Chad M. Barrett

Yesterday I read about half of the SMARTER Balanced Assessment Consortium's draft content specifications for mathematics. My initial reaction is that the consortium has made a thoughtful attempt to revolutionize mathematics education in the United States. The consortium, it seems to me, plans to assess mathematics in very different ways based on a very different approach to the domain. They are moving to center stage the habits of mind, or the ways of thinking, that students will need in order to successfully use mathematics in college or the workplace. A colleague told me that there is a fundamental shift taking place in mathematics education - away from focusing on how mathematics is taught and toward how mathematics is learned. After reading the first half of this document I agree with her.

In its draft content specifications the consortium identified four major claims that will map assessment targets to the Common Core State Standards. These claims are provided below.

• Claim #1 - Students can explain and apply mathematical concepts and carry out mathematical procedures with precision and fluency.
• Claim #2 - Students can frame and solve a range of complex problems in pure and applied mathematics.
• Claim #3 - Students can clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others.
• Claim #4 - Students can analyze complex, real-world scenarios and can use mathematical models to interpret and solve problems.

These claims, in my opinion, define what important habits of mind students will need in college and the workplace. These claims are supported by the Common Core State Standards and how that document is organized. However, the consortium took a very interesting additional step. They are proposing that these claims become the reporting categories for the assessments that they are developing. The table below, taken from the draft specifications document, shows how this would look.

I find this recommendation to be both revolutionary and intriguing. This is revolutionary because I am not aware of a state summative assessment that organizes reporting categories in any way other than the content domains. I have grown accustomed to seeing reporting categories such as: number and operation, algebra and functions, geometry, and statistics and probability. I find the recommendation intriguing because, as an assessment content developer, I find myself challenged to meet the expectations of this design. I think I will enjoy whatever role I will play in trying to make this work.

What do you think?

Reference

Burkhardt, H., & Schoenfeld, A. (2011). Content specifications with content mapping for the summative assessment of the common core state standards for mathematics. Review Draft, SMARTER Balanced Assessment Consortium, Retrieved from http://www.k12.wa.us/SMARTER/ContentSpecs/MathContentSpecifications.pdf

Photo Credit - Image: photostock / FreeDigitalPhotos.net

This morning I began, in earnest, a journey of discovery into the topic of computational fluency. The genesis for this journey came over a month ago. I was reviewing a list of emphasis areas in the Common Core State Standards that included a brief discussion of computational fluency. After conducting some preliminary research I became interested in trying to describe appropriate methods for evaluating computational fluency in large-scale assessment. So, after letting the idea languish for a month or more, I have decided to start my research.

The definition of computational fluency provided by the National Council of Teachers of Mathematics is my motivation for this investigation. The organization, in its Principles and Standards for School Mathematics, defined computational fluency this way.

Computational fluency refers to having efficient and accurate methods for computing. Students exhibit computational fluency when they demonstrate flexibility in the computational methods they choose, understand and can explain these methods, and produce answers efficiently.

There are elements of this definition, including flexibility in choosing methods and the ability to explain these methods, that I am not sure are a focus of current assessment. Testing for computational fluency is focused on efficiency, which is often assessed through a timed test of computational questions. One thing I hope to do is challenge the notion that assessing computational fluency means evaluating efficiency. A timed test may assess efficiency, however, I believe there are assessment methods that can get evaluate a student's flexibility and understanding. Identifying these methods will be a focus of my research.

If this is an area of interest please leave me a comment. I am interested in connecting with other educators and researchers interested in computational fluency.

References

National Council of Teachers of Mathematics. (2000). Principles and Standards for School Mathematics. Reston, Virginia: National Council of Teachers of Mathematics.

Image: anankkml / FreeDigitalPhotos.net

The term balanced assessment continues to be a buzzword in the area of educational assessment. But, what does balanced assessment mean? First, I must express my preference for the term balanced assessment system.  A balanced assessment system integrates many different assessment types in order to provide the best possible data regarding what a student knows and can do.

Balanced assessment systems synthesize data collected from three assessment types. Each assessment type is described below. I credit Tracy Huebner's 2009 Educational Leadership article titled Balanced Assessment with helping me provide brief descriptions of each assessment type.

• Summative Assessment - Summative assessments are delivered at the end of instruction and provide data that can be used to evaluate a program or some entity (e.g., school, district, state).
• Interim Assessment - Interim assessments are delivered at fixed points during instruction (e.g., at the end of a grading period) and provide information about whether a student or group of students are on track to pass the summative assessment.
• Formative Assessment - Formative assessments are delivered at frequent intervals during instruction and provide information to the teacher about any need there may be to change instruction.

In my opinion the concept of a balanced assessment system is not new. I learned very early in my educational assessment career is that we (i.e., the assessment community) recommend that stakeholders use multiple measures to determine what a student knows and can do. I believe that the term multiple measures is a predecessor to balanced assessment.

Balanced assessment systems may move from concept to reality over the next few years. The federal government jump started the conversation when defining the rules for the Race to the Top Comprehensive Assessment Competition. The two consortia, in their proposals, provided visions for balanced assessments that are aligned with the Common Core State Standards.

Until we get a better idea of the consortia's plans for balanced assessment, if you are implementing the concept of a balanced assessment system, please leave a comment and let us know the direction your work is taking.

References

Huebner, T.A. (2009). Balanced assessment. Educational Leadership, 67(3), 85-87.