preschool population and necessitate unique educational considerations in the preschool setting. PCF V. 1., p. 5 Universal design provides for multiple means of representation, multiple means of engagement, and multiple means of expression. Multiple means of representation refers to providing information in a variety of ways so the learning needs of all children are met. For example, it is important to speak clearly to children with auditory disabilities while also presenting information visually such as with objects and pictures. Multiple means of expression refers to allowing children to use alternative ways to communicate or demonstrate what they know or what they are feeling. Recognizing that children follow different pathways to learning, this framework incorporates a concept known as universal design for learning PCF, Vol. 1, p. 13 ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). 05/2013

Universal Design for Learning
Multiple means of representation Multiple means of engagement Multiple means of expression Although this curriculum framework presents some ways of adapting or modifying an activity or approach, it cannot offer all possible variations to ensure that a curriculum meets the needs of a particular child. Of course, the first and best source of information about any child is the family. Additionally, there are several resources available to support inclusive practice for young children with disabilities or other special needs. The resources, Web sites, and books listed in Appendix D are recommended for teachers’ use. PCF, Vol.1, p 13 For more information on Universal Design for Learning, see UDL Number Rock INTENT: Participants have a “brain break” while experiencing an activity that illuminates Universal Design for Learning. OUTCOMES: Participants will experience multiple means of engagement and representation while dancing and/or singing to Steve and Greg’s the Number Rock. MATERIALS REQUIRED: Access to Steve and Greg’s the Number Rock (via You Tube or computer download), Number Rock Envelope with direction cards and necessary materials (scarves), PPT notes TIME: 5 minutes PROCESS: Invite table groups to open the Number Rock Envelope and read the direction card within. When participants are ready, let them know that we will be doing the number rock, but that we will all be engaging in different ways. Play the song and watch all participants as they engage with the song in different ways (i.e., some will be standing and dancing, some will be tapping out the song with fingers, etc.)After the song debrief with possible questions: How did this activity represent Universal Design for Learning? How many different ways did we engage in this activity? How many different ways did we represent numbers? If you did this activity without the direction cards, what forms of engagement and representation might you see in your classroom? SUMMARY: Participants will engage in Number Rock activity. Number Rock

Research Highlight Read the Highlight on Page 251 Discussion Points What strategies have you seen children use to solve arithmetic? Of those strategies, what types of representation are used? Research indicates that the ability to reason about numbers starts as early as infancy. Five-month-olds show sensitivity to the effects of addition or subtraction of items on a small collection of objects. Toddlers viewing three balls put into a container, and then one being removed, know to search for a smaller number of balls, and many search for exactly two balls. By the time children are in preschool, prior to having any formal lesson in arithmetic, they use a variety of strategies to solve simple addition and subtraction problems. They may use manipulatives or fingers to represent the numbers in the problem and count out loud to find out the answer. As they get older, they rely less and less on finger counting. To solve an addition problem such as presented with concrete objects (e.g., color crayons), the child may count all objects “one, two, three, four” and then continue with the second set of objects “five, six” and find out there are a total of six. At a later stage, the child may “count on” from the second set of objects. Knowing the number of objects in the first set (e.g., “four”), the child starts with “four” and continues to count “five, six” to find out the total number of objects, rather than starting to count from “one” with the second set of objects. PCF, Vol. 1, p. 251 Handout 5: Teacher Support Strategies

For example… For example, when three pictures showing 1, 2, or 3 dots are placed in front of a six-month-old child, and three drumbeats are sounded, the child will most likely focus on the picture with three dots! Preschoolers possess informal mathematical abilities (i.e., develop number and geometry abilities, counting objects, making shapes, and use math knowledge every day). Educators must nurture these informal math abilities, or risk missing opportunities to support children in the early stages of their mathematical development.

Glossary Term: The act of subitizing supports the development of counting, adding, and subtracting. (Clements & Sarama, 2007) 20 minutes – Slides 39-54 Early number sense is not counting, but recognition of number. Recall the infants with the three dots; there is another example from the research done by by Starkey, Spelke & Gelman, This comes from page 17, Counting section in Engaging Young Children in Mathematics by Dr. Doug Clements. Also, recognition of number is misinterpreted by many as meaning reading numerals “3” or “2.” Instead, it means seeing a small group of objects and understanding how many are in that group. (NOTE: Apprehend means to understand – Doug Clements) The size and number of objects to be quantified can have a significant role in the child’s ability to subitize, but most children are able to subitize one or two objects spontaneously. Clements, D. H., & Sarama, J. (2007). Chapter 12: Early childhood mathematics learning. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning :A project of the national council of teachers of mathematics (pp ). Charlotte, NC: Information Age Pub.

