Are you a math teacher? Are you a parent of a child or teen who is taking a mathematics course? If yes to either question, then I’m sure you’ve seen students struggle with word problems. It’s so frustrating to watch and we want so badly to help them.

A perennial complaint of mathematics teachers is that students are unable to cope with word problems. This inability to deal with such problems often becomes a major stumbling block to success in mathematics courses (Nolan 1984). National trends in mathematics problem-solving, as measured by the 1986 National Assessment of Educational Progress, indicate that students, even 17-year-olds, have difficulty solving word problems (Dossey et al. 1988).

When asked, many students who have trouble with word problems say that

a) they cannot decide what is important in the problem and what is not,

b) they cannot determine which information in the problem will help them and which information is just put in there as a distractor, and/or

c) they cannot figure out how to compute the solution once they have figured out what the problem is.

As Kresse (1984, 598) cited: “Research using “students not solving (word) problems correctly” indicated 95% of the sixth graders tested could read all the words correctly, 98% knew the situation the problem was discussing, 92% knew what the problems was asking you to find, yet only 36% knew how to work the problem (Knifong and Holtron, 1977).”

There are many reasons why students have this difficulty, including semantic, syntactic, contextual, and structural characteristics (Silver and Thompson 1984). One possible approach to overcoming some of these difficulties is to “rewrite” the problems so that the question appears first, instead of last.

Teachers of reading often ask questions of students before having them read–so that the students will know what to look for, and thereby have better comprehension. It makes sense that this same strategy will also enhance mathematics students’ comprehension of word problems. Teachers in the mathematics classroom are not expected to be reading teachers, but it behooves us to draw on strategies that have been found beneficial by reading teachers in our quest to enable students to solve word problems correctly–and without the dread so many of them feel.

So…it is worth a try the next time you observe a young person who is mixed up about what to do next when confronted with a word problem in his/her mathematics classroom. Encourage the student to jump to the question first, then come back to the beginning of the problem and use that knowledge to determine what to do.

You’ll observe success – and will feel your own relief – and theirs!

**References**

Dossey, John A.; Mullis, Ina V. S.; Lindquist, Mary M.; & Chambers, Donald L. The mathematics report card: Are we measuring up? Trends and achievement based on the 1986 National Assessment. Princeton, N.J.: Educational Testing Service, 1988.

Kresse, Elaine Campbell. “Using Reading As a Thinking Process to Solve Math Story Problems,” Journal of Reading 27, (1984): 598-601.

Nolan, James F. “Reading in the Content Area of Mathematics.” In M. DuPuis (Ed.), Reading in the Content Areas: Research for Teachers (pp. 28-41). Newark, DE: International Reading Association, 1984.

Silver, Edward A. & Thompson, Alba G. “Research Perspectives on Problem Solving in Elementary School Mathematics.” The Elementary School Journal 84, (May 1984): 529-545.

Stiff, Leo V. “Understanding Word Problems.” Mathematics Teacher 79, (March 1986): 163-165, 215.

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Many students consider mathematics to be a difficult and scary subject. Difficulties can be overcome when you replace your fear with curiosity. If you give proper attention to this subject you will surely begin to like it. Math becomes very easy once you stop hating it.

But why should you take the pains to study it? What is the importance of math in real life? In fact, its scope is far beyond daily calculations and planning your monthly expenditure. It is said that all biology is ultimately chemistry; all chemistry is ultimately physics and all physics is ultimately mathematics. Today economics is one of the most popular subjects. Every curriculum pertaining to economics also has math as its integral part. At an advanced level its applications are incredible. For instance, the Nash Equilibrium (in Economics/Statistics) can be used to predict stock market trends and even in resolving war between countries. Learning math improves your mental skills. If you are good at math you will be able to solve day to day problems easily. This is because your thinking becomes logical when you properly study it.

Very few students have an aptitude for this subject. Nevertheless, everyone has the basic capabilities that are needed to study the subject at the school level.

Yet all the theorems, axioms and formulae sound like double-dutch to most of us. This problem could be because of two things. First of all, your knowledge of the subject’s basics is not sound. Secondly, it could be because of your faulty approach to the subject.

