Tag: <span>mathematics</span>

09 Jan

20 Tips And Tricks To Teach Mathematics At The Primary Level
Posted in Education by anshbookstore on January 9, 2022 @ 8:36 pm

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

  1. Ambience plays a very significant role. It is your responsibility to see that a classroom is properly ventilated with ambient light.
  2. 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.
  3. Cultivate the students’ interest in Mathematics by letting them know about the power, structure and scope of the subject.
  4. Hold the students’ attentions from the get go! Introduce the topics with some fun facts, figures or interesting trivia
  5. Chalk out the lesson plan effectively keeping time and content allotment in mind
  6. Use audio and visual aids wherever possible
  7. Draw on the board if required (especially, lessons like geometry, shapes and symmetry)
  8. Call students to work on the blackboard (engagement of every child is necessary and not just a select few!)
  9. Ask for a student’s opinions and thoughts on concepts and mathematical ideas.
  10. Give them time to discuss important concepts and study the text of the chapter too before taking on the problems themselves.
  11. Teach more than one way or approach to solve a problem.
  12. 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.
  13. Reward them! Whenever students perform well, be generous and offer them an incentive to continue working harder.
  14. Let children enjoy Mathematics and not fear it.
  15. Instill in them the practice to do mental math.
  16. 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)
  17. Present challenging questions to students so as to develop their analytical and deduction abilities
  18. Keep taking regular tests to cement knowledge.
  19. Teach at a consistent pace. Do not rush with any topic. Before proceeding, be confident that the students are clear with the prior topics.
  20. Play games to create a fun filled classroom teach and learning experience.



Source by Paul Genee

10 Dec

Finding a Mall Parking Spot Using Mathematics – Part II
Posted in Education by anshbookstore on December 10, 2021 @ 8:25 pm

If you read the previous article on this topic, then I imagine you were quite piqued by the nature of its contents. How we use mathematics to find a mall parking spot is not a typical thing you would hear people discussing at their Christmas parties. Yet I think anyone with a modicum of human interest would find this a most curious topic of conversation. The reaction I usually get is one of “Wow. How do you do that?”, or “You can really use mathematics to find a parking spot?”

As I mentioned in the first article, I was never content to get my degrees in mathematics and then not do anything with them other than to leverage job opportunities. I wanted to know that this newly found power that I studied feverishly to obtain could actually inure to my personal benefit: that I would be able to be an effective problem solver, and not just for those highly technical problems but also for more mundane ones such as the case at hand. Consequently, I am constantly probing, thinking, and searching for ways of solving everyday problems, or using mathematics to help optimize or streamline an otherwise mundane task. This is exactly how I stumbled upon the solution to the Mall Parking Spot Problem.

Essentially the solution to this question arises from two complementary mathematical disciplines: Probability and Statistics. Generally, one refers to these branches of mathematics as complementary because they are closely related and one needs to study and understand probability theory before one can endeavor to tackle statistical theory. These two disciplines aid in the solution to this problem.

Now I am going to give you the method (with some reasoning–fear not, as I will not go into laborious mathematical theory) on how to go about finding a parking spot. Try this out and I am sure you will be amazed (Just remember to drop me a line about how cool this is). Okay, to the method. Understand that we are talking about finding a spot during peak hours when parking is hard to come by–obviously there would be no need for a method under different circumstances. This is especially true during the Christmas season (which actually is the time of the writing of this article–how apropos).

Ready to try this? Let’s go. Next time you go to the mall, pick an area to wait that permits you to see a total of at least twenty cars in front of you on either side. The reason for the number twenty will be explained later. Now take three hours (180 minutes) and divide it by the number of cars, which in this example is 180/20 or 9 minutes. Take a look at the clock and observe the time. Within a nine minute interval from the time you look at the clock–often quite sooner–one of those twenty or so spots will open up. Mathematics pretty much guarantees this. Whenever I test this out and especially when I demonstrate this to someone, I am always amused at the success of the method. While others are feverishly circling the lot, you sit there patiently watching. You pick your territory and just wait, knowing that within a few minutes the prize is won. How smug!

