Curriculum evaluation
for Statistical Models

Dr. Silvio Fanzon
S.Fanzon@hull.ac.uk

University of Hull

Outline

Evaluation of module Statistical Models across the themes

  1. Curricular Context
  2. Assessment & Feedback Design
  3. Inclusive & Decolonised curriculum
  4. Sustainability in the curriculum
  5. Global Competence in the curriculum


Video presentation available on YouTube

Curricular Context

Micro Context

Module details:

  • Module Title: Statistical Models
  • Module Level: 2nd Year BSc Mathematics T2 (L5)
  • Class size: 20 Students
  • Format: 5h contact per week
    • 2 Lectures of 2h
    • Tutorial of 1h
  • Assessment Strategy:
    • 10 weekly Worksheets + Portfolio of statistical analyses

My experience: Taught this module once in T2 2023/24

Mathematics Programme Competencies

Programme Competency Description
PC1 Performing calculations and manipulating equations in core areas of mathematics and some more advanced topics
PC2 Solving mathematical problems in well-defined contexts by selecting and applying the appropriate techniques
PC3 Solving real-world problems by abstracting the essentials and formulating them mathematically, obtaining solutions by appropriate analytic or numeric methods, and interpreting the results
PC4 Logical reasoning, including identifying assumptions made and conclusions drawn, and giving proofs in well-defined contexts
PC5 Communicating with specialists and non-specialists by contributing to discussions, and accurately, clearly and appropriately presenting arguments and conclusions in written and oral form
PC7 Using computer technology from a range of given methods to obtain numerical solutions to problems, analyse data, and write mathematical documents
PC8 Learning and working independently when given some guidance, solving problems with patience and persistence and managing time appropriately

Mapping PC to Statistical Models

PCs Programme Competency Summary Mapping to Statistical Models
PC1 Performing calculations Study how Linear Models work
PC2 Solve mathematical problems Study why Linear Models work
PC3 Solve real-world problems Ability to analyse large datasets
PC4 Logical reasoning Interpret results of Linear Models
PC5 Communication with experts and non-experts How to report the findings
PC7 Using computer technology to obtain numerical solutions How to use Linear Models in statistical software (R)
PC8 Learning and working independently Promoted through Assessment

Meso Context

Statistical Models is part of the Data Science Pathway

Macro Context

  • Statistical Models is part of BSc in Mathematics

  • BSc in Mathematics at Hull meets standards of the

    • Quality Assurance Agency (QAA)
    • As detailed in the Subject Benchmark Statement for MSOR
    • MSOR: Mathematics, Statistics & Operations Research

  • BSc in Mathematics at Hull is accredited by

    • Institute of Mathematics and its Applications (IMA)
    • IMA accredits courses which meet its requirements
    • Graduates attain the IMA Chartered Mathematician status

Assessment &
Feedback Design

Evaluation of Assessment & Feedback

Assessment Structure

Type Percentage of final grade
Coursework Portfolio 70%
Homework 30%

Analysis backed by the following resources:

  • Inclusive Education Framework (IEF) of Hull University (Link)

  • Inclusive Assessment, Marking & Feedback Policy of Hull University (Link)

Evaluation Framework:

  • Inclusive Education Framework Checklist (Link)

Inclusive Education Framework Checklist

Highlights of Evaluation

Good example #1

Students are given choices within their assessments to allow for personalisation

  • 10 Worksheets: marked and returned to students with feedback
  • Maths Department Policy: Students allowed to miss small # of Worksheets
    (avoiding the University’s mitigating circumstances process)
  • Allows students freedom to prioritise their preferred topics
    (all topics are eventually assessed via Coursework at the end of the module)

In line with Hull IEF Assessment & Feedback

  • Be mindful of student workload and anxieties around assessment

Highlights of Evaluation

Good example #2

Module uses a range of assessment formats

  1. 10 weekly Worksheets:
    • Purpose: To provide continuous summative and formative feedback
    • Each Worksheet accounts for a low percentage of final grade
    • Including low-stakes regular assessments is an inclusive assessment for learning practice

Highlights of Evaluation

Good example #2

Module uses a range of assessment formats

  1. Coursework Portfolio:
    • Perform statistical analyses of real-world datasets
    • Report + Discuss statistical analyses
    • Exactly the same as statisticians working in industry would have to do
    • Opportunity to demonstrate depth of understanding

In line with Hull IEF Assessment & Feedback

  • Give students authentic opportunities to demonstrate their skills, knowledge and self-awareness

Highlights of Evaluation

Area of Enhancement

Mathematics assessment is designed at the programme level, giving students a manageable assessment load

Assessments sometime clash:

  • Mathematics assessment is indeed designed at the programme level

  • Managing assessment load is tricky

    • Due to inherently high amount of content for Maths disciplines

  • Example: Statistical Models students in T2 had

    • At least 1 more module with 10 Weekly Assignments
    • At least 1 more module with Coursework due in last week of T2

Inclusive &
Decolonised curriculum

Evaluation of Inclusivity

Evaluation Framework: Inclusive Education Curriculum Checklist (Link)

Highlights of Evaluation

Good example

My teaching resources are made available in appropriate accessible formats in advance of scheduled teaching sessions wherever possible

Digital Slides:

  • Statistical Models: I inherited teaching material in the form of PDF format slides

  • I wanted to use something more accessible than PDFs for my slides

  • Employed digital publication framework Quarto to write slides
    (The present set of slides is made with Quarto)

Highlights of Evaluation

Good example

My teaching resources are made available in appropriate accessible formats in advance of scheduled teaching sessions wherever possible

  • Statistical Models digital HTML slides are available at
  • Digital slides can be viewed in browsers
    • Allows for easy viewing on various devices, including smartphones
    • Facilitates the use of accessibility features on smart devices
      (e.g. text magnification, contrast enhancement)

Highlights of Evaluation

Good example

My teaching resources are made available in appropriate accessible formats in advance of scheduled teaching sessions wherever possible

  • Digital format allows for compatibility with text-to-speech software
    (overcoming the limitations often encountered with PDFs)
    • Beneficial to auditory learners
    • Beneficial to students with visual impairments
  • My slides are also available in PDF version on Canvas
    • Easy to print

In line with Hull IEF Curriculum: Demonstrate inclusion where possible

Highlights of Evaluation

Area of Enhancement

I work with students as active partners in curriculum design and delivery

(Sometimes) Low engagement in Tutorials:

  • Statistical Models comprises weekly 1-hour Tutorials
  • Lecturer reviews solutions to the previous week’s worksheet
  • Traditional format which often leads to passive learning
    • students receive explanations for exercises they may have already completed
    • low attendance and engagement

Possible solution

Involve students by having them present their solutions

  • I successfully implemented this approach in past modules

  • Led to more popular and well-attended tutorials

  • Students engaged in friendly competition, debating their solutions

  • Fostered a sense of active participation in curriculum delivery

Goal: Apply the same approach to the Statistical Models tutorials

Possible solution

Major impediments:

  • Many exercises in Statistical Models require coding in R
  • Most students lack access to laptops
    (raising concerns about digital exclusion)
  • Holding all classes in computer labs is not feasible

Positive observation:

  • Every student has access to a smartphone or tablet

Exploring the literature

Addressing Digital Exclusion: Reference [1]1

  • Explores challenge of integrating technology into teaching

  • Offers practical guidance through 5 real-world examples

  • Real-world example #2

    • Promoting self-directed learning through interactive presentations with hyperlinks

Sustainability
in the curriculum

Evaluation of Sustainability

Evaluation Framework: Evaluated curriculum against



Framework 1 - SDGs

Statistical models meets SDGs 4 and 8

Goal 4: Quality Education

Ensure inclusive and quality education for all and promote lifelong learning


Goal 8: Decent Work and Economic Growth

Promote inclusive and sustainable economic growth, employment and decent work for all

Good examples

SDG 4: Quality Education

Perform statistical analyses of real-world datasets:

  • Task aligns with SDG 4 by fostering high-quality education
  • Equips students with competencies in data interpretation + critical thinking
  • Prepares students for real-world challenges

Report + Discuss statistical analyses:

  • Students develop communication skills and ability to convey findings

  • Students become better prepared for future professional roles

  • Supports SDG 4 by ensuring that students are not just consumers of knowledge but active contributors

