Standards for Mathematical Practice Portfolio

The Standards for Mathematical Practice describe procedural, conceptual, and abstract reasoning skills that teachers should be intentional about developing and enhancing in their students’ mathematical understanding. Some of the standards are broad, overarching ideas about mathematics such as “make sense of problems and persevere in solving them” and “model with mathematics.” These standards can be met by a variety of classroom activities or tasks. Other standards are focused on a more specific set of skills such as “attend to precision” and “look for and express regularity in repeated reasoning.” All the Standards for Mathematical Practice are important for teachers to consider because they provide a diverse set of skills for learners at all levels. As they develop their mathematical thinking and reasoning, students can grow their skills in all areas of mathematics, from second grade to high school, from geometry to calculus. The Standards for Mathematical Practice are not written as standards that must be met to a certain degree of difficulty, but rather as guides for helping teachers grow their students’ skills in many ways.

The tasks that I completed for this portfolio were fun and challenging. I enjoy the puzzle-like nature of most math problems and have the appropriate knowledge and skills to complete the tasks without trouble. This is not necessarily true for most middle school math students. Middle school students come to the math classroom with a wide variety of experiences with mathematics, some positive and some negative. Some students may enjoy math, probably because it comes easy to them or because a previous teacher provided a positive environment for learning math. Other students may be less confident in their skills and find math to be difficult or frustrating. I experienced the math tasks as an enjoyable process and some students may share that opinion, but others may not. I think what’s most important is how I, the teacher, present the tasks, support students who need extra help, and extend the tasks for students that are ready for additional challenge.

By doing the work of completing the tasks, I was forced to reflect on my method of solving the problems and identify potential stumbling blocks for students. This, seemingly small thing, was a surprisingly valuable experience. Sometimes, as teachers, we can look at a math problem or task and quickly determine how we might solve the problem or what a reasonable answer might be. However, by actually doing all of the steps to complete the task, a teacher can find specific steps or numbers that might make the task difficult for middle school students. Identifying potential difficulties can inform a teacher about the foundational skills that students will need to successfully complete the tasks so that they can support them appropriately. Completing the tasks also showed me where there were entry points for additional challenge to enhance the learning of highly skilled students. It also illuminated the idea that there are multiple ways to think about, represent, and solve each of the tasks.

As I was choosing tasks for the portfolio, I tried to find problems with real-world application. Since they are written as general skills and understandings about mathematics, there are many, many tasks that can develop the skills of each of the Standards for Mathematical Practice. This allows teachers to choose developmentally appropriate tasks that have some application to their students’ lives. I find the “when am I going to use this?” question to be an annoying, but completely relevant question for students to ask. Finding tasks that can be applied in the real-world or looking out for those “teachable moments” when you can apply the knowledge and skills of the Standards for Mathematical Practice to something that the students are actually doing and living, provides a piece of relevance for students and shows them how they can use math concepts in the things that are already important to them. This relevance can make learning math more enjoyable for all students.

References

Standards for mathematical practice. Standards for Mathematical Practice | Common Core State Standards Initiative. (n.d.). Retrieved April 10, 2022, from http://www.corestandards.org/Math/Practice/