Engaging Young Children in Mathematics
When six-month-old infants are shown a series of pictures that always depict three (3) objects they eventually get bored. But… CLICK TO NEXT SLIDE. Clements, D.H., Engaging Young Children In Mathematics, 2004, pg. 17.

Engaging Young Children in Mathematics
If the configuration of the objects depicted in the pictures is then changed from three (3) to two (2) or four (4), infants notice the change and become interested again. They can “see” small configurations of objects nonverbally. This is called subitizing. By 18 months of age, infants can notice which of two collections contains more objects (Cooper 1984). This provides and early perceptual basis for number, but it is not yet “number knowledge.” Clements, D.H., Engaging Young Children in Mathematics, 2004, pg. 17.

How many dots do you see? That’s Subitizing!

Learning Trajectory for Subitizing
Can perceive group without counting Can use pattern of group To determine the number (e.g., domino pattern) Can make small collection Can name small collection When working on a skill it is important to remember the trajectory, continuum, or developmental sequence. The trajectory for subitizing is: Can name small collection Can make small collection Can use pattern of group to determine the number (e.g., domino pattern) Can perceive group without counting Learning Trajectory for Subitizing

Subitizing Games Subitizing: Let’s Play
INTENT: Participants practice subitizing knowledge through game play and analyze games with regard to the foundations, Dual-language strategies, the DRDP©, and Universal Design for Learning. OUTCOMES: Participants will practice multiple games to be used in a preschool classroom. MATERIALS REQUIRED: Subitizing Game handouts, Subitizing Game materials, PPT notes TIME: 20 minutes PROCESS: Invite participants to take out and read through the subitizing game packet. Walk around and provide support for participants to practice each game. Allow enough time for this exploration (10-12 min). Regroup participants and demonstrate how to apply the game knowledge to the chart using Handout 6: Subitizing LET’S PLAY Worksheet. Walk around while participants think about and complete this handout. Invite participants to share out their “aha” moments. Presenter can share out “aha” moments that they hear while walking around. SUMMARY: Participants will play subitizing games and participate in activity.

Teacher Role Think back to the ice breaker. Encourage counting during everyday interactions and routines. Learning the sequence of number words in English involves the rote learning of the first 13 number words and later the rules for producing the subsequent “teens” number words and the beyond-twenty number words. This may proceed slowly and require a lot of practice because learning number names in order takes practice. PCF, Vol. 1, p. 244 Ask questions that encourage purposeful counting. Use counting to determine quantity and answer a child’s question within context: “I wonder how many stickers Ana has? One, two, three, four. She has four.” To compare two quantities, the teacher might ask, “Which table has more children? How many more?” To create a set with a number of objects, the teacher could suggest, “Derek needs four sticks.” Or to solve addition and subtraction problems, ask “How many blocks do we have altogether? How many are left?” Combine counting with pointing or touching objects to reinforce the concept. PCF, Vol. 1, p. 245 Teachers have an extremely important role in supporting children’s understanding of number relationhips and operations. ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). 05/2013

Observe Children Counting
Observe children’s spontaneous counting and note their developmental level. PCF, Vol.1, p. 244 Observe Children Counting Observing preschool children’s spontaneous counting and reasoning will enable teachers to assess and successfully plan to meet the needs of all children, including those with special needs. See “Sample Developmental Sequence of Counting” on page 242 of the PCF. Reflect on Teacher Support Strategies handout. Which strategies might be beneficial for the dual-language learners in your classroom? (Spend at least five minutes reflecting and facilitating this conversation). ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). 05/2013

Developmental Counting Sequence
As teachers observe the children throughout the day, they are likely to encounter a great deal of spontaneous counting and reasoning about numbers. PCF, Vol. 1, p. 242. Developmental Sequence INTENT: Participants obtain a better understanding of the counting developmental sequence. OUTCOMES: Participants will practice identifying the counting developmental sequence. MATERIALS REQUIRED: Number line, Preschool Curriculum Framework (PCF). Table materials: Developmental Sequence Envelope, Developmental Sequence Cards TIME: 10 minutes PROCESS: Invite participants to find the Developmental Sequence Card Envelope. Allow time for participants to put these steps in order as a table group. When all tables have completed the task, invite participants to turn to page 242 of the PCF to check their work. Share out any interesting findings or discussion points from the group. Highlight how this knowledge may help teachers in gathering better evidence for the DRDP© measures. Debrief: Discuss how children may represent these developmental sequence levels differently. Think back to the Number Rock activity. How might your experience with this activity impact how you consider the developmental sequence? SUMMARY: Participants will practice the counting developmental sequence. ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). 05/2013

