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Are We Measuring Mathematical Understanding — or Merely Examination Performance? — A Francis K. A. Baccah Study

An in-depth study in Mathematics calling all stakeholders in education — W.A.E.C., G.E.S., M.o.E. to rethink Mathematics assessment in Ghana, and a must-read for all Mathematics educators in Ghana.

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Are We Measuring Mathematical Understanding — or Merely Examination Performance? — A Francis K. A. Baccah Study

1. Introduction: A National Mathematics Education Concern

In my recent teaching experience, I taught a learner who sat the Mathematics examination three times before eventually passing. Unfortunately, her grade was still insufficient for admission to her desired nursing programme. Her experience raises an important question about how learners' mathematical competence is developed, demonstrated and assessed.

The concern extends beyond individual learners. Figures attributed to the Ghana Education Service (GES) and the Volta Regional Education Directorate in August and September 2026 reportedly indicate that 18 public Senior High Schools (SHSs) recorded a 0% tertiary-progression rate in the 2025 West African Senior School Certificate Examination (WASSCE). Of 26,544 candidates in the region, 4,067 reportedly met the qualification requirements for tertiary progression, representing approximately 15.32%. Core Mathematics was reported to have a pass rate of 24.99%.

These figures should be verified against official reports, but if confirmed, they highlight the urgency of investigating persistent Mathematics underachievement in Ghana.

In my professional view, the problem requires us to examine not only what learners are taught and how they learn, but also the extent to which conventional teaching and assessment approaches contribute to their disaffection for Mathematics.

2. The Cognitive Emphasis and Learners' Disaffection for Mathematics

Mathematics is necessarily abstract. However, when teaching focuses predominantly on symbols, formulas, procedures and written examination preparation without sufficient practical exploration or connections to everyday life, some learners struggle to find meaning in what they are learning.

The deep-seated disaffection for Mathematics among many senior high school learners is particularly concerning. Some approach the subject with anxiety, low confidence or the belief that it is beyond their ability. When mathematical concepts appear disconnected from their experiences, learners may lose interest and struggle to develop lasting understanding.4

I contend that the dominance of abstract teaching and cognitively oriented written examinations may contribute to this problem. When examination performance becomes the principal measure of success, classroom teaching can become increasingly focused on reproducing procedures rather than exploring mathematical ideas through varied experiences.

This is not an argument against abstraction, cognitive development or written examinations. These are essential to mathematical competence. The concern is whether they are sufficiently supported by practical, creative, experiential and life-connected learning opportunities.

Ghana must therefore investigate whether its approaches to teaching and assessing Mathematics adequately support learners' understanding, engagement and ability to apply mathematical knowledge.

3. Are We Measuring the Full Range of Mathematical Understanding?

Conventional written Mathematics examinations provide important evidence of learners' knowledge, reasoning, accuracy and problem-solving abilities. However, written performance may not capture every relevant way learners can demonstrate mathematical competence.

Learners can also engage with mathematical ideas through practical activities, visual representations, verbal explanations, creative problem-solving, mathematical communication and real-life applications. These approaches should complement, not replace, the development of formal mathematical knowledge and reasoning.

For example, learners can explore percentages through mobile money transactions, discounts and savings; ratios through recipes and mixtures; and geometry through buildings, local crafts and the environment. Such experiences can help connect abstract concepts to meaningful contexts.

The central question is whether an assessment system dominated by written cognitive performance provides a sufficiently comprehensive picture of mathematical learning.

4. Lessons from the Assessment of Other Subjects

Other subjects demonstrate that learning can be explored through different forms of evidence, including practical work, projects, presentations, creative products and performance-based activities.

Mathematics should likewise investigate appropriate opportunities for learners to demonstrate understanding through more than one mode, where the learning objectives permit it.

This does not mean that every mathematical concept can or should be assessed through performance. Nor does creativity automatically demonstrate mathematical mastery. Rather, different forms of assessment should be selected according to the knowledge, skills and competencies being measured.

A balanced approach could help teachers identify learners' strengths and difficulties more comprehensively while maintaining clear standards of mathematical accuracy and reasoning.

5. Can Creativity and Performance Complement Written Mathematics Examinations?

Mathematical understanding can sometimes be demonstrated through constructing models, interpreting data, explaining patterns, solving practical problems or presenting mathematical reasoning.

Carefully designed tasks could provide additional evidence of learners' ability to apply concepts, communicate ideas and connect Mathematics with everyday situations.

However, any proposal to incorporate such approaches into high-stakes national examinations must be supported by research into validity, reliability, fairness, feasibility, cost and examination security. These approaches should not be introduced simply because they appear engaging; they must demonstrate that they assess meaningful mathematical learning.

