Tools for Presenting and Evaluating Mathematics

OnlineAjnu Jacob, Travis Miller and Sean Scott of

Overview

• Maple T.A. progress report• Adaptive Questions• Maple worksheets & MapleNet

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What is Maple T.A.?• A mathematically intelligent assessment

system• Supports multiple question types• Algorithmic templates for questions• Grade management

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Algorithmic variables• Variables can be assigned random values

– set a range such as x from [-1,1] in 0.01 increments– select an object from a (weighted) list– create a matrix with a certain rank– a set of plots

• Impose conditions– x > y or (x+y) > 0– rank ≠ 0

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Question Database• Managed (mostly) by MFCF• Several master repositories in different

disciplines• Several thousand questions and growing

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Question Database• Every question is tagged with its location

in the database• Question attributes can be assigned, e.g.

difficulty, course, keywords, etc.

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Assignments• Several types available• Allows question “pools”• Controlled access with proctoring• Includes a “proctored” browser option

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Usage• Assignments Finished :

2010 95,9062011 174,0472012 198,224

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Math Readiness Test• 1500 students using the system in a 6

hour period• Repeated the next night in Engineering• Didn’t even break a sweat.

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Availability• Paid for by Mathematics, Engineering &

Science faculties. Free for all courses in those faculties

• Other faculties pay a per-student charge• Course setup, training documentation and

“getting started” support provided by MFCF

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Adaptive Questions

Features• Deepens student comprehension

• Guidance for those who give incorrect response to a question.

• Walk the student through the problem one step at a time.

• Increases understanding of concepts.• Let the student try a simpler version of the

question before retrying the original problem.

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Features• Instructors can control the behavior of the

question• Number of attempts at each stage.• Credit the student gets for incomplete answers and

penalty for repeated attempts.• If the correct answer should appear after the

problem has been attempted max times.• When to move on to the next question in the

assignment.

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Implementation• Drill down (easy to hard)• Drill up (hard to easy)• Multiple attempts

• Additional hints• Decreasing grades

• Partial grading

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Self Evaluation

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Self Evaluation

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Self Evaluation

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Self Evaluation

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Self Evaluation

Self Evaluation

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Self Evaluation

Maple Worksheets &MapleNet

Key Features1) Users Do Not Need to Understand Maple• Work shifted from users onto developers.• Easy to use.• Easy to redistribute.

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Key Features2) User Input with Automatic Calculations

Video:Partial Differentials and Tangents Part 1

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Key Features3) 3D Plots, and Animations

Video:• Partial Differentials and Tangents Part 2• Parameterization• Hooke’s Spring Law

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Key Features4) Interactive Practice with Randomization

Video: System of Equations

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Key Features5) MapleNet Online Viewing

Video: Quadric Surfaces

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Recap Advantages• Interactive and Fun• Users do not need to understand, own, or

install Maple• One worksheet = hundreds of examples• Dynamic solution feedback• Possible replacement for textbooks?

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Recap Advantages• MapleNet online viewing and integration

with D2L.• Server does the work, not the client.• Easy to modify and redistribute.

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Statistics• Average about one week to create a

worksheet. (12-16 worksheets per co-op per term)

• One day to create a video version.• Currently have 15+ worksheets online.

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Possible Uses• Calculus• Algebra• Statistics• Physics

• Economics• Chemistry• Biology

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Questions?

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