Curriculum expectation and classroom reality in manipulative use by JHS mathematics teachers in Amansie Central Ghana

1 Introduction

Mathematics occupies a privileged position in national curricula worldwide, serving both as a gateway to further education and as a foundation for technological and economic development (Charles-Ogan and Otikor, 2016; Kilpatrick et al., 2001). In Ghana, mathematics is a compulsory core subject from basic school through pre-university education, reflecting its centrality to national development ambitions in science, technology, engineering, and commerce (Ministry of Education, 2020). Performance in mathematics at the end of basic education, as measured by the Basic Education Certificate Examination (BECE), therefore remains an important concern for policy-makers, curriculum developers, and schools.

This concern is evident in the Amansie Central District of the Ashanti Region, a predominantly rural district in which small-scale gold mining and agriculture are important livelihoods; 87.6% of its population lives in rural localities and 85.3% of households are engaged in agriculture, while gold is mined on a small scale at Apitisu, Amamom, Jacobu and other locations in the district (Ghana Statistical Service, 2014). Between 2022 and 2024, BECE mathematics failure rates in the district rose from 55.1% (2022) to 57.8% (2023) and 59.4% (2024), an increase of approximately four percentage points over two years, and were higher than the concurrent failure rates in English (34.2%–41.7%) and Science (39.6%–43.8%) (Ghana Education Service, 2024). These figures are presented as the educational context that motivated the study. Examination performance is shaped by many factors, including pupil, home, school, and system characteristics, and the present study did not test whether manipulative use is associated with BECE performance. The figures are therefore not interpreted as evidence of the consequences of any particular instructional practice.

The Common Core Programme mathematics curriculum (MOE, 2020) expects teachers to use mathematical manipulatives—concrete, physical objects that pupils can see, touch, and manipulate to make sense of abstract mathematical ideas—in teaching mathematics across JHS 1 to 3. The curriculum calls for a learning-centred classroom offering learners meaningful “hands-on” activities (MOE, 2020, p. xxii) and requires that “learners are given frequent opportunities to interact with varied sources of information, teaching and learning materials” (MOE, 2020, p. xxiii). Specific manipulatives are written into the content standards and exemplars themselves — for example, modelling number quantities “using graph sheets, isometric papers and multi-base blocks” (B7.1.1.1.1, p. 2) and modelling repeated factors “using counters or bottle tops” (B7.1.2.3.1, p. 13). This expectation is consistent with developmental and cognitive accounts of learning that emphasise movement from concrete experience towards abstract reasoning (Fyfe et al., 2014; Piaget, 1952), and with research reporting positive, though variable, effects of manipulative-based instruction on mathematical learning (Carbonneau et al., 2013; Laski et al., 2015).

Much is already known about manipulatives. Internationally, meta-analytic and review evidence indicates that manipulatives can support learning, but that their effectiveness depends on how they are used, including the level of instructional guidance and the explicitness of the links between objects and mathematical ideas (Carbonneau et al., 2013; Laski et al., 2015; McNeil and Jarvin, 2007). Studies of teachers' practice show that manipulative use varies considerably, tends to decline as grade level rises, and is sometimes treated as an enjoyable supplement rather than as integral to mathematical sense-making (Moyer, 2001; Uribe-Flórez and Wilkins, 2010). In Ghana, recent survey evidence indicates that many commonly recommended manipulatives are rarely available in basic school classrooms (Padmore et al., 2025), and earlier work has documented limited attention to the practical teaching of early mathematics in initial teacher preparation (Akyeampong et al., 2013) and difficulties in implementing mathematics curriculum reforms (Mereku, 2004).

What remains less well understood is how teachers' reported practices relate to what actually happens in classrooms, and how resource conditions and professional development are implicated in that relationship. Research on teachers' manipulative use frequently relies on teachers' self-reports (e.g.,Padmore et al., 2025; Uribe-Flórez and Wilkins, 2010), yet self-reported measures of instructional practice do not necessarily correspond to observed practice (Mayer, 1999). In the Ghanaian JHS context, and particularly in rural districts, little evidence brings together teachers' reported use, observed classroom enactment, the supply of materials, and teachers' access to professional development within a single study. The contribution of the present study lies in combining questionnaire, interview, and observation evidence so that reported practice can be compared directly with enacted practice and the discrepancy interpreted in light of teachers' and other stakeholders' accounts of their working conditions.

Accordingly, the study addressed the following research questions: (1) What types of manipulatives do JHS teachers report using in teaching different mathematics topics? (2) How do teachers obtain manipulatives? (3) What teaching methods do teachers report and employ when using manipulatives? (4) What benefits do teachers perceive from manipulative use? (5) What challenges do teachers perceive in using manipulatives in practice? In addition, the quantitative and qualitative strands were integrated to examine the extent to which teachers' reported use of manipulatives and teaching methods converged with observed classroom practice.

