Teaching Mathematical Reasoning across the Curriculum

Amruth N. Kumaramruth@ramapo.edu

Course: Comparative Programming LanguagesJunior/Senior CourseContent: Design of programming languagesPracticum: C++, LISP, Java, Prolog projectsBalanced with mathematical reasoning

Mechanism: Course Enrichment ComponentStudents study after class

No in-class instruction“If you build, they will come”

NOT!Extra credit question on mid-term, final

Mid-term – String Theory7 problems

1 & 2: One concept3, 4 & 5: Two concepts6 & 7: Three concepts

Average time spent by students: 40 min

Mid-term Results

1 2 3 4 5 6 70

2

4

6

8

10

12

14

16

MidtermDelayed

Mid-term ResultsOne concept problem score > Two/Three

concept problem scoreDelayed test scores went up or down by 1 for

most students

Final – Parameter Passing Mechanisms3 problemsStudents asked to:

Identify parameter modesWrite ensures and requires clauses

Average time spent by students: 41.43 min

Final Results

1.a(i) 1.a(ii) 1.b 2.a 2.b 2.c 3.a 3.b0

0.1

0.2

0.3

0.4

0.5

0.6

Final

Final

Final ResultsParameter modes were easy except:

Clears – no one got itReplaces – Only 25% got it

Ensures/Requires clauses: Score dropped dramatically if answer

contained more than one partMay be provide a hint about the multi-part

nature?

ConclusionsWorthwhile to introduce formal reasoning

Even as a self-study componentWith no supplementary classroom instruction

“If you require it, they will study”