Dealing with the first problem is more difficult. You will not be able to understand anything about Conditional Probability if your concepts of Permutations and Combinations are not clear. You will have to do extra work to make up for it. Speak to your teacher about any such problem and seek their guidance. You can always take the help of your friends. If possible, try to consult books from the previous term. You should deal with this problem as soon as possible. The longer it persists the harder it gets.

As far as your approach is concerned, you should never attempt to learn math. The only way to learn mathematics is by understanding it. Try to make it a pleasant experience. Reward yourself with, say, a candy every time you make even a small success. Practice it as often as you can. Our brain learns new things by observing and repeating. There is no alternative to persistent practice.

It will become a lot easier if you try to understand it in practical terms, as opposed to theory. For instance, let us speak in terms in LPP (Linear Programming Problems.) There you have to express practical situations, such as rate of production of a certain machine, as a mathematical expression. A proper understanding of both practical and algebraic form of the problem is required in such cases.

Math is easy if you let it be so. You should try to like it and you will. Otherwise you will be stuck with it regardless.

Remember that if you do well in mathematics, you will have many exiting and promising career opportunities. People with goods mathematical skills are always wanted in computer related fields. Even animation can’t be done without programing that involves a high level mathematics.

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What is really happening today is that tests do not reflect the students’ abilities. This has disastrous consequences. When unqualified students go to do a mathematics degree and eventually become mathematics teachers or researchers they lead to the decline of future generations in mathematics.

What is happening in schools today is that administrators are applying pressure on teachers and the teachers pass this pressure on to the students. The teachers teach the students only to prepare them for the test. The point is not to make the students understand the concepts. After all this pressure exerted on the teacher he only cares that the students score high on the test. One of the main issues that face the teachers when they do that is that parts of the syllabus are skipped on the test and thus left out untaught by the teacher. However, though these parts that are skipped do not come in the exam they are important for understanding the other parts of the syllabus. This is enough to cripple the students’ understanding of the material. The teachers teach the students some tricks and mechanical drills that allow them to automatically solve exams without understanding.

Tests will be driving standards and curricula in the near future. This is why special attention should be given in how to design tests. In other words, there should be precise definitions of the concrete objectives of the subject and how to quantify the measure of success.

This problem has two sides. One side is the tests and this side is the dominant side due to pressures on schools to have good scores. The second side is the teachers. To drive the teachers to really get the students to understand rather than do mechanical work the exams should be designed to filter the students’ capabilities.

The test should be composed of several sections that cover all the different parts of the syllabus. Each section should contain questions that reflect the students’ abilities in using the different techniques taught. The student should know which technique suitable for which problem. The section should contain problems that examine the students’ abilities in using mathematics in solving real life problems. After all how good is mathematics if one does not know how to apply it to real life.

Part of the exam should be a project on an application of mathematics in real life. The student should use his earned mathematics skills to solve some real life problem in a project. The project should have two supervisors, one supervisor from the student’s school and one supervisor from another school. The students should be exposed to the many innovative software calculators that they can use to complete their projects.

When exams reflect the true abilities of students mathematics teachers would not concentrate on how to beat the system and would concentrate on developing the students’ abilities in the subject.

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The primary Math education is a key determinant and I must say the very foundation of the computational and analytical abilities a student requires for a strong secondary education. It is the very base on which secondary education is built on. This is why it is mandatory that the teaching techniques and methods we employ as teachers and educators be of such rich quality that the development of a child with respect to his mathematical abilities be wholesome, practical and balanced.

Being a Math teacher is not easy. It is usually the favourite of a few and the nemesis of many. It has been observed that children mostly try to escape doing Math work. While there is a section of students who absolutely love mathematics enough to pursue a career in it, many students live in fear of it. Today we are going to give our teachers some helpful tips and tricks to make teaching math an enjoyable and interesting experience not only for the kids.

