Enhancing Students Learning Using Random Number Generation By
Enhancing Students’ Learning Using Random Number Generation By Arthur Dryver, Ph. D 1 and Wasita Boonsathorn, Ph. D 2 1 Graduate School of Business Administration, NIDA Email: dryver@gmail. com URL: www. Learn. Via. Web. com 2 School of Human Resource Development, NIDA
My Background – High Level Presently teaching within the School of Business Administration at NIDA, Bangkok Thailand (Been there over 9 - years) Worked in consulting in America for 4 years – first firm worked for was Price. Waterhouse. Coopers Ph. D. in Statistics from Pennsylvania State University Undergraduate at Rice University, TX
School Work ASAP Due one week or more Feedback a month… Sometimes immediate feedback also
The amount of examples for going from confusion to understanding differs for each student
I often ask myself two main questions 1. How can I give all my students at least access to all the examples they may need to understand at least the basic material? 2. How do I enhance learning for all students without simply forcing everyone to do a ton of examples?
This presentation is mostly about answering those 2 main questions Finally, I’ll go over the direction I selected and why.
Outline �The power of random number generation �Some platforms for leveraging random number generation: � R, Sweave, and La. Te. X � Microsoft Excel � Online and JSP �Summary
The power of random number generation With a focus on teaching statistics
Why use random number generation? Simulate realistic from small to large datasets. One can’t find real data and many examples for everything taught. Creating numbers just off the top of your head is limited and can be time consuming in its own way when trying to think of all the scenarios and making a good dataset for students to work with. Impossible if want a large dataset
Random Number Generation for Teaching Applied Statistics � Teachers, wanting to avoid present students copying from previous batches of students in their class, would have to create new problems, at least new numbers for the problems each year. � Even further individual assignments so no direct copying. Many students consider knowing the answer as understanding, which is often not true. For example, there is a big difference between knowing that 2+2=4 and understanding addition.
Random Number Generation for Teaching Applied Statistics To provide students with an ample number of problems to practice and homework, quizzes, etc. , can be a large amount of work for the teacher each year. For a concrete example of how even something simple as reading computer output could require a lot of examples imagine a one sample t-test. How many different scenarios are there when looking at two -sided p-value from computer output?
How many different scenarios are there when looking at two-sided p-value from computer output? There are 5, a two-sided test and then 4 different scenarios for converting the two-sided p-value into a 1 -sided: pval 2 s stands for 2 sided p-value Thus for only 3 examples of each possible scenario of a one sample t-test the instructor needs to create 15 examples.
Workload Using Random Number Generation All from data simulation to analysis, even grading SPSS
Leverage 1 st leverage the power of the computer 2 nd leverage your own work/code HA: µ<75 coded easy to modify code for HA: µ>75 coded, etc.
Thus Imagine Using Random Number Generation Imagine having nearly an unlimited supply of applied statistical problems for each problem type to use. Imagine the freed up time from making up numbers and solving each problem individually. Imagine the ability to focus on the problem types, scenarios accompanying the numbers.
R, Sweave, and La. Te. X Using R, Sweave an R function, and La. Te. X one can create PDF files with tons of examples
Why: R, Sweave, and La. Te. X are all free of charge. Many people already know R and La. Te. X, for those people learning the R function Sweave will not be difficult. Those with a lot of lecture notes in La. Te. X this can directly fit into your existing notes. R has a ton of advanced statistical functions already built in. For teaching advanced statistics and wanting to use random number generation this is one of the easiest platform to use. Much easier than C++, JAVA, etc. Something to consider if you are coding things yourself
R, Sweave, and La. Te. X Combining R, Sweave, and La. Te. X one can create an almost unlimited number examples, in terms of numbers. Using the package Sweave one can create a PDF file directly from within R. A version of La. Te. X must also be installed.