So what guarantees that you will get one of those spots in the allotted time. Here is where we start to use a little statistical theory. There is a well-known theory in Statistics called the Central Limit Theory. What this theory essentially says is that in the long run, many things in life can be predicted by a normal curve. This, you might remember, is the bell-shaped curve, with the two tails extending out in either direction. This is the most famous statistical curve. For those of you who are wondering, a statistical curve is a chart off of which we can read information. Such a chart allows us to make educated guesses or predictions about populations, in this case the population of parked cars at the local mall.

Charts like normal curve tell us where we stand in height, let us say, with respect to the rest of the country. If we are in the 90th percentile in regard to height, then we know that we are taller than 90% of the population. The Central Limit Theorem tells us that eventually all heights, all weights, all intelligence quotients of a population eventually smooth out to follow a normal curve pattern. Now what does “eventually” mean. This means that we need a certain size population of things for this theorem to be applicable. The number that works very well is twenty-five, but for our case at hand, twenty will generally be sufficient. If you can get twenty-five cars or more in front of you, the better the method works.

Once we have made some basic assumptions about the parked cars, statistics can be applied and we can start to make predictions about when parking spots might become available. We cannot predict which one of the twenty cars will leave first but we can predict that one of them will leave within a certain time period. This process is similar to the one used by a life insurance company when it is able to predict how many people of a certain age will die in the following year, but not which ones will die. To make such predictions, the company relies on so-called mortality tables, and these are based on probability and statistical theory. In our particular problem, we assume that within three hours all twenty of the cars will have turned over and be replaced by another twenty cars. To arrive at this conclusion, we have used some basic assumptions about two parameters of the Normal Distribution, the mean and standard deviation. For the purposes of this article I will not go into the details regarding these parameters; the main goal is to show that this method will work very nicely and can be tested next time out.

To sum up, pick your spot in front of at least twenty cars. Divide 180 minutes by the number of cars–in this case 20–to get 9 minutes (Note: for twenty-five cars, the time interval will be 7.2 minutes or 7 minutes and 12 seconds, if you really want to get precise). Once you have established your time interval, you can check your watch and be sure that a spot will become available in at most 9 minutes, or whatever interval you calculated depending on the number of cars you are working with; and that because of the nature of the Normal curve, a spot will often become available sooner than the maximum allotted time. Try this out and you will be amazed. At the very least you will score points with friends and family for your intuitive nature.



Source by Joe Pagano

10 Nov

What Skills Should a Teacher of Mathematics Teach His/Her Students?
Posted in Education by anshbookstore on November 10, 2021 @ 8:09 pm

Before the advent of universal secondary education, the mathematics teacher had a select group of students who were most likely, in terms of Gardner’s Multiple Intelligences, maths-logic thinkers. So there was no real need for the Mathematics teacher to change the pedagogue away from “chalk and talk” and lots of exercise practice.

But the second half of the twentieth century saw most students progress to secondary schools. Soon, most students were continuing on to complete their secondary education with most continuing to study Mathematics. This meant that these students had a variety of learning styles which we might equate to Gardner’s Multiple Intelligences.

This meant that teachers of Mathematics had to expand their pedagogue and teach new skills to help all students in their mathematical development. At this time, I was the head of a Mathematics Department in a large school going through the introduction of new syllabuses designed to bring Mathematics teaching into a position where it could cater for these different learning styles.

The syllabus content was being modernised. The use of computers, scientific and graphics calculator along with the Internet became mandated. This lead I to think about the additional skills my students needed to develop. Other teachers in other subject areas were most likely wanting to develop them, too.

The request from another school to have me explain how my department coped with a change from 40 minute to 70 minute periods began me thinking about these skills. I discussed my list and gained its acceptance at the workshop.

