OELCS 2005 Math Module 1 Speaker Notes

OELCS 2005 Math Module 1 Speaker Notes
Teaching Young Learners with the Ohio Early Mathematics Standards in Mind Sponsored by the Ohio Department of Jobs and Family Services in collaboration with the Ohio Department of Education Instructor should provide some background of the history of Ohio standards– first K-12 and later the addition of early learning standards so now Pre-K to 12. In the early learning standards, first to be published were language and literacy and now we have math, science and social studies. Collaboration between ODE and ODJFS to bring an understanding the standards around Ohio to early childhood professional communities. Introductions: Use some means of introducing participants. Raise your hand if you are from a childcare center … Head Start … public Pre-k … pre-K special Education … Family-child care Module One

Overview of Seminar Module 1 What are Standards, benchmarks and indicators? Supporting Children’s Early Concepts of Number Module 2 Early Addition and Subtraction Patterns and Algebraic Reasoning Module 3 Geometric Reasoning through Children’s Play Teaching Mathematics through Activity – Measurement & Data Analysis Instructor talks to participants about the content but also some of the themes that will be emphasized that are traditional early childhood values [for example – on next slides -- play, investigation, intentional teaching within play and investigation, looking at math across the curriculum, using children’s literature ]. The goal of the series is to understand how the standards with developmentally and culturally appropriate practice.

Themes for the Sessions
OELCS 2005 Math Module 1 Speaker Notes Themes for the Sessions Play Inquiry & projects Home-school connections Adaptations for diverse learners Integration across the curriculum The connected nature of mathematical knowledge Role of conversation and questioning 3 levels of representational thinking Play – how is children’s play a context for their mathematical learning? How can the teacher interact in the course of play to support and enhance learning? Inquiry, & projects– ideas for capitalizing on what we see in play with extended small group investigations Home environment; culturally relevant pedagogy – home/school connections. How do we bring children’s lives into the classroom? Integration across the curriculum means seeing and creating opportunities for math learning in dramatic play, blocks, art, literacy, sensory and manipulative materials, transitions and routines for daily life, music and movement. Etc. Mathematical knowledge as connected/integrated – when we are sorting we are also counting, when we are counting we are also patterning, when we are estimating we are also developing number sense. Number and number sense is a repeated theme throughout the series because of its foundational role. Talk is crucial-- explanation/justification, making connections – What can we expect from kids at this age– not to be “right” but to develop the habit of justifying their thinking… Instructors should detail the 3 levels of human representation: concrete, pictorial/transitional, symbolic.

Overview of Module 1 What are the Ohio Early Learning Content Standards? What are the benefits of using standards? What are some of the challenges of using standards? Instructor should emphasize that standards will guide us.. Provide a map .. But not take us away from traditional early childhood philosophies, methods, values. Standards do not mean standardization in any sense of that word.. We will look at the power of standards to advance the field but we will also look at the pitfalls of standards if we don’t understand them or if they are misused.

The Ohio Standards What are the Ohio early learning content standards?
How do standards, benchmarks, and indicators relate to one another? How should teachers think about using them?

Imagine… The Teacher as gardener The Learner as the growing plant
Standards as a grower’s guide Early content standards as roots Environment and circumstances as sun, water, soil, geography…

We all begin young and full of potential
Seeds and seedlings need much care. The younger the plant, the greater the need for careful observation and responsiveness. The child as learner needs similar support and responsiveness.

We need strong roots… The roots of the plant develop first and are critical to further growth, but they also continue their importance throughout the life of the plant.

an appropriate environment…
The sunlight, temperature, water, proximity and types of other plants, soil, fertilizer, and other environmental factors influence the development of the plant. A child’s environment influences the development of his or her math thinking

…and a gardener who knows our unique needs. A grower’s guide is a generic guide for how MOST plants grow. It provides benchmarks in the life of a plant, and it gives assistance to the novice gardener. It can’t predict with certainty all the specific needs of one particular plant. A skilled gardener adjusts directions in order to create the best environment for her particular plant. How does this relate to standards?

There are many plants and many learners.

Ideas to Keep In Mind… We can’t depend on a guide to provide the schedule of care for each day. Too much of a good thing can be damaging. The analogy is somewhat limited because children influence their environment. Tomato plants do not influence their environment.

Ideas to Keep In Mind (Cont.) …
What worked with one plant will not necessarily work with another; individualization is important. Patience is important for the gardener.

