Competency-based education in mathematics

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What is competency-based education?

Competency-based education (CBE) is a student-centered methodology of instruction that incorporates elements of constructivist philosophy, 21st century skills education, and flexible learning models.

CBE teaching methods differ from traditional teaching methods in pacing, structure, and goals. The end goal is not for students to “cover the content,” pass a test, or prepare for college or a specific career, but rather master skill sets that will allow students to successfully pursue their goals, no matter what they choose to do in life.

For more information about CBE, consider reading our other CBE blog posts and be on the lookout for upcoming research pieces on CBE.

How is mathematics different in a CBE environment?

Traditionally, mathematics education has relied on memorization and repetition, drill and practice, with little emphasis on why things are the way they are or with different approaches to learning mathematical procedures. This type of approach lends itself to students acquiring sharp computational skills but generally poorer complex problem-solving skills and conceptual understanding of mathematics itself.

CBE mathematics courses focus on mathematical literacy, which is defined as, “a person’s ability to apply their mathematical knowledge to practical situations.” It takes more than simply knowing a mathematical procedure to be highly mathematically literate. For instance, if you read a child a book multiple times and the child eventually memorizes the words, you would not define that child as necessarily literate.

While there are minor differences depending on who you ask, there is broad consensus amongst educators and researchers regarding the major competencies that are critical for a student to be mathematically literate. The following is a synthesis of what competencies are deemed critical to mastering mathematics skills and will likely be present in one form or another in almost any CBE math course:

  • Thinking and reasoning mathematically – To reason with mathematical logic to assess evidence or arguments, check a given justification, or provide a justification; as well as have the ability to devise a mathematical strategy to solve problems arising from the task or context.
  • Posing and solving mathematical problems – To transform a real-world problem into a mathematical problem and interpret mathematical information in problem-solving situations. 
  • Mathematical modeling and representation – To create or use mathematical objects or relationships, including equations, formulas, graphs, tables, diagrams, and textual descriptions. 
  • Making use of mathematical symbols and formalisms – To understand, manipulate, and make use of symbolic expressions (e.g., algebra), and use procedures and definitions appropriately.
  • Communicating mathematically – To read, decode, and interpret statements and math information, as well as have the ability to explain, present, and argue with mathematics.
  • Making use of tools and technology – To use tools and technology that aid in mathematical procedures, such as analysis of data and complex calculations.

Most CBE math courses will cover these core competencies while addressing age-level appropriate content. For example, a second grade student’s math competencies regarding problem-solving are not the same as a tenth grade student. These are the things that students need to master in order to be able to effectively make use of their mathematics education.

How Do I Make Sure That My Student Succeeds?

CBE courses can be challenging for many students because of the change in pace, as well as structure, and can require that learners make adjustments. In order to make sure that students can be successful in CBE mathematics courses, consider the following:

Mastery

Mastery of a skill includes conceptually understanding a mathematical procedure (e.g., why we use the order of operations, and why it is important). It also includes being able to effectively replicate a procedure and apply calculating skills and conceptual knowledge to solve realistic problems. Understand that while learning can feel like trial and error, students often have as many attempts at displaying mastery of a skill as they can muster.

Emphasis on solving problems and applying skills

Learning mathematics has shifted away from the memorize, drill, and repeat method that many parents participated in; there is a higher emphasis now on problem-solving. The more students possess these aforementioned competencies, the more able they will be to make use of their mathematical knowledge to solve problems that they are likely to face in the real world. 

Grading

Students are “graded” on how well they progress in a specific area of competencies, if they have achieved mastery, or how close they are to achieving it. This means that students pass courses when they have displayed sufficient evidence of mastery of the competencies covered in the course. They may master some competencies faster than others as progress and pace vary for each student. 

Resources and tools for students 

While a student’s most valuable resource should be their instructor, here are some helpful tools and resources for students participating in CBE math courses. They include repositories of videos, explanations, and study aids for instances when a student may be trying to “figure it out” on their own without the assistance of a teacher, as well as interactive tools and simulations that can assist in calculations or better understanding of a concept or process.

Final Thoughts

A CBE math course may be a different animal than what many parents and students are prepared for, but the payoff for adapting to the learning curve is well worth it. Research has indicated that mastering mathematics competencies will enable our students to better solve problems in a variety of settings and that these competencies should be directly targeted by curriculum and teachers in math courses. 

For more information on CBE, check out our previous blogs about classroom challenges and CBE and how CBE is designed for student success.

Competency-Based Education Blog Series

In our Competency-Based Education Blog Series, we explore CBE in terms of tools for parents, teachers, and students. Next month’s topic will be student resources for success in science CBE courses. Stay up to date on future blogs in this series by signing up for email notifications!

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Nikolas McGehee

Nikolas McGehee

Dr. Nikolas McGehee received his doctorate in Exceptional Learning and STEM Education from Tennessee Technological University. He has worked as a high school science teacher, university researcher, analyst, and project manager, as well as a STEM Education program manager. His professional career is focused upon improving educational processes and products by performing sound research and making data driven decisions.

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