Good examples

SDG 8: Decent Work and Economic Growth

Analysis of the ENRON scandal by looking at dataset of stock prices:

  • Task directly addresses SDG 8 by focusing on an instance of corporate governance failure

    • ENRON scandal had significant implications for economic stability and ethical business practices

  • Students understand the impact of statistical analyses on business ethics and policy-making

  • Equips students with knowledge to contribute positively to economic growth and decent work environments in their future careers

Framework 2 - ESD Competencies Checklist

ESD Competencies

Good examples

Systems thinking

  • Statistical regressive models are designed to understand relationships between variables

  • Nested models are used to compare relationships on different scales

  • All Statistical Models can handle uncertainty

Anticipatory or Future thinking

  • Module includes statistical analyses of real-world examples in Economics and Finance

  • Outcome of statistical analyses is used to inform policy decisions

ESD Competencies

Area of Enhancement

Collaborative working

Little room for collaboration in Lectures:

  • Statistical Models comprises 2 weekly 2-hour Lectures

  • Current lectures design:

    • Lecturer delivers content with slides and whiteboard
    • Lecturer fosters engagement with direct questions

  • This traditional format tends to

    • foster passive learning
    • lacks opportunities for student collaboration

Exploring the literature

Strategies to foster collaboration: Reference [2]1

  • Discusses the role of assessment in education

  • Explores collaborative learning in formative assessment

  • Team tasks

    • Students work collaboratively towards solvinga a problem task

  • Students as Teachers

    • At the end of the problem task students explain solution to each other

Global Competence
in the curriculum

Uni of Hull Global Competence definitions

# Global Competency Description
1 Global Challenges Recognises challenges from a local to global level, such as the issues highlighted in the Sustainable Development Goals or the Earth Charter, acknowledging that such challenges cannot be tackled in isolation of each other.
2 Critical Awareness Has the capacity to reflect critically, effectively evaluating the importance and accuracy of information, continuously seeking to enrich their knowledge base.
3 Historical/Cultural Awareness Is aware of the past influences on current situations, the present complexities of our different traditions, cultures and nations and has a deep understanding of the challenges of our collective future horizons.
4 Respect and Understanding Perspectives Respects the views of others, by reflecting on and articulating alternative perspectives and approaches, and has the capacity to integrate new perspectives into their world view.
5 Equity and Inclusion Aspires to attain an unwavering ethical attitude towards social justice, equity, diversity and inclusivity believing in the transformative power of these principles, by welcoming differences from diverse backgrounds and giving everyone a voice.
6 Positive / Real World Action Motivated by planetary challenges, has the capacity for sustained positive action, from a local to global level and drive change, united against intolerance, ignorance and discrimination in all its forms.
7 Lifelong Personal Growth Understands that individual growth is an endless journey, and requires adaptability, ongoing self-reflection, self-regulation, lifelong learning, empathy, connection and action as well as the ability to work effectively within teams.

Mathematics Programme Competencies

Programme Competency Description
PC1 Performing calculations and manipulating equations in core areas of mathematics and some more advanced topics
PC2 Solving mathematical problems in well-defined contexts by selecting and applying the appropriate techniques
PC3 Solving real-world problems by abstracting the essentials and formulating them mathematically, obtaining solutions by appropriate analytic or numeric methods, and interpreting the results
PC4 Logical reasoning, including identifying assumptions made and conclusions drawn, and giving proofs in well-defined contexts
PC5 Communicating with specialists and non-specialists by contributing to discussions, and accurately, clearly and appropriately presenting arguments and conclusions in written and oral form
PC7 Using computer technology from a range of given methods to obtain numerical solutions to problems, analyse data, and write mathematical documents
PC8 Learning and working independently when given some guidance, solving problems with patience and persistence and managing time appropriately

Mapping PC to Global Competencies


Programme Competencies Global Challenges Critical Awareness Historical / Cultural Awareness Respect & Understanding Perspectives Equity and Inclusion Positive / Real World Action Lifelong Personal Growth
PC1 ❌ ❌ ❌ ❌ ❌ ❌ ❌
PC2 ❌ ✔️ ❌ ❌ ❌ ❌ ❌
PC3 ✔️ ✔️ ❌ ❌ ❌ ✔️ ❌
PC4 ❌ ✔️ ❌ ❌ ❌ ❌ ❌
PC5 ❌ ✔️ ❌ ✔️ ✔️ ✔️ ✔️
PC7 ❌ ❌ ❌ ❌ ❌ ❌ ❌
PC8 ❌ ✔️ ❌ ❌ ❌ ❌ ✔️

