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Teaching Mathematical Reasoning across the Curriculum

Teaching Mathematical Reasoning across the Curriculum. Amruth N. Kumar amruth@ramapo.edu. Course: Comparative Programming Languages. Junior/Senior Course Content: Design of programming languages Practicum: C++, LISP, Java, Prolog projects Balanced with mathematical reasoning.

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Teaching Mathematical Reasoning across the Curriculum

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  1. Teaching Mathematical Reasoning across the Curriculum Amruth N. Kumar amruth@ramapo.edu

  2. Course: Comparative Programming Languages • Junior/Senior Course • Content: Design of programming languages • Practicum: C++, LISP, Java, Prolog projects • Balanced with mathematical reasoning

  3. Mechanism: Course Enrichment Component • Students study after class • No in-class instruction • “If you build, they will come” • NOT! • Extra credit question on mid-term, final

  4. Mid-term – String Theory • 7 problems • 1 & 2: One concept • 3, 4 & 5: Two concepts • 6 & 7: Three concepts • Average time spent by students: 40 min

  5. Mid-term Results

  6. Mid-term Results • One concept problem score > Two/Three concept problem score • Delayed test scores went up or down by 1 for most students

  7. Final – Parameter Passing Mechanisms • 3 problems • Students asked to: • Identify parameter modes • Write ensures and requires clauses • Average time spent by students: 41.43 min

  8. Final Results

  9. Final Results • Parameter modes were easy except: • Clears – no one got it • Replaces – Only 25% got it • Ensures/Requires clauses: • Score dropped dramatically if answer contained more than one part • May be provide a hint about the multi-part nature?

  10. Conclusions • Worthwhile to introduce formal reasoning • Even as a self-study component • With no supplementary classroom instruction • “If you require it, they will study”

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