Below is a list of the additional skills I believe we, Mathematics teachers, should strive to develop as early as possible. (A short explanation may be included with each skill.)

They are:

  • Communication skills. One of the aspects of some new syllabuses is the introduction of problems in unfamiliar contexts which need the solutions to be fully communicated.
  • Calculator skills. The calculator enables the student to do necessary calculations quickly. Students need to be taught checking and estimation skills to facilitate their use correctly. Graphics calculators have in-built programs that allow more in depth real life problems.
  • Computer skills.
  • Internet skills.
  • Skills in how to concentrate effectively in class. This is important as there is less time allocated to the teaching of Mathematics than in the past. This should incorporate skills in how to be a powerful listener.
  • Textbook skills. This is the student’s first option in consolidation of the classroom learning. The student needs to know how best to use it.
  • Homework and study skills.
  • Examination skills including how to go about solving a problem and how to develop an examination technique that helps guarantee the best results.
  • Problem solving/critical thinking skills. And
  • In the senior school where life becomes extremely busy, organisational skills.

These skills cannot be developed overnight. There must be a commitment by all Mathematics teachers to introduce them from day one of the student’s secondary school life as the opportunity arises. Separate lessons on the skills are not the best options. Dropping different skill ideas into day to day lessons is a better option since the student will see it in an everyday event, not a contrived one.

What I have suggested here in many ways is a “Wish List”. If all the Mathematics teachers adopt the need for these skills, they will gradually, over the years, become a natural part of the student’s Mathematics persona.



Source by Richard D Boyce

11 Oct

What Pedagogue Should a Mathematics Teacher Used to Cater for Different Learning Styles?
Posted in Education by anshbookstore on October 11, 2021 @ 7:54 pm

Universal secondary education is the norm in most parts of the world with most students graduating from secondary school. Most students will continue to study Mathematics in some form right to the end of their secondary schooling.

This means that the teacher of Mathematics must have an expanded group of pedagogue to use in the classroom to cater for the different learning styles of the whole school population as suggested by Gardner’s Multiple Intelligences. This article will detail many types of pedagogue that can be successfully used in the Mathematics classroom.

Let me begin by saying that “Chalk and talk”/teacher lecture has its place within the teaching pedagogue along with doing practice exercises.

The important issue is to keep students engaged in their learning of Mathematics by making it life related wherever possible. The new syllabuses contain new topics that relate well to real life situations.

There are many strategies that a teacher may use to engage the students but they must fit the topic being taught.

Here are a few ideas:

  • Team teaching. Different teachers approach topics from different angles unconsciously thus giving students a wider view of the topic. Sometimes another teacher might have an expertise in the topic under investigation.
  • A guest speaker adds a real life dimension to the topic under discussion.
  • Computer lesson using software especially with Functions often lessens the time to create an understanding of the topic with students;
  • An internet lesson;
  • Library research especially on a new topic;
  • An excursion;
  • Hands on lessons;
  • Doing a survey as part of a statistics unit;
  • A film, video, or DVD lesson;
  • A Quiz is a great way to revise particularly if there is a competitive element to it.
  • Setting up a revision program to help teach students how to prepare for an examination.
  • A practice exam with a review.
  • Regular, short sharp fun problem solving exercises
  • Play on words to teach students to think “outside the box”.
  • Assessment that reflect the teaching pedagogue.

Incorporating different pedagogue in a lesson adds interest and keeps the students involved looking for the next episode in the lesson. There is little chance of the students or the teacher getting bored with the lesson or being distracted.



Source by Richard D Boyce

11 Sep

Mastering Mathematics – Absolute Value
Posted in Education by anshbookstore on September 11, 2021 @ 7:38 pm

Absolute value is an important concept in mathematics. The duality of absolute value makes this concept problematic and hard to grasp for students. Yet this need not be the case. When looking at absolute value for what it really is, that of the distance from a given point to 0 on a number line, we can put this abstraction into its proper perspective. Let us explore this topic in more detail so that it never presents a problem again.

