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Digital resources for middle school mathematics.

Abstract

Middle school mathematics have traditionally been a turning point for many students as they transition from the relative "safety" of elementary school arithmetic to the more challenging demands of high school algebra, pre-calculus and statistics. This paper reviews a number of digital educational resources, available as CD-ROMs or Internet websites and chosen to conform to Massachusetts Department of Education curriculum standards, which may help teachers, students and their parents meet these challenges and smooth the transition from middle school to high school mathematics.

Introduction

American schools and math teachers at all levels continue to grapple with the almost indefatigable disdain that many students feel toward the study of mathematics and science. While studies have shown that proficiency in mathematics is a key component for success in a computer-based economy (Olson, 2006), all but the most gifted American students continue to lag behind their European and Asian counterparts in mathematical ability. The prevailing attitude among many young people is that math is boring and for "nerds" only, a prejudice that is unfortunately reinforced in the popular media. To counteract this attitude many educators contend that math activities should be made fun or "cool" to encourage students to participate. However, this approach fails to recognize that students are often intimidated by the perceived difficulty of math and that many lack the self-confidence to stay motivated and master mathematical concepts (McCallister, et.al., 2003). This anxiety toward math can be compounded at the middle school level as students transition from elementary arithmetic to intermediate mathematics concepts like algebra, geometry and probability. To address math anxiety and build self-confidence, student performance must be improved through skill-building exercises that strengthen problem solving abilities and through instruction that provides the feedback necessary to master more difficult concepts.

This paper reviews a number of digital educational resources, available as CD-ROMs or Internet websites, which can be used in the classroom, or independently at home, to improve student performance in math and build self-confidence in problem solving. The purpose of this paper is not to endorse any particular product, but to provide examples of resources that satisfy general criteria that the author has proposed to meet the challenges of middle school mathematics instruction. Reviews are based on the author's independent use of each resource, and in each case an Internet web address is indicated through which the reader may access a demonstration version of the resource for further investigation.

Challenges of Middle School Mathematics

A number of factors conspire to make middle school mathematics instruction challenging for teachers, students and parents alike. Teachers at the middle school level are generally faced with students emerging from different elementary schools and with varying backgrounds and competency in all subjects, including math. Students taking math at the middle school level are transitioning from the familiar skills base of elementary school arithmetic into the more challenging study of pre-algebra and geometry, whose concepts and "formalisms" (equations and data representations) can be intimidating and confusing at first even to the best students (Booth, 1988). Finally, for parents of middle school students this level of mathematics can often present the first real performance obstacle to children who had previously done well in school, and parents will naturally seek to provide both the right encouragement and the right resources to help their children succeed.

Mathematics Curriculum Standards

The digital resources reviewed in this paper were chosen to conform to the Massachusetts Department of Education curriculum framework for students in grade 7 (Mass DOE, 2004) which is representative of standards used around the country at the middle school level. These standards require that students demonstrate skills in (i) number sense and operations (e.g., fractions, percentages, estimation), (ii) patterns, relations and algebra (e.g., simple linear equations), (iii) geometry (e.g., congruent angles, Cartesian coordinates), (iv) measurement (e.g. area/perimeter of polygons), and (v) data analysis, statistics, and probability (e.g., graphical representations of data, mean, median and mode). Within each subject area students are required to interpret the problem they are being asked to solve, and frequently to represent their solution graphically using computer-based applications like graphing calculators.

Digital Resource Selection Criteria

In reviewing the educational CD-ROMs and Internet websites below consideration was given to selecting mathematics resources that can be used to address the concerns of middle school teachers, students and parents described above. To ensure that resources effectively address these concerns the following criteria are proposed:

Resources must provide the means for students with weaker backgrounds in certain areas to catch up to their more experienced classmates. By satisfying this criterion mathematics resources should "level the playing field" for students coming from weaker elementary school instruction, and make the job of teaching a "performance diverse" student population easier. Such resources should force weaker students who require additional "drill and practice" to improve basic math skills and become solid problem solvers, thereby improving their self-confidence in math.