Using the Standards Wisely The standards are like the grower’s guide. Teachers make educated judgments about necessary conditions for math learning. Each child is different. We reap benefits when we opt not to push children too hard or too quickly. Teachers need patience and direction. Instructor emphasize: The child care provider is the PROFESSIONAL making decisions based on the children with whom s/he is working.

What is an early math standard?
Standards are what we expect students to know and be able to use as they progress through school. Standards outline the foundational content and processes in mathematics.

Standards are both content and process
OELCS 2005 Math Module 1 Speaker Notes Standards are both content and process Number, number sense and operations Measurement Geometry and spatial sense Patterns, functions and algebra Data analysis and probability Mathematical processes Instructor emphasize: Process Standards are delineated on slides 21 & 22.

What is an indicator? Indicators are specific skills and understandings that students demonstrate across the grade levels These indicators let us know that the student is making progress toward the benchmarks

What are benchmarks? Benchmarks are particular indicators that are “grouped” in developmental chunks to indicate where students should be by a particular grade. For early childhood math, the benchmark is second grade.

Number, Number Sense and Operations Standards (by grade 12)
OELCS 2005 Math Module 1 Speaker Notes Number, Number Sense and Operations Standards (by grade 12) Students will demonstrate number sense, including an understanding of number systems and operations and how they relate to one another. Students compute fluently and make reasonable estimates using paper and pencil, technology-supported and mental methods. Note: This is the verbatim ODE standard. See page 28 of Early Number Standards book. Definition of operation – addition, subtraction, multiplication, and division.

2nd grade benchmark for number standard
OELCS 2005 Math Module 1 Speaker Notes 2nd grade benchmark for number standard There are 13 indicators that a student has reached the 2nd grade standard for number, number sense, and operation. For example: recognize, classify, compare and order whole numbers Model, represent and explain subtraction as comparison, take-away, and part-to-whole Instructors– Participants have the indicators – take a look at these indicators with participants and help the participants put these into everyday language and brainstorm behavioral indicators for preschool. The indicators help us to know whether the students have attained the benchmark at 2nd grade.

Mathematical Processes Standard
OELCS 2005 Math Module 1 Speaker Notes Mathematical Processes Standard Students use mathematical processes and knowledge to solve problems. Students apply problem-solving and decision-making techniques, and communicate mathematical ideas. Problem solving, Communication, Connections, Representation, & Reasoning and Proof Note: This is the verbatim ODE standard. Mathematical processes are ways to help children learn mathematics. They are also outcomes of learning mathematics. For example, we learn mathematics by communicating our mathematical observations and by solving problems. And by studying math we learn to communicate mathematically and problem solve efficiently.

Benchmark for process standard
OELCS 2005 Math Module 1 Speaker Notes Benchmark for process standard Example indicator (there are 9 all together): Use a variety of strategies to understand problem situations, e.g., discussing with peers, stating problem in own words, modeling problems with diagrams or physical materials, identifying a pattern. Note: This is the verbatim ODE standard.

Achieving Balance Children construct their own knowledge through play Teachers provide lots of time for free play with math materials Teachers place math related materials in every part of the room With Intentional Teaching, teachers can pay attention to curriculum standards and benchmarks as they prepare environments Teachers plan math experiences based on the standards, with developmental levels and culture in mind. Teachers assess where children are and provide next step experiences Here we emphasize that on the left side of the balance scale, we see children playing and investigating the physical world around them and spontaneously showing us their discoveries: “Look I made a design” (red/blue, red/blue). With intentional teaching and knowledge of the standards, we would take that opportunity to talk about it– “Wow look what you created– a color pattern! What other patterns can you make with color?” Other examples could come from dramatic play, art, sensory etc…. Examples of spontaneous discovery where the intentional teacher seizes the opportunity. On the right side of the scale– an intentional teacher chooses children’s storybooks with the standards in mind or plans a small group game that has them in mind. But these plans are always mindful of what she has observed the children thinking about during play. Finally, it is important that we support students in realizing their full potential. For some students the indicators are minimal and they will already have knowledge and skills that exceed them.

Backmapping How do we know we are providing experiences that support students’ progress toward the benchmark? We backmap!! Backmapping is a regular routine where you look back at curricular experience and ask: which indicators have we been supporting? Instructors should emphasize also allows you to reveal gaps so you can “forward map” to provide balanced across the domain of mathematics. So, part of being intentional is to provide experiences that “fill the gaps” we notice. Backmapping may be thought of as an iterative process. Instructors: Emphasize that we will be practicing this skill… BREAK FOR LUNCH following this discussion.