The absolute value of a number is simply its distance to 0 on a number line. The symbol used for absolute value is the straight brackets “| |” with a number or variable placed inside. Thus |3| = 3 because 3 is 3 units from 0 on the number line. The duality of absolute value comes into play because the absolute value of both 3 and its additive inverse, or -3, are the same, namely 3. Both 3 and -3 are 3 units from 0 on the number line.

The only thing to remember with absolute value is that if a number is positive then the absolute value is equal to the given number; however, if the number is negative, then the absolute value is the negative or opposite of the number. This seems all too simple. So why does this concept present problems?

Well introduce a variable into the absolute value expression and all hell breaks out—literally. The reason is simple: a variable stands for some unknown number. The key word in the previous sentence is unknown. That is, we do not know whether the variable stands for a positive or negative number. Take the expression |x|. What does this equal? Well that all depends. Is x negative or positive?

If x is positive, then the expression |x| is simply equal to x; however, if x is negative, then the expression |x| is equal to -x because the “-” symbol in front of x makes this quantity positive. Remember two negatives become a positive. Read the preceding again because this is where all the “sticky-ness” comes into play. Most students will say erroneously that the |x| = x because they fail to consider the duality of absolute value. That is, when we do not know what is inside the absolute value symbol, we need to consider both cases; that is, when what is inside is positive, and when it is negative. If we do this, then absolute value will never be a problem again. To make this clear let x = 3. Then |x| = |3| = 3 = x; however, if x = -3, then |x| = |-3| = -(-3) = 3 = -x.

So do not cower when you see or hear absolute value. Just remember that all this means is the distance to 0 on a number line, and that one needs to consider both the positive and negative cases when dealing with a variable expression. If you do this, you will never shrink before such expressions. You can then add yet another feather to your mathematical cap.



Source by Joe Pagano

12 Aug

Teaching High School Mathematics in One Hour Time Slots
Posted in Education by anshbookstore on August 12, 2021 @ 7:24 pm

In the mid-1990s, the administration of the school in which I taught decided to change from using 40 minute teaching periods to 70 minute periods. It allowed the administration to gain extra teaching time from each teacher within the industrial award provisions. In fact, it allowed the administration to have English, Science and Mathematics teachers teach an extra class without having more time in the classroom.

My school became one of the first to do this and became an example for other schools to follow in the following years. As a result of this, I was asked to present a workshop to a nearby high school Mathematics Department explaining how my Mathematics Department had gone about adjusting to this major change.

Below is a synopsis of what I spoke about during this workshop.

For the teachers, personally:

  • It is hard work.
  • The class time must be regarded as “untouchable” and you must fight to prevent it being “borrowed” even by the administration.
  • Detailed planning is essential. It is easy for the teacher to waste/lose time without realising it is happening.
  • They need to develop a strategy to cope with absent students as even one period missed is a great chunk of their learning time.
  • Additionally, teachers need to develop a strategy for any absences they may have. In fact, teachers would be tempted to teach on even when they are not well so as to not lose valuable teaching time.
  • Their lessons must become a series of mini lessons to cover the course and to survive physically.
  • It is possible to teach a whole unit in one period.
  • They need to work smart. They must use every available tool or pedagogue to get the message across to the students.
  • Group planning by teachers will improve the quality of lessons presented to the students.

For the teachers and students:

  • There is a lack of continuity created by less teaching periods spread over the week. (In some schools, there was a two week rotation of periods.)
  • It is difficult to create a work ethic when you see the class less frequently.
  • Learnings skills must be taught more thoroughly because students must become more accountable for their learning, homework and study.
  • Learning to think mathematically must become a priority to help the students accept more accountability for their learning.
  • Mentoring becomes a useful tool to consolidate learning.
  • Learning the basic skills and procedures is paramount to gaining worthwhile success in their learning.
  • There is time to pursue problem solving in unfamiliar contexts provided the teacher’s planning covers the mandated learning.

