Sunday, February 20, 2011

Embracing Meaning: Algorithms with Understanding

I recently had the pleasure of hearing a talk by Marilyn Burns about our societies singular devotion to the use of specific algorithms, called "traditional algorithms," when teaching students how to compute numbers. The computation of numbers fall into the domains of mathematics called Number Sense and Operations. I have often thought about the irony of those labels and how we generally do not impart a good sense of numbers or meaning when teaching students how to "operation" on numbers. Instead we teach the "rules," steps or procedures for algorithms to "relieve" learners of the burden of having to develop a useful, flexible understanding of numbers, their magnitude, meaning, and relationships to other quantities.

Some educators might disagree or take offense to my aforementioned point, saying things such as:
  • "We were taught this way, and we are fine."
  • "This is simple for my struggling learners to follow. They can get the answer. I will save these other methods for my advanced learners."
  • "They get it. See they can all use the algorithm and get the right answer."
I cannot tell you how many times I have heard these lines or similar one with the same sentiments, but I sense a change in many educators. I am finding that more and more teachers are willing to ask about the meaning behind various algorithms that they teach. They realize that, as a society, "we are not fine." In the report, "Diploma to Nowhere," they note, "One of the most important to prepare students for college. In the knowledge based economy of the 21st century, students need a post-secondary degree...most...students who enroll lack basic math..." They go on to document, "...achievement in elementary schools is low, with barely 40 percent of 4th graders scoring at or above proficient in mathematics on the 2007 National Assessment of Educational Progress (NAEP). Only 41 percent of 8th graders in 2005 enrolled in gateway classes such as Algebra."

The challenge and pressure that many educators face and feel stem from standardized exams and performance expectations. Aside from the fact that many teachers do not know how to approach teaching algorithms with meaning, they are also concerned with the time it will take their students to understand the concepts involved. Additionally, in many schools, it is often not the work of grade level teams to look at how algorithms are taught and/or seeking alternative strategies that might help students understand the mathematics embedded within the algorithm. Furthermore, few school districts are like Chets Creek Elementary and Schultz Center Academy of Mathematics, and do not make building teacher content-knowledge around this topic a priority.

To help us better understand this issue...our need for a systematic and efficient approach to solve a problem, we are going to have a conversation with Ms. MaryAnn Wickett, co-author of, "This Is Only a Test: Teaching for Mathematical Understanding in an Age of Standardized Testing", and we are going to focus on the question of, "What are the benefits of teaching algorithms with conceptual understanding?"

Interview with Ms. MaryAnn Wickett:

Interview with a parent who has a child in Ms. Wickett's 3rd grade class:

Additional books by Ms. MaryAnn Wickett:

One last word - a statement from the Introduction to the Common Core State Standards for Mathematics: "There is a world of difference between a student who can summon a mnemonic device to expand a product such as (a + b)(x + y) and a student who can explain where the mnemonic comes from. The student who can explain the rule understands the mathematics, and may have a better chance to succeed at a less familiar task such as expanding (a + b + c)(x + y). Mathematical understanding and procedural skill are equally important, and both are assessable using mathematical tasks of sufficient richness."