2 Theoretical framework and review of related literature

2.1 Defining manipulatives in mathematics education

Mathematical manipulatives are concrete, physical objects—whether commercially produced or improvised from everyday materials—that teachers and learners use to illustrate, explore, and understand mathematical concepts (Van de Walle et al., 2013). The category has expanded to include pictorial representations and virtual manipulatives (Cooper, 2012), although physical manipulatives remain the primary focus of Ghanaian curriculum guidance (MOE, 2020). Across these typologies, the central purpose of manipulatives is to make abstract mathematical ideas perceptible and open to manipulation, bridging concrete experience and symbolic representation (Laski et al., 2015).

2.2 Teachers' perceptions and practices: clarifying the constructs

Research on teachers' thinking distinguishes several related constructs. Thompson (1992) described teachers' conceptions as a general mental structure encompassing beliefs, meanings, concepts, propositions, rules, mental images, and preferences. Capturing conceptions in this broad sense requires instruments and analyses designed for that purpose, which the present study did not employ. The study therefore does not claim to measure teachers' conceptions. It focuses instead on two narrower and directly measured constructs. Teachers' perceptions are operationalised as teachers' levels of agreement (agree, disagree, uncertain) with statements about the benefits of, and challenges to, manipulative use. Teachers' reported practices are operationalised as teachers' self-reported use of manipulatives across 13 syllabus topics, the sources and frequency of supply, and the teaching methods they report using with manipulatives. These are distinguished from enacted practice, operationalised as the use of manipulatives and the teaching methods recorded during classroom observation. Table 1 (Section 3.3) summarises how each construct relates to the research questions, data sources, and analyses.

Table 1. Alignment of research questions, constructs, data sources, and analyses.

RQ, research question.

2.3 Curriculum enactment as the guiding framework

Because the central phenomenon of the study is the way teachers take up a curricular expectation under contextual constraints, the study is framed primarily by research on curriculum enactment. Stein et al. (2007) distinguished between the written curriculum, the curriculum as intended by teachers, and the curriculum as enacted in classrooms, noting that each transformation is shaped by teachers' knowledge and beliefs and by the conditions in which they work. Remillard (2005) characterised teachers' use of curriculum as a participatory relationship in which teachers interpret and adapt curriculum resources rather than simply implementing them. Building on this work, Remillard and Heck (2014) differentiated the official curriculum, set by education authorities, from the operational curriculum, which includes the teacher-intended curriculum and the curriculum enacted with students. From a policy-implementation perspective, Spillane et al. (2002) similarly argued that implementers make sense of policy through their existing knowledge, beliefs, and situations, so that the policy enacted may differ from the policy designed.

This framework informed the study in three ways. First, it guided the selection of variables: the curriculum expectation for manipulative use (MOE, 2020) represents the official curriculum; teachers' lesson-note entries and questionnaire reports can be read as indicators of the teacher-intended or documented curriculum; and observed lessons represent the enacted curriculum. Second, it identified the conditions that may shape the movement from intended to enacted curriculum—the availability and supply of materials, teachers' access to professional development and guidance, time, and class size—which were examined as sources of supply and perceived challenges. Third, it provided the lens through which discrepancies between reported and observed practice are interpreted in the Discussion: not as simple non-compliance, but as the outcome of teachers' interpretation of curriculum requirements within particular resource and accountability conditions.

2.4 The learning rationale for manipulatives

The rationale embedded in the official curriculum for using manipulatives draws on accounts of how pupils learn mathematics. Piaget (1952) argued that children's mathematical understanding is initially rooted in concrete experience and that abstract reasoning develops through interaction with objects. The concrete–representational–abstract (CRA) sequence operationalises this idea in teaching by moving learners from concrete manipulation to pictorial representation and then to symbolic reasoning (Sousa, 2008), and research on concreteness fading provides further support for a gradual transition from concrete to symbolic representations (Fyfe et al., 2014). At the same time, manipulatives do not automatically produce understanding: their benefits depend on whether pupils are helped to connect the objects to the mathematical ideas they represent (Laski et al., 2015; McNeil and Jarvin, 2007). This rationale explains why the curriculum values manipulatives and why the manner of their use—including the teaching methods that accompany them—was examined in this study. It is not, however, used to test effects on pupils' learning, which the study did not measure.

2.5 Evidence on the benefits of manipulative use

Research reports a range of potential benefits of manipulative-based instruction. In a meta-analysis of 55 studies, Carbonneau et al. (2013) found small-to-moderate positive effects of teaching with concrete manipulatives compared with instruction using abstract symbols only, with effects moderated by instructional features such as the level of guidance provided. Boggan et al. (2010) argued that manipulatives help students move from concrete experiences to abstract reasoning. In an action research project with eighth-grade students, Goracke (2009) reported that four students who failed the numerical portion of a test on adding and subtracting polynomials scored 100% on the corresponding manipulative portion. Green et al. (2008) found that short-term instruction using manipulatives helped to reverse pre-service teachers' arithmetic misconceptions, and Rosli et al. (2015) described how manipulatives can support mathematical problem solving and problem posing.

