EDU 320

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EDU 320

• Chapter 15
• Data Analysis

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Understanding Relevant Learning Frameworks

• According to researcher Friel, Curcio, and Bright
  (Statistics) and Jones, Langrall, Thornton, and
  Mogill (Probabilitity) There has been very little
  research on how learners develop data analysis
  knowledge. Because this is a developing field,
  current research opt to identify their finding as
  framework rather, than theory. Before 1990 very
  few experiences with data analysis were included
  in typical primary curricula.

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Underlying Facts

• There six underlying facts about the learning and
  teaching of data analysis.

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• First, a problem-solving approach to teaching is
  consistent with how learners develop data
  analysis knowledge.
• Second, concept knowledge must be developed
  before developing procedural or conventional
  knowledge.
• Third, concepts and procedures are heavily
  interdependent.

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• Fourth, Statistical representations can become
  more and more sophisticated as students have more
  experiences dealing with data and as their
  knowledge of probability ideas such as likelihood
  become more sophisticated.
• Fifth, data organization can be greatly aided by
  appropriate use of technology.
• Sixth and last, there are certain early
  experiences that lay the foundations for the more
  sophisticated ideas behind data analysis

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The importance of Students -Generated Data

• Early learning experiences with data analysis is
  the opportunity to work with data that make sense
  to the learner.
• It is critical that students be encourage to and
  allowed the time to engage in explorations with
  an eye toward making sense of the the data-hence,
  data analysis.

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• Students must see how relationships exist between
  data pieces and understand for themselves what is
  going on.
• The content is in some ways unpredictable, so
  students must truly understand the concepts
  before thinking about applying procedures.
• This information simply cannot be rotely
  memorized.

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Statistics Framework

• According to Friel, Curcio, and Bright students
  progress through three kinds of analysis.
• 1. Extracting information from data
• 2. Finding relationships in data
• 3. Moving beyond data to make claims

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Organizing concepts

• Students must first understand the concept of
  data before extracting information from them.
• As students work with their own data they should
  be prompted to think about different ways to
  organize and reorganize, the data in the sample.
• By creating and studying several different
  organizations, students are more able to see
  relationships within and between the data.

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• Students might note that one kind of value
  occurred more often than another. They might
  organize information into two or more groupings
  rather than looking at individual pieces of data
• By rearranging data, they develop the capacity to
  see relationships.
• Once students have an understanding of
  organization and making representation students
  can interpret data by making generalizations.
  
  
  
  

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Probability Framework

• According to Jones, Langrall, Thornton, and
  Mogill. Students progress through four levels of
  thinking
• 1 subjective
• 2 transitional
• 3. Informal quantitative
• 4 numerical

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• Subjective Students (level 1) tend to think
  narrowly and inconsistently about information
  under investigation. They might be swayed by
  their own experience.
• Transitional students (level 2) seem to recognize
  some usefulness to quantifying or organizing
  information to make a general statement. But are
  not sure enough or experienced enough to justify
  their claims and can still be convinced of
  subjective claims.

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• Informal quantitative students (level 3) use
  quantitative reasoning. Students make sense of
  multistep problems and organize information in a
  structured manner. They are also less swayed by
  subjective claims and can concentrate on several
  aspects of a single event.
• Numerical students (level 4) make abstract
  connections and precise calculations about the
  nature of the probability situation.
• Table 15.2)

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Recognizing Development Through Likelihood

• The concept of likelihood is the level of
  certainty of an event.
• (level 1) Understanding of the concept of
  certain as opposed to impossible is the launching
  point for probability.
• (Level 2) Students grow to include notions of
  most likely or least likely in thinking about
  probability.

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• (Level 3) Students develop more sophisticated
  thinking, attaching notions of more likely or
  less likely as opposed to notions of most likely
  or least likely. (more comfortable justifying)
• (Level 4) Students learn to attach a numerical
  estimation (probability) to the degree of
  likelihood of an event.

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Recognizing Development through Randomness

• Being able to calculate the degree of likelihood
  of an event requires awareness of the concepts of
  randomness.
• According to Horvath and Lehrer Understanding of
  the general nature of gathered data in an
  experimental trial, as a viable representation of
  the situation, must be consciously developed.

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• Subjective learners level 1 think about possible
  outcomes from a situation by listing only
  familiar outcomes.
• At level 2, learners begin to list complete sets
  of outcomes and can begin to understand and make
  sense of situations that may have two steps.
• Level 3 students list outcomes from a situation,
  no matter how complicated.
• By level 4 learners are able to generate
  strategies for listing the the outcome set rather
  than mechanically writing down all possible out
  comes.

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Comparing Probabilities

• Experimental probability - (example) when
  forecasting weather
• Theoretical probability- (example) pulling B7
  from a bingo cage that contains 75 different
  chips 1/75

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Organized Counting(Pascals Triangle)

• Pascals triangle is a useful tool when it is
  necessary to count possible outcomes in a variety
  of situations so you can calculate probabilities
  and make a prediction.

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Using Student-Generated Data

• When we teach about data analysis, it is critical
  to used students generated data.
• Teacher aid materials (pictures
• Modeling
• provide stimulate that students can relate to and
  are familiar with.

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• When data gathering that require dice or coins
  you might want to provide students with a shoebox
  lid to lesson the noise of the flipping and
  rolling of dice or coins being used.

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Type of Concrete Materials

• Two-Color Counters-plastic poker chips, colored
  sticks, spray-painted lima beans
• Dice
• Spinners

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http// pbskids.org/cyberchase/parentsteachers/le
ssons_web.html
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By Demi