By: Jeff Heyck-Williams
Anyone who has had a conversation with me about education or has taken time to read any of my previous posts on this blog knows that I am passionate about what I have come to describe as expanded outcomes for education. This idea is at the heart of the mission of Two Rivers and of what we believe defines innovative education for the 21st century. My earlier writings on our mission, on the nature of curriculum, and about the types of tasks and experiences that we need to provide for our students are founded on this idea.
So what is this idea?
To explain, I’ll share my reactions to a report that I recently finished reading on the state of math education in the United States and recommendations for improvement. Adding It Up: Helping Children Learn Mathematics is a report written by the Mathematics Learning Study Committee of the National Research Council published in 2001. As I read, I was struck that this report both reaffirmed my commitment to expanded outcomes and disheartened me as I considered how little has changed in the 10 years since this report was published. Both reactions are part of my own response to the state of education in the US and where we need to go. Together they illustrate what I mean by a new vision for proficiency as the outcomes for education.
Ironically the same year that the National Research Council published Adding It Up, Congress passed the Elementary and Secondary Education Act known as No Child Left Behind (NCLB). I say ironically because as Adding It Up laid a firm rationale for an expanded vision for what it means to be mathematically proficient, Congress passed a well intentioned law that ultimately reinforced and calcified an existing reductionist view of the outcomes for math education. To be fair, NCLB does not dictate what it means to be mathematically proficient. It leaves that up to the states. However, NCLB did force states to create state standards in two areas, math and reading that raised these two subjects over all others in the curriculum. On their own initiative, states created standards and aligned assessments that too often reinforced a limited view of what it means to be mathematically proficient. Namely that most of what students needed to develop was rote procedural fluency in mathematics (i.e. quick arithmetic). Thus over the ten years since the publication of Adding It Up and the enactment of NCLB, we find ourselves nationally with possibly a more limited view of educational outcomes than when we started.
However, Adding It Up is a clarion call for a broader vision for what it means to be mathematically proficient. In the report, the authors argue that mathematical proficiency is defined by five interwoven strands. They include conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and a productive disposition. While proficiency does include the ability to solve standard computational problems efficiently, procedural fluency is encompassed in only one aspect of what it means to be proficient. Unfortunately most state assessments only test students procedural fluency in a multitude of strands of mathematics. However, students also need to be able to make sense of what they are doing when computing or solving a problem and demonstrate understanding of the underlying concepts. They need strategies for solving non-routine problems and an ability to reason effectively about both their methods and solutions. Finally the report argues that an equally important outcome is productive disposition. In other words, students need to love math or at very least see it as a useful worthwhile discipline in which to engage.
As Adding It Up addresses what it means to be well educated in mathematics, works like Frank Levy and Richard Murnane’s The New Division of Labor: How Computers are Creating the Next Job Market and Bernie Trilling and Charles Fadel’s 21st Century Skills: Learning for Life in Our Times address what it means to be proficient more generally across disciplines. Two Rivers has taken the terms expert thinking and complex communication from Levy and Murnane’s work to describe what these expanded learning outcomes look like. However, regardless of the terms we use, the point is the same. To fully realize the potential for all of our students and to provide each of them with rich and varied options for their futures, we must see beyond providing proficiency on any single test. We must have a new vision of proficiency that encompasses the cognitive, interpersonal, and intrapersonal skills of life-long learning. To do anything less is truly leaving our children behind.
Ironically the same year that the National Research Council published Adding It Up, Congress passed the Elementary and Secondary Education Act known as No Child Left Behind (NCLB). I say ironically because as Adding It Up laid a firm rationale for an expanded vision for what it means to be mathematically proficient, Congress passed a well intentioned law that ultimately reinforced and calcified an existing reductionist view of the outcomes for math education. To be fair, NCLB does not dictate what it means to be mathematically proficient. It leaves that up to the states. However, NCLB did force states to create state standards in two areas, math and reading that raised these two subjects over all others in the curriculum. On their own initiative, states created standards and aligned assessments that too often reinforced a limited view of what it means to be mathematically proficient. Namely that most of what students needed to develop was rote procedural fluency in mathematics (i.e. quick arithmetic). Thus over the ten years since the publication of Adding It Up and the enactment of NCLB, we find ourselves nationally with possibly a more limited view of educational outcomes than when we started.
However, Adding It Up is a clarion call for a broader vision for what it means to be mathematically proficient. In the report, the authors argue that mathematical proficiency is defined by five interwoven strands. They include conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and a productive disposition. While proficiency does include the ability to solve standard computational problems efficiently, procedural fluency is encompassed in only one aspect of what it means to be proficient. Unfortunately most state assessments only test students procedural fluency in a multitude of strands of mathematics. However, students also need to be able to make sense of what they are doing when computing or solving a problem and demonstrate understanding of the underlying concepts. They need strategies for solving non-routine problems and an ability to reason effectively about both their methods and solutions. Finally the report argues that an equally important outcome is productive disposition. In other words, students need to love math or at very least see it as a useful worthwhile discipline in which to engage.
As Adding It Up addresses what it means to be well educated in mathematics, works like Frank Levy and Richard Murnane’s The New Division of Labor: How Computers are Creating the Next Job Market and Bernie Trilling and Charles Fadel’s 21st Century Skills: Learning for Life in Our Times address what it means to be proficient more generally across disciplines. Two Rivers has taken the terms expert thinking and complex communication from Levy and Murnane’s work to describe what these expanded learning outcomes look like. However, regardless of the terms we use, the point is the same. To fully realize the potential for all of our students and to provide each of them with rich and varied options for their futures, we must see beyond providing proficiency on any single test. We must have a new vision of proficiency that encompasses the cognitive, interpersonal, and intrapersonal skills of life-long learning. To do anything less is truly leaving our children behind.
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