Download The fair use of graphing calculator in introductory statistics

The fair use of graphing calculator in
introductory statistics courses
WEI WEI*
KATHERINE JOHNSON
MATHEMATICS DEPARTMENT
METROPOLITAN STATE UNIVERSITY
SAINT PAUL, MN
Outline
 The Use of TI calculators in an introductory statistics course
 Our goal of the research
 Assessments
 Results
Functions used in an introductory statistics course
 1-Var-Stats: Descriptive statistics
 Functions for distribution
 Binomcdf: probabilities related to binomial distribution
 Normalcdf: probabilities related to normal distribution
 Invnorm: find the x value given a probability under a normal distribution
 Functions for confidence intervals
 Tinterval: confidence interval for mean
 1-PropZInt: confidence interval for proportion
 Functions for hypothesis tests
 1-PropZTest
 2-PropZtest
 T-test
 2-SampTTest
2
 𝜒 -Test
Our goal
 Pros
 Help students to get accurate results quickly
 Reduce math anxiety
 Cons
 Some students are good at technology while some are not
 May hinder students’ understanding of certain important concepts if relying on
calculators too much
Our goal
 Helped with normal probability calculation?
 Normalcdf vs.
 Standard Normal Distribution Table
 Hindered the understanding of normal transformation?
 Helped with hypothesis testing?
 T-test, 2-PropZTest, 2-SampTTest etc. vs.
 calculating test statistic and p-value using normalcdf
 Hindered the understanding of p-value, especially the one-tailed and
two-tailed p-value?
 Reduced short-term retention?
Our Assessments
 Two instructors and four sections
 Instructor one->calculator section
 Instructor one->non-calculator section
 Instructor two->calculator section
 Instructor two->non-calculator section
 Two Quizzes and Three Final Exam questions
Our Assessment
 Quiz one:
 Given after introducing normal distribution and the calculation of normal
probabilities
 One multiple choice question and two calculation questions
The multiple choice question is related to standard normal transformation
 The calculation questions are finding Z-score and probabilities under a normal distribution

Our Assessments
 Quiz two
 Given after introducing two-sample tests
 One multiple choice and one calculation
One multiple choice question related to the understanding of p-value
 One calculation question related to two-sample proportion test (null and alternative
hypotheses were given)

Our Assessments
 Final exam questions
 One multiple choice question related to normal transformation
 One multiple choice questions related to p-value
 One calculation question on one-sample T-test
Results
 Quiz one-multiple choice question (conceptual understanding of normal
Proportion of correct answers
transformation)
 Mantel-Haenszel test
 No significant difference between the two instructors (p=0.66)
 The proportion of correctness from the calculator sections was
significantly higher than the non-calculator sections (p=0.030)
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
One
Two
Instructor
Results
 Quiz one-calculation questions (finding probabilities under a normal distribution)
 The mean grade from the calculator sections was significantly higher than the mean
Average grade (percentage)
grade from the non-calculator sections (p=0.0099)
 No significant interaction between instructor and pedagogy
 No instructor effect
Results
Quiz two- multiple choice question (conceptual understanding of p-value)
Mantel-Haenszel test
No significant difference between the two instructors (p=0.31)
The proportions of correctness were not significantly different between the
calculator and non-calculator sections (p=0.990)
Proportion of correct answers




1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
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One
Two
Instructor
Results
 Quiz two-Calculation question (two-sample Z-test)
 Two-way ANOVA
 The mean score from the calculator section was significantly higher than the mean score
Average grade (percentage)
from the non-calculator section (p=0.0017)
 A significant interaction between instructor and pedagogy (p=0.0024)
 Significant difference between two instructors (p=0.0074)
Results
 For short-term retention (analysis of final exam question)
 Multiple choice question-Normal transformation
Mantel-Haenszel test
 No significant difference between the two instructors (p=0.15)
 No significant difference between calculator and non-calculator sections (p=0.44)
Proportion of correct answers

1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
One
Two
Instructor
Results
 For short-term retention (analysis of final exam question)
Multiple choice question-p-value
Mantel-Haenszel test
 Significant difference between the two instructors (p=0.0067)
 For instructor one: proportion of correctness from the calculator section was significantly higher
(p=0.025)
 For instructor two: proportions of correctness are not significantly different between the calculator
1
and non-calculator sections (p=0.11)

Proportion of correct answers

0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
One
Two
Instructor
Results
No instructor effect (p=0.54)
 No pedagogy effect (p=0.99)
 No significant interaction (p=0.27)

Average grade (percentage)
 For short-term retention (analysis of final exam question)
 Calculation question-one sample T-test
 Two-way ANOVA
Conclusion
 The TI calculator significantly helped students with the calculation of
normal probabilities and understanding of normal transformation
 It did not significantly helped with hypothesis testing or short-term
retention, but it did not hinder students’ understanding
Questions???