Other claimed benefits include support for conceptual understanding and knowledge construction (Cooper, 2012; Dennis, 2011), improved motivation and reduced mathematics anxiety (Cope, 2015), and opportunities for cooperative learning and communication (National Council of Teachers of Mathematics, 2000). Many of these benefits correspond to learning goals in the Ghanaian mathematics curriculum (MOE, 2020), which is why teachers' perceptions of them were examined in this study.

2.6 Challenges and barriers to manipulative use

Research also documents a persistent gap between the advocated and actual use of manipulatives. Moyer (2001) found that teachers often used manipulatives for enjoyment or as rewards, and distinguished such activities from what they regarded as “real” mathematics. Uribe-Flórez and Wilkins (2010) reported that teachers' manipulative use varied with grade level and teacher background, with less frequent use in higher grades—a pattern of particular relevance to JHS classrooms. Swan and Marshall (2010) emphasised that teachers need guidance and training to use manipulatives effectively, and Pham (2015) found that teachers viewed manipulative-based instruction as time-consuming and logistically demanding.

In sub-Saharan Africa, and in Ghana specifically, structural conditions add to these challenges. Akyeampong et al. (2013) found that initial teacher preparation in several African countries, including Ghana, gave limited attention to how to teach early mathematics in classrooms. Mereku (2004) described difficulties in implementing mathematics curriculum reforms in Ghana, and Padmore et al. (2025) reported that many recommended manipulatives were rarely available to Ghanaian JHS mathematics teachers, with insufficient funding among the obstacles to both procurement and improvisation. These studies suggest that the resources and professional support that condition curriculum enactment (Section 2.3) warrant examination alongside teachers' reported practices.

3 Methodology

3.1 Research design

The study employed a convergent mixed-methods design (Creswell and Plano Clark, 2018) within a cross-sectional timeframe. In a convergent design, quantitative and qualitative data are collected in the same phase of the research, analysed separately, and then merged to determine whether, and in what ways, the findings converge or diverge. This design was selected because the research aim required both breadth—patterns of reported use, supply, methods, benefits, and challenges across the district's teachers—and depth, in the form of observed practice and stakeholders' explanations. Neither strand alone could establish whether teachers' reported practices corresponded to classroom enactment.

Timing. Both strands were conducted during the 2024–2025 academic year. The questionnaire was administered first, with a one-month completion window; classroom observations were conducted during the same term; interviews with observed teachers took place immediately after the observed lessons; and interviews with head teachers, pupils, and the district mathematics coordinator were conducted during the same period. Priority. The two strands were given equal priority, because the key research outcome — the comparison of reported and enacted practice — required both. Integration. Integration occurred at three points (Fetters et al., 2013). At the design level, the questionnaire, interview schedules, and observation protocol were aligned to the same research questions and constructs (Table 1). At the analysis level, observation data on manipulative use and teaching methods were compared with the corresponding questionnaire items, and interview data were used to explain the patterns identified. At the interpretation level, the findings were merged in a joint display (Table 7) that classifies each dimension as convergent or divergent and states the resulting meta-inference.

3.2 Setting, population, and sampling

The study was conducted in public JHSs in the Amansie Central District of the Ashanti Region of Ghana. The district is predominantly rural, and its schools operate in resource-constrained conditions at the 2010 census, 21.9% of the district's population aged 3 years and over had never attended school (GSS, 2014), making it a relevant setting for examining the enactment of curriculum-mandated instructional practices.

The target population comprised JHS mathematics teachers, head teachers, pupils, and the district mathematics coordinator associated with the district's 62 public JHSs. Fifty-six schools were accessed; six were excluded because teachers were absent, engaged in examination duties, or declined to participate. Questionnaire sample. A total of 108 questionnaires were distributed and 97 were returned, a response rate of 89.8%. The sampling frame comprised all 108 mathematics teachers in the 56 accessible schools, and a questionnaire was distributed to every teacher in the frame; the questionnaire sample was therefore a census of the accessible teacher population rather than a probability sample.

Interview sample. Purposive sampling was used to select five mathematics teachers, ten head teachers, fifteen pupils (selected to represent a spread of academic performance levels identified during classroom observation), and the district mathematics coordinator (31 interview participants in total). The five teachers were selected from among the observed teachers so as to include both those who used manipulatives in the observed lesson and those who did not, and the ten head teachers were selected to represent schools across the district's circuits and a range of school sizes. Observation sample. Classroom observations were conducted with sixteen teachers in sixteen schools. The sixteen schools were selected purposively from the 56 accessible schools to represent the district's circuits and schools of differing size, and one mathematics teacher was observed in each. Relationship among samples. All sixteen observed teachers were among the 97 questionnaire respondents, and the five interviewed teachers were among the sixteen observed teachers; the comparison of reported and enacted practice can therefore be read at the individual as well as the group level.

