By Norma Evans, consultant
Children’s numeracy skills matter for their academic success and long-term well-being. A paper I wrote to feed into the 2024 Spotlight Report on universal basic education completion and foundational learning in Africa, Learning counts, looked at the importance of four pedagogical inputs to make numeracy work: curriculum, textbooks, teacher guides and assessments – in Mauritania, Niger, South Africa, Uganda and Zambia.
Just as important as having these four inputs in place is the need for them to be aligned by which I mean three things. First, the content should be aligned across each of these materials. Second, the pedagogical approach woven into the textbooks and teachers’ guides needs to be aligned with the pedagogical principles outlined in the curriculum. And third, the national documents should align with the global research on the important mathematical concepts students need to develop, and the optimal progression and pacing of that learning, over time.
In putting its accent on alignment, the research in the second Spotlight research cycle focused on whether key, foundational mathematics competencies were found in each of the national pedagogical inputs analysed. It also looked, for example, at the relative importance given to different mathematical domains (e.g. algebra vs geometry), the cognitive difficulty of the activities proposed in textbooks, and the pacing of key concepts over time – in other words, which competency was taught at which grade.
In order to map the alignment across different inputs in these five African countries, I looked at documents in the third grade and the last grade of primary school.
Curricula
The analysis of the curriculum across the five focus countries and the two grade levels focused on six key points of comparison. Firstly, countries differ significantly in the scope of their curricula. English-speaking countries cover more mathematical domains, particularly at the grade three level, than French-speaking ones, which generally do not address probability and statistics. The role that algebra plays in primary also varies significantly across countries. In most countries, anywhere between 4% and 8% of competencies focus on this domain. The exception was Niger, where 20% competencies in grade 3 and 25% of competencies in grade 5 focus on that domain.
Secondly, curricula are different in how they specify learning outcomes. Some curricula, such as in Mauritania, South Africa, and Zambia, provide detailed, measurable learning outcomes. Others, such as in Niger, provide broader or more general statements of content teachers are to cover (e.g. subtraction), making curriculum implementation and assessment more challenging.
Curricula also differ in the extent to which they indicate how students are expected to learn mathematics. Some clearly stipulate the use hands-on learning (e.g. using objects to explore or represent mathematical concepts), while others communicate the results of learning – for example being able to add two digit numbers with regrouping – without providing any indication of how students are to develop the competency.
Across the five countries the pace of learning in the curriculum generally aligns with the Global Proficiency Framework for Mathematics (GPF-M), although some important variations were noted. In some countries, for example students are expected be able to add, subtract, multiply and divide numbers one or more years prior to when students are expected to demonstrate the same competency in the GPF-M. This is not an issue if national, regional or international assessments show that students are able to demonstrate mastery of these competencies at earlier grade levels than proposed in the GPF-M.
Lastly, there were a few incidences of misalignment between curriculum, textbooks and teacher guides. For example, Niger’s curriculum omits logic and reasoning, while the textbook deals with this concept extensively. Country representatives generally attributed these incidences to misalignment in funding cycles, where funding is available to develop and distribute a new textbook prior to a new curriculum being validated (or vice-versa).
Textbooks
Different types of activities are proposed in textbooks. They study examine three different types of activities, 1) learning activities, i.e., activities require students to move beyond the confines of the textbook, for example using objects or manipulatives to explore or represent concepts, carrying out a survey, measuring the length of objects in the classroom or school grounds, or identifying two- or three-dimensional shapes in the environment, 2) exercises or problems and 3) explanations. The relative weighting of the three types of activities in textbooks varies by country. In early primary, for example, very few of the activities in the Zambia, Uganda, South Africa, and Mauritania textbooks were classified as learning activities. At the end of primary, except for Uganda, the percentage of textbook activities that can be labelled “learning activities” is less than 10%. Most activities are exercises or problems.
How textbooks explain mathematical concepts to students also differs across countries. Grade 3 textbooks in Niger rely heavily on text or narrative-based explanations, a practice that prevents students with weak reading skills from accessing important information. Uganda, on the other hand, makes extensive use of worked examples and graphics and illustrations to explain mathematical concepts, formats that are more accessible to students with limited reading skills. At grade 5, both Uganda and Niger used worked examples to explain concepts, although both countries, along with Zambia, continued to use narrative-based explanations. Mauritania was an outlier in the analysis. Its grade 3 and grade 5 textbooks provided few explanations for students. Overall, the over reliance on narrative-based explanations across the five countries, as opposed to less language-intense worked examples and graphic explanations, presents language barriers that can prevent students from accessing necessary information.
The cognitive demand of the activities proposed in textbooks also differs across countries, suggesting that students do not have equal opportunities to develop higher level thinking skills in mathematics. Both in lower and upper primary, students in Mauritania are presented with significantly more higher-level thinking activities than students in Zambia.
Teacher guides
Lastly, the analysis of teacher guides also provided insights. It is worth noting that although grade 3 textbook activities in Uganda and Zambia do not require high-level thinking skills, the same is not true of the activities proposed in the teacher’s guide. At least one third of all the proposed grade 3 and grade 5 teacher guide activities require higher level thinking skills. If students in these two countries are to have the same opportunity to develop higher level thinking skills as their counterparts in Mauritania, their teachers must use the activities in the teacher guide in addition to those in the textbook and use them as intended. If teachers rely primarily or solely on the student textbook, students’ opportunities to develop higher-level thinking skills may be compromised.
These guides differ in the amount of instructional support provided. Most provide lesson plans for the entire school year, and all were structured, meaning that they identified activities teachers were to carry out and the order in which they were to carry them out. However, the quality and comprehensiveness of lesson plans varies by country.
The approach in Niger is unique in that the government clearly states that the teacher’s guide is the primary reference teachers are to use. However, the structure of the teacher’s guide, which is organized by domains (number, geometry, measurement), may hinder its effective use. Teachers must search through the teacher’s guide to find the guidance related to the day’s targeted competency.
Only Zambia’s teacher guides offer specific support to help teachers differentiate their instruction according to the level of the student.
As pointed out above, teacher’s guides also differ in the cognitive demand expected of teachers. Zambia’s teacher guides encourage higher-order thinking skills more than the textbooks, while Mauritania’s documents move in the opposite direction: most of the higher-level thinking skill activities are found in the student textbook, not in the teacher’s guides.
With the exception of South Africa, none of the guides provided teachers with guidance on how to carry out summative assessment. Most teacher guides lack guidance on assessing student learning aligned with the curriculum.
Conclusion
Achieving alignment between the intended curriculum, the implemented curriculum, and the assessed curriculum is crucial for effective mathematics learning. This paper found significant variation in the alignment of curriculum, textbooks and teacher guides across the five focus countries. Key areas of concern include the limited emphasis on higher-order thinking skills in some textbooks, insufficient support for differentiated instruction, and mismatches between the curriculum and the content of teaching and learning materials. Addressing these misalignments is critical for ensuring that all students have the opportunity to develop strong foundational numeracy skills.
Follow the links to the five countries’ document analyses and the summary background paper on the page of the Spotlight report, Learning counts.
