Introduction
Ontario’s elementary mathematics curriculum is “designed to help students build the solid conceptual foundation in mathematics that will enable them to apply their knowledge and further their learning successfully” [i]. Educators have the important task of supporting students to “develop mathematical understanding; learn important facts, skills, and procedures; develop the ability to apply the processes of mathematics; and acquire a positive attitude towards mathematics” [ii].
Comprehensive Math Program
To achieve this mandate, educators must teach within a comprehensive math program, which takes into consideration the individual learners, the learning environment, and the learning experiences. The following video provides viewers with the opportunity to explore how the York Region District School Board created a comprehensive math program to enhance math outcomes for all students, including those with LDs.
Click here to view the transcript of this video.
This module focuses on the learning experiences, or the design and delivery of content to support students in developing foundational skills. More specifically, this module explores the Concrete-Representational-Abstract (CRA) approach, an evidence-based practice in mathematics instruction for students with LDs.
Conceptual, Procedural, and Declarative Knowledge
In addition to focusing on the learning, the environment, and the learning experience, an effective comprehensive math program balances the emphasis placed on different types of knowledge [iii].
| Declarative Knowledge: information that students retrieve from memory or know “at a glance”
EX: addition or multiplication facts Procedural Knowledge: ability to follow a set of sequential steps to solve computation problems, word problems, or real-world tasks EX: following an algorithm to calculate an answer Conceptual Knowledge: involves a deep understanding of the meaning of mathematics and the connections among concepts, which helps students generalize their learning to other situations EX: Students may learn to link two previously learned concepts or they may link a new concept to a previously learned concept. [iv] |
The CRA approach is distinctive in this regard, as it provides an explicit link between conceptual and procedural knowledge [v]. This is particularly important for students with LDs; conceptual knowledge is fundamental to success in math and for problem solving in a variety of contexts [vi]; yet, research has demonstrated that interventions for students with disabilities have historically focused on computational skills and procedures instead of conceptual knowledge [vii].
References
[i] Ontario Ministry of Education, 2005, p. 4
[ii] Ontario Ministry of Education, 2005, p. 3
[iii] Miller & Hudson, 2007
[iv] Miller & Hudson, 2007
[v] Agrawal & Morin, 2016
[vi] Miller & Hudson, 2007
[vii] Bottge, 2001