1. EDU 320
Chapter 15
Data Analysis

2. 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.

3. Underlying Facts
There six underlying facts about the learning and teaching of data analysis.

4. 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.

5. 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

6. 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.

7. 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.

8. 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

9. 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.

10. 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.

11. 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

12. 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.

13. Informal quantitative students (level 3) use quantitative reasoning
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)

14. 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.

15. (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.

16. 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.

17. 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.

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

19. Organized Counting (Pascal’s Triangle)
Pascal’s 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.

20. 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.

21. 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.

22. Type of Concrete Materials
Two-Color Counters-plastic poker chips, colored sticks, spray-painted lima beans
Dice
Spinners

23. http:// pbskids.org/cyberchase/parentsteachers/lessons_web.html

24. By Demi