1. Mathematics for Young Children
Jennifer Kearns-Fox, Mary Lu Love & Lisa Van Thiel
Institute for Community Inclusion
University of Massachusetts Boston

2. Update
8:00-8:10

3. Session Goals
Apply understanding of how children develop mathematical concepts to curriculum
Use rich language to expand vocabulary
Implement Houghton Mifflin Pre-K math curriculum, differentiating instruction to support children along a developmental continuum
2 minutes
8:10 to 8:15

4. Teaching Young Children Mathematics
What math concepts might children be learning in each center?
Hang chart paper on the wall. Ask participants to list mathematics that might come up in this area.
DP, Blocks, Art, Books, Manipulatives, Science, Sensory
Record their responses on chart paper.
Now let us review what the National Council of Teachers of Mathematics emphasizes in teaching young children mathematics.
As discussed at our last PD, curriculum that is integrated and intentional has been linked to positive learning outcomes.
5 minutes
8:15 to 8:20

5. Standards of the National Council of Teachers of Mathematics
Emphasize a vision of mathematics for young children that:
builds upon young children’s experiences with mathematics,
establishes a solid foundation for the further study of mathematics,
incorporates assessment as an integral part of learning events,
develops a strong conceptual framework that provides anchoring for skill acquisition,
The Houghton Mifflin math program is designed to build upon young children's experiences with mathematics.
The curriculum establishes a solid foundation for the further study of mathematics, and incorporates assessment as an integral part of learning events, so that children develop a strong conceptual framework anchoring skill acquisition. At the end of each unit there is an observation checklist.
2 minutes

6. NCTM emphasizes a vision of mathematics for young children that:
involves children in doing mathematics,
emphasizes the development of children’s mathematical thinking and reasoning abilities,
includes a broad range of content, and
makes appropriate and ongoing use of technology, including calculators and computers.
Involves children in "doing mathematics" (small group, whole group, and center time) when authentic opportunities arise, such as figuring out how many students need lunch or counting out the number of plates needed for snacks.
Emphasizes the development of children's mathematical thinking and reasoning abilities. Engages children in conversations that encourage them to express their mathematical thinking and reasoning by asking questions such as, “How do you know? How many? How did you come up with that?”
Includes a broad range of content (math cuts across all content areas). Revisit the list about what, when, and how do you teach mathematics (math can be integrated across the curriculum and in preschool is often part of science, writing, and English Language Arts activities, e.g., classifying, writing numerals, collecting and analyzing data).
Makes appropriate and ongoing use of technology, including calculators and computers. If you have computers in your classroom use technology to support children’s foundation skills in mathematics. Jumpstart other computer games.
2 minutes

7. Process Standards Problem-Solving Connections Reasoning Representation
Communication
The National Council of Teachers of Mathematics organizes their curriculum standards around focal points based on their guiding principles and process standards. These include communication, reasoning, representation, connections, and problem-solving. NCTM curriculum standards and principles provide teachers with many activities to engage children in developing mathematical thinking.
NCTM takes a comprehensive approach to mathematics experience, preparing students for whatever comes their way. Think about teaching mathematics as an opportunity to equip children with the skills necessary for solving many problems faced in daily life and throughout their education.
Juanita Copley states that Early Childhood teachers are often unaware of the essential processes of mathematics, specifically reasoning, problem-solving, and the connections between mathematics and the world of the young child. As children develop conceptual understanding, they are also developing critical communication skills for problem solving. (academic language of logic and mathematics)
Often, knowledge, beliefs, and instructional strategies used to teach mathematics are focused on computation skills rather than problem-solving, which generally demonstrate procedural steps to solutions. When teaching mathematics the focal point should be on listening to children’s methods and reasoning.
Our goal today is to engage you in reflecting on some of the Houghton Mifflin Pre-K math activities, the NCTM process standards, and developmental levels of young children’s mathematical thinking to assist you in considering curriculum tailored to children using planned learning experiences.

