Elizabeth M. E. Nelson
I was always "good at math." In elementary school, I was able to memorize basic arithmetic facts. I caught on quickly to the traditional algorithms for addition, subtraction, multiplication, and division. I carried when I needed to carry and borrowed when I needed to borrow by following the set of rules established and communicated to me. As procedures got more complicated, I excelled at following a series of processes as outlined in a textbook and reapplying them to a new set of numbers. After being admitted into an advanced math program, I was able to finish calculus by my sophomore year of high school and test out of the general math requirements for college. It wasn't until I was in graduate school taking a course in "Teaching Mathematics in the Elementary School" that I came to the shocking realization that my problem-solving and mathematical-thinking skills were really quite limited. If asked to solve a math problem without being able to use the tried and true algorithms, I found that I was fairly lost. In my personal math education, I was not taught
why
I did all those procedures I did so well or
how
they worked so well. Unfortunately, I was not alone.
Fortunately, there has been a general trend in math education to focus on more than just the traditional algorithms to help ensure that students understand the "hows" and "whys" of solving a range of mathematical problems. This trend is quite evident with the implementation of the Common Core State Standards (CCSS) in which emphasis during a student's early elementary years is placed on using a variety of strategies to meaningfully represent and understand the concepts of addition and subtraction.
1
If this strong foundation is set, students should eventually be able to use the most efficient and accurate strategies to solve a range of problems. Their mathematical-thinking, problem-solving, and higher-order thinking skills should allow them to interpret and solve real-world problems and be able to express their mathematical thinking. CCSS provides a framework that should ideally ensure that students do not end up like me. Ideally, they will understand
why
they are doing the procedures they are doing and not just plugging in new numbers to the same old algorithm, as I had been accustomed to doing.
While CCSS are well intentioned, teachers at all levels are struggling to get their diverse groups of learners to meet the high expectations outlined by the established standards. Having taught in various urban elementary schools with a variety of curricula, I can say that I have yet to find any one curriculum that adequately helps
students
develop, discuss, and use a variety of strategies to solve problems in a meaningful way, as CCSS demands. Time and time again, I find that, while many components of these resources can be beneficial, there are major voids that do not promote mastering the skills and concepts that students will need down the road. It is no secret that it is extremely challenging to build up students' skills when their foundation has not been established. Being a first-grade teacher of a diverse group of English language learners, I want to be able to do all that I can in order to establish a strong foundation upon which later elementary and high-school educators will be able to build. If the expectations of CCSS can be met, our students will be much less likely to make it all the way to grad school believing that they are exceptional math students unless they are actually doing some critical and mathematical thinking.
