Session 2 Schooling and Theories on Thinking

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Session 2 Schooling and Theories on Thinking
Learning

• What is the purpose of school?
• What is your role as the teacher?

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Focus Activity Do We Have Enough?

• K 1 Focus
• Your school has been collecting canned food to
  donate to the community. When a box is full your
  class will pack it up and send it to City
  Harvest. City Harvest wants to know how many
  cans you collected into the box each time it got
  full. What would you do to keep track? How might
  you find out the total number of cans you have
  donated in all?

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Questions for us to consider?

• What mathematical concepts is this activity
  asking students to grapple with?
• How might this word problem become relevant?
• How did you go about solving the problem.
• How would you show others to get this job done as
  well?
• Is there information that might be missing?
• What questions might you be able to build off of
  this initial set of information?

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How do Children Learn Math?
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Socio - Transformative Constructivism

• Alberto J. Rodriguez - San Diego State Univ.
• STC Teachers are informed, and use, theories of
  learning (socio-constructivism) and theories of
  justice (multiculturalism, critical pedagogy,
  transformation)

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Constructivism

• Piaget's theory is based on the idea that the
  developing child builds cognitive structures--in
  other words, mental "maps," schemes, or networked
  concepts for understanding and responding to
  physical experiences within his or her
  environment. Piaget further attested that a
  child's cognitive structure increases in
  sophistication with development, moving from a
  few innate reflexes such as crying and sucking to
  highly complex mental activities.
• Piaget's theory identifies four developmental
  stages and the processes by which children
  progress through them. The four stages are
• 1. Sensorimotor stage (birth - 2 years
  old)--The child, through physical interaction
  with his or her environment, builds a set of
  concepts about reality and how it works. This is
  the stage where a child does not know that
  physical objects remain in existence even when
  out of sight (object permanance).

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Constructivism

• 2. Preoperational stage (ages 2-7)--The child is
  not yet able to conceptualize abstractly and
  needs concrete physical situations.
• 3. Concrete operations (ages 7-11)--As physical
  experience accumulates, the child starts to
  conceptualize, creating logical structures that
  explain his or her physical experiences. Abstract
  problem solving is also possible at this stage.
  For example, arithmetic equations can be solved
  with numbers, not just with objects.
• 4. Formal operations (beginning at ages
  11-15)--By this point, the child's cognitive
  structures are like those of an adult and include
  conceptual reasoning.

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Representation
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Multiple Intelligence Theories

• Gardner defines an "intelligence" as a group of
  abilities that
• Is somewhat autonomous from other human
  capacities. Has a core set of information-processi
  ng operations. Has a distinct history in the
  stages of development we each pass through.Has
  plausible roots in evolutionary history
• While Gardner suggests his list of intelligences
  may not be exhaustive, he identifies the
  following seven (or eight)
• 1. Verbal-Linguistic--The ability to use words
  and language
• 2. Logical-Mathematical--The capacity for
  inductive and deductive thinking and reasoning,
  as well as the use of numbers and the recognition
  of abstract patterns
• 3. Visual-Spatial--The ability to visualize
  objects and spatial dimensions, and create
  internal images and pictures
• 4. Body-Kinesthetic--The wisdom of the body and
  the ability to control physical motion

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Multiple Intelligences, cont.

• 5. Musical-Rhythmic--The ability to recognize
  tonal patterns and sounds, as well as a
  sensitivity to rhythms and beats
• 6. Interpersonal--The capacity for
  person-to-person communications and relationships
• 7. Intrapersonal--The spiritual, inner states of
  being, self-reflection, and awareness
• 8. Naturalistic-- has to do with nature,
  nurturing and relating information to one's
  natural surroundings

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Socio-Historical Constructivism

• Humans are social beings, situated within culture
  and history.
• These realities shape our thinking processes.

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Socio-Historical Constructivism

• 1. Culture makes two sorts of contributions to a
  child's intellectual development. First, through
  culture children acquire much of the content of
  their thinking, that is, their knowledge. Second,
  the surrounding culture provides a child with the
  processes or means of their thinking, what
  Vygotskians call the tools of intellectual
  adaptation. In short, according to the social
  cognition learning model, culture teaches
  children both what to think and how to think.
• 2. Cognitive development results from a
  dialectical process whereby a child learns
  through problem-solving experiences shared with
  someone else, usually a parent or teacher but
  sometimes a sibling or peer.

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Socio-Historical Constructivism

• 3. Initially, the person interacting with child
  assumes most of the responsibility for guiding
  the problem solving, but gradually this
  responsibility transfers to the child.
• 4. Language is a primary form of interaction
  through which adults transmit to the child the
  rich body of knowledge that exists in the
  culture.
• 5. As learning progresses, the child's own
  language comes to serve as her primary tool of
  intellectual adaptation. Eventually, children can
  use internal language to direct their own
  behavior.