3.3 Instruments and data collection

Three instruments were used. First, a structured questionnaire captured the types of manipulatives teachers used across 13 mathematics topics in the GES syllabus, the sources and frequency of supply, the teaching methods employed, perceived benefits of manipulative use (seven statements), and perceived challenges (eight statements). Benefit and challenge statements used a three-option response format (agree, disagree, uncertain); the instrument also included ranking items and open-ended questions. A one-month completion period was provided to accommodate teachers' schedules.

3.3.1 Development and validation of the questionnaire

The questionnaire items were developed from the literature reviewed in Section 2 and from the 13 topics of the GES junior high school mathematics syllabus. Content validity was established through review by a panel of experts in mathematics education at the University of Education, Winneba, whose comments led to the rewording of ambiguous items and the removal of redundant ones. The revised instrument was pilot-tested with JHS mathematics teachers in the neighbouring Amansie West District, a district with a comparable rural, farming and small-scale-mining profile that was not included in the main study; the pilot informed the final wording of the topic list and of the benefit and challenge statements. Reliability coefficients were not computed for the benefit and challenge statements, because each statement was analysed as a single item rather than as part of a summed scale; this is acknowledged as a limitation in Section 6.1.

Second, semi-structured interview schedules were administered individually to the mathematics coordinator, five teachers, ten head teachers, and fifteen pupils. The interviews explored participants' perspectives on manipulative use, supply and resource challenges, teaching methods, and pupils' learning experiences. Third, unannounced classroom observations, each lasting a full lesson period (approximately 70 min), were conducted to record whether manipulatives were used and which teaching methods were employed, independently of teachers' self-reports. Each teacher was observed once. Observations were recorded on a structured checklist covering the topic taught, whether manipulatives were used and by whom (teacher only, pupils, or both), the materials used, the dominant teaching method (lecture, discussion, activity, or problem solving), and whether the teacher explicitly linked the materials to the mathematical ideas; accompanying field notes recorded the lesson sequence and pupils' participation. Teachers were informed of the researcher's intention to observe but not of the specific observation dates, in order to reduce reactivity to observation.

3.4 Data analysis

3.4.1 Quantitative analysis

Questionnaire data were entered into IBM SPSS Statistics (Version 27). Reported use of manipulatives by topic, sources of supply, and teaching methods were analysed using frequencies and percentages, and a matrix-ranking method was used to identify the most frequently named manipulatives for each topic. Because use by topic was recorded as a categorical variable, frequencies and percentages, rather than means and standard deviations, are reported as the principal descriptive statistics.

For each of the seven benefit statements and eight challenge statements, a one-sample chi-square goodness-of-fit test was used to examine whether teachers' responses were evenly distributed across the three response options. The null hypothesis for each test was that the proportions of agree, disagree, and uncertain responses were equal, giving an expected frequency of 97/3 = 32.33 responses per category and 2 degrees of freedom. Tests were conducted at α = 0.05; because 15 tests were conducted, results were also checked against a Bonferroni-adjusted threshold of.05/15 = 0.0033. A significant result indicates only that responses were not evenly distributed; the direction of the pattern is interpreted from the observed percentages. These tests describe the distribution of teachers' perceptions. They do not measure pupils' learning outcomes and cannot establish any effect of manipulative use on learning. Cohen's w, calculated as √(χ²/N), is reported alongside each test as a measure of how far the observed distribution departs from an even one.

3.4.2 Qualitative analysis

Interview transcripts and observation field notes were analysed using the six-phase thematic analysis described byBraun and Clarke (2006): familiarisation, generating initial codes, searching for themes, reviewing themes, defining and naming themes, and producing the report. A hybrid coding approach was used: the research questions provided initial deductive categories, and codes within those categories were generated inductively from the data. Coding was carried out by the author, and a second researcher independently coded a subset of the transcripts; coding disagreements were resolved through discussion until consensus was reached, and the decisions were recorded in coding memos. Initial codes were grouped into themes on the basis of shared meaning — for example, the codes “no supply from GES”, “buying materials personally”, and “using bottle tops and stones” were grouped into the theme “dependence on improvisation”. Trustworthiness was addressed through triangulation across participant groups and data sources, an audit trail of coded transcripts and analytic memos, and peer debriefing with a colleague familiar with the district context (Nowell et al., 2017). Observation field notes were coded for the presence or absence of manipulative use and for the dominant teaching method, and these codes were compared with the corresponding questionnaire responses as part of the integration described in Section 3.1.

3.5 Ethical considerations

Written permission was obtained from the Amansie Central District Education Directorate prior to data collection. Ethical approval was granted by the Ethics Committee of the University of Education, Winneba (Ref. No. __________). Head teachers introduced the researcher to teachers and facilitated access to classrooms. All participants were informed of the purpose of the study, the confidentiality of their responses, the academic use of the data, and their right to withdraw at any time without penalty. No questionnaire requested participants' names, and pseudonyms or role descriptors are used in reporting.