Resources must allow students to transition more successfully from basic arithmetic to the challenges of pre-algebra. By satisfying this second criterion resources should take some of the anxiety out of pre-algebra study, and make students more confident in tackling subjects that at first might appear intimidating. These resources should also serve as applications that students can "grow into" in subsequent grades so that skills mastered at the entry level can be applied to studying more complex subjects later on.

Resources must demonstrate to students that skills acquired in mathematics can be applied in an engaging fashion to other areas including science and social studies. By satisfying this third criterion resources will show students that mastery of mathematical skills can be applied in a meaningful context, which is important for children at the middle school level who are just beginning to define the interests they will carry into their professional lives. This element should encourage students to look more broadly at the ways in which mathematics can be applied toward their own emerging interests.

Resources must be straightforward for students and teachers to use and offer educational opportunities not easily found in other classroom resources. These final considerations address the practical side of using digital resources in the classroom, or at home, by acknowledging that learning to use these applications often requires a considerable time investment on the part of the teacher and the student, as well as a monetary investment for school districts and parents. To make the time and money invested worthwhile, digital resources should offer a unique learning opportunity and not simply duplicate the kind of instruction already available through textbooks and pencil-and-paper exercises. Resources must also be easy to use so that students can devote their time to learning the concepts and not to figuring out how to use the software or website.

Exemplary Digital Mathematics Resources

Each digital resource reviewed below is first characterized by its purpose, target audience, method of delivery, the company that created the resource, the web address of its product description and any available online demonstration. These items are followed by a description of the mathematics concepts presented and how the software or website functions to instruct students about these concepts. Each resource is also evaluated with respect to the general criteria above and specifically by any unique opportunities that the resource might bring to mathematics instruction for students and teachers. Given the volatility of educational resources, especially on the Internet, only resources from companies or educational groups that are well-established or have exhibited long-term "staying power" are considered.

Destination Math Mastering Skills & Concepts IV." Advanced Mathematics Destination Math Mastering Skills & Concepts V: Pre-Algebra Drill-and-practice and problem-solving exercises for grade 6-8. Available as CD-ROMs or via a subscription website from Riverdeep Corporation. Demo versions available at www.riverdeep.net.

Course IV is a comprehensive mathematics program that teaches basic skills, math reasoning, conceptual understanding and problem solving for the following math topics: fractions, decimals, percents, integers and operation order. Course V is a comprehensive mathematics program that teaches the fundamentals of algebra, geometry, radicals and exponents, ratio and proportion, statistics and probability. Each set of topic exercises begins with a concept review section followed by three levels of increasingly challenging word problems that are set in an imaginary place but have real-life applicability. The review section may be skipped and students can choose the desired level of difficulty for the problem sets. Students solve the problems by choosing between multiple choice items or by inputting short answers. The multiple choice format serves as excellent training for standardized tests and often includes wrong answers that result from common mistakes. Excellent explanatory and interactive feedback is available for each problem that allows students to solve the problem as the software reveals the solution. The software is easy to use and navigate, and the animated graphics are attractive and sufficiently "cool" for middle school students and do not overwhelm or detract from the instruction. Both packages serve as excellent examples of how drill-and-practice software tools can elevate weaker students into the realm of problem solving, as well as strengthen the math skills of students at all proficiency levels. The corrective interactive feedback offered for each problem provides a detailed level of explanation that could probably not be replicated by the most patient of teachers.

Hotmath.com

Website hotmath.com with free and subscription access offering mathematics homework assistance and skills practice for students in grades 6 through college. Maintained by the HotMath Corporation.

