Preparing for excellence in Mathematics

03/21/2011  |  Jill Rosenblum
Mathematics
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The Challenge

Among the 13 southeastern states, 10 currently have an Algebra I graduation requirement, and two more will have one in the 2011–2012 school year. This means that every student graduating from high school will need to succeed in algebra. 

All students must not only pass an Algebra I class, they must demonstrate proficiency on a statewide End-of-Course Assessment. Current pass rates on those exams range from as low as 61 percent to as high as 94 percent. This leaves thousands of students unprepared to graduate from high school, both without the grades/scores needed, and without the mathematics knowledge and skills deemed necessary for success in the 21st century.

Policy Rationale

“Algebra emphasizes relationships among quantities, ways of representing those relationships, and the analysis of change. Algebraic understanding builds on concepts of number and helps to understand concepts in geometry and data analysis. It is important mathematics, useful in post secondary education and on the job.”

“Excellence in mathematics education requires equity — high expectations and strong support for all students.”

(Principles and Standards for School Mathematics, NCTM, 2000)

For many years, the National Council of Mathematics has promoted algebra for all students and their recommendations are reflected in state standards and accountability programs and in the work of Partnership for 21st Century Skills.

The mandate is clear. Algebra is important and we must support all students in learning it. We must believe both that algebra is relevant and valuable and that all students are capable and deserving of learning it. The challenge is also clear. The goals laid out over the past 20 years must now be achieved. This year and next, the high school graduation and future of our students depend upon it.

Approaches

Teachers, schools, districts, and states are working in a variety of ways to assist all students in meeting Algebra I standards. These include explicit strategies for providing additional instruction and support to students who are at risk of failure. These efforts must be tailored and targeted in order to be successful.

“Support” Class

Georgia’s approach to “Algebra for All” comes in the form of a graduation requirement for all students to complete three years of integrated mathematics, Math 1, 2, and 3. Each course includes algebra, geometry, and probability and statistics standards, and the program is built around a set of Learning Tasks. To accommodate the range of high school math learners, schools offer three “versions” of each year’s math course. In addition to Math 1, there is a Math 1 Support course and an Accelerated Math 1 class. Students enrolled in Math 1 Support are also enrolled in Math 1. The Math 1 Support class can do more than provide extra time for students to complete Math 1 assignments, in addition to slowing the pace of Math 1 instruction. With appropriate materials and support for teachers and students, the Math 1 Support class can systematically identify and introduce or review the pre-requisite skills necessary for success in Math 1, in real time. On a daily basis, students can review pre-requisite skills and concepts and preview upcoming lessons and activities. This approach allows students to achieve success in their “core” course in ways that simply providing more time cannot. Many Georgia school districts are implementing materials that let teachers support their students by addressing identified pre-requisite mathematics, coordinated with the “core” curriculum and supported by best-practice research.

‘Foundations’ Class

North Carolina tackles the challenge of all students achieving proficiency in algebra somewhat differently. Their ninth grade students who enter high school with a Level 1 or low Level 2 score on the mathematics section of their statewide Grade Eight assessment are assigned to a Foundations of Algebra course. As the title implies, this course addresses the fundamental concepts that underpin algebraic understanding. The class may be team-taught by a math instructor and a special educator, and the instructional approaches address both the fundamental nature of the content and effective pedagogy. The course offers students hands-on experiences and opportunities for discourse that develop and illuminate the central constructs in order to develop their mathematical thinking and understanding. The intent is to engage students with algebra in a concrete and meaningful fashion and to develop their sense of the structures found within mathematics. This is not merely a middle school math review. It is a purposeful sequence of experiences to build or shore up the fundamental, “foundational” mathematics concepts. In an effective version of the course developed in Wake County, North Carolina, course materials employ a cycle of concrete, conceptual, and communicative/representational experiences. It includes various hands-on activities that generate data and create models that allow students to explore, develop, and reinforce fundamental math concepts. Foundations of Algebra focuses on the mathematics and pedagogy needed for success in Algebra I.

Summer School or Credit Recovery

Districts in many states offer students the opportunity to pass the Algebra I requirement and/or earn the associated credit through evening, weekend, or summer school classes. The key to success in these settings is an acknowledgement that the initial course-taking experience didn’t work. Summer school classes that march students through the same textbook that they used in their Algebra I course are unlikely to be effective. The materials and approaches need to be different. One powerful difference can be opportunities for students to see the mathematics applied in realistic, relevant contexts. Another is a cooperative learning approach where students work together to solve rich, complex problems requiring the application of algebraic thinking.

Direct instruction, infused into problem-solving sessions that serve to review and clarify the necessary (relevant to the task-at-hand) algebra concepts and strategies, builds the students’ understanding and skill set within the context of problem solving. Taking responsibility for approaching the students and the content differently in summer school/credit recovery is key. Then a deliberate effort to connect with student interests, making the classroom experience and the instructional contexts engaging, will go a long way in ensuring their success in the class and in future math courses.

Online Instruction and Test Prep

More and more districts and states are incorporating some form of technology-based instruction into their Algebra I programs. In particular, online tutorials are used for students who are struggling, and online practice tests are used in advance of high stakes tests. In either case, the challenge of effective online instruction is the need to take advantage of the capabilities and advantages of technology. Delivering traditional paper and pencil assignments via a computer, doesn’t exploit the capacity of an online environment to engage students and convey concepts.

Effective online programs are responsive. They adjust to fit the students in a variety of ways. Most importantly, they must possess the ability to identify student learning difficulties — matching student responses to common misconceptions and errors — so that they can deliver appropriately differentiated instruction. Immediate feedback is helpful and targeted follow-up — not just “wrong,” but “looks like you switched x and y, would you like to try again?” — is a great motivator.

Technology enables all kinds of adaptations, from enlarging print to defining or reading aloud terms that are clicked on. Tools for constructing answers, such as selecting words or creating images, support students’ communication. This minimizes reading and writing barriers, and allows students to focus on the mathematics.

Technology-based instruction that exploits the medium, rather than using it to deliver conventional materials, holds great promise.

What’s Working?

In order to realize the vision of all students succeeding in Algebra I and beyond, effective instruction is essential. And in order to make instruction effective, a number of distinctions must be attended to. For example:

Use the extra time afforded by a Support Class to introduce or review important pre-requisite concepts, setting students up for success, rather than just spending more time on class assignments.

Use a “Foundations” course to engage students with the key underpinnings of algebra, helping them to construct or shore up their understanding of mathematics as a system, rather than simply reviewing middle school math.

Use cooperative grouping and realistic, relevant problems to involve summer school/credit recovery students, rather than repeating the same lessons using the same materials.

Use technology’s unique capacities to provide responsive learning opportunities and to minimize challenges, rather than to deliver traditional lessons and assignments.

Jill Rosenblum taught for 10 years in public schools and is currently Vice President of Education at Walch Education. For more information visit www.walch.com.
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