Because the pupils who were interviewed and whose lessons were observed were minors, additional procedures applied. Written informed consent was obtained from parents or guardians through the schools before pupils were interviewed, and pupils gave verbal assent after the study had been explained to them in age-appropriate language; pupils were told that they could decline to take part or stop at any time. The study adhered to the ethical guidelines of the University of Education, Winneba and the Ghana Education Service research protocol.

4 Results

4.1 Demographic profile of teacher participants

Of the 97 teacher participants, most were male (79.4%). The sample was relatively young: 36.1% were aged 20–25 years and 38.1% were aged 31–35 years. Most held a degree (70.1%), 23.7% held a diploma, and 4.1% held a postgraduate degree (MEd or MPhil); qualification was not recorded for two teachers (2.1%). In terms of experience, 63.9% had taught mathematics at the JHS level for between three and eight years (Table 2).

Table 2. Demographic characteristics of teacher participants (N = 97).

Data were collected during the 2024–2025 academic year. Frequencies within each variable sum to 97; percentages may not sum to exactly 100 because of rounding. No participant reported an age of 26–30 years or 9–15 years of teaching experience, and the two teachers whose qualification is not recorded did not respond to that item.

4.2 Teachers' reported use of manipulatives by mathematics topic

Across all 13 topics, large majorities of teachers reported using manipulatives, ranging from 85.6% (Powers of Numbers) to 96.9% (Sets; Shapes and Space). Table 3 reports the frequency and percentage of teachers who reported using manipulatives for each topic, together with the most frequently named materials.

Table 3. Teachers' reported use of manipulatives by mathematics topic and most frequently named materials (N = 97).

“Did not report use” includes teachers who indicated non-use and any teachers who gave no response for the topic. Manipulatives are ranked by the frequency with which teachers named them.

The matrix-ranking analysis showed that teachers mostly named manipulatives that were available in the immediate school environment or could be improvised at low cost. Bottle tops, stones, sticks, cut-out shapes, and graph paper were named across multiple topics, whereas commercially produced manipulatives such as Cuisenaire rods, geoboards, AngLegs, and attribute blocks ranked consistently lower; in interviews, head teachers and the district mathematics coordinator attributed this to the limited availability of commercially produced materials in school stores. These patterns suggest that accessibility and familiarity were prominent considerations in teachers' choice of materials.

4.3 Reported and observed use: observation evidence

The comparison of questionnaire and observation data revealed a marked discrepancy. Although large majorities of teachers reported using manipulatives (Table 3), only two of the sixteen observed teachers (12.5%) used manipulatives during the observed lesson. The remaining fourteen teachers taught using lecture or discussion methods, and neither they nor their pupils handled concrete materials. In the two lessons in which manipulatives were used, one teacher used a coin and dice to teach probability, and the other used cut-out shapes to teach the properties of quadrilaterals, both of which are consistent with the curriculum. No inferential test was conducted to compare reported and observed use; the discrepancy is described, not statistically tested.

Teachers offered explanations for this discrepancy in post-observation interviews. One teacher stated: “I did not use my manipulatives stated in the lesson notes because there is no time, and using manipulatives takes too much of the lesson, so I used the discussion method to treat topics more often.” Another explained: “It is a normal practice to indicate the type of manipulatives you intend to use in teaching every topic, but in reality most of us teachers don't use them because they are simply not available.” These accounts suggest that lesson-note entries about manipulatives may document compliance with curriculum requirements without reflecting classroom enactment. Head teachers' interview accounts indicated that supervision focused on lesson-note preparation rather than on classroom observation.

4.4 Sources and supply of manipulatives

Table 4 shows that improvisation by teachers and pupils was the main source of manipulatives for 78.4% of teachers, whereas MOE/GES supply was the main source for 12.4%. With respect to frequency of supply, 78.4% of teachers reported never receiving manipulatives from the MOE/GES, and only 1.0% and 3.1% reported termly or yearly supply, respectively. The district mathematics coordinator stated: “Since I entered into this office, I have never received any budgetary allocation for the supply of manipulatives for teachers, and when I ask the office, they simply tell me no funds have been allocated for that purpose.” Taken together, these data indicate that, in this district, the provision of manipulatives depended largely on teachers' and pupils' own improvisation.

Table 4. Main sources of manipulatives and frequency of supply by source (N = 97).

The “main source” column sums to 97 teachers, each of whom identified one principal source. Frequency-of-supply percentages are calculated for all 97 teachers for each source. Each teacher identified a single main source, and the frequency-of-supply items were answered separately for each of the four sources. MOE, Ministry of Education; GES, Ghana Education Service; NGO, non-governmental organisation; PTA, Parent–Teacher Association.

