WP2: Modernization of Math Courses for STEM Education in GE/AM Universities

Ishkhan HovhannisyanNational Polytechnic University of Armenia

14 March 2016, Yerevan, Armenia, Yerevan State University

Outline

• Overview

• Activities

• Outcomes

14 March 2016, YSU

Role of Math and Statistic in STEM Education

❖ Math is the key subject for STEM disciplines❖ Basic math competencies are prerequisites for many technical skills

❖ lower entrance math standards❖ Students tend to underestimate the role of math in technical studies

❖ Investigations show that the level of math knowledge is the primary factor for success or failure in technical education

14 March 2016, YSU

MathGeAr Project• Modernization of Mathematics curricula for Engineering and Natural

Sciences studies in South Caucasian Universities by introducing modern educational technologies

• WP2: Modernization of Math Courses for STEM Education in GE/AM Universities

Math Courses in GE/AM Universities:Number of Math Courses: 3-5 (Bach), 0-? (Master)Credits: 15-54Assessment: 20+2*20+40=100, 10+2*20 +50=100Grading: 60-70-80-90-100, 40-60-80-100Form of exams: oral, written, testDeterioration of STEM education in the 90sCurrent trend on reducing the amount of math hours

Math courses in EU and GE/AM Universities

❖ No significant differences, when it comes to: ❖ Learning content (courses and topics) ❖ Number of credits (ECTS) ❖ Course compositions (lecture/practice/independent work) ❖ Course size and teacher availability• EU and US are heavily investing in ICT-

enhanced Math educational solutions and have promising results

14 March 2016, YSU

Differences❖ In EU, the system is more elastic:• universities have more freedom in terms of modifying their

courses if necessary;• there is a standard practice of student-based course evaluation,

which provides consistent and timely feedback.❖ In EU, the universities also phase the problem of low math

competencies of new students, but• there is common solution - Bridging Courses❖ In EU, usage of e-Learning technologies and tools is much broader❖ In EU, math for engineers is taught in a much more applied way:• focus is made on learning how to use math as a tool when solving

practical engineering problems, not on theorem proving

14 March 2016, YSU

Outline

• Overview

• Activities

• Outcomes

14 March 2016, YSU

Approach

The approach is two-fold1. Structural improvements of Math curricula in

line with the Bologna principles and best EU practices

2. Introduction of new educational technologies for new pedagogical approaches

14 March 2016, YSU

Activities❖ Participation in study visits and investigation EU best practices in math education❖ Comparative analyses between the EU and the GE\AM courses according to the defined methodology: Duration, hours, credits; Descriptions; Major Outcomes; SEFI Level; Curriculum aims and objectives; Problem solving abilities; Assessment systems; Recommendations;

14 March 2016, YSU

Recommendations 1 (TUT)

• Changing syllabus (contents and the way of presentation, "theorem-to proof" style could be slightly modified by putting more emphasis on applications )

• Adding topics, applications, examples related to engineering disciplines to improve engineering student's motivation to study mathematics.

• Using mathematical tool programs (Matlab, Scilab, R-, etc) for solving problems.

14 March 2016, YSU

Recommendations 2 (TUT)

• Finding the courses, or parts of the courses, or activities related with the courses that can be best studied using MathBridge.

• Adding (small) student project works to the course. Use of web resources, and open data would add student motivation.

• Finding complementary ways of assessment that would measure competencies corresponding to SEFI list.

14 March 2016, YSU

GTU - Calculus 2; Statistics and Probability; Discrete mathematicsUG - Pre-calculus; Calculus 1ATSU - Calculus 1; Modelling and optimization for Technological Processes (Master Pr.)BSU - Linear Algebra and Analytic Geometry; Discrete MathematicsNPUA - Calculus 1; Probability Theory and Statistics 1, 2ASPU - Linear Algebra and Analytical Geometry; Calculus 1

List of modified courses

14 March 2016, YSU

SEFI FRAMEWORK• One of the key purposes is to modernize selected national

math courses based on SEFI criteria after comparing these with corresponding EU courses. The SEFI framework for math curricula in STEM education provides the following list of competencies: 

• thinking mathematically• reasoning mathematically• posing and solving mathematical problems• modeling mathematically• representing mathematical entities• handling mathematical symbols and formalism• communicating in with and about mathematics• making use of aids and tools.

14 March 2016, YSU

Implementation ❖ We cannot address all problems, we have chosen:

• Modification of course materialto focus on more applied competenciesSyllabi change (GTU, NPUA, …)Bridging courses (GU, GTU, NPUA, …)

• Introduction of e-Learning technologies Math-Bridge TEL classrooms, equipment • Students Mobility

14 March 2016, YSU

Math-Bridge

Outline

• Overview

• Activities

• Outcomes

14 March 2016, YSU

Large-scale Evaluation

• Fall, 2015: Teach the selected course in the traditional way.

• Implement updated courses within Math-Bridge.• Fall, 2016: Teach modified versions of the selected

course.• Compare student performance, analyze the results

and verify the impact of the modified courses.

14 March 2016, YSU

Our ObjectivesCompleted Objectives• Implement a comparative analysis of the national math

curricula for STEM disciplines• Modernize math and statistics curricula for a selected set of

engineering and sciences studies• Localize the European TEL (Technology-Enhanced

Learning) tools for GE\AM UniversitiesCurrent Objectives• Build a capacity to effectively implement, maintain and

develop TEL for math education.• Conduct pilot a evaluation of the impact of the new curricula

on the quality of studies in math and statistics, as well as on quality of engineering and sciences education in general.

• Disseminate the results of the project.14 March 2016, YSU

Conclusions

The applications and the use of ICT tools makes the course more interesting.

Students will spend much more time to do experiments around the questions given by the teacher.

Students feel the importance of the course and this would assist for students’ progress.

Improved Math programs• TOPIC 1: NUMERIC SEQUENCES (Lecture 1-4)– Bounded and unbounded numeric sets. Bounds of sets.

Theorem on existence of infimum and supremum. Limit of a sequence. Examples related to engineering disciplines and applications.

– Uniqueness of the limit and boundedness of a convergent sequence. Using mathematical tool programs for finding limit of a sequence.

– Infinitely small and infinitely large sequences. Properties of infinitesimals.

– Monotonic sequences. Criteria of limit existence, examples. The number e, application of natural number e in engineering disciplines.

14 March 2016, YSU

Project website: Project Twitter channel:http://www.mathgear.euhttps: // twitter.com/MathGeAr

Thank you

Շնորհակալություն