8. Word Problem There are 7 girls on a bus. Each girl has 7 backpacks.
In each backpack, there are 7 big cats.
For every big cat, there are 7 little cats.
How many legs are there on the bus?
When you read this question, what was your first response? What did you feel? What did you do?
What Problem-Solving skills did you use? Try to make the problem into an operation. Graphically depict, break it into a unit/part.
What Connections did you make? Comprehend the word problem.
What Reasoning did you use: Logic, follow directions, step by step.
Did you use any Representation? Use diagram.
How did you use Communication? Notations, communicate logic.
Do you think the answer or the process gave you more insight into solving the problem? What does this tell you about your role in thinking about the process standards when implementing Houghton Mifflin?
The answer is 10,990
ACTIVITY TAKES ABOUT 20 minutes (5 minutes to share)

9. Debriefing What was your first response when you read the question?
What problem-solving skills did you use?
How did you connect to the problem?
What reasoning skills did you use or follow?
Did you use any forms of representation to assist you? If so, what?
Describe how communication impacted your thinking.
When you read this question, what was your first response? What did you feel? What did you do?
What Problem-Solving skills did you use? Try to make the problem into an operation. Graphically depict, break it into a unit/part.
What Connections did you make? Comprehend the word problem.
What Reasoning did you use: Logic, follow directions, step by step.
Did you use any Representation? Use diagram.
How did you use Communication? Notations, communicate logic.
Do you think the answer or the process gave you more insight into solving the problem? What does this tell you about your role in thinking about the process standards when implementing Houghton Mifflin?
The answer is 10,990
ACTIVITY TAKES ABOUT 20 minutes (5 minutes to share)

10. Content and Process Standards
Algebra
Patterns can be used to recognize
relationships and can be extended
to make generalizations.
Number & Operations
Numbers can be used to tell us how many, describe order, and measure; they involve numerous relations, and can be represented in various ways.
Operations with numbers can be used to model a variety of real-world situations and to solve problems; they can be carried out in various ways.
Problem Solving
Connections
Geometry
Geometry can be used to understand
and to represent the objects, directions,
and locations in our world and the
relationships between them.
Geometric shapes can be described,
analyzed, transformed, and composed
and decomposed into other shapes.
Communication
Data Analysis
Data analysis can be used to classify,
represent and use information to ask
and answer questions.
Debrief 7 cat using Clements and Sarama visual representation.
Problem solving: Students need to develop a range of strategies for solving problems. The use of diagrams, looking for patterns, or trying special values can help children solve problems. These strategies need instructional attention. Problem-solving strategies should be embedded across the curriculum. Teachers play an important role in developing students' problem-solving dispositions. They must choose problems that engage students and create an environment that encourages students to explore, take risks, share failures and successes, and question one another. In such supportive environments, students develop the confidence needed to explore problems and the ability to make adjustments in their problem-solving strategies.
Reasoning & Proof: Through the use of reasoning, students learn that mathematics makes sense. As they explore, justify, and use mathematical conjectures, they develop mathematical reasoning as a habit of mind.
Communication: Provide children with opportunity to discuss their mathematical thinking. This provides teachers with an opportunity to model how to organize and consolidate their mathematical thinking through communication.
Helping children to be able to clearly community their mathematical thinking to peers, teachers, and others provides them with an additional learning strategy to use as they engage in problem solving.
When mathematical opportunities present themselves in the classroom, engage children in analyzing and evaluating mathematical thinking as well as the strategies used by others. In this way, teachers model the language of mathematics and how to express mathematical ideas using teachable moments.
Representation allow students to communicate mathematical approaches, arguments, and understanding to themselves and to others. Through communication, students recognize connections among related concepts and apply mathematics to problems. It is important to encourage students to represent their mathematical ideas in ways that make sense to them, even if those representations are not conventional. Of course it is also equally important for students should learn conventional forms of representation in ways that facilitate their learning of mathematics and their communication with others about mathematical ideas.
Connection: Help children to recognize and use connections among mathematical ideas. Mathematical ideas are incorporated across the curriculum (science, literature, social studies). Take each opportunity that presents itself to interconnect ideas, such as number of side/shapes identification, or in doing puzzles. (Looks like the pieces you are missing have four flat sides of equal length, so what shapes do you think might fit here? Two small rectangles or one square.)
Conjecture is a mathematical statement which appears resourceful, but has not been formally proven. Once a conjecture is proven it is elevated to the status of theorem and may be used afterwards without risk in the construction of other formal mathematical proofs.
Reasoning
Measurement
Comparing and measuring can be used to specify
“how much” of an attribute (e.g., length) objects
possess.
Measures can be determined by repeating
a unit or using a tool.
Representation
Clements and Sarama, 2004

