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Fostering Mathematical Excellence in Early Childhood Education

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Title: Fostering Mathematical Excellence in Early Childhood Education


1
Fostering Mathematical Excellence in Early
Childhood Education
  • Dr. Susan Looney
  • looneyconsulting_at_comcast.net
  • www.looneymathconsulting.com

2
PSSM
  • Most students enter school confident in their own
    abilities, and they are curious and eager to
    learn more about numbers and mathematical
    objects. They make sense of the world by
    reasoning and problem solving, and teachers must
    recognize that young students can think in
    sophisticated ways. Young students are active,
    resourceful individuals who can construct,
    modify, and integrate ideas by interacting with
    the physical world and with peers and adults.
    They make connections that clarify and extend
    their knowledge, thus adding new meaning to past
    experiences. They learn by talking about what
    they are thinking and doing and by collaborating
    and sharing ideas.

3
- Andrews and Trafton, 2002
  • When children make sense of mathematics, they
    develop deep understanding of important ideas by
    making connections with their informal
    mathematical knowledge and making connections
    among mathematical ideas.
  • Children surprise us by learning mathematics
    beyond our perceptions and they learn it better.

4
The Handshake problem in Kindergarten?????
  • Start with 4 or 5 students in a group. How many
    handshakes will there be if each person in your
    group shakes the hand of every person once?
  • Tell who was in your group.
  • How did you get your answer?
  • Try to show your solution on paper.
  • How many handshakes will there be if 1 more
    person joins your group?
  • What if 2 more join? 3 more join?
  • Do you see a pattern in the numbers? Describe the
    pattern.

????? Joey Kim Connor Trina





5
Partnership for the 21st Century Skills
  • An organization leading the way ..

6
Rainbow

7
Learning and Innovation Skills
  • Creativity and innovation
  • Critical thinking and problem solving
  • Communication and collaboration

8
Counting on Frank by Rod Clement
9
Problem Solving Choose a problem to solve. Show
and tell how you arrived at your answer.
  • 1. The boy calculates that 24 Franks (his pet
    dog) could fit into his bedroom. What if, in
    addition to these 24 Franks, 30 Franks could fit
    into the boys parents bedroom, 25 in the living
    room, 10 in the bathroom, and twenty in the
    kitchen? How many Franks in all would fit into
    the boys house?
  •  
  • If there were 24 Franks in the bedroom,
    how many ears would there be? How many Frank paws
    would there be?
  •  
  •  
  •  
  •  
  • 2. If the boy accidentally knocks 15 peas off
    his plate each night, how many peas would he
    knock off in one week? Two weeks? What about for
    the last 8 years as stated in the story?
  •  
  •  
  •  
  •  
  • 3. The tree in the boys yard grows 6 feet
    each year. If he had grown at the same speed, he
    would be almost 50 feet tall. How old is the boy
    in the story? How tall would you be if you grew
    at this rate?

10
Characteristics of Sense-making Classrooms
  • Children take ownership of task and problems,
    letting them use their own approaches and
    strategies / over time with sharing, immature
    strategies become more mature
  • Sufficient time repeated opportunities
  • Reflect and communicate
  • Variety of tools available at all times
  • Teachers role of observer when to let children
    work and when to provide info and closure /
    questions and genuine interest
  • Respect for childrens ideas and belief that all
    children can learn mathematics

11
How do I Teach Students to make connections in
their solutions?
  • After students complete a task, brainstorm what
    types of connections they can go back and add to
    their work.
  • After students complete a task, request that they
    make an eye noticed statement about their
    solution.
  • Ask good questions and give rich tasks that will
    provide opportunity for students to make
    connections.
  • Spotlight students who make connections, either
    by giving them a mathematics award, or just a pat
    on the back.
  • Give students opportunities to self assess, then
    revise their work.

12
Motivating Students to keep thinking .
  • Focus on the outcome vs. the performance.
  • You answered the question vs. good job
  • You did it! You wrote that!
  • What you did vs. how you did
  • Check-in points You did half of the problems.
  • Rationale Releases a brain chemical called
    dopamine which increases motivation to continue
    because the students feels good.

13
Characteristics of Rich Tasks
  • Open ended
  • High demands
  • Novel
  • What else???

14
Consider the two classrooms.
  • What skills are necessary for the students to be
    successful in classroom A? Classroom B?
  •  
  • How would you describe the level of challenge in
    Classroom A? Classroom B?

