2 OutcomesParticipants 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.
3 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 PlanTIME: 10 minutesPROCESS: 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.
5 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.
6 Domain OrganizationThe 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
7 Common Core NCTM Alignment California Learning Foundations Number SenseUnderstanding Number QuantityUnderstanding Number Relationships and OperationsCommon Core StandardsNCTM Focal Points for PrekindergartenCommon Core NCTM AlignmentThe 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.
8 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="http://www.youtube-nocookie.com/embed/EYaLrPNtD8I?rel=0" frameborder="0" allowfullscreen></iframe>Dr Clements Says
9 Trends in International Mathematics and Science Study 2011 Forward GrowthCompared 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 ComparisonsAt 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)-BELFor a full report go to:Full Report
10 International Growth Over Time Highlights:Unites States changed an average of 23 points in overall scorePortugal changed an average of 90 points in overall scoreThe Czech Republic changed an average of -30 points in overall scoreThe 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 scoreFull Report
13 Map of the FoundationsHandout 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 TakingINTENT: 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 minutesPROCESS: 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.
19 Universal Design for Learning Multiple means of representationMultiple means of engagementMultiple means of expressionAlthough 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 13For more information on Universal Design for Learning, see UDLNumber RockINTENT: 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 notesTIME: 5 minutesPROCESS: 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
20 Research HighlightRead the Highlighton Page 251Discussion PointsWhat 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 sub- traction 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. 251Handout 5: Teacher Support Strategies
21 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.
22 Glossary Term:The act of subitizing supports the development of counting, adding, and subtracting. (Clements & Sarama, 2007)20 minutes – Slides 39-54Early 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.
23 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.
24 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.
26 Learning Trajectory for Subitizing Can perceive groupwithout countingCan use pattern of groupTo determine the number(e.g., domino pattern)Can make small collectionCan name small collectionWhen working on a skill it is important to remember the trajectory, continuum, or developmental sequence. The trajectory for subitizing is:Can name small collectionCan make small collectionCan use pattern of group to determine the number (e.g., domino pattern)Can perceive group without countingLearning Trajectory for Subitizing
36 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 minutesPROCESS: 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.
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