4.5 Teaching methods used with manipulatives

On the questionnaire, the activity method was the most frequently reported approach when teaching with manipulatives (67.0%), followed by discussion (15.5%), problem solving (13.4%), and lecture (4.1%). Classroom observations, however, showed that most observed teachers used lecture or discussion methods, with manipulatives seldom used. One teacher explained: “Activity or problem-solving methods of teaching using manipulatives is time-consuming … also, most of us were not trained that way, therefore it is difficult for us to use, though it is stated in the syllabus.” In interviews, pupils reported that they did not understand topics well when lessons relied on lecture alone and that they understood better when manipulatives and activities were used. These are pupils' perceptions of their learning rather than measured learning outcomes.

4.6 Teachers' perceived benefits of manipulative use

As Table 5 shows, most teachers agreed with all seven benefit statements. Agreement was highest for “helps pupils relate real-world situations to mathematics” (96.9%) and “improves understanding; pupils construct their own knowledge” (93.8%). For every statement, responses were not evenly distributed across the three options (all p < 0.001), with agreement as the dominant response. The lowest level of agreement concerned the statement that manipulative use saves time: 32.0% of teachers disagreed, suggesting that some teachers who recognise the instructional value of manipulatives also regard them as time-consuming.

Table 5. Teachers' perceived benefits of manipulative use and chi-square goodness-of-fit results (N = 97).

One-sample chi-square goodness-of-fit tests with equal expected frequencies (32.33 per category); df = 2. All results remain significant at the Bonferroni-adjusted threshold of.0033. Significant results indicate that responses were not evenly distributed across the three options; they reflect teachers' perceptions and do not measure pupils' learning outcomes. Cohen's w (√[χ²/N]) is reported as an effect size, where.10,.30 and.50 denote small, medium and large departures from an even distribution.

Interview and observation data provide pupils' perspectives on this issue. After one of the two lessons in which manipulatives were used, a pupil said: “I was happy because I understood everything master was doing … I can now solve problems on my own.” In lessons in which manipulatives were not used, post-lesson exercises completed by 31 pupils showed that only 9 scored 2 out of 5 marks and only 1 scored full marks. Comparable exercise data were not collected in the two lessons in which manipulatives were used. These observations are descriptive. The exercises were not standardised measures of achievement, no comparison was made under controlled conditions, and pupils' scores cannot be attributed to the absence of manipulatives.

4.7 Teachers' perceived challenges to manipulative use

Table 6 shows that the challenges most frequently endorsed by teachers were lack of continuing professional development (71.1%), the high cost of preparing improvised materials (66.0%), non-availability or inadequacy of manipulatives (61.9%), and inadequate user guides (59.8%). By contrast, most teachers disagreed that limited knowledge of how to use manipulatives (72.2%), heavy workload (64.9%), or insufficient lesson time (58.8%) were challenges. For large class size, responses were divided between agreement (41.2%) and disagreement (47.4%); the significant chi-square result for this item reflects the small proportion of uncertain responses rather than a clear majority view. Because all 15 chi-square tests were significant, the tests mainly confirm that teachers held definite views on each statement; the substantive interpretation rests on the direction and size of the percentages.

Table 6. Teachers' perceived challenges to manipulative use and chi-square goodness-of-fit results (N = 97).

One-sample chi-square goodness-of-fit tests with equal expected frequencies (32.33 per category); df = 2. All results remain significant at the Bonferroni-adjusted threshold of.0033. A significant result indicates an uneven distribution of responses, not that a majority agreed that the statement is a challenge; the direction of each pattern should be read from the percentages. Percentages may not sum to 100 because of rounding. Cohen's w (√[χ²/N]) is reported as an effect size, where.10,.30 and.50 denote small, medium and large departures from an even distribution.

Interview data contextualised these perceptions. The district mathematics coordinator stated: “We all know that the use of manipulatives helps in lesson delivery and helps improve pupil performance in the subject. The teachers know this and that is why they indicate manipulatives to be used in every lesson note they prepare.” The coordinator also reported: “The GES or MOE, or any other bodies, have never organised CPD programmes on manipulatives for teachers in this district, and this does not even encourage mathematics teachers to see the need for using manipulatives in teaching.”

4.8 Integration of quantitative and qualitative findings

Table 7 presents a joint display that merges the two strands. The strands converged on the dimensions of supply, professional development, and perceived benefits, and diverged on reported versus observed use, teaching methods, teacher knowledge, and time.

Table 7. Joint display of quantitative and qualitative findings.

CPD, continuing professional development; MOE, Ministry of Education; GES, Ghana Education Service.

5 Discussion

This study compared teachers' reported use of manipulatives with observed classroom practice in the Amansie Central District and examined the supply, professional development, and perceived conditions surrounding that practice. The principal finding is a marked discrepancy between the curriculum as documented and reported by teachers and the curriculum as enacted in the observed lessons. The discussion interprets this discrepancy through the curriculum-enactment framework set out in Section 2.3.

