Teachers are being asked to instruct students in ways that they were neither taught during pre-service training nor learned as students themselves. They struggle with pulling away from teaching procedures versus having students independently discover mathematical ideas precipitated by time restraints and the pressures of high-stakes testing. However, teachers need support to be successful in this shift in instructional practices. Even when districts purchase math curriculums that publishers tout as being aligned with the common core and teaching mathematics conceptually, teachers struggle with providing inquiry-based versus exercise-oriented lessons. As a first-year teacher admitted, his students struggled consistently in solving story problems or any problem that did not have an obvious equation to solve. Teaching conceptually requires teachers to attend to student’s questions, anticipating obstacles, capitalizing on opportunities, and making connections. The Common Core and NCTM standards require this connection which fosters content retention for high-stakes testing and being successful in the 21st-century workplace. After analyzing observations and lesson plans used by three third-grade teachers in separate schools, of the 168 activities added to their lessons that were not part of the original conceptual lesson plan provided, 68 percent were procedural and 31 percent were conceptual in nature. The teachers admitted during interviews that they did not receive the support necessary to implement this new time-demanding technique of guided discovery or conceptual understanding. This study highlights that teaching mathematics procedurally is almost a subconscious act that requires teachers to recognize first that it exists allowing them to embrace change.
Questions to consider:
Are teachers modeled how a conceptual mathematics lesson should look like which harmoniously incorporates the NCTM standards?
Are trainers available to observe lessons to provide immediate feedback to teachers that struggle with a procedural mindset?
Are teachers encouraged to adapt their lessons to include real-world tasks that encourage problem-solving?
Do teachers have faith in their students to allow them to persevere without being told the steps necessary to solve real-world tasks?
Mahovsky, K. (2018). A Procedural Mindset in a Conceptual World of Mathematics. Mathematics Teaching- Research Journal, 10(N1), 19. http://www.hostos.cuny.edu/MTRJ/archives/volume10/issue1/A%20Procedural%20Mindset%20in%20a%20Conceptual%20World%20of%20Mathematics.pdf
With 10 years’ elementary teaching experience, Kim currently instructs students on conceptual teaching methods in mathematics. Connect with Kim on Twitter, @kimmahovsky