**20 Tips and Tricks to Teach Mathematics at the Primary Level**

- Ambience plays a very significant role. It is your responsibility to see that a classroom is properly ventilated with ambient light.
- Ensure that Mathematics class is neither before lunch break (when children concentrate more on the Tiffin than studies) nor the last period where students wait more for the bell to ring (not to mention start feeling sleepy!) Keep Math class when the children are active and fresh.
- Cultivate the students’ interest in Mathematics by letting them know about the power, structure and scope of the subject.
- Hold the students’ attentions from the get go! Introduce the topics with some fun facts, figures or interesting trivia
- Chalk out the lesson plan effectively keeping time and content allotment in mind
- Use audio and visual aids wherever possible
- Draw on the board if required (especially, lessons like geometry, shapes and symmetry)
- Call students to work on the blackboard (engagement of every child is necessary and not just a select few!)
- Ask for a student’s opinions and thoughts on concepts and mathematical ideas.
- Give them time to discuss important concepts and study the text of the chapter too before taking on the problems themselves.
- Teach more than one way or approach to solve a problem.
- Give regular homework exercises making sure that the questions are a mixed batch of easy, medium and difficult) Children should not feel hopeless. Easy problem questions evoke interest.
- Reward them! Whenever students perform well, be generous and offer them an incentive to continue working harder.
- Let children enjoy Mathematics and not fear it.
- Instill in them the practice to do mental math.
- Also, never give a lot of homework. Children are already burdened with assignments to work at home in almost all school subjects, it is thus your duty to make sure that the homework you delegate to them is fair sized or little. (This trick will inculcate in them the motivation to complete math homework first)
- Present challenging questions to students so as to develop their analytical and deduction abilities
- Keep taking regular tests to cement knowledge.
- Teach at a consistent pace. Do not rush with any topic. Before proceeding, be confident that the students are clear with the prior topics.
- Play games to create a fun filled classroom teach and learning experience.

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There is no need to go very far to find cases of successful applications with mathematical models of use in mining, which produce enormous savings to the industry, not only applicable in planning mining, but in extraction and processing of minerals. Generally, when we refer to the use of applied mathematics in industry, we imply the use of numerical analysis techniques to implement proven mathematical theory.

Very widely used and of great value is the use of optimization problems for which the solution is characterized by the largest or smallest value of a numerical function depending on several parameters. Such a function is often called the objective or goal function. Many kinds of problems can be expressed in optimization, i.e, finding the maximum or the minimum of a goal function. In mining it is frequently used to determine allocation of laborers to work areas and also to calculate optimum load extraction based on expected total output production volume and ore grade requirements.

Many other prototypical solutions involve theory based on non-linear analysis, numerical integration, function evaluation, complex numbers, boundary value solutions, eigenvalue solutions, and differential equations. A few cases to mention: Underground mining operations requiring construction of platforms to carry assorted equipment with specific dimensions; Exploratory drilling tasks for obtaining sample core bits in a formation where several methods of combined drilling are used in somewhat complex geological sections and finding stress concentrations around holes; Use of the fourth-order Runge-Kutta integration methods to resolve polluted reservoirs exacerbated by large-scale earth disturbances and acid drainage and find acceptable levels of concentration of the pollutants as fresh water would replenish the reservoir; Applications in underground mining for tubing diameter variations due to diametric contractions regarding site temperatures; Applications in Cut-and-Fill stoping mining methods problems using rock mechanics techniques including finite element, finite difference and boundary integral methods.

Many mathematical functions used in numerical computation are defined by an integral, a recurrence formula, or a series expansion. While such definitions can be useful to a mathematician, they are quite complicated to implement in a computer. For one, not every mining engineer knows how to evaluate an integral numerically (most do), and then there is the problem of accuracy, and the evaluation of a function as defined mathematically involves complexity. Plus programming expertise is paramount to produce application module solutions that are accurate, useful and timely.

This being the case, the mathematical representation via numerical modeling represents a major challenge. The importance of applied mathematics in the mineral industry is so significant that future generations of mining engineers need to be very knowledgeable in numerical analysis procedures, possess solid command of high level programming languages and feel comfortable with mathematics reasoning in general.

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