5.1 The reported–enacted discrepancy

Only two of sixteen observed teachers (12.5%) used manipulatives during instruction, whereas at least 85.6% of questionnaire respondents reported using them for each topic. In terms of the framework adopted, the official curriculum (MOE, 2020) and the teacher-intended curriculum, as documented in lesson notes and questionnaire responses, largely aligned with the expectation of manipulative use, but the enacted curriculum in the observed lessons did not (Remillard and Heck, 2014; Stein et al., 2007). Teachers' own explanations—that manipulatives were written into lesson notes as “a normal practice” but not used because of time and availability—suggest a discrepancy between documented curriculum compliance and observed instructional enactment. Consistent with Spillane et al. (2002), teachers appear to have interpreted the curriculum requirement in light of their circumstances, satisfying its documentary dimension, which supervision reportedly checked, while adapting classroom practice to the materials and time they perceived as available.

The discrepancy is consistent with international evidence that manipulatives are often treated as peripheral to mathematics teaching (Moyer, 2001) and that manipulative use becomes less frequent in higher grades (Uribe-Flórez and Wilkins, 2010). It also underlines the methodological point that self-reported measures of instructional practice need to be interpreted alongside observational evidence (Mayer, 1999). Two cautions apply. First, the observation data came from 16 teachers, each observed in a single lesson, so the observed rate of use is an indication rather than a precise estimate of district practice. Second, questionnaire items asked about use in teaching each topic, whereas observation captured use in a particular lesson; some of the discrepancy may reflect this difference in reference period. Nonetheless, teachers' own accounts corroborate that the discrepancy is not solely a measurement artefact.

5.2 Supply of manipulatives as a structural condition

Improvisation by teachers and pupils was the main source of manipulatives for 78.4% of teachers, and 78.4% of teachers reported never receiving manipulatives from the MOE/GES; the district coordinator likewise reported no budgetary allocation for this purpose. Within the curriculum-enactment framework, the availability of materials is one of the conditions that shapes whether the intended curriculum can be enacted (Remillard and Heck, 2014). When materials required by the curriculum are not supplied, the responsibility for providing them shifts to teachers, who must improvise with their own time and resources; 66.0% of teachers identified the cost of preparing improvised materials as a challenge. These findings are consistent with recent Ghanaian evidence that many recommended manipulatives are rarely available in JHS classrooms and that funding constraints limit both procurement and improvisation (Padmore et al., 2025), and with earlier accounts of resourcing difficulties in implementing mathematics curriculum reform in Ghana (Mereku, 2004).

5.3 Professional development and pedagogical knowledge

A lack of continuing professional development was the challenge most frequently endorsed by teachers (71.1%), and the coordinator reported that no CPD on manipulatives had been organised in the district. At the same time, 72.2% of teachers disagreed that limited knowledge of manipulatives was a challenge. Pedagogical knowledge was not directly measured in this study, so these findings cannot establish teachers' level of knowledge. One possible interpretation is that teachers may feel confident about what manipulatives are and why they are recommended, while having had limited opportunity to develop the more specialised knowledge needed to use them within activity-based or problem-solving lessons (Ball et al., 2008). This interpretation is tentatively supported by a teacher's statement that activity-based methods are difficult because “most of us were not trained that way,” by the prevalence of lecture and discussion in observed lessons, and by the 59.8% of teachers who reported inadequate user guides. It is also consistent with evidence that initial teacher preparation in several African countries, including Ghana, gave limited attention to the practical teaching of early mathematics (Akyeampong et al., 2013).

Carbonneau et al. (2013) reported that the effects of manipulative-based instruction were moderated by instructional features such as the level of guidance, and Laski et al. (2015) emphasised the importance of explicitly connecting materials to mathematical ideas. Such findings suggest that the provision of materials alone may be insufficient without professional development that addresses how manipulatives are used. Research on effective professional development points to features such as a focus on content, active learning, coherence with teachers' needs, sustained duration, and collective participation (Desimone, 2009), which could inform the design of CPD in contexts such as Amansie Central.

5.4 Time as a contested condition

The joint display (Table 7) shows a divergence concerning time. Most teachers disagreed that lesson time was insufficient (58.8%) or that heavy workload prevented manipulative use (64.9%), yet time was the explanation that observed teachers gave for not using the manipulatives listed in their lesson notes, and 32.0% of teachers disagreed that manipulatives save time. One interpretation is that teachers do not regard the timetable as generally inadequate but perceive manipulative-based activities as demanding more time than lecture or discussion within a given lesson, which is consistent with Pham’s (2015) findings. Because this divergence emerged from a small number of interviews, it should be treated as a question for further research rather than a firm conclusion.