BREAK TIME

Early number Concepts What understandings are young learners developing as they are developing their concepts about number? How do you support these early competencies? Later we will look at what it means to have mature concept of number and the complex knowledge underlying number concept. BUT what are children learning before and along side of their emergent sense of number? This is what we call early concepts and they can be nurtured and supported thru intentional teaching. What are prenumber concepts? (mention them here because they will be explained more fully later) Sorting and grouping by various “attributes” .. Classifying and labeling (e.g., these are the big ones these are the little ones, these are the blue ones these are the red ones) The beginning language of math– “more” “less” “some”.

Early number -- sorting
OELCS 2005 Math Module 1 Speaker Notes Early number -- sorting Free sorting activities – what are they? Teacher’s roles: providing sortable materials, conversation/questioning “ What did you find?” • “What kinds of groups did you make?” • “How did you put them together in different groups?” • “I see you sorted them into colors!” Instructors: Emphasize the importance of lots of experience with free sorting of all kinds of materials (buttons, shells, chips, geometric shapes) Point out that geometric shapes do not need to be named (squares, rectangles) but can be described (“the shape with the pointy top”) The value of free sorting is really the children’s explanation of how they sorted them… see what they say about their own groupings.. ACTIVITY: [YOU ARE PROVIDED SORTING MATERIALS FOR 5 GROUPS OF PARTICIPANTS. IF PARTICIPANT NUMBERS ARE LARGE YOU MAY BE PROVIDED MORE MATERIALS AS NEEDED.] Provide each group with various sorting materials and 2 loops (yarn). Have participants sort materials and explain how they sorted the materials. Ask: Can you sort them in another way? Back map – using the ODE early learning content standards. Which indicators can we help students move toward with these activities?

Structured Sorting Activities
OELCS 2005 Math Module 1 Speaker Notes Structured Sorting Activities “In the Loop”: The leader (adult or child) places one piece in the loop. Everyone else finds pieces from their pile to add to the loop “Guess my rule”: The leader places several pieces in a loop – everyone else guesses what s/he is thinking Instructors– Use same materials for these activities. Emphasize that we recommend this kind of game AFTER children have had lots of experience with free sorting. It can be played one-on-one with a child during free play (at the table) or in a small group that emerges spontaneously or that is planned. Free sorting materials and explaining one’s reasoning is crucial to developing these early and important competencies. ACTIVITY: At their tables, participants try activities (i.e., “In the Loop” and “guess my rule”) and backmap to the early learning standards.

As early number concepts develop further
OELCS 2005 Math Module 1 Speaker Notes As early number concepts develop further Classification – sorting according to attributes Patterns Comparisons of sets (more than & less than) Ordering Sets (smallest to largest) SUMMARY: Instructors explain what each of these are and how they emerge over time with lots of experience. These competencies do not necessarily depend upon number concepts. Do not rely on numbers but provide a foundation for later number concepts and skills. Define conservation --

As early number concepts develop further (Cont.)
OELCS 2005 Math Module 1 Speaker Notes As early number concepts develop further (Cont.) Conservation - Conservation is the recognition that the number, length, quantity, mass, area, weight, and volume of objects and substances are not changed by transformations in their appearance. Beginning to recognize how many in a small set without counting SUMMARY: Instructors explain what each of these are and how they emerge over time with lots of experience. These competencies do not necessarily depend upon number concepts. Do not rely on numbers but provide a foundation for later number concepts and skills. Define conservation --

Early Counting Concepts and Skills
OELCS 2005 Math Module 1 Speaker Notes Early Counting Concepts and Skills What do you see when children count? How is learning to count similar to learning to read? Groups discuss these questions (and record on table post-its) from their experience and come back to whole group to discuss. Instructor points out that rote counting to 10, 20 or even 100 is like knowing the alphabet and doesn’t mean children understand counting..

Seven Candies While watching the children, notice what they do to count the candies What do they show us about their understanding of number and counting Take notes about individual children’s: Strategies Physical behaviors Knowledge and competencies Misunderstandings or limited experience This slide provides instructions for participants as they view videos on the following slides. Discuss what participants will be doing as they view the children’s counting behaviors. You may want to view individual clips and then have a discussion OR view several and then discuss. Show participants video clips of children’s early efforts to count; take note of children’s individual behaviors (Video clips are from -- Hersch, Cameron, & Fosnot PreK-3 – Fostering children’s mathematical development) Notice what children do to count the candies. What are there strategies? What do they know? What do they need to learn about counting? What are the individual student’s competencies? What are some of the errors they make?