This website offers math homework assistance by providing solutions to odd-numbered problems in many of the leading mathematics textbooks used at the middle school through college levels. Recognized publishers include McGraw-Hill, Prentice-Hall, and Holt, Rinehart and Winston, and with a subscription students can access each problem page in a participating textbook. In addition the "Hotmath Team" offers an extensive series of "free-access" problems that cover expressions, operations, number theory, fractions, pre-algebra, geometry, statistics and probability. Solutions to all problems are explained first by offering students hints and then revealing steps in the solution in a hint-then-solution step fashion. The solution graphics are spare but sufficient and include only text, equations and simple line graphs. In addition to homework solutions and explanations, the site also offers exercises designed specifically for graphing calculators, and can provide students with access to online math tutors. Math textbooks often include answers to problems "in the back of the book" as a way for students to check their work independently, however, the answers themselves often do not offer any insight into the solution process. Hotmath.com provides students with a unique service by expanding answers to math problems into full-blown step-by-step explanations, giving students the homework help they need and reinforcing their understanding of key concepts and solution strategies. The website also offers more motivated students a unique "look ahead" to advanced mathematics topics taught at the high school and college level like advanced algebra, pre-calculus and calculus.

HomeSchoolMath.net

Free website www.homeschoolmath.net providing links to homeschooling math resources for students in K-12. Created and maintained by former math teacher and homeschooler Maria Miller.

This website is advertised as a comprehensive math resource site for homeschooling parents and teachers. It offers links to a number of other math resource websites as well as downloadable math worksheets, interactive tutorials, games and curriculum guides. Because the website is geared toward homeschoolers it can provide students and parents (who may wish to augment their children's classroom instruction) with access to math instruction tools from a variety sources that have been found to be effective for home-schooled students who function essentially as "independent learners".

Math Arena Advanced

Pre-algebra games for grades 7 through 10 available on CD-ROM from Sunburst Technology. Online demonstration available at store.sunburst.com.

Math Arena Advanced offers twenty kinds of games at two levels (easy and hard) that allow students to practice a variety of pre-algebra concepts. In a first set of games called "time trials" students race against the clock to solve visual math problems of data graphing, linear equations, line graphs, algebra and manipulation of 2-D and 3-D shapes. A second set of games called "buzzins" allow students to compete against each other to solve probability, order of operations, data graphing, and translating word problems into equations. The graphics are humorous and attractive and are accompanied by snazzy background music. Like its popular "younger sibling" Math Arena for grades 4 through 7, the Advanced package provides students at all performance levels with engaging drill-and-practice activities that require them to hone their math skills and visualize mathematical concepts in unique ways.

Shodor Project Interactivate

Free website www.shodor.org/interactivate offering interactive Java-based mathematics simulations for grades 6 through 8. Created and maintained by the Shodor Education Foundation.

This website is a great online resource for both teachers and students that offers lesson plans and Java-based activities designed to support number and operations, geometry and measurement, functions and algebra, and probability and data analysis concepts. The wide range of activities provided in each subject area progress from simple interactive simulations that introduce fundamental concepts to more challenging simulations and games that build on earlier concepts to teach complex topics and develop higher problem-solving skills. In all cases activities use standard equations to represent mathematics problems and simple animation and graphics to illustrate both simple and advanced concepts. Many activities are also correlated to specific lessons found in established middle school mathematics textbooks. Project Interactivate activities emphasize higher problem solving over skill building and challenge students at all levels of mathematical ability with unique interactive visualizations of math concepts that cannot be replicated with classroom chalkboard discussions.

Graph Master

Data graphing toolkit for grades 4 through 8 available on CD-ROM from Tom Snyder Productions. Online tour and trial version available at www.tomsnyder.com.

Graph Master is a versatile and easy-to-use toolkit for graphing, analyzing and comparing data with nine different graph types, including linear x-y plots, histograms, pie charts, etc. In addition to a number of data sets included with the package, a number of ready-made data CDs are also available with social studies, nature and geography data applications. A related resource website also provides links to a number of other sources of data for analysis (see DASL below). Graph master can serve as a practical math tool with which students can investigate, compare and interpret data in various graphical representations, and it also allows students to export their data graphs for use in multi-media presentations. The toolkit serves as a good "prequel" to Microsoft Excel and its plotting features, and the built-in data library demonstrates that math can be applied to the study of a wide range of subjects.

