By Yasin Memis, a former teacher of mathematics in middle schools with a PhD degree in mathematics education from Anadolu University (Turkey).
A curriculum can be described as a roadmap, answering questions such as what, why and when students should learn in the learning process. In the world of mathematics, it gives us direction on how to progress from current skills to desired ones.
Finding answers to the key questions about what we want students to learn from their curriculum has gained renewed importance in mathematics education after COVID-19, as well as in other disciplines. But because curriculum design requires the consideration of many phenomena, from pedagogy to technology and from policy to diversity as the title figure in this blog shows, so answers to these questions may not be simple. Mathematics involves many interconnected ideas, so there can be a number of different routes between current and target points.
Having said that, while there may be many alternative ways to teach mathematics and researchers are constantly seeking better approaches, students may still experience limited choices. Some students may need to spend more time on things that other students do not need, or may choose to take circuitous routes that keep their attention. Moreover, just as there are individual differences between students, there might be differences between teachers. Similar to roads in city plans, we need to indicate the critical junctures in curriculum design and provide enough alternative side roads and connections to allow teachers to choose what they think is best. Coherence might be an essential guide in ensuring that this process is carried out as effectively as possible.
Less is more: Coherence
Coherence is derived from co-haerēre, a compound Latin word that means to stick together; to be in harmony; to be closely attached. The origin and meaning of this word provide insight into what makes a curriculum semantically meaningful. From a mathematics education perspective, Schmidt et al., note that, “a set of content standards must evolve from particulars (e.g., the meaning and operations of whole numbers, including simple math facts and routine computational procedures associated with whole numbers and fractions) to deeper structures inherent in the discipline”.
In order to present the curriculum as a meaningful whole, it is critical to first pare down the content within a framework of big ideas, akin to a roadmap for learning. Of course, reducing content should not be perceived as simplification. On the contrary, an overcrowded curriculum is likely to be experienced superficially; covering less allows for the possibility of deeper mastery. To the extent that we can harmonise the curriculum, we can go beyond the “miles-wide-inches-deep” criticism, which claims that having only surface level knowledge of multiple elements is not as good as an in-depth knowledge of the essentials.
Moreover, a curriculum that lacks coherence and includes a sequence of poorly related learning outcomes will increase content overload. Due to the difficulty of getting to the desired point in the midst of so many disconnected outputs, teachers are more likely to misunderstand the purpose of the curriculum and use it in an ineffective manner. Thus, considering the philosophy that less is always enough, coherence can address the problem of curriculum overload.
In curriculum design, there is often a concern that covering fewer topics will lead to lower standards of student achievement. In current reforms in mathematics education, therefore, coverage of broad knowledge content is often preferred to in-depth learning, resulting in ‘more learning’ rather than ‘deeper learning’. But this trend goes against the findings on the most effective way to learn mathematics: research shows that studying fewer topics in greater depth for longer periods of time allows for the development of deeper knowledge of the topics as well as high mathematical achievement. The countries with the highest TIMSS mathematics scores (such as Singapore, Korea, Japan and Hong Kong) have similar characteristics in terms of focusing on key mathematical ideas in their curriculum and covering fewer topics per grades.
An effective curriculum should be more than a series of objectives; it should focus on big ideas and be well articulated across key stages. A strongly connected structure with a small number of key ideas will give students enough time to master their skills. To ensure coherent learning experiences for each student, content should consider student development and be responsive to their needs. Nevertheless, ensuring curricular coherence might be an effective guide to adjusting the balance between breadth and depth, which remains a major challenge facing education reform in many countries.