11. Break
Can rest or keep your mind going looking for Waldo

12. Every Day Conversations about Math
December 19, 2008
Math Continuum
Line up according to your comfort with math.
phobic
genius
Math Phobia Continuum
Discuss how individuals’ feelings of competency impact our interest in and ability to teach young children. Discuss the importance of being willing to be a learner and to celebrate where we are along the continuum as a starting point.
Boston Ready

13. Continuum for Mathematics
What should every four- year-old know and be able to do?
Number Sense & Operations
Algebra
Geometry
Measurement
Data Analysis
Young children’s mathematical thinking is sequential. Knowing where a child is along the developmental continuum equips teachers with information for differentiating instruction. Knowing where each child is permits us to structure students’ learning based upon students’ past knowledge and experience. To assist each student in achieving his/her full potential, we must set benchmarks for ourselves and our students.
The Houghton Mifflin Pre-K math program is a three year old curriculum and clearly promotes differentiated instruction. Let us take a few minutes to reflect on the scope and sequence of the curriculum and to begin to develop a continuum of learning. We know what it looks like for our youngest members, and we can use the Massachusetts Curriculum Frameworks to know what the expectation is at the end of kindergarten, but what we need to know is what it looks like for children attending their second year of preschool.
Our task is go to develop stepping stones or establish milestones for building skills between 1st-year preschoolers and kindergarten-age children. What do we think every returning preschool child should know and be able to do by the end of their second year of preschool? (Primarily 4 year olds.)
Let us use the scope and sequence and the curriculum frameworks to establish this continuum for students in our classrooms. What do we expect at the end of their second year of preschool? This alignment will assist us in differentiating our curriculum. It may also inform curriculum alignment across grade levels.

14. Developing a continuum
Count off by fives.
Work with other group members in pairs or triads. (10 minutes)
Join small group. Select a recorder, facilitator, and reporter. (10 minutes)
Establish benchmarks for 4-year-olds in your strand.
Develop a list of potential vocabulary to expand children’s academic language.
Prepare to share with the larger group.
Chart papers on walls with following labels: Number Sense, Operations Algebra, Geometry, Measurement, and Data Analysis
Let us begin our work by counting off by fives and working in pairs or triads. Try to find someone new to work with. We will give you about 10 minutes to work in pairs or triads and an additional 10 minutes to work in strand small groups. Each strand will need to select a recorder, facilitator, and reporter. We will then ask each group report out. 20 minutes to report out. 4 minutes each group.
Link this back to September training and developmental continuum. We want to drill down skills (task analysis of what children are learning).

15. Continuum for Mathematics
What should every four- year-old know and be able to do?
Number Sense & Operations
Algebra
Geometry
Measurement
Data Analysis
Pass out alignment sheet and share findings on chart paper. Show developmental continuum of math to participants in their packets. Discuss the need to scaffold learning based on what we know about individual children in our classrooms. Jen records what is reported out. Collect sheet from groups.

16. Facilitating Mathematical Thinking
Assess
Choose learning outcome
Plan experience for learning
Select materials and resources
Facilitate learning experience
Assess what learners have learned
(Brewer and Kallick, 1997)
Teachers are seen as facilitators supporting children’s construction of knowledge. Conceptual knowledge is attained by integrating new knowledge with that which is already known to the child. That is why it is so important to know where each child is on the developmental continuum. Individual-level data is used to scaffold learning and engage children in applying known reasoning skills to more complex problems.
The HM math program does provide many examples of provoking questions that may be presented to the group as games or challenges. Teacher can model with children how to solve these problems by helping children to make connections through the use of concrete materials and real-life problems that arise in the classroom.
Knowing where each child is along the continuum can assist us in ensuring that all children are challenged and learning to their full potential. Each unit includes an observation assessment checklist and each activity includes modifications for ELL, easier, and harder.
CLASS two dimensions: Concept Development and Quality of Feedback.