Example Sweave Code – Matrix Inverse <<echo=FALSE, results=hide>>= <<load. Pkg, echo=FALSE>>= library(lattice); library(xtable) ## DATA GENERATION y 2<-matrix(floor(runif(9, min=-20, max=20)), nrow=3, byrow=T) ## QUESTION/ANSWER GENERATION @ begin{question} Solve for the determinant and inverse of the following matrix Sweave. Opts{echo=false} <<results=tex>>= print(xtable(y 2, caption="X matrix"), include. rownames=FALSE, include. colnames=FALSE) @ begin{solution} The determinant equals $Sexpr{det(y 2)}$ and the inverse is: \ Sweave. Opts{echo=false} <<results=tex>>= print(xtable(solve(y 2), caption="The inverse of the X matrix", digits=4), include. rownames=FALSE, include. colnames=FALSE) @ end{solution} Not a lot for Matrix Inverse but you definitely need to be comfortable with R and La. Te. X end{question}
Example R Code �The below 2 commands are perhaps an over simplification of what is needed to run the package Sweave and create a PDF file you literally only need 2 lines of code. 1. Sweave(file 1) 2. texi 2 dvi(file=file 1, pdf = TRUE, clean = TRUE, quiet = TRUE, texi 2 dvi = get. Option("texi 2 dvi"), texinputs = NULL) � Reminder – See PDF file form my Regression Class
Microsoft Excel
Why: Microsoft Excel �Most people that work with data will use Excel for at least basic statistics like the average and basic graphs/chats. �It is easy to use. Can also be used with Power. Point lecture notes very easily. �One negative is for advanced statistics you’ll need to purchase an add-in package. � For example: http: //www. xlstat. com
How: Microsoft Excel �Using random number generation in Microsoft Excel, it is possible to create many basic math and statistics problems. �The words would not change but the function “rand()” could be used to create random numbers for each problem. �The teacher could use the copy and paste function in Excel to create multiple problems from a single problem template in this manner. � Static: The teacher could copy paste special as values to make the numbers static. � Dynamic: The teacher can refresh the numbers on demand to change the numbers in the problem.
Microsoft Excel Example For updating and automatic grading for homework
For updating and automatic grading for homework using Microsoft Excel First, create a template sheet with random numbers for questions and formulas for checking answers.
Step 1: Create the problems in Excel. Create answer boxes for students to enter their Answers. I highlighted mine in yellow.
Sum of correct to get total score. Correct answers using formulas. Change numbers and answers are still correct. Students answers using linked to yellow boxes Check if number equals correct answer within your given margin of error of 0. 02 or whatever you choose. 1 if correct, 0 otherwise
Highlight All Cells and “Lock” them.
Select all the “student answer cells” at once, hold “ctrl” button to select multiple cells – the ones in yellow. Right click and click on format cells. Go to protection and “unlock” – remove the check mark. This is necessary so that when you protect the worksheet students can still enter their answers on the yellow boxes.
Highlight everything you don’t want the student to see. Right click and click on “Hide” to hide the answers and stuff you want hidden, like their scores.
Right click on the sheet you wish to protect – make unchangeable except the answer boxes. Then click “protect sheet. ” Enter a password and now only you can access the “locked “cells.
Check what you want users to be able to do. Then Enter password.
Re-enter password microsoft asks twice. Also do not forget the password. If students ever get your password they can get the answers thus be careful about this. You’re Done!!!!!
For Grading Just unprotect and unhide the answers the students send back. Reminder: Go over example with Excel. Right click on the sheet you wish to unprotect – after students return their answers via email and then unhide to get the grade on the students homework.
Online
Why: Online � Using the Internet we can offer a near unlimited audience to a near unlimited set of problems. Online is also easier to combine efforts across teachers. Immediate feedback – automatic grading Can force students to complete each problem type X number of times correctly in a row before moving forward. Basically wrong answers causes students to work harder and learn without forcing the instructor to grade/work more. I offer my online homework free to those interested From Descriptive statistics to Simple Linear Regression You personally can easily add questions to my database to ultimately use.
Online and JSP – Students Use �Reminder: go over my online homework: �http: //www. learnviaweb. com/teachstat/ Examples, from my website: �http: //www. learnviaweb. com/teachstat/q 12 geg. jsp
Online and JSP – Professors Use Examples, from my website for making question types: �http: //learnviaweb. com/teachstatbeta/editquestinfobet a. jsp? qtype=1&qname=Descriptive%20 Statistics �Examples of getting grades: �http: //www. learnviaweb. com/teachstat/adminlogon. jsp �Example grade file
Summary Concluding Remarks
Summary – Concluding Remarks Through random numbers we can offer students a nearly unlimited supply of problems to work out. We can force students to demonstrate “mastery” of a topic before allowing them to move forward. Think of the saying, “Practice makes perfect. ” �We can do this without creating an unbearable amount of extra work for the instructors. � We can even eliminate grading and automate it.
My Choice I have tried all of these and I think online is the best. I mainly teach MBA students and Ph. D students within the school of business. My online system is also presently used in the Human Resource Department by another professor also as online homework for her class on research methodology. Why I think online is the best Automatic feedback Don’t allow students to decide not to learn a topic. Forcing students to do the problems over and over until they demonstrate the ability to do it correctly. I require 5 times in a row correct before moving forward. Students focus on how to do not grades. I give full credit if done on time, some students still don’t do it on time because it isn’t easy. Those interested in using my website may contact me at dryver@gmail. com
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