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Making Mathematical Reasoning Fun. Jason Hallstrom (Clemson), Joan Krone (Denison), Joseph E. Hollingsworth (IU Southeast), and Murali Sitaraman (Clemson) This workshop is funded in part by NSF grant DUE-1022941 . Goals. Reasoning Across the Curriculum Not just in Discrete Math

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Making mathematical reasoning fun

Making Mathematical Reasoning Fun

Jason Hallstrom (Clemson), Joan Krone (Denison), Joseph E. Hollingsworth (IU Southeast), and MuraliSitaraman(Clemson)

This workshop is funded in part by NSF grant

DUE-1022941


Goals
Goals

  • Reasoning Across the Curriculum

    • Not just in Discrete Math

    • Fundamental part of CS

    • Motivating example: binary search “proven” correct

  • Supporting Tools

  • Supporting Methods

  • Applicable to both large universities and small colleges


Partners
Partners

  • Alabama

  • Clemson

  • Cleveland State

  • Denison

  • Depauw

  • IU Southeast

  • Ramapo College

  • Virginia Tech NVC

  • Western Carolina



Why?

  • Current software is too large for one person to understand.

  • Students need tools for dealing with all sizes of projects.

  • Maintenance makes up the majority of jobs.

  • Students need to separate specifications from implementations.


Courses at all levels
Courses at All Levels

  • Beginning level: CS110 – Intro to Programming, CS174 – Discrete math at Denison, (others – CPSC101 – CSI, CPSC102 – CS2, Discrete Math at Clemson)

    • Use of collaborative approach

    • Use of specifications

    • Reasoning assistant tool


  • Intermediate level: CPSC215 – Software Foundations, (others: CPSC212 – Data Structures) at Clemson

    • Contract specifications – comparing informal specs with formal specs

    • Mathematical modeling – abstraction

    • Generating test data from specs

    • Reasoning assistant tool



All levels
All Levels and CS349 – Software Engineering at Denison, CP372 – Software Engineering at Clemson

  • Collaborative Approach

    • Pairs or small groups

    • In class or homework


Collaborative method
Collaborative Method and CS349 – Software Engineering at Denison, CP372 – Software Engineering at Clemson

  • Pairs or small groups

  • With or without tools

  • Each team presents their findings

  • Collaboration both within teams and among teams


Selective adaptation
Selective Adaptation and CS349 – Software Engineering at Denison, CP372 – Software Engineering at Clemson

  • Pick and choose appropriate reasoning concepts and/or tools

  • Faculty expertise

  • Student background


One example software engineering course
One Example: Software Engineering Course and CS349 – Software Engineering at Denison, CP372 – Software Engineering at Clemson

  • Usual Topics

    • Requirements analysis

    • Design and specification

    • Component-based implementation

    • Quality assurance

  • Formal Reasoning


Objectives
Objectives and CS349 – Software Engineering at Denison, CP372 – Software Engineering at Clemson

  • Read formal specifications

    • Create test points from the specs

  • Use component specifications to build larger systems

    • Work in teams

  • Carry out formal verification of components

    • Use automated rules


Methods
Methods and CS349 – Software Engineering at Denison, CP372 – Software Engineering at Clemson

  • Collaborative learning

    • Teams of 2 to 4 members

    • Read specs

    • Implement specs

    • Verify implementations

    • Build larger systems.


Using the tools
Using the Tools and CS349 – Software Engineering at Denison, CP372 – Software Engineering at Clemson

  • http://www.cs.clemson.edu/group/resolve


Summary
Summary and CS349 – Software Engineering at Denison, CP372 – Software Engineering at Clemson

  • Importance of Reasoning across the Curriculum

  • Tools to Support Reasoning

  • Collaborative Pedagogy includes collaboration between students and between students and faculty


Some work
Some Work and CS349 – Software Engineering at Denison, CP372 – Software Engineering at Clemson

  • Binary search specifications

  • Java

  • C++

  • Any other language

  • Are the algorithms correct?

  • Do the implementations work?

  • What’s the difference?


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