17. Concept Development and Quality of Feedback
Robert Pianta
CLASS two dimesions: Concept Development and Quality of Feedback.
Concept development encourages children to focus on the process of learning, rather than concentrating solely on the rote instruction and recall of facts. High-quality concepts development provides students with opportunities to use analysis and reasoning in their approach to problems, to think about the how and whys of learning, and to explore their world through experimentation and brainstorming. Concept development also encompasses an intentional approach by teachers to tie together concepts across activities and bring concepts to life by applying them to students’ everyday worlds.
Quality of Feedback: Students learn the most when they are consistently given feedback on their performance. Feedback works best when it is focused on the process of learning, rather than simply focused on getting the right answer. Higher-quality programs provide students with specific information about their work and help them reach deeper understanding of concepts than they could get on their own.
Pass out two sheets from class booklet on concept development and quality of feedback.
Bridget Hamre, Robert Pianta, and Karen LaParo.
Bridget Hamre
Karen LaParo

18. What Research and Literature Tell Us
What research tells us, slides (15 min)

19. Consider wait time as think time
Result of using 3-second pause:
For children:
Larger number of correct answers
Longer answers
Fewer “I don’t know” answers
For adults:
Ask more varied questions
Ask additional questions for more complex processing
(Stahl, 1994)
The concept of "wait-time" as an instructional variable was invented by Mary Budd Rowe (1972). The "wait-time" periods she found--periods of silence that followed teacher questions and students' completed responses--rarely lasted more than 1.5 seconds in typical classrooms. She discovered, however, that when these periods of silence lasted at least 3 seconds, many positive things happened to students' and teachers' behaviors and attitudes. To attain these benefits, teachers were urged to "wait" in silence for 3 or more seconds after their questions, and after students completed their responses (Casteel and Stahl, 1973; Rowe, 1972; Stahl, 1990; Tobin, 1987).
For example, when students are given 3 or more seconds of undisturbed "wait-time," there are certain positive outcomes:
The length and correctness of their responses increase.
The number of their "I don't know" and no answer responses decreases.
The number of volunteered, appropriate answers by larger numbers of students greatly increases.
The scores of students on academic achievement tests tend to increase.
When teachers wait patiently in silence for 3 or more seconds at appropriate places, positive changes in their own teacher behaviors also occur:
Their questioning strategies tend to be more varied and flexible.
They decrease the quantity and increase the quality and variety of their questions.
They ask additional questions that require more complex information-processing and higher-level thinking on the part of students.
The convention is to use 3 seconds as the minimum time period because this time length represents a significant break-through (or threshold) point: after at least 3 seconds, a significant number of very positive things happen to students and teachers. The concern here is not that 2.9 seconds is bad, while 3 seconds is good, and 5.3 seconds of silence is even better. The concern is to provide the period of time that will most effectively assist nearly every student to complete the cognitive tasks needed in the particular situation. The teacher's job is to manage and guide what occurs prior to and immediately following each period of silence so that the processing that needs to occur is completed.

20. Foster math communication
Provide opportunities for informal reflection to express reasoning
Facilitate problems during center time (versus being the answer giver)
Connect knowledge to prior knowledge
Connect tasks/routines to mathematics
Ask questions to promote problem solving, prediction, reflection
Use and encourage use of math terms
Cooke, B.D. & Buchholz, D. (2005). Mathematical Communication in the Classroom: A Teacher Makes a Difference
Early childhood teachers can foster math language by creating a comfortable, inviting classroom environment that encourages students to interact with them and other students. They can act as models as they use math language. Moreover, strategies such as providing materials for young children to explore and asking them math-related questions should be utilized to generate verbal participation. Additionally, use of appropriate questions can stimulate children's reasoning abilities as they respond to your inquiries while exploring objects in their world. Children should be encouraged to use math language in their responses.
Children come to school with a variety of experiences (Baroody, 2000). Many of these experiences can be related to mathematics (e.g., relating children's understanding of a seesaw to a balance scale). Therefore, teachers need to provide opportunities for young children to make connections between new and prior math experiences (Gallenstein, 2003). Encouraging children to discuss and share ideas can enhance the assimilation of new and old experiences and can facilitate the use of appropriate, informal mathematical communication.
Go back to problem-solving activity from AM and give examples. 20

21. Levels of Understanding:
Knowledge
Comprehension and
Application
Analysis, Synthesis, Evaluation
Higher Level Thinking:
1. knowledge (or rote)—remembering basic information.
To Popham, all other questions are open, requiring children to show their understanding of knowledge through responses that indicate they are developing critical thinking skills.
2. comprehension—understanding the basic information, being able to phrase it in one’s own words.
3. application—using the information in a concrete way to solve a problem or complete a task.
Bloom’s taxonomy higher-order questions began with the analysis level and included synthesis and evaluation because they required children to do more intense thinking. (Taxonomy = things arranged in a hierarchical structure)
4. analysis—breaking apart the information, sorting out facts, and drawing conclusions.
5. synthesis—putting together knowledge in novel, creative ways.
6. evaluation—judging content based on standards, which may be set by the learner or the teacher.
Popham, W. James Classroom Assessment: What Teachers Need to Know. Boston: Allyn & Bacon Inc.
Popham (2002)

