Curricular Coherence in the Age of Open Educational Resources
By Matt Larson, NCTM President
August 22, 2016
From its very founding, NCTM has actively promoted the use of high-quality curricular materials to support effective mathematics teaching and student learning. A critical feature of high-quality curricular materials is that they are coherent. Coherence, with respect to mathematics curriculum, generally means that connections are clear and receive emphasis from one year to the next, from one concept to another, and from one representation to another. High-quality materials are coherent pedagogically, logically, and conceptually.
More than 15 years ago, NCTM enunciated the Curriculum Principle in Principles and Standards for School Mathematics (NCTM, 2000): “A curriculum is more than a collection of activities: it must be coherent, focused on important mathematics, and well articulated across the grades.” Fourteen years later, NCTM reinforced the importance of curricular coherence in Principles to Actions: Ensuring Mathematical Success for All (NCTM, 2014): “An excellent mathematics program includes a curriculum that develops important mathematics along coherent learning progressions and develops connections among areas of mathematical study and between mathematics and the real world.”
NCTM is certainly not alone in advocating curricular coherence. The authors of the Common Core State Standards for Mathematics identified coherence as one of their guiding principles and organized the content standards into clusters and domains that weave content together from grade to grade or topic to topic to make conceptual connections and coherence more obvious to teachers and curriculum developers alike.
The increasing availability of online instructional materials—some of which are of high quality and some of which are not, and many of which can be downloaded at no cost—has added a new dimension to the curricular landscape for mathematics teachers and school districts. Some of the most engaging conversations about mathematics teaching today are taking place within online communities where teachers share instructional resources and ideas that they have either created themselves or found on their own online. A recent survey by the RAND Corporation found that the vast majority of math teachers, at both the elementary and secondary levels, reported they used materials that they developed or selected themselves to implement the Common Core State Standards for mathematics. There is no question that this practice is widespread.
The dilemma is that while districts, schools, and teachers have greater access than ever to tools and resources for selecting and developing instructional materials, the skill required to develop a high-quality curriculum is both complex and often underappreciated. The widespread availability of online tasks therefore makes having and working with a coherent curriculum at the school and district level even more important because it is the curriculum that establishes the learning goals in a coherent progression and helps teachers see and understand the multiple pathways that students might take through the progression.
NCTM itself has published online materials that provide examples of curricular resources that encourage teachers to integrate high-quality mathematical tasks and problems into their mathematics instruction. These materials stand as examples for teachers and schools in cases where the core materials may lack highly engaging, high-cognitive demand tasks or lessons. NCTM’s recent publication of exemplar Activities with Rigor and Coherence (ARCs) is an example of one such online resource. Each ARC is a series of lessons that addresses a mathematical topic and demonstrates the vision of instruction that Principles to Actions describes in detail. ARCs integrate a wide array of NCTM resources and include community features that offer opportunities for social interaction, feedback, and ratings.
Ideally, teachers who select online instructional resources and engage in online community discussions would not be working in isolation but within well-developed professional learning communities in their schools. This sustained colleague-to-colleague communication would increase the likelihood of the selection of high-quality tasks that fit within mathematical learning trajectories and support the school and district’s curricular goals for students. Whether such collaborative task selection is feasible or not, the selection of online materials should be done in such a way that the instructional materials used in classrooms are situated within an overall coherent curriculum. That lessens the chance that students’ learning experiences devolve into a mere “collection of activities” rather than a coherent, well-designed curriculum.
Stated very simply, the danger in online curricular selection is the undercutting of curricular coherence by the introduction of disjointed tasks that are of questionable quality, do not fit within the mathematical learning progression, and are incoherent. Perhaps the greatest danger is the potential for vast inconsistencies in instruction and highly variable learning experiences for students that in turn can lead to differences in student learning outcomes.
Without question, curricular coherence is highlighted and enhanced when teachers work collaboratively and regularly with colleagues at the school level to plan instruction, implement the task, anticipate student work, respond to student learning needs, and provide consistency in curricular aims and instruction for students—no matter what teacher students might be assigned. Easy access to online tasks and communities makes the need to work collaboratively with colleagues in local professional learning communities more critical than ever before in the interest of safeguarding consistency in student learning experiences and outcomes.
Acknowledgement
I would like to thank NCTM’s Emerging Issues Committee for its thoughtful work on a framing paper that was the basis for this President’s Message.
References
National Council of Teachers of Mathematics. (2000). Principles and Standards for School Mathematics. Reston, VA: Author.
National Council of Teachers of Mathematics. (2014). Principles to Actions: Ensuring Mathematical Success for All. Reston, VA: Author.