Mathematical Instruction and Learning
April 27, 2021

There has been considerable attention placed on mathematics – as there should be. Mathematics plays an important part in the educational system and in the lives of everyone. Whether it is a particular mathematical concept (i.e., geometry), instructional approach (i.e., constructivist), learning theory (i.e., growth mindset), educators are doing all they can to support students in making meaning and communicating their understanding. Truly, I believe that teachers cannot work any harder than they already are. Yet, many teachers are feeling frustration that their efforts are not paying off in terms of student achievement.

So, appreciating the workload on teachers and how they have their students’ best interests as their instructional goals, I have decided to start a blog. Through this blog I will share strategies, tasks, and/or ideas that will help teachers achieve their instructional goals and support students in strengthening their mathematical understanding. I will share instructional and learning strategies that are not only effective, but are also manageable and sustainable for the teacher. It is about working smarter not harder.

When discussing instruction and learning, I think it is important to consider it from three spaces: instructional, thinking, and physical. As shown in the diagram below, it is where these three spaces overlap that we have an approach to mathematics that can be a difference maker and give us the value added that we are looking for.

Instructional space examines the instructional decision-making of teachers. How teachers approach a lesson influences the mathematical experiences of students. The lesson plays a large part in determining how students engage with mathematical concepts, including the choice of problems offered to students, whether students work individually or with others, and what counts as successful completion of the problem. It is through the planning of the lesson, the delivery of the lesson, and the atmosphere created by the lesson that teachers determine how students encounter and work with mathematical concepts.

Thinking space examines the characteristics of a literate environment from the perspective of student thinking. Such a perspective involves more than how students solve a problem or complete a task. The thinking space includes how students approach the problem, how they frame their thinking, how they support this thinking, and then how they navigate the problem to completion. Within the thinking space is how students approach the problem by thinking like mathematicians.

Physical space examines the actual arrangement of the classroom and how it contributes to a literate environment. How the classroom is structured can have a great impact on both the instructional practices of teachers and the learning experiences of students. Whether it is the set- up of desks, how displays are crafted and used, or the availability of resources, the physical space plays a significant role in the literate environment.

What I would love for readers to do is to post a comment to this blog with topics that they would like to see explored. Another option is to email me at with any suggestions.

(Source – Using What Works: Strategies for Developing a Literacy-Rich Environment in Math)

Subscribe To Our Newsletter

Join our mailing list to receive the latest news and updates from Dr. David Costello.

You have successfully subscribed!