15
Classroom A
  • Classroom A
  •  
  • Check of last nights homework
  • Demonstration of how to add with regrouping
  • Students work on 20 similar problems
  • Teacher reminds students how to compute
  • Assigns remainder of problems for homework plus
    word problems at the end of the page
  •  
  •  
  •  
  • Word problem Sarah and John went apple picking.
    Sarah picked 23 apples. John picked 38 apples.
    How many apples did they pick all together?
  •  

16
Classroom B
  •  
  • Students enter room and are asked to immediately
    begin working in small groups on the task as
    described by the teacher. They will have the
    entire period to work on this task, and they may
    quietly get whatever paper, tools, or
    manipulatives they will need to complete the
    task.
  • Task Collecting Shells
  • Paul and Amy love to collect seashells. The first
    time they went to the beach they each found 5
    shells. The second time they went to the beach
    Paul found 6 shells and Amy found 4 shells. The
    third time they went to the beach Paul found 15
    shells and Amy found 17 shells. Amy said that she
    found the most shells while Paul argued that they
    both found the same amount of shells. Who was
    right? Show how you know.
  •  
  • During class the teacher questions various
    groups, provides hints about how to proceed, but
    never shows students exactly how to go about
    solving the problem.
  •  
  • At the end of the period, none of the groups are
    finished with the task, but they are all actively
    engaged in problem solving.

17
Depth of Knowledge (DOK)
  • Level 1 (recall) conduct basic math
    calculations perform routine procedures
  • Level 2 (skill / concept) solve routine
    multiple-step problems organize, represent, and
    interpret data
  • Level 3 (strategic thinking) apply a concept in
    other contexts, compare, non-routine problems,
    strategic thinking, logical arguments
  • Level 4 (extended thinking) apply math model to
    illuminate a problem, to inform, and to solve
    design, critique, prove

18
Task Sort
  •  
  • Identify which Depth of Knowledge level for each
    of the tasks described below.
  •  

19
Task A Grade 1
  • Sam bought 4 cookies for 10 cents a piece. How
    much money did he spend?
  • Recall Skill Strategic thinking Extending
    thinking

20
Task B Grade 1
  • 3 7
  • 4 6
  •  
  • Recall Skill Strategic thinking Extending
    thinking

21
Task C Grade 3
  • John is making rectangles using square tiles. He
    has 24 tiles. How many different rectangles can
    he build?
  • Show all your work.
  • Recall Skill Strategic thinking Extending
    thinking
  •  

22
Task D Grade 2
  • Write a word problem that would be solved by this
    equation
  • 23 45 68
  • Recall Skill Strategic thinking Extending
    thinking
  •  

23
Task E Grade 2
  • Using base-ten blocks, solve the following
    addition problem
  •  
  • 23 45 68
  • Recall Skill Strategic thinking Extending
    thinking

24
Task F Kindergarten
  • Start with 4 or 5 students in a group. How many
    handshakes will there be if each person in your
    group shakes the hand of every person once?
  • Tell who was in your group.
  • How did you get your answer?
  • Try to show your solution on paper.
  • How many handshakes will there be if 1 more
    person joins your group?
  • What if 2 more join? 3 more join?
  • Do you see a pattern in the numbers? Describe the
    pattern
  • Recall Skill Strategic thinking Extending
    thinking

25
Questions for analyzing student work
  • What can we say about each students response?
  • What does this students response tell us he knew
    about ___?
  • What questions might we ask the student to better
    understand his reasoning?
  • What mathematical concepts or procedures might
    the student use to answer this question
    correctly?
  • What might we do to further explore this
    students ability to communicate what he knows
    about ____?
  • What other mathematical ideas could we assess
    with this task?
  • In what ways could we use information learned
    from this task to plan for the next lesson with
    this students?

26
Task Student work
  • Look through the student samples and highlight
    where the student went beyond the demands of the
    task.
  • Identify what makes each task a rich task

27
Summary
  • Choose rich tasks
  • Find time to enrich and extend
  • Explicitly teach children to persevere
  • Allow for revisions
  • Use student work to inform instructional
    decisions
  • Celebrate and share excellence

28
Conclusion
  • The attitudes children develop in the early
    years will strongly influence their future
    mathematical performance. If children experience
    connections and sense-making mathematics, they
    will come to think of mathematics as a
    sense-making experience. If they experience
    interesting, powerful mathematics, they will come
    to view mathematics as the interesting and
    powerful endeavor it can be.

29
Resources
  • Problems from Exemplars www.exemplars.com
  • Clement, Rod (1991). Counting on Frank.
    Milwaukee, WI Gareth Stevens Publishing.
  • Principles and Standards for School Mathematics,
    NCTM 2000.
  • Andrews and Trafton (2002). Little Kids
    Powerful Problem Solvers. NH Heinemann.
  • Fosnot (2007). Investigating Number Sense,
    Addition, and Subtraction, Unit Beads and Shoes,
    Making Twos. NH Heinemann.
  • Seeley (2009). Faster Isnt Smarter. CA Math
    Solutions.
  • NCTM (2001). Assessment Sampler, Grades PreK 2.
    VA NCTM.
  • http//www.21stcenturyskills.org/
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