but…does it work? do students truly learn the material better?

But…does it work? Do students truly learn

the material better?

Nathan Tintle, Dordt College

Small liberal arts college: 1350 undergraduate students

Statistician within Department of Math, Stat and CS

Class size: Stat 131 (30 students), 5-6 sections per year

3 hours per week in computer or tech-enabled classroom

What we know about randomization approaches

What we don’t

What it means

Overview

Tintle et al. flavor (2013 version)◦ Unit 1. Inference (Single proportion)◦ Unit 2. Comparing two groups

Means, proportions, paired data Descriptives, simulation/randomization, asymptotic

◦ Unit 3. Other data contexts Multiple means, multiple proportions, two

quantitative variables Descriptives, simulation/randomization, asymptotic

Our approach

Qualitative

◦ Momentum: Attendance at conference sessions, workshops Publishers agreeing to publish the books Class testers/inquiries People doing this in their classrooms (clients,

colleagues) Repeat users

Appealing “in principle” and based on testimonials to date

What we know about it

Quantitative assessment

Tintle et al. (2011, 2012)◦ Compare early version of curriculum (2009) to

traditional curriculum at same institution as well as national sample

◦ 40 question CAOS test◦ Results

Better student learning outcomes in some areas (design and inference); little evidence of declines


Post-test answer

National sample

Hope -2007 Hope-2009

Small p-value 68% 86% 96%


Sample sizes: Hope ~200 per group; National Sample 760

P<0.001 between cohorts

Pre-test: 50-60% correct

Example #1. Proportion of students correctly identifying that researcherswant small p-value’s if they hope to show statistical significance

What we know about it 2012-13 results

14 instructors, 7 institutionsTotal combined sample size of

783

Instructor (Inst, Class size)

Pre-test Post-test Change Sample size

1 (LA, Med) 70% 97% 27% 33

2 (LA, Med) 73% 95% 22% 26

3 (Univ, Med) 23% 95% 72% 40

4 (LA, Med) 70% 96% 26% 127

5 (LA, Sm) 28% 92% 64% 11

6 (Univ, Med) 37% 96% 59% 49

7 (Univ, Sm) 39% 73% 34% 23

8 (LA, Med) 60% 97% 37% 35

9 (LA, Med) 29% 96% 67% 95

10 (HS, Med) 24% 74% 50% 38

11 (Univ, Large) 68% 97% 29% 101

12 (LA, Med) 63% 93% 30% 92

13 (LA, Med) 28% 95% 68% 18

14 (LA, Med) 56% 97% 41% 78


Institutional diversity in student background (pre-test)

Post-test performance very good for most (over 90%)

A couple of exceptions◦ Both first time instructors with curriculum who will

use it again this year


Example 1 (continued).

First quiz, 2.5 weeks into course; Simulation for a single proportion

119 people played RPS, 11.8% picked scissors

Evidence that scissors are picked less than 1/3 of time in long run?


The following graph shows the 1000 different “could have been” sample proportions choosing scissors for samples of 119 people assuming scissors is chosen 1/3 of the time in the long run.


Would you consider the results of this study to be convincing evidence that scissors are chosen less often in the long run than expected?


No, the p-value is going to be large 8%

No, the p-value is going to be small 2%

Yes, the p-value is going to be small 77%

Yes, the p-value is going to be large 9%

No, the distribution is centered at 1/3. 4%

Suppose the study had only involved 50 people but with the same sample proportion picking scissors. How would the p-value change?


It would not change, the sample proportion was the same

22%

It would be smaller 11%

It would be larger 66%

Not enough information 1%

Single instructor (me), on 92 students, across 4 sections and 2 semesters

Example #2. Moving beyond a specific item to sets of related items and retention

Tintle et al. 2012 (SERJ)+JSE

◦ Improvement in Data collection and Design, Tests of significance, Probability (Simulation) on post-test

◦ Data collection and Design and Tests of significance improvements were retained significantly better than in consensus curriculum


Retention significantly better (p=0.02)


Pre-test Post-test 4-Months Later50

55

60

65

70

75

Retention of knowledge about tests of significance (6 items from CAOS)

Randomization

Consensus

Example #3. How are weak students doing?