Interaction and Strategies Graphing with children
Encourage preschool children to collect data, tally totals, and graph the results. Use graphing with children. Encourage preschool children to collect data, tally totals, and graph the results. Children enjoy taking an active part in this process. Invite children to collect and record numerical information (e.g., the number of children who have pets, the number of people in each child’s family). Create a chart or graph, using real objects, to represent numerical information collected by children. Discuss with children the information presented in the graph. Graphs lead naturally to making comparisons: “Which group has more?” “Which group has fewer?” “Can you tell without counting?” “How many more are in this group?” PCF, Vol. 1, p. 255 NOTE: Think back to the ice breaker activity again. How could we facilitate and maximize graphing in this activity? Revisit the handout and add ideas for facilitating the various substrands with the ice breaker activity. How would you use it? Reflect on the Teacher Support Strategies handout. Which strategies might be beneficial for the dual-language learners in your classroom? (Spend at least 5 minute reflecting and facilitating this conversation). ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). 05/2013

Let’s Play Counting Sequence Games.
Participants stay at their own table to do this one.

Exposure to Preschool Mathematics can increase language ability; and has lasting effects into Kindergarten Dr. Clements, Society for Research and Development, 2013 Dr Clements After one and two years of a preschool experience with math curriculum, language skills were assessed in Kindergarten to determine if the extra time spent on Math was harmful to language development. Results demonstrate that language actually benefits, specifically the ability to produce independent language, produce complex grammar, and retell details of a story. -Dr Clements, Society for Research and Development, 2013. ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). 05/2013

Interaction Strategy Introduce preschool children to the concepts of addition and subtraction through literature, songs, and games. Stories, songs, and games provide a playful way to introduce “adding-to” and “taking-away” operations, and part–whole relationships. Experiences with concrete sets of objects, in particular, can illustrate for children addition and subtraction concepts and enable children to solve simple addition and subtraction problems by counting objects. For example, when telling the flannel board story Rooster’s Off to See the World, the teacher says, “One rooster met two cats,” and she places one flannel rooster next to two cats and asks the children, “How many animals do we have altogether?” The story continues, “The rooster and the cats met three frogs.” The teacher places three flannel frogs, “One, two, three,” next to the rooster and cats and asks, “How many do we have now?” The flannel board story provides the context for introducing the “adding-to” concept. PCF, Vol. 1, p. 255 Introduce preschool children to the concepts of addition and subtraction through literature, songs, and games. PCF, Vol. 1, p. 255 ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). 05/2013

Pair Share Your Knowledge
What are your favorite books to enhance Number sense? What are your favorite songs to enhance number sense? Play a counting song and hit pause when it pauses the person you are standing closest to will become your partner. Answer the questions with them. One Example includes: (Make this example a technology enhanced example.) Revisit the Foundations Chart one more time. What new ideas to you have to add? ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). 05/2013

Books and Number Sense Play Books and Number Sense
INTENT: Apply and integrate number sense knowledge with math vocabulary. OUTCOMES: Participants will analyze the use of books and math vocabulary to enhance number sense in the classroom. MATERIALS REQUIRED: Dot Book Video, Handout 4: Foundation Chart, Handout 8: Math Vocabulary, Math books for tables (Feast for 10, 10 Black Dots, Let’s Eat) TIME: 20 minutes PROCESS: Model reading a book that is rich in Math Vocabulary. Guide participants to find the Math Vocabulary handout. Discuss the math vocabulary that was used in the book. Tell participants that we will watch a video and then try ourselves. Watch the Dot Book video together. Highlight the use of the counting book to support math language and spontaneous counting and adding. Invite participants to choose the math book they will use. Table groups read the math book they chose and use the Math Vocabulary handout to reflect on which math vocabulary is used in the book. Take out the Teacher Support Strategies handout and discuss which strategies might best benefit dual-language learners in your classroom. Take out the Foundation Chart and add ideas or notes around specific foundations that participants want to return to regarding this activity. SUMMARY: Participants will experience integrating literacy and math.

What might be an appropriate use of technology to enhance this activity? Counting books elicit spontaneous counting PCF, Vol. 1, p. 244 ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). 05/2013

What are you going to hang on to from today?
What was very new to you? What was really interesting? What can’t you wait to try? What are you still curious about? ©2013 California Department of Education (CDE) with the WestEd Center for Child & Family Studies, California Preschool Instructional Network (CPIN). 05/2013

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