Many of the ideas raised above had become part and parcel of Mathematics teaching since the late 1980s brought about by the introduction of new syllabuses in Mathematics that opened up the teaching of Mathematics moving away from the traditional “Chalk and Talk” Maths lesson to lessons using a variety of pedagogue.

Personally, I found teaching with 70 minute periods challenged me to use a greater degree of teaching pedagogue. Initially, I found I was rushing to cover the course. I did find that teaching had become more stimulating.

As head of Mathematics in my school, I did not see any significant change in the standard of the work produced by teachers and students. It just goes to show how adaptable teachers and students can be.



Source by Richard D Boyce

13 Jul

How Mathematics Helps You To Find The Best Porta Potty
Posted in Education by anshbookstore on July 13, 2021 @ 7:10 pm

The next time you get in line to use one of the portable restrooms at a fair, concert or any event, you might want to use mathematics to pick your potty. Yes, you heard it right, Maths.

The Secretary Problem, a Mathematical theory could be your best solution for this. But if you literally shit in your pants hearing the name of Maths, and no one’s blaming you there, you can always pick the best porta potty without an equation; just use Porties!

But for the sake of having some harmless fun, let’s go back to the toilet mathematics:

MATHS OF TOILET: A DEMONSTRATION

No need to panic the next time you have too much Pepsi to drink at a concert or festival and have to make a beeline to the portable toilets. According to a sequence of recent mathematical experiments, there is an ideal value that can be considered. For instance, consider a design model that consists of 3 different toilets. Let us label the toilet on the far left as Number1. Toilet 1 is amazingly clean, the very cleanest of the 3. The middle toilet is labeled Number 2 and is slightly dirtier than the first one. Toilet Number 3? A complete disaster zone. For obvious reasons, the toilets in real-time aren’t going to be limited to 3 nor will they be so pleasantly ordered. However, for this demo, we will stick with the 3 ordered toilets.

There are 6 different permutations; the different number of possible ways a group of toilets can be arranged in this model. This means that the probability of you hitting toilet number 1 gets worse as you keep adding more and more toilets. However, with just 3 toilets you have a 50% chance of picking toilet 1 if you follow the golden rule of rejecting the first toilet you check out and go for the portable potty that is, in your guess, the best so far. In all 6 probabilities, there is an average 50% chance of hitting the jackpot.

WHAT IF THERE ARE MORE TOILETS IN THIS CASE:

As mentioned before, adding more toilets decreases the odds of picking the most delightful toilet of all. If the demonstration given above had 4 toilets to choose from instead of 3, the percentage of success will drop to around 46 percent. With each new toilet thrown into the model your odds of succeeding drop by about 4%. The simulation illustrated works decently in limited toilet situations, obviously. However, many events offer far more toilets. In order to work on a bigger scale, another mathematical answer arises. Go through the text that is followed to learn the real trick (other than just using Porties) to find the best porta potty among a larger selection by using mathematics.

THE BEST SHOT

Mathematical theories suggest that you will have the best shot at finding the cleanest toilet by scoping out exactly 37% of the toilets out of the total number of toilets. After checking out at 37%, you can then follow the ‘best so far’ rule. After 37% of the restrooms have been tested, go for the very next toilet you find that seems better than all those you already tested. For example, if there are 100 toilets at a music concert, you must peek inside 37 of them to get past the tipping point. Only then your choice of whichever toilet after that appears better than all the restrooms you saw before, with a higher rate of a positive result in doing so.

There you have it now on how to use mathematics when trying to choose the best porta potty. No one can ever imagine in their wildest dreams that toilets and math had so much to do with each other. The next time you get into a hazardous toilet situation, test out this Secretary Problem mathematical theory. You might get surprised at how a little mathematics can help you go a long way when it comes to picking the most delightful toilet.



Source by Ana Waghray