Pretest Posttest25

30

35

40

45

Performance on CAOS for lowest 1/3 of students (2007 vs. 2009)

Consensus

Randomization

2012-2013


Group Pre-test Post-test Change

Lowest (n=210; 13 or less)

38% 55% 17%

Middle(n=329;14-17)

52% 60% 8%

Highest(n=250; 18+)

66% 69% 3%

All changes are highly significant using paired t-tests (p<0.001)

**Among those who completed course; anecdotally we’reseeing lower drop out rate now than with consensus curriculum

Example #4. Understand new data contexts?

Old AP Statistics question

10 randomly selectedlaptop batteries; testedand measured hoursthey lasted


To investigate whether the shape of the sample data distribution was simply due to chance or if it actually provides evidence that the population distribution of battery lifetimes is skewed to the right, the engineers at the company decided to take 100 random samples of lifetimes, each of size 10, sampled from a perfectly symmetric normally, distributed population with a mean of 2.6 hours and standard deviation of 0.29 hours. For each of those 100 samples, the statistic sample mean divided by the sample median was calculated. A dotplot of the 100 simulated skewness ratios is shown below.


What is the explanation for why the engineers carried out the process above?


This process allows them to determine the percentage of the time the sample distribution would be skewed to the right

3%

This process allows them to compare their observed skewness ratio to what could have happened by chance if the population distribution was really symmetric/normally distributed.

64%

This process allows them to determine how many times they need to replicate the experiment for valid results

10%

This process allows them to compare their observed skewness ratio to what could have happened by chance if the population distribution was really right skewed.

23%

Analysis of all (free-response) class tests is ongoing

Integrate observed statistic and simulated values to draw a conclusion?


Summary

◦ Preliminary and current versions showed improved performance in understanding of tests of significance, design and probability (simulation) post-course, and improved retention in these areas

◦ These results appear stable across lower-performing students with older and newer versions of the curriculum

◦ Some evidence of student ability to apply the framework of inference (3-S) to novel situations


Summary

◦ Some instructor differences, but also preliminary validation of “transferability” of findings across different institutions/instructors; new instructors?

◦ **Note: Some evidence of weaker performance in descriptive stats in this earlier curriculum; substantial changes to descriptive statistics approach to combat this.


What’s making the change◦Content?◦Pedagogy?◦Repetition?

How much randomization before you see a change?

Are there differences student performance based on curricula? Are they important?

What don’t we know

What are the developmental learning trajectories for inference (Do they understand what we mean by ‘simulation’)? Other topics?

Low performing students; promising---ACT, GPA

Does improved performance transfer across institutions/instructors? What kind of instructor training/support is needed to be successful?

Using CAOS (or adapted CAOS) questions, but do we still all agree these are the “right” questions? Is knowing what a small p-value means enough? What level of understanding are they attaining?

Why do students in both curriculums tend to do poorly on descriptive statistics questions? Or areas where we see little difference in curricula?

What we don’t know

Preliminary indications continue to be positive

You can cite similar or improved performance on nationally standardized/accepted/normed tests for the approach

Tag line for peers and clients:◦ We are improving some areas (the important ones?) and doing no harm

elsewhere

Still lots of room for better understanding and continued improvement of approach

Student engagement (talk yesterday)

Next steps: Larger, more comprehensive assessment effort coordinated between users of randomization-based curriculum and those that don’t. If you are interested let me know.

What it means

Author team (Beth Chance, George Cobb, Allan Rossman, Soma Roy, Todd Swanson and Jill VanderStoep)

Class testers

NSF funding

Acknowledgements

Tintle NL, VanderStoep J, Holmes V-L, Quisenberry B and Swanson T “Development and assessment of a preliminary randomization-based introductory statistics curriculum” Journal of Statistics Education 19(1), 2011

Tintle NL, Topliff K, VanderSteop J, Holmes V-L, Swanson T “Retention of statistical concepts in a preliminary randomization-based introductory statistics curriculum” Statistics Education Research Journal, 2012.

References

but…does it work? do students truly learn the material better?

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