Mathematical and Quantitative Reasoning

Mathematical and Quantitative Reasoning

July-November, 2026

 Lectures:  Tuesday, Thursday at 12:00 PM

 Office Hour: TBD

Evaluation:

Minor Examination - 25%

Major Examination - 40%

Quizzes - 20%

Assignments/Project – 15%

Quizzes will be held on August 27 and October 24.

Attendance Policy:

A student is expected to have full attendance in the course unless the student takes a leave of absence for valid medical or bona fide reasons. In any case, at least 75% attendance in the course is mandatory.

Objectives

The instructor will:

1.     Introduce basic mathematical & quantitative reasoning for practical usage and large-scale surveys and databases in the domain of education.

2.     Provide knowledge and capacities required to analyze, interpret, and communicate quantitative data to deduce conclusions using numerical and graphical representations.

3.     Enable learners to think critically about data and use quantitative reasoning to solve real-life problems.

Learning Outcomes

At the end of the course the students will be able to:

1.     Adapt mathematical reasoning to solve problems in the real world and explain some fundamental ideas and tenets in this field

2.     Interpret numerical and graphical representations like formulas, graphs, or tables to deduce conclusions.

3.     Analyze educational data to inform pedagogical decision-making.

4.     Demonstrate critical thinking and problem-solving skills using mathematical and quantitative reasoning methods.

Contents

1. Introduction to mathematical and quantitative reasoning (6 lectures): Meaning, nature and scope of mathematical and quantitative reasoning; Significance of mathematical and quantitative reasoning; Types of quantitative reasoning; Use of mathematical and quantitative reasoning; Mathematization

2. Data in Education (9 lectures): Data and Sources of Data; School enrolment data: Gross Enrolment Ratio (GER), Net Enrolment Ratio (NER), Dropout rate, Measures of literacy; Indian census: Data elements; Nationwide and International sample surveys or tests: National Achievement Survey (NAS), ASER, PISA; UDISE data

3. Data Analysis & Interpretation (11 lectures): Data interpretation (equation, diagram, graph, tables); Statistical analysis of data in educational context and its applications: Measures of central tendency, measures of variability, percentile; Visual and numerical representation of data and its application (bar diagram, histogram, pie charts, mean/median/mode, standard deviation, range); Learning analytics (LA): concept, types, levels, and its applications in educational context (e.g., LA Dashboards).

Textbook:

1.Ruth Ravid, Practical Statistics for Educators, Sixth Edition, Rowman & Littlefield

References:

1. Madison, B. L., & Steen, L. A. (Eds.). (2008). Calculation Vs. Context: Quantitative Literacy and Its Implications for Teacher Education: June 22-24, 2007, Wingspread Conference Center, Racine, Wisconsin. Mathematical Association of America.

2. Duraisamy, p. (2012). Statistics on Education: Advantages and Limitations for Studies on Social Groups. https://learnos.files.wordpress.com/2012/10/statistics-education-iids-seminar-duraisamy.doc

3. GoI (2024): UDISE Plus Data and Reports for various years https://udiseplus.gov.in/udisereport http://udise.in/flash.htm (various reports)

4. Mehta A. C. (2023). Decoding UDISE+ 2021-22 Enrolment Ratios under Samagra Shiksha https://educationforallinindia.com/decoding-udise-2021-22-enrolment-ratios-under-samagra-shiksha/

5. Ferguson, R. (2012). Learning analytics: drivers, developments and challenges. International journal of technology enhanced learning, 4(5-6), 304-317.

6. Verbert, K., Govaerts, S., Duval, E., Santos, J. L., Van Assche, F., Parra, G., & Klerkx, J. (2014). Learning dashboards: an overview and future research opportunities. Personal and Ubiquitous Computing, 18(6), 1499-1514.

7. Steen, L. A. (2001). Mathematics and democracy: The case for quantitative literacy. National Council on Education and the Disciplines.

Course

📅 August 2026

• Week 1 (Jul 27 – Aug 2)

  • Jul 30 (Thu): Introduction to the Course: Statistics – Meaning and Use

• Week 2 (Aug 3 – Aug 9)

  • Aug 4 (Tue): Measures of central tendency and Variability

  • Aug 06 (Thu): Percentiles

• Week 3 (Aug 10 – Aug 16)

  • Aug 11 (Tue): Organization of Data

  • Aug 13 (Thu): Graphical Representation of Data

• Week 4 (Aug 17 – Aug 23)

  • Aug 18 (Tue): Linear Correlation

  • Aug 20 (Thu): The Normal Curve

• Week 5 (Aug 24 – Aug 30)

  • Aug 25 (Tue): The Normal Curve

  • Aug 27 (Thu): How do we Grade in IITJ? (Quiz-I)

📅 September 2026

• Week 6 (Aug 31 – Sep 6)

  • Sep 01 (Tue): Prediction and Regression

  • Sep 03 (Thu): Prediction and Regression

• Week 7 (Sep 7 – Sep 13)

  • Sep 08 (Tue): t-Test

  • Sep 10 (Thu): t-Test

• Week 8 (Sep 14 – Sep 20)

  • Sep 15 – Sep 20: Minor Examination

• Week 9 (Sep 21 – Sep 27)

• • Sep 22 (Tue): Data in Education

  • Sep 24 (Thu): Data in Education 

📅 October 2026

• Week 10 (Sep 28 – Oct 4)

  • Sep 29 (Tue): Chi-Square Test

  • Oct 01 (Thu): Chi-Square Test

• Week 11 (Oct 5 – Oct 11)

  • Oct 06 (Tue): How to choose the right Statistical Test?

  • Oct 08 (Thu): How to choose the right Statistical Test?

• Week 12 (Oct 12 – Oct 18)

  • Oct 13 (Tue): Using Statistical Tests to Analyze Survey Data

  • Oct 15 (Thu): Using Statistical Tests to Analyze Survey Data

  •  

• Week 13 (Oct 19 – Oct 25)

  • Oct 20 (Tue): ❌ NO CLASS (Dussehra Holiday)

  • Oct 22 (Thu): Learning Analytics

  • Oct 24 (Sat): 🔄 EXTRA Thursday Class: LA Dashboards (Quiz-II)

• Week 14 (Oct 26 – Nov 1)

  • Oct 27 (Tue): Class Project Presentations

  • Oct 29 (Thu): Class Project Presentations

📅 November 2026

• Week 15 (Nov 2 – Nov 8)

  • Nov 2 – Nov 8: ❌ NO CLASSES (Mid-Semester Break)

• Week 16 (Nov 9 – Nov 15)

  • Nov 10 (Tue): Class Project Presentations

  • Nov 12 (Thu): Class Project Presentations

·       Week 17 (Nov 16 – Nov 22)

• • Nov 17 (Tue): Class Project Presentations

·       

November 19, 2026 – November 26, 2026: Major Examination.