Seven Candies Seven Candies: Go through all of the children’s video clips. Have participants work in groups. Notice what children do to count the candies. What are there strategies? What do they know? What do they need to learn about counting? What are the individual student’s competencies? What are some of the errors they make?

Developing Early Concepts of Number
OELCS 2005 Math Module 1 Speaker Notes Developing Early Concepts of Number What do you do to foster children’s early development of counting? Brainstorm in groups ideas for fostering number knowledge with your children across the curriculum. Where does counting informally and easily appear (singing, play in blocks, children’s books, puzzles etc etc.) Use Intentional teaching language here.

Components of Early Number Knowledge - Counting Principles
OELCS 2005 Math Module 1 Speaker Notes Components of Early Number Knowledge - Counting Principles Production of numbers (standard list of counting words) One-to-one correspondence (one object for each number) Ordering or seriation (small to largest) Cardinality principle (last number is the number in the set) Which object in the set you start with doesn’t matter Conservation– number stays constant even if objects are rearranged Instructors should show complexity of counting– which seems so simple – by going thru this list of concepts behind it.

Groups of 5 counters are arranged in the following 3 patterns. Discuss the students’ knowledge of counting principles on each of the following slides The next set of slides provides more context for participants to quickly discuss student’s competencies and weaknesses. Participants could be asked to go into the ODE Academic content standards to state the indicators the child is close to attaining or needs work in attaining, etc. What are the student’s weaknesses and competencies in the following slides? What would be the next experience you would provide each of these children in your classroom?

A conversation with Stephen
OELCS 2005 Math Module 1 Speaker Notes A conversation with Stephen T: Are there more red, blue, or yellow counters? S: More blue. T: How do you know? S: I can tell by looking. T: How many of each? S: One, two, three, four, five... five red. One, two, three, four, five...five blue. One, two, three, four, five...five yellow. T: Five of each? S: Yes. T: Do you still think there are more blue? S: Yes, I can just see there's more blue. What do you know about Stephen from this conversation? How would you interact with him based on this understanding?

A conversation with Rebecca
OELCS 2005 Math Module 1 Speaker Notes A conversation with Rebecca T: Are there more red, blue, or yellow counters? R: They're the same. T: How do you know? R: I counted them. T: How many of each? R: One, two, three, four, five...Five red. Five blue. Five yellow. T: Five of each? R: Yes. ditto

Counting Principles: Stephen
OELCS 2005 Math Module 1 Speaker Notes Counting Principles: Stephen T: Here are some blocks in a row. Start with this one on the end and count them. S: One, two, three, four, five, SIX. There are six blocks. T: What if you start at the other end of the row and count them? S: One, two, three, four, five, SIX. There are six. The fact that the student needed to recount the blocks is indicative that s/he does not yet understand that the order in which we count doesn’t matter to the number of objects in the set.

Counting Principles: Rebecca
OELCS 2005 Math Module 1 Speaker Notes Counting Principles: Rebecca T: Here are some red blocks in a row. Start with this one on the end and count them. S: (Touches each of the 5 blocks) One, two, three, five, six. Six red blocks T: Now count these blue blocks. S: (Touches each of the 4 blocks) One, two, three, five. Five blue blocks.

Counting Principles: Sally
OELCS 2005 Math Module 1 Speaker Notes Counting Principles: Sally T: Here are some blocks in a row. Start with the one on this end and count them. S: One, two, three, four, five, six. There are six. T: What if you start at the other end of the row and count them? S: I already counted them! There are six!

Counting Principles: Brenda
OELCS 2005 Math Module 1 Speaker Notes Counting Principles: Brenda T: Here are some red blocks (4) in a row. Start with this one on the end and count them. S: (Points to each but says two numbers with each point) One, two, three, four, five, six, seven, eight. Eight red blocks.

Number Standard Age 3 Counts Collection of 1 to 4 items Begins to understand cardinality Group recognition for collections of 1 to 3 Adds and subtracts non-verbally low numbers Age 6 Counts and counts out collections up to 100 using groups of 10 Group recognition for patterned collections of up to 6 items Adds and subtracts using counting-based strategies such as counting on for numbers and totals less than 10 Adapted from Early childhood mathematics: Promoting Good beginnings – NAEYC & NCTM Emphasize that this is consistent with the ODE standards FINAL ACTIVITY: BACKMAP ALL THAT WE COVERED THIS DAY ONTO THE ODE STANDARDS..

OELCS 2005 Math Module 1 Speaker Notes

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