Table of Contents

  1. Rationale
  2. Aims
  3. Content and Organization
  4. Using and Navigating MathDEN
  5. Relationship to the Information Technology IRP for 1996
  6. Incorporating MathDEN into your class curriculum

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Many mathematics students find themselves bored in their regular classes because they already understand the concepts presented, or they find that they are lagging behind. Teachers and schools are increasingly introducing the concept of self-paced mathematics units, in which the student has a great deal of control over his or her learning. The benefits of immediate interactive feedback are well-known, as students can see right away whether they understand the concepts.

MathDEN assists teachers and students to develop individualized programs. At the same time, MathDEN can also be used very effectively as a collaborative tool. Adults who wish to refresh their mathematical skills, or eager students who wish to study on their own also find MathDEN helpful. MathDEN's content is geared specifically for students age 12-18. However, individuals outside of this group have been known to enjoy it as well.

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MathDEN has five basic aims. They are:

Different students will likely find different aspects of MathDEN helpful. Some will wish to focus on the word problems, an area in which many students seek to improve their abilities. Other students may wish to increase their mental calculating skills using Hot Math Tips. In a low-pressure setting like MathDEN, students have the opportunity to see their mistakes and improve their mathematical skills without embarrassment. All students will find it helpful to review their skills.

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MathDEN's content and organization

MathDEN's Four Stages:

MathDEN has four stages, each of which roughly corresponds to a specific grade level. These stages are meant to be flexible. Students may often find they can review old concepts by going down a level or two.

This stage corresponds roughly to Grades 7-8 in the U.S. and Canadian school systems, or ages 12-14. This stage includes computational questions, introductory geometry, and elementary algebra. Abstract reasoning and word problems are emphasized.
This stage corresponds to Grades 9 - 10, or ages 13 - 15. Some linear functions are introduced, and there is an emphasis on geometry.
This stage corresponds to Grade 11, or ages 15 - 17. This stage does not include logarithms or trigonometry, but includes functions such as parabolas, circles, hyperbolas, and ellipses. Complex word problems are included.
This stage corresponds to Grade 12, or ages 16 - 18. This stage focuses on many different aspects of precalculus mathematics, including logarithms and trigonometry.

MathDEN's Other Features:

Hot Math Tips are simple-to-understand calculating tricks. Despite the widespread use of calculators, students still need to know how to do mental math quickly. Each tip includes an accompanying set of examples and a practice quiz.
One problem per week, generally of a light and amusing nature, is presented. The problems are often solved through logical, rather than strictly mathematical, reasoning. Readers can submit their solution, and if it is correct, they will be given credit the following week, when the solution is posted.
The best of mathematical web sites from around the world are listed on this page. An ideal spot for advanced students to begin exploration of more difficult mathematical subjects. Or, a great starting point for anyone seeking mathematical humour, software, and more.
Students can keep track of their cumulative results in each Stage (level). The information is private, and cannot be accessed by anyone who does not possess the User ID and Password.

This icon gives a brief, lighthearted description of MathDEN and its intended purpose. A great way to get students acquainted with the features in MathDEN.

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Using and Navigating MathDEN

MathDEN's Navigation Buttons:

Click on this button to go to the next problem in the set. This is used in Stages 1-4, and in the Hot Math Tips.
Click on this button to go to the preceding problem in the set. This button is used in Stages 1-4, and in the Hot Math Tips
This button leads the user back to the MathDEN menu page.
This button is used in Hot Math Tips and leads the user to the examples that accompany the lesson.
This button is used in Hot Math Tips and leads the user to the practice problems that accompany the lesson.
This button returns the user to the main DEN page, which give the user a choice of MathDEN, GraphicsDEN, InternetDEN, and NewsDEN.

Completing a Question Set:

Students click on the Stage they want or are assigned.

If a student clicks on Stage 1, he or she will be given the choice of a number of different question sets. Each set contains a mix of different problems suitable for that grade level. Question sets that have already been completed by the student will be indicated using a gold star. A new question set is added every week.

In general, each question set is expected to take about 30 to 40 minutes to complete, although some students may need more or less time. Some of the questions may require a pencil and paper to work out the answers, and occasionally a calculator can be helpful. If conserving online time is a factor, the student can disconnect from the Internet once he or she has downloaded a question set. Once every question has been filled in with the chosen answer, the student can reconnect to the Internet (if necessary), and click on the button.

The student then receives his or her score, and is able to look at the solutions for each problem. The student's score is added to the progress report, which is automatically updated upon the completion of a question set.

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How does MathDEN fit into the objectives of the Information Technology IRP for 1996?

