Is There Really Such a Thing as a Negative Number?

When you were about two years old you probably learned to hold up two fingers when you were asked how old you were. Two fingers are real and in this case represented two years of time. From the very beginning of civilization numbers were meant to count real things, like the number of sheep when sheep were being sold or traded. Then zero meant none, no sheep. In today's mathematics numbers that are greater than zero are called positive numbers.

Let's think about subtraction for a minute where we "take away" a number. Pretend you want to buy some music CD's from your friend who has 8 CD's for sale. While there are 8 CD's for sale you want to buy just 6 of them. You "take away" 2 CD's and the math is 8 - 2 = 6. Another way to look at your CD trading transaction is -2 or negative 2. Is the negative number real? Your friend who was selling CD's still has 2 CD's so it's okay to decide that the negative number is real.

The idea of negative numbers has been around for a long time. The ancient Chinese people used negative numbers in the marketplace. In fact they used red counting rods for positive numbers and black counting rods for negative numbers. It wasn't until centuries later, in the 16th century, that mathematicians outside of China started using negative numbers.

Are you familiar with the term sea level? The location of sea level is determined by scientists. Picture yourself standing on a high cliff looking out over the ocean and feeling the nice ocean breezes. How far is it down to the water? If it's 30 feet to the water you are 30 feet above sea level. But the exact science of sea level is a bit more complicated than this simple example.

The tallest mountain in the world, Mount Everest, is 29,035 feet above sea level. Flat areas in the middle of the United States sometimes are only 600 feet above sea level! The lowest point in the United States is Death Valley which is located in both California and Nevada. Death Valley is 282 feet below sea level or -282 feet in relation to sea level.

Based on the examples of selling CD's and sea level, you know that negative integers make sense. But does it make sense to have a negative decimal number like -17.56? It certainly does!

Negative numbers are used a lot in banking and finance. It's easy to think of positive numbers as plus or addition and negative numbers as minus or subtraction. Do your parents use an ATM machine? Money doesn't flow from an ATM machine by magic, does it? Your parents deposit money in the bank and when they withdraw money from the bank at the ATM machine, the amount is subtracted from their account. Basically any withdrawal from a bank account is a negative number. Since dollars and cents are shown as decimal numbers, it's easy to see that negative decimal numbers make sense.

In fact, all electronic banking transactions are based upon the idea of positive and negative numbers. Banks really don't transfer actual dollar bills very often. Banks send computer messages to each other that credit an account with a positive number or debit an account with a negative number. But when banks or other financial companies prepare printed statements, they use the opposite color scheme from the ancient Chinese. Today black is used for positive numbers and red is used for negative numbers.

So, negative numbers are extremely important in you and your family's everyday life. Now you know that negative numbers exist for sure.

Tips for Reinforcing Good Problem Solving Skills

A big part of the job as an educator is to discover effective ways to help children make it through the difficult times of their academic lives. Students must have the ability to problem solve effectively is very important in helping them learn self-respect and self-esteem, overcome feelings of helplessness, and promote a generalized sense of capability. Equipping students with the right problem solving skills will promote resiliency and solution-focused problem solving shifts away from emphasizing problems and toward helping students discover the considerable power and possibilities they have in themselves.

The solution-focused problem-solving perspective emphasizes that children can become stuck by focusing on their past and current "bad" behavior and failures versus focusing on future solutions. It is important that educators will increase student performance by removing obstacles to student learning. Children accomplish more when they concentrate on their successes and strengths rather than their failures and deficits. There are so many advantages for students who know how to constructively problem solve. Students should be looked at as being good and capable of rational thought but without any influence from teachers or significant adults a student will likely focus more on their own negative side.

Once educators begin to shift to the positives of the good things that are going on in a student's life, the student's usually will switch to that, open up and talk about it too. Students do have the capacity to act on common sense if given the opportunity to identify common sense problem-solving strategies. Solution-focused problem solving is based on the theory that small changes in behavior lead to bigger changes in behavior. Solution-focused problem solving emphasizes a role shift for students. Small shifts in role by a student will cause shifts in other places. The best advice that can be given to an educator in regards to teaching problem solving skills to a student is to develop an alliance with the student and work together to determine the problem and the cause. Identify the student's strength, everyone has at least one, and then they can build strengths and foundations which will lead to positive changes. When the plan does not seem to be working and the student seems to be repeating the same pattern or does not have the ability to control compulsive behaviors then the educator has to watch for a pattern and reinforce with positive.

Solution-focused problem solving pursues the positive and students are more likely to find a solution to a problem when they concentrate on their successes rather than their failures. Students must realize that they play a huge part in the success of their problem solving process and that change will occur. Once the changes begin to happen then the student will realize that their lives can be very different. Then it is time to have the students set goals and then monitor their progress. Good problem solvers use a variety of processes and strategies as they read and represent the problem before they make a plan to solve it. They then use comprehension strategies to translate the linguistic and numerical information in the problem and come up with a solution. For example, good problem solvers may read the problem more than once and may reread parts of the problem as they progress and think through the problem. They identify the important information and even underline parts of the problem.

A systematic, research-based problem-solving program makes problem solving easy to teach. Students are provided with the processes and strategies that make problem solving easy to learn, and they become successful and efficient problem solvers. They also gain a better attitude toward problem solving when they are successful and develop the confidence to persevere.