Highlights of Evaluation

Good example

Critical Awareness

Assignment: Evaluating the Effectiveness of Education Interventions

  • Students are given
    • dataset containing student performance metrics (i.e. test scores)
    • details about different educational interventions (i.e. tutoring programs)
  • Task:
    • use regression analysis to evaluate data
    • determine which interventions have the most significant impact on student outcomes

How is the Competency met

  • Critical Reflection: Students must critically assess the effectiveness of various educational interventions

  • Evaluating Accuracy of their regression models

    • checking for potential biases
    • checking that model assumptions are met

  • Continuous Improvement:

    • Assignment encourages students to seek out additional methodologies to refine their analysis
    • E.g. they may need to explore advanced regression techniques to improve their evaluation

Highlights of Evaluation

Areas of Enhancement

  • Global Challenges
  • Historical / Cultural Awareness
  • Respect & Understanding Perspectives

Exceptional Example: Undergraduate supervision

  • I supervised an undergraduate dissertation
    • used methods taght in Statistical Models
    • statistical analysis of Formula 1 races
    • advanced the econometric understanding of Formula 1 modelling
  • Dissertation resulted in a publication in a prestigious economics journal [3]

How are Global Competencies met

Global Challenges

  • Relevance:
    • Paper addresses a problem with broader societal or global implications (e.g. sports modelling, economic forecasting, climate modelling)
  • Impact:
    • Paper contributes to the broader application of statistical and econometric methods in real-world scenarios (e.g. Formula 1 racing)

How are Global Competencies met

Historical / Cultural Awareness

  • Contextual Understanding:
    • Paper contextualizes current research by exploring the historical development and use of statistical models (e.g. in sports analytics)

Respect & Understanding Perspectives

  • Inclusion of Different Views:
    • Paper considers and address different perspectives
    • Paper offers comparisons to existing alternative methods
  • Effective Communication:
    • Present complex mathematical ideas clearly to a broad audience

Exploring the literature

Devising Marking Rubric: Reference [4]1

  • Critical role of clarity in academic writing, particularly in mathematical papers
    • Enhance a researcher’s visibility
    • Increase the likelihood of citations
  • Provides a comprehensive guide to the publication process in mathematics
    • Structuring a paper
    • Proper referencing
    • Effective writing styles (Maths)
    • Tips for using LaTeX
  • Insights from [4] + My own experience can be used to design Marking Rubric

References

[1]
T. Betts, Technology, tools and tips for active learning: Five innovative ideas for integrating technology with your teaching, in: T. Betts, W. Garnham, P. Oprandi (Eds.), Disrupting Traditional Pedagogy: Active Learning in Practice, Brighton: University of Sussex Library, 2019: pp. 141–171. https://doi.org/10.20919/9780995786240.
[2]
H. Pokorny, Assessment for Learning, in: H. Pokorny, D. Warren (Eds.), Enhancing Teaching Practice in Higher Education, London: Sage, 2021: pp. 79–106.
[3]
J. Fry, T. Brighton, S. Fanzon, Faster identification of faster formula 1 drivers via time-rank duality, Economics Letters. 237 (2024) 111671. https://doi.org/10.1016/j.econlet.2024.111671.
[4]
I. Pak, How to write a clear math paper: Some 21st century tips, Journal of Humanistic Mathematics. 8 (2018) 301–328. https://doi.org/10.5642/jhummath.201801.14.

Link to Annotated Bibliography

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License

This work is licensed under CC BY 4.0

For attribution please cite this work as:

Fanzon, Silvio (2024). Curriculum evaluation for Statistical Models.
https://www.silviofanzon.com/2024-Curriculum-Design-Slides/

BibTex citation:

@electronic{Fanzon-Curriculum-Design-2024,
    author = {Fanzon, Silvio},
    title = {Curriculum evaluation for Statistical Models},
    url = {https://www.silviofanzon.com/2024-Curriculum-Design-Slides/},
    year = {2024}}

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