jennifer kearns-fox, mary lu love & lisa van thiel institute for community inclusion university...

Jennifer Kearns-Fox, Mary Lu Love & Lisa Van Thiel

Institute for Community Inclusion University of Massachusetts Boston

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

What math concepts might children be learning in each center?

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,

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.

Problem-Solving Connections Reasoning Representation Communication

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?

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.

Content and Process StandardsNumber & 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.

AlgebraPatterns can be used to recognize relationships and can be extended to make generalizations.

Problem Solving

Geometry•Geometry can be used to understandand to represent the objects, directions,and locations in our world and the relationships between them.•Geometric shapes can be described,analyzed, transformed, and composedand decomposed into other shapes.

Measurement•Comparing and measuring can be used to specify “how much” of an attribute (e.g., length) objects possess.•Measures can be determined by repeatinga unit or using a tool.

Data Analysis•Data analysis can be used to classify,represent and use information to ask and answer questions.

Communication

Representatio

n

Reasoning

Connections

Clements and Sarama, 2004

Line up according to your comfort with math.

phobic genius

What should every four-year-old know and be able to do?

1. Number Sense & Operations

2. Algebra3. Geometry 4. Measurement5. Data Analysis

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.

What should every four-year-old know and be able to do?

1. Number Sense & Operations

2. Algebra3. Geometry 4. Measurement5. Data Analysis

Assess Choose learning outcome Plan experience for learning Select materials and resources Facilitate learning experience Assess what learners have learned

(Brewer and Kallick, 1997)

Robert Pianta

Bridget Hamre Karen LaParo

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)

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

Popham (2002)

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

The more we relinquish the role of problem solver, the more children will assume it. (Carol Gross)

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

As children engage in problem solving,teacher is thinking about:1. Where is the child now?2. What is the next logical step for the child

to learn? 3. What should the child do to accomplish

this objective?4. What materials should be used?5. Do the plan and materials fit the

expectation as indicated by the objective?6. Has the child learned?

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).

Watch the video. What process and

content standards are being taught?

What strategies are being used to teach the concepts?

Watch the video. What process and content standards are

being taught? What strategies are being used to teach the

concepts?

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?

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

Model and demonstrate Ask thought-provoking questions

◦ How do you know?◦ Tell me about your thinking.

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

Students feel secure and comfortable enough to: Share beliefs Ask questions Hypothesize Express ideas Make mistakes

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”!

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?

Teachers Instructional Partners

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

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?

What is one thought you will take away from today’s session?

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?