Teaching math focusing on competencies rather than content

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 discussed the benefits of teaching math by focusing on competencies.

In the video, the teachers highlighted 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,” has a good suggestion of how teachers can design lessons based on competencies rather than content. He proposes that teachers should not plan their lessons by dividing what students should learn into content units, such as fractions, multiplication, cardinal numbers, etc. However, he suggests considering a list of competencies related to each content and how they connect among them not only into the same content but also between contents. In this sense, while planning learning goals, teachers can work with more flexibility between competencies and contents.

The image below shows how to interview competencies (represented by the number indicating how the competency progresses)  from different content (represented by the different colors):

Source: Phil Stringer BCTM Vector article “Deunitization in the Mathematics Classroom.”

Therefore, by interviewing competencies and content, teachers have more flexibility to build different patterns of learning progression for their students. Moreover, as Phil describes from his experiences, students learn more deeply about the curriculum goals and tend to not forget the content since it reviews them throughout the whole academic year rather than just for a short time when the 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 for that since they allow both teachers and students to map what are the learning goals already developed and the ones that need more focus.

Identifying specific competencies can develop independence and confidence in students and make teachers work more efficiently. Teachers can use a simple Excel table or even more sophisticated platforms that link 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: