By: Shirin Lutfeali, Yasmin Sitabkhan and Wendi Ralaingita //
Imagine being a second grade student in a classroom with close to a hundred other children. It’s math class, and the teacher is instructing the class on how to solve a problem written on the board. You’re too far in the back to hear, and her instructions were so fast. Now she wants everyone to solve a new problem she has written. You have no idea what to do, so you just copy the numbers that you can see and hope she doesn’t call on you.
In early-grade classrooms across Asia and Africa, teachers struggle to teach math effectively, relying on techniques such as memorization and lecture to teach foundational skills. Children in these classrooms leave primary school with a shallow understanding of basic math concepts like addition and subtraction and often cannot solve problems beyond simple calculations. Teachers’ limited training, a lack of resources, and curricula that are out of step with children’s learning compound systemic issues such as overcrowding and teacher absenteeism, leading to students who are unable to do math at grade level. For example, a 2015 study from Ghana revealed that 22% of second grade students could not solve a single math problem (such as 4–1).
But, there is hope
This scenario can change. We know that math is important, especially in terms of building a foundation in the early years. And we know that students are struggling with both basic skills and problem-solving strategies. What are the specific areas we can improve, and how? A new guide produced by RTI International with funding from the Bill and Melinda Gates Foundation seeks to help policy makers, donors, and implementers design and manage effective early-grade math programs at scale. The guide, entitled Designing Effective Numeracy Programs in Low- and Middle-Income Countries, focuses on three elements of foundational math teaching and learning:
- curriculum and standards
- teachers and teaching
- teaching and learning materials
An Early Start
First, it is important to support math learning early, through preschool, and with sufficient attention in the early grades. This can close achievement gaps between children from different socioeconomic backgrounds and provide time for mastery in foundational areas such as counting and addition and subtraction, principles that have shown to impact later success in mathematics. Starting math education early can also foster positive attitudes toward math, particularly among girls, who are frequently steered away from math as a result of negative gender stereotypes.
The First Area: Curriculum and Standards
We should update curricula to be realistic and in line with what we know about how students learn. Math curricula in low- and middle-income countries (LMICs) are often not based on established learning progressions and can be overloaded. In Uganda, for example, second grade students are expected to know the multiplication table up to 6, division by 1, 2, 3, and 4, and how to add fractions—skills that are generally taught in third and fourth grade elsewhere. Further, in many LMICs, topics are taught just once, never to be addressed again during the school year. Adopting a “spiral” curriculum, which spaces out content and revisits concepts throughout the year, can support deeper learning of mathematical concepts. Additionally, a focus on conceptual understanding as a basis to build procedural fluency can help children understand math concepts and not just memorize a set of rules and procedures. This will serve students better in the upper grades, when content becomes more abstract and requires a deeper understanding of underlying concepts.
The Second Area: Teachers and Teaching
We should also provide teachers with the knowledge they need to be effective math teachers. Many teachers never received the right kind of support to build a solid foundation of math skills, particularly those that require conceptual understanding. Indeed, a survey across African countries found that although over 90% of teachers were able to solve basic addition problems, this number declined as content became more challenging and less procedural: only 11% were able to interpret data in a graph and only 15% were able to solve word problems. Teachers generally teach the way they have been taught—which, in many LMICs, is largely rote memorization and techniques that favor procedural fluency over conceptual understanding. An approach to teacher training that includes and connects content knowledge and pedagogical content knowledge would produce teachers who are better prepared to teach early-grade math concepts.
In the classroom, the instructional approach and strategies used by teachers has more impact on student learning. Teacher professional development should include high-impact strategies that support the development of students’ conceptual and procedural knowledge, including: discussing mathematics, incorporating questioning, explanation, and justification; using appropriate models and representations; linking informal and formal mathematics; using knowledge of students and learning progressions to target instruction; and incorporating assessment into instruction.
The Third Area: Teaching and Learning Materials
Instructional materials should be readily available to teachers who are teaching math, and teachers should be well trained in how to use them appropriately, for it has been shown that using materials to represent abstract concepts helps children reason more meaningfully and that the appropriate and systematic integration of materials into the math classroom can have positive outcomes on learning. However, in LMICs, textbooks and learning materials are often limited, and teachers frequently lack adequate training on how to lead constructive discussions around student observations and ensure the use of the materials leads to understanding.
Children who are learning foundational concepts should have access to materials that help them “see” the mathematics. To this end, teachers can be provided with locally sourced and low-cost resources (such as stones, string, and counting sticks), though it is equally important that they be trained on how to use each resource. As revealed by a study in Ghana, teachers who received materials and instructions on how to use them were more likely to employ high-impact teaching strategies compared to those who were asked to gather their own materials.
Changing the Status Quo
Teachers can be supported to teach effectively. But practices across the system must change—from math curriculum to teacher training institutions, and ongoing professional development and support. The efforts of the international community over the last decade and a half on improving reading skills in the early years has produced a body of research and tools to track student learning outcomes in LMICs. Teachers have benefited from training, supplementary reading materials, and assessment support to learn where students struggle and how to support them. Similar changes can, and should, take place in foundational numeracy. If policy makers and implementers embraced a careful focus on the three areas highlighted above, along with additional targeted research on math teaching and learning in LMICs, they could start to reap genuine benefits in terms of improved instruction and better learning outcomes. This how-to guide provides an important starting point in helping them to achieve this goal.