Exams and Mastery Learning in Mathematics

Web-based Proficiency Exams and Mastery Learning in Mathematics : 

Web-based Proficiency Exams and Mastery Learning in Mathematics John Lindsay Orr University of Nebraska - Lincoln

Slides : 

http://www.math.unl.edu/~jorr/presentations Slides

Goal : 

Answer the question: What is an Online Assessment Management System and why use it? Definitions Examples Core Features Five practical problems Goal

Who Am I and Why Am I Here? : 

Who Am I and Why Am I Here?

What is an OAMS? : 

An Online Assessment Management System is web-based software to manage student assessment: Student: Step through questions, answer questions, get grade report and feedback Instructor: Write questions, assemble assignments, review grades Varied question types and assignment types What is an OAMS?

Examples : 

Some Online Assessment Management Systems include: Maplesoft’s MapleTA Horizon Wimba’s EDU WebAssign from North Carolina State U WebWork from Rochester U Wiley’s WileyPlus Prentice Hall’s PHGradeAssist Examples

Core Features : 

The core features of an OAMS are: Automated grading, immediate feedback Range of question types Range of assignment policies (quiz, homework, test, etc.) Web interface for students to browse questions Grade reporting for student and instructor (grade book) Tools to create new questions Administrative tools (user management) Interface with other web applications (CMS) Core Features

Five Practical Problems : 

1. Students don’t always remember all the material from previous courses. 2. Some students scrape through on partial credit who shouldn’t. 3. I have some students in my class who shouldn’t be there. 4. I know what I said but I don’t know what they heard. 5. My students don’t all study as hard as I’d like them to. Five Practical Problems

Five Practical Problems : 

Five Practical Problems

Five Practical Problems : 

“Students don’t always remember all the material from previous courses” Practice more the first time Learn it until you’ve mastered it Review it until you’re as good as you were (or better) Five Practical Problems

Five Practical Problems : 

“Some students scrape through on partial credit who shouldn’t” Only award credit once they’ve mastered it Five Practical Problems

Five Practical Problems : 

“I have some students in my class who shouldn’t be there” Placement testing Five Practical Problems

Five Practical Problems : 

“I know what I said but I don’t know what they heard” “Just in time teaching” (www.jitt.org) Pre-class warm-ups – with feedback loop Five Practical Problems

Five Practical Problems : 

“My students don’t all study as hard as I’d like them to” “No pay/no play” Increased time-on-task Five Practical Problems

Some Pedagogical Strategies : 

1. Mastery Learning 2. Just-in-time Learning 3. Adaptive Learning 4. Increased time-on-task Some Pedagogical Strategies

A False Choice : 

A False Choice

How Technology Can Help : 

In addition to Automated grading and Immediate feedback an OAMS can provide 24/7 Access and Repeatable assignments How Technology Can Help

24/7 Access : 

24/7 Access

Repeatable Assignments : 

Each student on each attempt gets a different set of questions. 1. Permuted questions 2. Algorithmic questions Repeatable Assignments

Algorithmic Questions : 

Algorithmic Questions $a = range(4, 9); $k = decimal(2, rand(1, 2)); $right = sum(x, 1, $a, x($a-x)e^(-$k x)); $low = $right - 3; $high = $right + 3;

Case Studies : 

Some ways we’ve used OAMS at Nebraska: 1. Gateway Exams 2. Placement Testing 3. Keller Plan 4. Homework Case Studies

Gateway Exams : 

Precalculus, Calculus 1, Calculus 2 Require 80% fully correct for credit Credit is 5% of course total Daily retakes allowed for two weeks Proctored exams and unlimited practice Gateway Exams

Placement Testing : 

All incoming students take diagnostic test Proctored from UNL or high school Diagnostic assessment algorithm (Maplesoft + MAA product) Placement Testing

Keller Plan : 

Self-paced introductory psychology course Students progress through units by mastering tests Tests mix multiple choice and essay Both machine and human feedback available Keller Plan

Homework : 

Increased time-on-task Publisher and home-grown content Homework

Advantages/Disadvantages : 

Standardizes courses + Reduces grading work + Reduces grading budget + Enhances limited classroom time - Administration - Question creation Advantages/Disadvantages

EDU at UNL : 

Began project in 1996 at UNL Developed Wiley Webtests and then eGrade 1.0 for John Wiley & Sons Developed EDU for Brownstone Learning (now Horizon Wimba) Became core of Maplesoft’s MapleTA EDU at UNL

EDU at UNL > Courses : 

EDU at UNL > Courses Fall 2003 170 active classes set up

EDU at UNL > Disciplines : 

EDU at UNL > Disciplines Accounting Curr & Instruction Psychology Ag. Marketing Educational Psych. School of Music Agro. & Hort. Electrical Eng. Veterinary Science Anthropology Entomology Lincoln High School Architecture Family & Consumer Science Astronomy Geography Biochemistry Geosciences Biological Sciences History Bio Systems Eng. Industrial Eng. Children, Family & Law Libraries Chemistry Mathematics Civil Engineering Modern Languages Communication Studies Natural Resource Sciences Computer Science Physics Const. Management Political Science

EDU at UNL > Students : 

Fall 2003 Student accounts: 10,650 Active (5+ sess.): 7,075 Spring 2004 Student accounts: 8,863 Active (5+ sess.): 5,310 EDU at UNL > Students

EDU at UNL > Assignments : 

Fall 2003 Total assignments: 277,148 Daily average: 2,500 Spring 2004 Total assignments: 292,888 Daily average: 2,650 EDU at UNL > Assignments

EDU at UNL > Value Added : 

Fall 2003 Total assignments: 277,148 GTA hourly rate: $20 GTA assignments/hour: 10 Cost of human grading: $554,296 EDU at UNL > Value Added

OAMS for Maths : 

What’s specific to math for online assessment? Grading formulas and expression on content; CAS Powerful question types Mathematical notation in display and entry LaTeX or WYSIWG question creation Sophisticated algorithms (“ x+-2 ”) OAMS for Maths

Questions : 

Questions

Questions : 

Questions

Questions : 

Questions

Questions : 

Questions

Questions : 

Questions

Questions : 

Questions

Questions : 

Questions

Questions : 

Questions

Questions : 

Questions

Questions : 

Questions

Questions : 

Questions

Demos : 

MapleTA 2.51 MapleTA 3.0 (Beta) EDU at UNL Demos

Goal : 

http://www.math.unl.edu/~jorr/presentations Goal