22. Understanding that… Focuses on knowledge level:
Fails to capture creativeness
Classroom is humdrum
Teaching becomes mundane
Focuses on higher– order thinking:
Classroom is more interesting
Children show more enthusiasm for learning
Children discover knowledge and concepts

23. Child as Problem Solver
The Irony of Problems
The more we relinquish the role of problem solver, the more children will assume it. (Carol Gross)
Teacher as Problem
Solver
Child as Problem Solver
Children who come to expect help with every problem lose faith in their intuition and never develop the confidence needed to tackle problems alone.
When children’s intuitions are respected and valued, and when they are encouraged to listen to other children explain how they answer questions, they naturally pick up more advanced ways of solving problems.
Getting correct answers is important, but it is the process of getting those answers that is key in getting children to build and trust their intuitions.
Jung, M., Kloosterman, P., McMullen, MB, (2007)

24. Five Steps to Problem Solving
Understand the problem
Devise a plan
Carry out the plan
Answer the question
Evaluate the answer
Talk through the adult language to facilitate each step:
Understanding the problem
Devising a plan
Implementing the plan
Arriving at an answer
Evaluating the answer
Teachers can use self talk (talking about what they are doing) or parallel talk (talking about what children are doing) to model this process.
You may also want to ask children to discuss a problem and explain how they are going to go about solving it with one another. Encourage children to talk about their thinking with one another.
Discuss how this process helps in thinking about feedback loops and conversations with children about their mathematical ability. Remember to give children time to talk about their thinking.

25. Adult Talk During Problem Solving
Language should describe children’s thinking, as best you understand it
Suggest possible solution – tentatively (What if…?; Have you thought about…?)
Encourage multiple ways to get to answer
Reflect on the process of problem solving
Encourage children to talk about how they arrived at their answer to a mathematical problem.

26. Problem Solving & Posing
As children engage in problem solving,
teacher is thinking about:
Where is the child now?
What is the next logical step for the child to learn?
What should the child do to accomplish this objective?
What materials should be used?
Do the plan and materials fit the expectation as indicated by the objective?
Has the child learned?
Charlesworth and Lind (200X) suggested that teachers attend to the following ass children engage in problem-solving activities:
Assess - Where is the child now?
Choose objectives - What should the child learn?
Plan experiences - What should the child do to accomplish this objective?
Select materials - What materials should be used?
Teach - Do the plan and materials fit the expectation as indicated by the objective?
Evaluate - Has the child learned what was taught?
In the Pre-K math they give some ideas for differentiated instruction: making it easier, harder, or supporting ELL learners.

27. Universal Design for Early Childhood Education
Multiple Means of Representation
Multiple Means of Engagement
Multiple Means of Expression
The concepts of multiple intelligences fit nicely with research on Universal Design for Early Childhood Education which says that the three key components of Universal Design are
Multiple Means of Representation: provide children with varied ways to explore and process information, including moving, seeing, hearing or touching
Multiple Means of Engagement: support learners’ interests, and provide adequate motivation and challenge for learning
Multiple Means of expression: learners have various opportunities to demonstrate what they know and teachers use assessment and documentation of changes in children’s development and learning over time
Show me, tell me, represent it.
Making connections across the curriculum in centers is one way to support Universal Design.
Using multiple settings for explicit math instruction, such as small group, whole group, and individually working with children.
Reflecting on informal observational data on how the student learns best.

28. Differentiated Instruction
Differentiated instruction is a teaching theory based on the premise that instructional approaches should vary and be adapted in relation to individual and diverse students in classrooms (Tomlinson, 2001).
The model of differentiated instruction requires teachers to be flexible in their approach to teaching and to adjust the curriculum and presentation of information to learners rather than expecting students to modify themselves for the curriculum. Many teachers and teacher educators have recently identified differentiated instruction as a method of helping more students in diverse classroom settings experience success.
While we now have established benchmarks for both three- and four-year-olds in our classroom, we must also recognize the need to differentiate instruction to accommodate diverse learners.
In each of the HM math themes each activity lists ways to support ELL, make the task easier, and make it harder, and discusses what to observe and how to support.
The key elements of HM math are:
Identify as learning goals:
Each activity lists the specific math and process standards as well as related vocabulary.
This is your framework on which you add your knowledge of individual children and adapt or scaffold the activity to support each child’s development.
How do you regularly observe and document children’s knowledge and skill?
How is this information used to inform instruction?
How have you differentiated math instruction in your classroom?
Give example information on three students’ ability to count. Discuss each student and their development. Then discuss why differentiating math instruction may be helpful. How can these be implemented? Whole or small group?
(Differentiated instruction CAST)