MathDEN provides an excellent opportunity for students to practice their Internet skills. They learn navigational techniques, use of forms, and online tracking. Students will benefit from doing mathematics problems on the computer. To learn more about the British Columbia government's information technology objectives for students, follow these links.

Information Technology K-7 Integrated Resource Package 1996
Grade 8 to 10 IRP
Grade 11 to 12 IRP

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Incorporating MathDEN into your class curriculum

The following are some suggestions for using MathDEN in your classroom:

Problem Attack Strategies: Individual, Pair, and Group

One teacher uses MathDEN as a tool to analyze problem-solving strategies. Students work in pairs to solve difficult problems. They keep a written log of the steps they used to achieve a solution and then report their findings to the class. Having students explain their work clarifies mathematical concepts to the students themselves and others in the class.

Individualized Testing and Problem Sets

Most math teachers distribute the same problem set to every student. The possibility of collaboration is great, thus making it difficult to determine if students are relying on their own math skill, or their friends'. MathDEN's numerous question sets make it possible for an instructor to assign every student his or her own question set.

Students who are at different levels can use question sets from different Stages. Advanced students can study on their own and practice with a question set from a higher Stage than their grade level. Other students may find it beneficial to review skills they learned earlier.

Printing out MathDEN Sets

It is easy to print out specific questions. If you are using Netscape or Microsoft Internet Explorer, go to the "File" Menu, and select"Print." An entire question set will be rather lengthy to print, due to the spaces that have been added to make the set legible for the web. If you are interested in obtaining a question set in print format, e-mail Minus the Math Shark for more information.

Creativity, Problem Creation, and Problem Solution

Some students view mathematics as rigid, with no creativity possible. That is definitely not the case, and some of the exercises suggested below will show students that creativity and mathematics are not mutually exclusive.

Hot Math Tips

As a straight-forward exercise, Hot Math Tips are good for improving calculating ability. Another way to use Hot Math Tips is to have students devise a word problem that fits each numerical problem provided. This is a reversal of the presented situation, but it can be an interesting alternative.

Suppose the student is told to do the problem:

50 x 101 = ?

This problem is from Hot Math Tips lesson on Multiplying by 101.

What might "50 x 101" represent? One possibility is 101 tropical fish at $50 each. Or perhaps it represents wages of $50 per day for 101 days. Students are sure to think of an unlimited number of possibilities. Maybe "50 x 101" means the total number of humans abducted, if 50 humans are abducted by space aliens per day for 101 days.


The same principle works for the Stages. Here is a typical problem from Stage 2:

The figure consists of a square inside a circle with diameter of 16. Find the area of the green region.

The figure could represent a farmer building a square fence inside a circular area with a diameter of 16 meters. Or, perhaps a square swimming pool is going to be built in a circular courtyard.

If the question was

1/8 + 0.3 + 1/16
the corresponding word problem could be "How much of a pie is eaten if pieces of 1/8, 0.3 and 1/16 are served?".

This numerical expression could also be related to the following word problem, "Jane used 1/8 of the gas in the tank when driving to school. She used another 0.3 of the gas in the tank when driving to the library. She used another 1/16 when driving to a friend's house. How many liters did she use if a full tank of gas has 60L in it?"

The idea is for the student to recognize that mathematics is more than abstract, randomly extracted numbers, but that it also represents a concrete reality.

Quantities in Our Daily Lives

Another exercise is for a student to think of a physical object, say a car. What are some mathematical quantities related to a car? There are many:

mass, weight, # of passengers, amount of fuel, fuel efficiency, amount of oil, rate of oil loss, water required (radiator fluid, etc.), number of horsepower, acceleration, speed, manufacturing specifications, height, width (and how many could be packed in a certain sized area), friction-speed connection, tire rotation and tire size, etc.

For cars in a lot:

what quantity are green, blue, white, domestic, imports, four-door, two-door, etc.

Thinking of these mathematical quantities makes it easier to devise a problem. Students need not restrict themselves to tangible objects. Another possibility, for example, is weather. A few quantities related to weather include: wind speed, precipitation levels, humidity levels, and so on. Having students create word problems encourages independent thinking and fosters an understanding of how abstract mathematical concepts are directly related to concrete physical problems.

Varied Solutions to a Problem

Another possibility is to look at how many different ways a problem can be solved, and to detail the steps. If your math class incorporates computer programming into the curriculum, you could have students write a program that would solve a given problem (or class of problems). Even without actual computer programming, you can use the problems to introduce the concept of an algorithm and flow-charting, and have the students devise a series of steps that will solve the relevant problem, or class of problems.

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