Focus on Math
Mathematics continues to be a tough subject, both to learn and to teach. This subject requires that students not only understand the fundamental concepts, but that they are also able to apply these rudimentary ideas to solve problems and progress to more advanced levels. This progression often requires that students receive extra assistance in comprehending and utilizing these concepts; however, with the number of students in each class continually increasing, tutoring students individually becomes a real challenge for instructors. In addition to receiving extra help from parents and peers, students may sharpen their math skills with a number of math software programs. This month's Focus On details mathematical solutions that cater to all levels, skills, languages and state standards.
Assessing students' abilities and guiding them in the selection of appropriate study material is a time-consuming challenge for teachers. Luckily, certain educational software programs allow students to test their level of knowledge in a certain area, and provide level-appropriate lessons to help them learn concepts. A Web-based solution for K-12 math, Aleks delivers precise, comprehensive diagnostic assessments of students' math knowledge, directs them to study material, and records their progress toward mastery of curricular goals. Aleks delivers a graphic report analyzing the student's conceptual understanding, relevant to his or her grade level based on specified standards. The report also recommends concepts on which the student can begin working by clicking on any of the listed items. The course management system interacts with the student much as a human tutor would - moving between explanation and practice as needed, correcting and analyzing errors, defining terms and changing topics on request.
Also included in the system is a teacher module where students' progress can be monitored and educational standards can be adapted to a particular district, school or class. Teachers may view and print reports for one or several students with a summary of information for each student, view and edit standards for their class, edit student registration data, and retrieve forgotten passwords. Administrators may do everything a teacher can do. They may also view and print lists of classes and teachers, and view and edit the default standards used by individual classes or the entire school. In addition, the entire Aleks system, including the assessment module, can be used in several languages, such as Chinese, Russian, French, Spanish, English and German.
While computers provide a wonderful resource for enhancing learning, convincing students to spend quality time using educational programs at home, as well as in the classroom, can be a formidable task. This is why Educational Insights, Inc. has created Geosafari Knowledge Pad - The Math Series. The series consists of Beginning Math (K-first grade), Addition and Subtraction (first and second grade), Multiplication and Division (third and fourth grade) and Fractions, Decimals and Percentages (fifth and sixth grade). Each program is made up of arcade-style quiz games, entertaining graphics, sound effects and bonus round quizzes that are designed to engage students in learning. Pop-down window quiz instructions allow for easy navigation through the program, and an easy-to-use assessment tool keeps track of students' progress.
Beginning Math includes 48 learning games that focus on skills such as matching sets of numbers, identifying numbers, counting numbers, estimating, finding objects on a grid, adding money values, identifying attributes and matching number words to numbers. Addition and Subtraction includes 56 learning games that focus on rounding, adding two-digit numbers, subtracting two-digit numbers without regrouping, telling time, using coordinates to find objects on a grid, and adding and subtracting money. Multiplication and Division includes 56 learning games that focus on multiplying one- and two-digit numbers, choosing the correct operation, identifying missing factors, dividing, identifying remainders, completing word problems and calculating averages. Fractions, Decimals and Percentages includes 64 learning games that focus on identifying whole numbers and fractions, reducing fractions, adding and subtracting fractions, finding the lowest common denominator, rounding decimals, changing decimals to percents and changing fractions and mixed numbers to decimals.
In order for students to get the most out of their education, it is important that lessons appeal to their particular learning style. Prentice Hall's Interactive Math provides a solution for math teachers and students that offers students instruction based on the way they want to learn. Visual and auditory learners can watch video segments featuring on-screen instruction, verbal learners can read a description of concepts, and tactile/kinesthetic learners can complete the Read, Watch and Explore activities. The program is available for three levels - Basic Math, Introductory Algebra and Interactive Algebra. Delivered via CD-ROM and Internet applications, Interactive Math is aligned with a nationally recognized text.
Available with a customizable syllabus, the program allows teachers to select items that suit the students' level, to rearrange syllabus items, to insert instructor notes, to set the mastery level and to set forced order completion. Interactive Math can be used in a variety of environments, including the classroom, a self-paced lab or distance learning courses. In addition, all practice and assessed problems are algorithmically driven, giving students multiple opportunities for practice.
Prentice Hall provides schools that implement Interactive Math into their programs with a faculty trainer, who is an instructor already teaching with the program. The trainer addresses the specific course environment as he or she trains the instructor on how to use the program and how to succeed as a teacher in a computer-based learning environment. Users receive ongoing access to a faculty support consultant and a technical support team to assist with installation and ongoing technical support. User conferences are offered to provide the opportunity for further training.
