Mathematics has been known as one of the subjects that focus on content, and consequently, the procedures to achieve the right answer, rather than on competencies, or in other words, on the understanding of the procedure followed by students. However, these two ways should not be seen as irreconcilable!
As the National Research Council discussed in the book Adding it UP! Helping children learn mathematics, mathematics fluency is achieved through the development of five strands:
- conceptual understanding: comprehension of mathematical concepts, operations, and relations
- procedural fluency: skill in carrying out procedures flexibly, accurately, efficiently, and appropriately
- strategic competence: the ability to formulate, represent, and solve mathematical problems
- adaptive reasoning: capacity for logical thought, reflection, explanation, and justification
- productive disposition: the habitual inclination to see mathematics as
sensible, useful, and worthwhile, coupled with a belief in diligence and one’s
own efficacy.
Source: Adding it UP! Helping children learn mathematics
Therefore, both math content and competence are essential to achieve mathematics proficiency. Teaching math through competencies emphasizes how important conceptual understanding is to advance to high-level math. It also shows that content and procedures are used to build up understanding and not as isolated goals in the process of learning math.
The following video discusses some of the benefits of teaching math by focusing on competencies. In the video, the teachers highlight that math competencies allow lessons based on student-centered approaches and differentiation, giving space for students to learn at their own pace through pedagogical strategies.
Phil Stringer, in his BCTM Vector article “Deunitization in the Mathematics Classroom,” (pp. 38), suggests how teachers can design lessons based on competencies rather than content. He proposes that teachers should not plan their lessons strictly by dividing what students should learn into content units, such as fractions, multiplication, cardinal numbers, etc. He suggests teachers consider a list of competencies related to each content area and how they interconnect. In this sense, while planning learning goals, teachers can work with more flexibility between competencies and content.
By covering competencies and content, teachers have more flexibility to build learning progressions to support their students. As Phil describes from his experiences, students learn more deeply and tend not to forget the content since it scaffolds and is reviewed throughout the term or academic year rather than just for a short time while a specific content-based unit is been covered.
Regarding assessment, a great way to assess competency is to analyze students’ knowledge and skills in each competency. Competency trackers can be a helpful tool since they allow both teachers and students to map the learning goals already developed and the ones that need more focus.
Identifying specific competencies can build independence and confidence in students and support teachers’ planning. Teachers can use an Excel table or a more sophisticated platform that links students’ progression to real-time assignments.
Resources:
Open School BC and the Delta District develop many detailed resources for teachers to develop the following competencies in math:
Guest post by Peer Mentor Ariane Faria dos Santos (Ph.D. EDCP), Aug. 2024.
Social Justice Issues could be easily taught through Math.