For Windows users, NuCalc 2.0 (The Graphing Calculator for Windows) includes capabilities similar to SureMath.

## Turnkey material for problem solving lessons

Teachers, administrators and curriculum developers will find it useful to bookmark this page. It serves as the benchmark for developing a coherent approach to problem solving across the curriculum. There is an urgent need to embed mathematics in the K-12 curriculum. These web pages extend the ongoing reforms in education to include using mathematics in problem solving.
The following gives links to material which form organized lessons in problem solving. They lend themselves to thematic instruction. These lessons will open in a separate window. Examine as many successive pages as you wish. Return to this page by closing the last window opened.

An evolving problem solving text book
The book material develops the philosophy on which reliable problem solving is based. Examples are used to illustrate the ideas. The use of the material is appropriate at all grade level. At the elementary grades it introduces the student to sound, comfortable ideas associated with problem solving. It shows how problem solving is a natural process closely associated with everyday life. At more advanced levels it provides a way for students to overcome preconceptions about problem solving that have become imbedded in earlier years.

How to solve problems
The pages available from this menu describe the basics of problem solving in detail. Why students can't solve problems reliably is explained and the resolution of the difficulty is addressed. The cure of the "I can't solve word problems" syndrome and the Hierarchical nature of problem solving extend your understanding of problem solving. The menu on the page About Problem Solving leads to additional instruction in the concepts involved in reliable problem solving.

A Short Course in Problem Solving
The lesson provides a sequence of screens showing the principles of reliable problem solving by means of examples. The sequence starts with the simplest ideas and evolves to handle complex problems reliably. The resource can be introduced in early grades and returned to in successive grades. There is an index to select appropriate entering points on successive use of the material.

K4-K12 Problem Set
This is an extensive set of algebra problems starting with quite elementary problems. The problems are ordered in order of increasing grade level. This problem set forms the core of problem solving in algebra at all grade levels. Some of the problems are interactive.

Problem Solving Lesson Plans
This is a set of lesson plans that serve to introduce and embed the problem solving process. It fills a serious need for lessons plans that form a sound basis for problem solving. This will serve the student for a life time.

Problem Solving Manipulatives
Teaching problem solving is not complete without hands-on, minds-on material. This lesson provides problem solving manipulatives which gives even the most reticent student an exciting and meaningful tool for learn to solve problems reliably. These manipulative work together with the Lesson Plans described above to provide a complete approach to learning problem solving.

Making Sense of Story Problem
This inexpensive book has two parts. The Work Book and the Answer Book. The Answer Book serves as guide for the teacher. Students develop solutions to problems in the Work Book. The problems range from very simple problems to upper middle school problems. The emphasis is on embedding the basic problem solving principles. Once this is done, problems in more advanced courses can be solved reliably. The link above causes one of the more advanced problems from the answer book to be displayed.

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Guest Book
Comments in the the guest book show why the problem solving principles shown at 21st Century Problem Solving have become the world standard for problem solving.

Interactive lessons.
The lesson links below provide particular interactive material for learning the problem solving process. These provide ideal turnkey online lessons on problem solving.
An excellent lesson providing exercise in reliable problem solving
How to start a problem solution

SureMath
SureMath is a symbolic algebra program designed for problem solving using modern problem solving processes. In environments in which there is a commitment to including reliable problem solving in the curriculum SureMath greatly expands the students opportunities to learn not only problem solving but subject matter in all subjects, at all levels, that use mathematics for problem solving. Click here to make that move into the future.

SureMath is a Macintosh application. Those who are limited to using Windows can easily extend their resources. Click here to see how. Adding SureMath to your teaching resources is a step you will never regret.

The links above provide a systematic approach to implementing problem solving across the curriculum. Other material on the site provides additional problem solving experience. Encourage your students to explore the site. This is done by clicking on the image bar at the top of this page. Problems and their solutions in algebra, physics and chemistry are available.

Though this site deals specifically with problem solving in situations that use mathematics, the problem solving principles used apply equally well to problem solving in areas that use tools other than mathematics for problem solving.

School resources must necessarily be apportioned to many important courses and activities. Teaching the problem-solving approach described in these web pages, beginning in the early grades and continuing across the curriculum through high school and college, provides a continuity that eliminates much time that is lost in teaching special purpose problem-solving methods specifically limited to subjects.

The National Council of Teachers of Mathematics has said that, "The development of each student's ability to solve problems is essential if he or she is to be a productive citizen." (Curriculum and Evaluation Standards for School Mathematics)

The NCTM Standards also set objectives for precollege education:

"... the K-12 standards articulate five general goals for all students:
• that they learn to value mathematics
• that they become confident in their ability to do mathematics
• that they become mathematical problem solvers
• that they learn to communicate mathematically
• that they learn to reason mathematically"

## The practicalities of achieving these objectives across the curriculum

A unified approach to problem solving from one grade level to the next, in all subjects of the curriculum using mathematical methods for problem solving, is a superior pedagogical approach and saves time and money. An ideal combination.

Problem solving becomes confusing to students when special purpose techniques are taught in various subjects, appearing to be unrelated to their previous problem-solving experience.

The unified problem-solving principles shown in these pages provide much needed continuity for the students. With a solid foundation in problem solving, based on use of mathematics, students are empowered to discover mathematics.

The problem-solving principles set forth here can be adopted with no investment in facilities and simple training for teachers. When resources permit doing so, the addition of computer software is highly desirable.

## Using computer technology in our schools

As more and more of our schools become equipped with computers, it is extremely important that the software used with them is truly substantive as well as easy for teachers and students to use.

The SureMath software referred to in these pages can be used from early grades through graduate school and beyond. It is therefore economical of both financial resources and training time for teachers and students.

NCTM's recognition of the importance of computers in teaching mathematics is stated in these two short quotes, from the NCTM Standards:

"Computers are powerful problem-solving tools. The power to compute rapidly, to graph a relationship instantly, and to systematically change one variable and observe what happens to other related variables can help students become independent doers of mathematics."

[Computers and other technologies] "free students from tedious computations and allow them to concentrate on problem solving and other important content. ...As paper-and-pencil computation becomes less important, the skills and understanding required to make proficient use of calculators and computers become more important."

The problem-solving principles presented in these pages have solved the problem of solving word problems. SureMath software facilitates handling the mathematical functions. All examples in these web pages were solved using SureMath.

For more details,

1. Send e-mail to SureMath Publishing, Inc.