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Socio-Historical Constructivism

• 6. Internalization refers to the process of
  learning--and thereby internalizing--a rich body
  of knowledge and tools of thought that first
  exist outside the child. This happens primarily
  through language.
• 7. A difference exists between what child can
  do on her own and what the child can do with
  help. Vygotskians call this difference the zone
  of proximal development.
• 8. Since much of what a child learns comes
  form the culture around her and much of the
  child's problem solving is mediated through an
  adult's help, it is wrong to focus on a child in
  isolation. Such focus does not reveal the
  processes by which children acquire new skills.
• 9. Interactions with surrounding culture and
  social agents, such as parents and more competent
  peers, contribute significantly to a child's
  intellectual development.

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Problem Solving Centers

• 1.00 Words
• If a .01, b .02, c .03, and so on, what
  is the value of your first name?
• 2. Using the alphabet system, one of the days of
  the week is worth exactly 1.00. Which one is it?
• 3. Describe how you arrived at your answers for
  1 and 2.
• 4. Find other words that are worth 1.00. How
  about .75 words?

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Problem Solving Centers, cont.

• Counting Story
• Someone can read this aloud to their partner
  Three children are playing on the slide. Two
  children are playing in the sandbox. Count the
  children.
• Draw what you did to figure it out.
• Use the unfix cubes to create another counting
  story.
• Logical Breakfast
• Jonathan, Valerie, and Edwin each ate something
  different for breakfast. One had mangu, one had
  huevos rancheros, and one had a banana split.
  (the last one was allowed because the parents had
  to go to work early and abuelita was still
  sleeping)
• Jonathan, did not have huevos rancheros or a
  banana split. Valerie did not have huevos
  rancheros.
• Whose parents had to go to work early in the
  morning?

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What is Problem Solving?

• Problem any task or activity for which the
  students have no prescribed or memorized rules or
  methods, nor is there a perception by students
  that there is a specific correct solution
  method.
• It must begin where the students are
• The problematic or engaging aspects of the
  problem must be due to the mathematics that the
  students are to learn.
• It must require justifications and explanations
  for answers and methods.

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What is Problem Solving?

• Problem solving is a skill that cuts across
  academic and social contexts Where else in our
  lives might we need to develop problem solving
  skills?
• Problem solving is developmental, becoming more
  sophisticated and from different perspectives as
  we grow in our own numeracy.

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Venn Diagram of Problem Solving
Concepts
strategies
Skills
Problem Solving
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Handouts

• Polyas 4-Step Rule
• Discuss within the context of the first math
  problem.
• Problem Solving Strategies
• Differentiation for Problem Solving (Separate
  discussion)

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Understanding By Design Jay McTighe Grant
Wiggins
Geometric shapes can be seen in many places in
the world The concept of the pyramid has been
used by many cultures as a basic building
structure.
Worth being familiar with
Important to know and do
Students will understand how to draw geometric
shapes Students will be able organize a chart to
organize and present the different
characteristics of geometric shapes.
Enduring Understandings
SWU how to identify and describe the
characteristics and properties of geometric
shapes SWUT shapes are essential to living and
acting in the world.
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UBD Terms

• Backward Design A process to designing a
  curriculum or unit by beginning with the end in
  mind and designing toward the end.
• Enduring Understanding (EU) The important ideas
  or core processes that have lasting value beyond
  the classroom. Such understandings are generally
  abstract in nature, so they require un-coverage
  through sustained inquiry.
• Essential Questions (EQ) A provocative question
  designed to engage student interest and guide
  inquiry into the important ideas in a field of
  study.

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Unit Cover Page

• Title Geometry is Everywhere!

• Link to Content Standards
• Geometry Strand Students will use visualization
  and spatial reasoning to analyze characteristics
  and properties of geometric shapes.
• 4.G.1 Identify and name polygons, recognizing
  that their names are related to the number of
  ides and angles
• 4.G.5 Define and identify vertices, faces, and
  edges of 3-D shapes.

Brief Summary of Unit This unit is a review of
2-D shapes and deeper discussion/introduction of
3-D shapes.
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Identify Desired Results

• What enduring understandings are desired?
• Students will understand how to identify and
  describe the characteristics and properties of
  geometric shapes.
• Students will understand the relationships
  between geometric figures.

What essential questions will guide this
unit? What is the different between 2-D and 3-D
shapes? What are the parts of of 2-D and 3-D
shapes? How have people used 2-D and 3-D shapes
in real life?
Key knowledge and skills students will acquire
through this unit? Students will know
Students will be able to - Key terms
(vertices, edges, faces) - Identify and document
the characteristics of 2-D 3-D
shapes