Download
1 / 25
250 likes | 257 Views
Data Analysis and Statistical Reasoning. Geometric and Spatial Reasoning: Review & Sharing What is Statistical Reasoning? Statistical Reasoning Assessment (SRA) Statistics and Graphical Reasoning Data Analysis Problems. Today’s Agenda. Geometric and Spatial Reasoning Review.
E N D
Geometric and Spatial Reasoning: Review & Sharing What is Statistical Reasoning? Statistical Reasoning Assessment (SRA) Statistics and Graphical Reasoning Data Analysis Problems Today’s Agenda
Geometric and Spatial Reasoning Review • Pass around and look at student baseline assessments within your group. • Assess and sort according to students’ abilities with geometric and spatial reasoning • 0: no spatial reasoning skills exhibited • 1: some evidence of spatial reasoning • 2: fluent spatial reasoner. • Was there a correlation between students’ abilities with planar figures and the 3D isometric problems? • Are your good geometric reasoners also good at algebraic reasoning?
Geometric and Spatial Reasoning Review What did you learn most from the baseline and summative assessments? Describe at least two ways that you helped your students with geometric and spatial reasoning. Describe one classroom situation where you saw a student exhibit growth in thinking about proof.
Definition Statistical reasoning may be defined as the way people reason with statistical ideas and make sense of statistical information. This involves making interpretations based on sets of data, representations of data, or statistical summaries of data. (Garfield & Chance, 2000)
Mathematics vs. Statistics Many people think of mathematics and statistics as the same thing, and therefore confuse statistical reasoning with mathematical reasoning. Today’s leading statistical educators see these disciplines and types of reasoning as quite distinct. (Garfield & Gal, 1999)
Distinguishing Characteristics I • In statistics, data are viewed as numbers with a context, which can affect procedures and interpretation. • Statistics has “messy” data compared to the precision of mathematical reasoning and proof.
Distinguishing Characteristics II The fundamental nature of statistics problems is that they do not have a single mathematical solution. Rather, realistic statistics problems begin with a question and culminate with an opinion based on certain assumptions. The “correctness” of the answer is subjective, depending on the communities standards for techniques and reasoning.
Example of Context An economics teacher asks five students how much cash they are carrying in their pockets. The results are: $6.50 $7.10 $15.80 $7.30 $6.80 The teacher wishes to find the average amount of cash that each of the five students has. What is the answer?
Example of Context – Part II A physics teacher gives five students a stopwatch and asks them to time how long it takes for a ball to drop from the roof of a tall building to the ground. In seconds, the times were: 6.5 7.1 15.8 7.3 6.8 How should she average her students’ times to come up with the “average” observation?
SRA Joan Garfield developed the Statistical Reasoning Assessment (SRA) as part of the ChancePlus Project. You will take the assessment before discussing what it measures, to avoid any bias in your answers!
SRA Discussion Did you notice the built-in ambiguity with some of the questions and answers? Did you find any problems more difficult than others? Did you feel any were unfair?
What does the SRA measure?Correct Reasoning Skills: • Correctly interprets probabilities • 2. Understands how to select an appropriate average • 3. Correctly computes probability • a. Understands probabilities as ratios • b. Uses combinatorial reasoning • 4. Understands independence • 5. Understands sampling variability • 6. Distinguishes between correlation and causation • 7. Correctly interprets two-way tables • 8. Understands importance of large samples
What does the SRA measure?Misconceptions: • Misconceptions involving averages • a. Averages are the most common number • b. Fails to take outliers into consideration when • computing the mean • c. Compares groups based on their averages • d. Confuses mean with median • 2. Outcome orientation misconception • 3. Good samples have to represent a high percentage of the population • 4. Law of small numbers • 5. Representativeness misconception • 6. Correlation implies causation • 7. Equiprobability bias • 8. Groups can only be compared if they are the same size
Setup One of your clever and precocious students, Harvey, challenges you to a game: “I toss a coin 20 times. If 40-60% of all my tosses turn out heads, I win. Otherwise you win.” You are tempted to play, but wonder about the choice of 20 flips. On one hand, if you asked for 40 flips you have more chances to win. But you also think that the more times the coin is flipped, the more likely it is that about half of them will be heads, making you lose. Should you agree to play, but with fewer than 20 flips? Investigate this game on your handout!