DASL: The Data and Story Library

Free website lib.stat.cmu.edu/DASL sponsored by the Carnegie Mellon University Department of Statistics that offers access to real data sets for statistical analysis for grades 6 and higher.

The DASL data and story "library" was created as part of a larger effort to enhance the teaching of statistics using computers, and is one of the many data links suggested on the Graph Master resource webpage (above). The library's purpose is to provide data from a wide variety of topics so that statistics teachers can find real world examples that students will find interesting. Each dataset includes a "story" to explain why the information was collected and the original intent of the statistical analysis. This website offers data for all statistical skill levels and identifies data sets by appropriateness of analysis method, and gives students access to data that would be difficult, impossible or very time consuming for them to collect themselves. Some of the datasets are very unique: for example one is an 1854 "census" of the number of lunatics residing in each county in Massachusetts, and another dataset examines the relationship between human behavior and superstition on Friday the 13th. Much of the data and related "stories" are taken from social studies and historical contexts, and all data sets offer the opportunity to pursue advanced statistical analysis.

Conclusion

The digital resources reviewed in this paper were selected because they satisfy general criteria proposed to provide teachers and students with effective tools for mastering key middle school mathematics concepts. In particular, all resources support standard mathematics curricular objectives in ways that cannot generally be achieved via traditional teacher-at-the-chalkboard instruction or with pencil-and-paper homework assignments. The drill-and-practice and math gaming resources reviewed promote skill-building with the objective of turning all students into good math problem solvers. The online math homework support resource provides practical intervention for students who use a number of popular middle school textbooks. The homeschooling website provides links to math resources geared specifically toward independent learners. The interactive online resource uses unique graphical representations to illustrate and reinforce fundamental algebraic and geometric concepts. The data graphing toolkit and data library website provide true-to-life applications of math skills that demonstrate the utility of mathematics for all fields of study. With these tools in hand teachers and parents can effectively address the challenges of middle school mathematics and help former elementary school students develop the proficiency to succeed later at high school level mathematics.

References

Booth, Lesley R. (1988). "Children's Difficulties in Beginning Algebra". In Arthur F. Coxford & Albert P. Shuttle (Eds.), The Ideas of Algebra, K-12, 1988 Yearbook (pp. 20-32). Reston, VA: National Council of Teachers of Mathematics.

Massachusetts Department of Education (Mass DOE). (2004). "Supplement to the Massachusetts Mathematics Curriculum Framework Grades 3, 5 and 7 Grade Level Standards", May 2004. Retrieved November 2006 from www.doe.mass.edu/frameworks/current.html

McCallister, Deborah A., Adrian Mealer, Peggy S. Moyer, Shirley A. McDonald, John B. Peoples. (2003). "Chattanooga Math Trail: Community Mathematics Modules Volume 1", The University of Tennessee at Chattanooga, July 2003. Retrieved November 2006 from ERIC at www.eric, ed.gov/ERICDocs/data/ericdocs2/content_storage_01/0000000b/80/ 22/c1/d7.pdf.

Olson, Lynn. (2006). "Economic Trends Fuel Push to Retool Schooling: Leaders Want Tighter Links to Workplace, College Skills". Education Week, March 22, 2006, vol. 25, no. 28.

Shelley E. Scruggs, Boston University School of Education

Shelley E. Scruggs, Ph.D., holds a doctorate in electrical engineering and is a student in the Graduate Certificate in Instructional Technology program at Boston University.
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Author:Scruggs, Shelley E.
Publication:Academic Exchange Quarterly
Date:Jun 22, 2007
Words:3027
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