The objective is to broaden the evidence available for understanding mathematical competence without weakening academic standards.

6. The Mathematics Verse Assessment Framework (MVAF)

I propose that Ghana investigate the Mathematics Verse Assessment Framework (MVAF), developed within Transformative Poetic Mathematics Education (TPME) under Transformative Poetic Education (TPE).

MVAF is a proposed framework for examining mathematical learning through two complementary modules:

● Rubric-Based Assessment (RBA): Uses clearly defined criteria and performance levels to evaluate specified aspects of learners' work.

● Standards-Based Assessment (SBA): Evaluates learners' demonstrated competence against clearly defined mathematical learning standards.

The framework identifies five dimensions for consideration: cognitive, affective, psychomotor, creative and performative.

These dimensions would not all need to be assessed in every task. Cognitive assessment would continue to examine mathematical knowledge and reasoning, while other dimensions could be included where they provide valid evidence of relevant learning outcomes. For example, interest and confidence may inform understanding of learner engagement, but they cannot independently establish mathematical competence.

MVAF remains a proposal requiring systematic development, piloting, validation and evaluation. Its potential contribution should be judged by evidence of its effectiveness, not by its conceptual appeal alone.

7. Restoring Meaning and Enjoyment Through Verse Pedagogy

Assessment reform must be accompanied by attention to how Mathematics is taught and experienced.

Verse Pedagogy (VP), developed within TPE, offers an instructional ecosystem intended to connect mathematical learning with rhythm, language, exploration, practical experience, creativity and everyday life. It goes beyond poems and songs to incorporate methods, assessment, field education and other learning resources.

Its learning sequence is:

Enjoy → Discover → Explore → Practice → Connect → Reflect.

The sequence is intended to help learners engage with mathematical ideas, discover relationships, explore concepts, practise procedures, connect learning to meaningful contexts and reflect on their understanding.

The purpose is not to entertain learners at the expense of rigour. It is to investigate whether engaging and experiential approaches can strengthen conceptual understanding, participation and sustained interest in Mathematics.

Verse Pedagogy should therefore be subjected to appropriate classroom research and evaluation to establish its effectiveness across different learner groups and educational settings.

8. A National Call to WAEC, GES and the Ministry of Education

The reported WASSCE performance figures, together with teachers' experiences of learners' difficulties and disaffection, warrant a coordinated national response.

I call on WAEC, GES, the Ministry of Education, teacher education institutions and mathematics education researchers to:

1. Investigate persistent underachievement: Examine foundational learning gaps, teaching practices, learner engagement, learning resources and assessment demands.

2. Review the balance of Mathematics assessment: Establish whether the current emphasis on written cognitive performance adequately measures the intended learning outcomes.

3. Support innovative teaching: Strengthen teacher professional development in practical, experiential, creative and life-connected Mathematics education.

4. Research and pilot MVAF: Evaluate its validity, reliability, fairness, feasibility and potential contribution alongside existing assessment methods.

5. Evaluate Verse Pedagogy: Investigate whether its learning sequence improves engagement, conceptual understanding, mathematical competence and examination performance.

6. Protect standards and fairness: Ensure that any proposed assessment reform maintains mathematical rigour, transparent criteria, equitable opportunities and the integrity of national examinations.

These measures should form part of a broader national effort to understand why learners struggle with Mathematics and identify effective, evidence-based responses.

9. Conclusion: Beyond Examination Scores

Ghana's Mathematics education challenge cannot be addressed by focusing exclusively on examination results. We must also examine how mathematical understanding develops, how learners experience the subject and whether teaching and assessment practices provide adequate opportunities to demonstrate competence.

I contend that the strong emphasis on abstraction and written cognitive performance, when insufficiently balanced by meaningful and innovative learning experiences, may contribute to learners' disaffection for Mathematics. This position deserves serious investigation rather than automatic acceptance or dismissal.

The proposed Mathematics Verse Assessment Framework and Verse Pedagogy offer avenues for research into broader assessment and more engaging instruction. Their value must ultimately be established through evidence.

The national challenge is not to lower Mathematics standards, but to improve how Mathematics is taught, experienced and assessed so that learners can develop meaningful understanding and demonstrate what they know and can do.

Ghana must be willing to ask not only whether learners are passing Mathematics, but also whether our educational approaches are helping them understand, appreciate and use it.


Written by:

Francis K. A. Baccah

Educationist | Mathematics Educator | Researcher

atsubaccah@gmail.com 

0545271766 | 0243589166

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