5.5 Benefits perceived despite limited enactment

Most teachers agreed with all seven benefit statements, and the uneven distribution of responses (Table 5) indicates that these were widely shared perceptions. These results concern teachers' perceptions of benefit; they do not show that manipulative use improved pupils' learning in this study, which was not measured. Nonetheless, the perceptions are consistent with research reporting benefits of manipulative-based instruction under appropriate conditions (Boggan et al., 2010; Carbonneau et al., 2013; Goracke, 2009). Taken together with the observation data, they suggest that limited enactment in this district is unlikely to be explained mainly by teachers doubting the value of manipulatives. Rather, the combination of positive perceptions, limited supply, and limited professional development is consistent with the view, derived from the curriculum-enactment framework, that teachers' endorsement of a curricular expectation is not sufficient for its enactment when the conditions for enactment are weak (Remillard and Heck, 2014; Spillane et al., 2002).

6 Conclusions and recommendations

This study examined JHS teachers' reported and observed use of manipulatives, and their perceptions of the benefits of and challenges to manipulative use, in the Amansie Central District of Ghana, drawing on 2024–2025 questionnaire data from 97 teachers in 56 public schools, interviews with 31 participants, and observations of 16 teachers. Three conclusions are drawn.

First, there was a marked discrepancy between documented curriculum compliance and observed instructional enactment. Although most teachers reported using manipulatives across all topics and recorded them in lesson notes, only 2 of 16 observed teachers used manipulatives during the observed lesson.

Second, teachers attributed limited manipulative use mainly to structural conditions rather than to doubts about the value of manipulatives. Teachers widely perceived manipulatives as beneficial, while reporting that materials were seldom supplied by the MOE/GES, that improvisation was costly, and that continuing professional development on manipulative use was lacking.

Third, the rising BECE mathematics failure rates in the district (from 55.1% in 2022 to 59.4% in 2024) and the limited use of manipulatives observed in this study coexist within the same context, but they were not analytically linked. The study did not test a causal or correlational relationship between manipulative use and BECE performance, and many other factors may influence examination outcomes. Whether improving the conditions for manipulative-based instruction would improve pupils' achievement in this context is a question for future research using appropriate designs.

Based on these conclusions, the following recommendations are advanced. Because they derive from a single-district, cross-sectional study, they should be piloted and evaluated before wider adoption.

• Strengthen supply mechanisms. The MOE/GES should consider dedicated budget lines for mathematics teaching materials in JHSs, with transparent procurement and distribution processes, supplemented by school-level support for locally improvised materials.
• Provide sustained CPD on manipulative-based pedagogy. The MOE/GES, in collaboration with Colleges of Education and universities, should develop ongoing professional development focused on teaching mathematics concepts with manipulatives through activity-based and problem-solving approaches, drawing on established features of effective professional development (Desimone, 2009).
• Refocus supervision on enactment. Circuit supervisors and head teachers should complement lesson-note checks with regular classroom observation that includes explicit attention to the use of manipulatives and teaching methods.
• Engage PTAs and community partners. District education offices should facilitate partnerships among schools, Parent–Teacher Associations, local businesses, NGOs, and philanthropists to supplement the supply of materials.
• Develop and distribute user guides. Topic-specific guides on using recommended manipulatives, including low-cost improvised alternatives, should be developed and distributed to JHS mathematics teachers as part of curriculum support materials.

6.1 Limitations

Several limitations should be considered when interpreting the findings. First, the study was conducted in one district of the Ashanti Region, and the findings may not generalise to other districts, regions, or private schools. Second, the cross-sectional design captures practice at one point in time and cannot support causal conclusions about the relationships among supply, professional development, perceptions, and practice. Third, questionnaire data are self-reports and may be affected by social desirability bias, particularly because manipulative use is a curriculum expectation that is checked through lesson notes. Fourth, the observation subsample was relatively small (16 teachers), and each teacher was observed in a single lesson, so the observations may not represent teachers' typical practice across topics and over time. Fifth, although observations were unannounced, the presence of an observer may have altered teachers' and pupils' behaviour. Sixth, the study did not use a standardised, objective measure of pupils' achievement; the post-lesson exercises and pupils' statements reported here are descriptive and cannot be used to infer effects of manipulative use on learning. Seventh, the reliability of the questionnaire was not formally estimated, because the benefit and challenge statements were analysed as single items rather than as summed scales. Finally, BECE results were used only as contextual information; they were not linked to teachers or schools in the sample, and the design could not account for the many other factors that influence examination performance.

6.2 Future directions

Future research could observe a larger sample of teachers across multiple lessons, link observational data to individual teachers' questionnaire responses, and examine teachers' conceptions of manipulatives using instruments designed for that construct. Intervention studies with comparison groups, or longitudinal designs, are needed to examine whether structured CPD, improved supply of materials, or changes in supervision produce sustained changes in manipulative use and in pupils' learning, measured with standardised assessments. Comparative studies across Ghanaian districts with differing resource profiles, including urban–rural comparisons, would help establish whether the conditions identified here are district-specific or more widespread.

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Footnotes

Edited by: Sutrisno Sutrisno, Universitas PGRI Semarang, Indonesia

Reviewed by: Balwant Singh, Partap College of Education, India

Yanuar Hery Murtianto, Universitas PGRI Semarang, Indonesia