29. Break

30. How Many are Hiding? Watch the video.
What process and content standards are being taught?
What strategies are being used to teach the concepts?
Pull out Purple Paper Video Observations
Let take a few minutes to watch a short video clip. Think about how communication is being facilitated and how children are talking about their thinking in multiple ways. Watch the video clip and see if you can identify the content and process standards being taught. List the strategies the teachers uses to teach these concepts.
Start video 11:16 stop video at 15:54
Turn off the video and discuss what process and content standards are being taught.
How often were children being asked to explain their thinking? (what were some multiple ways?)
Then discuss the strategies used to teach them.
Number operation part/part whole
Process standard communication and representation
Physically acted out and discussed
Practice and talk
Represent and review
Video 5 minutes
Discussion 5 minutes
Total 10 minutes

31. Which is Heavier? Watch the video.
What process and content standards are being taught?
What strategies are being used to teach the concepts?
Now let’s take a few minutes to watch another video. This time, let’s identify the concepts the teacher is intentionally teaching. What types of questions does the teacher ask? How does she facilitate higher-order thinking? Listen for and document the mathematical language she uses.
Concepts related to standards:
Science: observable properties. Manipulative a wide variety of familiar and unfamiliar objects. Observe, describe, and compare using appropriate language.
Science: Explore and describe a variety of natural and manmade materials though sensory experiences.
Math: Listen and use comparative words to describe the relationship of objects to one another.
Use estimation in meaningful ways and follow up by verifying the accuracy of estimations.
Use non-standard units to measure length, weight, and amount of content in familiar objects.
Questions What do you remember? What happens if… Think about… What’s your prediction? What do you think?
Vocabulary: Tool, heavy/light, predict
Flexibility and acceptance of responses
Video 2.45
Reflect 1 minute
Discuss 5 minutes

32. Reflecting on student learning
Individually read the vignette.
In small groups, discuss:
What does the teacher say/do to support students’ learning? 
How does she respond differently to different students, and why? 
What else might you do to extend learning?
Participants will be given one of three vignettes to read.
After reading the vignette they will work in groups and discuss. 1. what they know about each child’s development, 2. identify strategies the teacher used to support learning, and 3. list additional strategies that might be used to support learning.
In your packets you also have several resources to assist you in reflecting on each child’s development. The Golden Rob color packets of information in packet labeled Children’s Mathematical Developmental and Vignette 1. This packet includes several charts you may want to use as references when considering a child’s current level of development as well as information on the next level of development and the target level for instruction.
There is a XX sheet of paper for you to individually and as a group record your findings.
5 minutes to read
10 minutes to discuss
5 minutes to collectively gather information to report to the group

33. Mathematical thinking is everywhere
Think about all the areas in your classroom. There are many opportunities throughout the classroom to engage children in mathematical thinking.
Dramatic play, how much, (grocery store) how long (which dress do you want to wear)
Blocks (geometry, measurement, spatial relationships)
Book corner (number books, shape books, pattern books, measurement books, operation books)
Math center: Attribute blocks (create, match, fill in)
Counting games, measurement games.
Art whole/part, shapes, numbers
Manipulatives: How many, how tall, comparing structures or patterns, puzzle spatial relationships.
Introduce new objects, games, & events
Add complexity to the task
Plan for the environment:
Manipulatives
Games
Construction materials

34. Use Books
Children’s literature creates a natural context for talking about mathematics (see Hellwig, Monroe, and Jacob, 2000; Moyer, 2000)
To launch conversation around the mathematical story line
To make meaning
To Illustrate use of process standards
Children’s literature involving mathematics creates a natural context for talking about mathematics (see Hellwig, Monroe, and Jacof, 2000; Moyer, 2000). 34

35. Promoting mathematical thinking
Model and demonstrate
Ask thought-provoking questions
How do you know?
Tell me about your thinking.
Meal time can be used to reinforce mathematical concepts such as counting, shape recognition, and making comparisons or classifications.
Model counting. Compare more or less. Classify or compare groups of objects and describe their characteristics. Ask children to describe their thinking and how they know.