While the main purpose of educational software should center on the learning benefits to the student, programs should also offer teachers support for incorporating the software into the curriculum. Designed to improve performance on standardized tests and to help students succeed in meeting educational goals, Summit Math Version 1.7 provides instructors with enhanced management system features, support for Solaris and Linux servers, user customization, additional activities and technical support options. Management system improvements in Version 1.7 include the ability to change the look and feel of the Summit program, the ability to assign activities to an entire group of students at once, and the ability to set preferences for individual users. If an error occurs, the system can be configured to send an e-mail automatically to Summit customer support with information at the time of the error.
The curriculum portion of the program contains comprehensive reading and mathematics instruction for grades three through eight, and includes more than 900 learning activities. Summit's management system gives detailed reports to instructors about objectives mastered, time spent on tasks, and the overall progress of each student.
The management system also provides proficiency-based assessment embedded within each activity. Summit Math Version 1.7 modules cover number concepts, measurement, fractions, decimals, percents and ratios, statistics and probability and algebraic ideas.
Integrating technology into a curriculum directly involves both the teacher and student. However, in order for a program to remain useful, students must engage in out-of-classroom practice. Unfortunately, teachers cannot be there to help solve difficulties that arise when the student practices at home. To help remedy this, Boxer Learning has engineered BoxerMath, an online math application for teachers, students and parents. Especially designed for parents, the program has a Point of Reference and a Parent-Teacher Forum section. To refresh their memories, parents may quickly click on the Glossary to reacquaint themselves with the meaning of a reciprocal. If additional help or referencing is required, access to other online math sites is embedded within the Point of Reference section, which provides a set of links for algebra and other math-related sites.
For teachers, BoxerMath presents a core curriculum for Algebra, Algebra II, geometry and trigonometry in the same way a textbook presents its content. The Tutorial Center allows for the selection of an appropriate level of math, a topic, and then instruction or practice. Because each lesson is comprised of both explanation and demonstration, teachers may use this material to facilitate classroom lectures or provide self-paced sessions for students.
Also new from Boxer Learning is the launch of the Boxermath.com Gymnasium. A new practice area of the Boxermath.com site with significant assessment activities for students and teachers, the Gymnasium adds more than 1,300 practice problems developed by experienced math teachers. In addition to the existing practice slides and tests in the Boxermath.com tutorials, the Gymnasium enables educators to reinforce tutorial concepts through more skill-based practice, and to provide more exercises for students having difficulty with particular math concepts. Educators can then track and assess student progress in the Gymnasium activities through the Boxermath.com ledger online management system.
Exploring advanced topics electronically requires advanced technology. Designed with the view that students of accelerated mathematics should work with the same full power software as technical professionals, Wolfram Research's Mathematica for Students 4.1 includes many new enhancements. Refined solvers, new functions and an improved pattern matcher and compiler allow students to solve more complex problems faster. MathML and HTML integration helps academics and technical professionals share their work over the Internet. J/Link allows the design of innovative applications and combines the strengths of Mathematica and Java.
New features of the program include greatly enhanced symbolic differential equation solvers, dramatic speed improvements in statistics functions, conversion between linear systems of equations and matrices, and support for saving in IBM techexplorer format. Further, the program offers faster import and export filters for Excel files, tabular data, compressed BMP, DXF and STL, support for real-time manipulation of 3D graphics on Linux and Unix platforms and routines for plotting graphics defined by inequalities. The program's advanced math capabilities include optimized algorithms for statistical computation, numericalization of root objects, continued fraction improvements, evaluation of roots for polynomials with algebraic number c'efficients, and implementation of GCD by Chinese remainders.
Because solving word problems requires interpretation, conceptualization, analytical skills and application of mathematical theories, this type of math befuddles many students. Carnegie Learning has created Cognitive Tutor Quantitative Literacy Through Algebra (QLTA) to enable students to develop their formal mathematical and problem solving skills. Nearly all of QLTA's problems are word problems that help students further develop both their math and reading skills. Students are taught to approach the problems in three ways: numerically,graphically and algebraically.
The program provides real world problem situations and detailed solution processes. The curriculum uses Carnegie Learning's Cognitive Tutor software, which follows students step-by-step as they solve problems, and provides help when needed so that students can work and learn at their own pace. Because QLTA enables student learning to be self-paced, it reaches all learners, from more advanced students to those who need more one-on-one attention. Unlike a supplemental software product, the Cognitive Tutor QLTA program is a full-course curriculum that features a complete system for the student, including a textbook, collaborative problem solving activities and student presentations.
Contact InformationAleksGlenc'e McGraw-Hill
Geosafari Knowledge Pad -
The Math Series
Educational Insights, Inc.
Upper Saddle River, NJ
Summit Math Version 1.7
The Denali Project
Mathematica for Students 4.1
Wolfram Research, Inc.
Cognitive Tutor Quantitative Literacy Through Algebra
Carnegie Learning, Inc.
This article originally appeared in the 04/01/2001 issue of THE Journal.