10 Tips for New Math Teachers

Starting out as a new teacher can be intimidating and even frightening. Some basic tips may help to eliminate the stress and anxiety from teaching a class of children. Students will give their trust easily if they like you.

Don't be too serious

Every new thing is kind of scary, so when you have to stand up and teach math it can be a little intimidating at first. Try not to frown or look to serious. It will discourage the students and they will be afraid of you. Humor can built a bridge that can make amends later on it the year. Remember that a good laugh is like medicine for the body.

Use discipline

There will be no teaching without controlling of your class. It is better to fall behind by a day or two early in the year to address discipline, than to have an uphill battle all year long over behavior. Let students know from the beginning what is acceptable behavior and what is not. This way they won't take chances.

Involve the students

Encourage the students to work in groups. In this way they can have a study partner and feel comfortable with one another and learn to trust each other. In the long run it will benefit your students if they all get along smoothly and there will be order in the classroom. Later on you can have competitions between the different groups as well.

Motivate your students

Be a motivation to your students. Identify early on what math they are struggling with and help them overcome those areas. Students are surrounded with negativity where ever they go. If you can give them a place to feel safe and comfortable they will give back to you a solid return by doing their best.

Make it interesting

Use every day examples to draw and hold their attention. Math can get very boring when the same patterns are followed every time. Be open to creativity and use basic things that aren't costly. Students can bring junk materials from home to use in their projects.

Prioritize

Get your priorities straight right in the beginning. A good diary can only be an investment and remember that you don't have to do everything just to accommodate others. If your schedule allows it, you can take on extra curricular activities.

Rest when possible

Teaching is hard work. Make time for yourself. If you are stressed out you cannot give your best. Take vacation time to sleep, eat and maybe read a good book once in a while. When you are rested you will benefit your students.

Be prepared

Preparation is of the essence. Take time every day to prepare for the following days lessons. This will pay tremendous rewards as you can then give your full attention to the subject at hand. Don't leave things and hope it will work out. Be prepared for all situations.

Organizational skills

Organizational skills are like a lifeline. Pack away stuff, clear desks, and make sure that you personally take tests from students. Organizing can save you a lot of time and trouble.

Planning goes a long way

Keep students busy. When they sit around they get bored and think of mischief. Plan extra activities that they can do. Something that will be a challenge to them. Some students finish quicker than others, give them extra assignments, perhaps let them read an article about math and set up a reward system for every 10 articles they read. This way they will be kept busy and won't bother each other.

What do graphs do for us in the business world?

Graphs sometimes do not always get the credit they deserve in the business world. Often, they are joked about as being silly visual aids. In reality, they provide great value. Graphics are typically used to better represent a set of results or patterns and help improve the presentation of a study. Serving as illustrative visuals they can improve cognitive reasoning and enhance the scope of how an evaluation has turned out. The concept of data visualization is a great tool that can help assess business performance. In the area of business management graphical analysis is essential in presenting crucial information and in taking appropriate remedial action. Reporting and tracking the market targets of companies is best managed by creating graphs and charts to visualize data and comprehend statistics.

You may ask how a mere diagram can achieve this goal, but you will be surprised by how powerful a visual pattern is in understanding financial reports that mere numbers and figures. Graphs logically represent information along several dimensions based on how one wishes to show the available statistics. The primary purpose of graphs is to show relationships among variables and this may include, in a business world, anything from profit and loss related information to sales and marketing figures. The common types of graphs are line and bar graphs, pie charts, scatter plots and bar diagrams. In general charts represent one type of information, for example, you may show the percentage of profits from various states in the country. Graphs on the other hand show one set of variables represented in a continuous flow against another variable entity, for instance, the annual sales numbers of the past 10 years or something similar. The increasing ease with which graphs can now be created as well as the scope of attractive visuals has created an impact in the business arena.

It is interesting to note that graphs can conceal or reveal information as is desired and will depend on the type of graph chosen and the level of detail structured. For instance, the pie chart might give a picture of relative quantities of each division, but if a precise numerical figure or percentage share is required it might be better to go in for a tabular format than a graph. Thus understanding the purpose of presenting the information is critical to selecting the right type of graphical display. Consider a simple line diagram to represent the pattern of goods sold over a period of time. A graph such as this very effectively reveals the pattern of sales, and can also be used to compare the values for several manufacturers.

So how does this help make the business better you wonder? It's a fairly straightforward approach really. If one were to view the individual sales values of a company over the years, assuming there has been a steady climb in sales, then one is likely to conclude that the company is marketing its products right. Now that is pretty basic. But a comparison of corresponding data from companies within the same industry may show a marked difference, which means your business is not doing as well as you anticipated! Although you may be able to infer this little piece of information by studying pages and pages of company reports, the ease with which a single graph can tell the whole story is undeniable. So now you know not only where your company stands but you will also be able to measure and set future targets for the next year.

The process of effective graphical construction begins with a simple analysis of the information available. Pattern detection comes in very handy to decide the right kind of visual that will best represent your data. Graph construction is an iterative process meaning that there is ample scope for trial and error to assess what works best. Given the popularity and flexibility of graphics and the importance of the patterns revealed by using images, graphs are key decision-making tools for any enterprise.