36. More strategies Facilitate support and enhance exploration
Open-ended and focused questions
Engage students in higher-order thinking
Predictions
Classification and comparison
Evaluation
Opportunities to explain their thinking and reasoning to others
Provide opportunities for children to plan, anticipate, reflect on, and revisit their own learning experience
Each day in Houghton Mufflin Math there is a question labeled Think and Talk.
The questions are open-ended and encourage children to talk about their thinking, giving you a window into their current level of development.
Open ended:
Tell me about your … shape.
How do you know?
Focused
How any sides are in your shape?
What comes before or after 3?
Use these daily questions to promote excitement around numbers. Example: Can anyone predict where they might be able to make a set of 9 today? Where might you be able to do that? Then after center time ask children to share their sets of nine with the whole group.
Each day there are suggestions for ELL, make easier, make harder. Observe and document children’s development and differentiate instruction for all young children.

37. Every Day Conversations about Math
December 19, 2008
Classroom Climate:
Students feel secure and comfortable enough to:
Share beliefs
Ask questions
Hypothesize
Express ideas
Make mistakes
CLASS looks at several components of classroom climate.
Climate: High climates: teachers and students are enthusiastic about learning and respectful to one another. Teachers and students have positive relationships with each other and clearly enjoy being together and spending time in the classroom.
Look at elements such as: Relationship: physical proximity, shared activities, peer assistance, matching affect (smiling, laughing) to social conversations. Affect: smiling, laughing, enthusiasm. Positive communication: verbal affection, physical affection, positive expectations. Positive communication: verbal, physical, positive expectations. Respect: eye contact, warm calm voice, respectful language, cooperation and sharing.
Regard for student perspective: High classrooms regard student perspectives intentionally and consistently place an emphasis on student interests, motivations, and points of view. In classrooms high on this dimension teachers promote students’ independence by providing meaningful roles for them within the classroom, encouraging them to talk and share ideas, and allowing them to make decisions for themselves when appropriate.
Boston Ready

38. Facilitate Discourse Questions - no incorrect answers
Allow time before sharing with classmates
Discuss ideas with a partner before sharing with entire group
Social learning is learning, not “cheating”!
Whether children are working in small groups, or talking about issues in larger groups, it’s important to get them involved in classroom discussions that lead them to share their ideas and solutions about problems as well as to respond to their classmates’ solutions. Classroom discourse influences students’ reasoning, problem-solving competencies, self-confidence, and social skills acquisition.
To facilitate active sharing of ideas, teachers should:
Create an environment where students feel secure and comfortable enough to share their beliefs, ask questions, hypothesize, and make mistakes.
Teachers may reduce students’ anxiety and increase their willingness to participate in discussions by asking questions that have no incorrect answers.
Arranging seats in a circle so that students can easily see classmates as they speak.
Letting students discuss their ideas with a partner before sharing them with the whole group, and
Giving students an opportunity to think about the problem before sharing their thoughts with their classmates. 38

39. Reflecting on this session
Does anyone want to add anything to the list?
Tell me about your thinking.
What is one take-away you have from this morning’s session?

40. Lunch

41. Small group exploration
Integrated approach to aligning OWL and HM Pre-K Math
Room 2039
Preview Pre-K Math activities and extensions; develop HOT language
Room Tigers Den Annex
Group will break up into two small groups. Teachers will look at aligning OWL and HM Math. Task: think about ways to integrate the curriculums. Will be asked to look at alignment, extension activities, vocabulary, and guidelines.
Assistant teachers will be given several HM activities and potential extension activities to preview and will be asked to review, reflect and develop language to use in interacting with children that promotes higher-order thinking skills.
Teachers
Instructional Partners

42. Ideas for involving families in mathematical language and literacy:
If you had a budget of $50.00, how would you engage families in literacy?
Describe the purpose and goals of your family literacy event.
How would you measure success?

43. Take-Away
What is one thought you will take away from today’s session?

44. Work Plans and Evaluation
Reflect on today’s professional development.
Establish a goal for yourself.
What are one or two ideas you will take away from today’s session?
Design an action plan for yourself.
What is your goal?
What supports will you need?
How will you use your coach as a resource?
What changes do you expect your coach to observe in the classroom?