Can We Can Improve the Learning of Mathematics?

There is, I think, sufficient data to indicate that, for both students and teachers, mathematics is the least popular subject in elementary schools, and this has been true since before I entered mathematics education over 40 years ago.

After a life time spent in mathematics education I have come to the conclusion that, despite the improvements in our understanding of how children learn, and new methods of teaching mathematics, students still leave school with a low level of numeracy. To be clear, numeracy is the ability to reason with numbers and other mathematical concepts, and includes number sense, operation sense, computation, measurement, geometry, probability and statistics. Numeracy also requires that students have an intuitive or emotional feel for mathematics that gives them confidence in predicting or calculating answers.

Many people would argue that there is no emotional aspect to mathematics, just obey the rules, get the right answer and move on. However most adults have a strong emotional response to anything related to school mathematics; unfortunately these responses are usually negative!

Intellectually students can deal with everyday calculations (after all, they are rarely without a calculator), but many lack the emotional understanding that gives confidence in predicting and calculating answers.

The problem does not lie directly with the teachers but more with the way we recruit and train potential teachers. We have a self perpetuating cycle; students don’t enjoy mathematics in school, graduate and go to university where they tend to avoid mathematics courses. They enroll in teacher education programs where they may or may not take a course on how to teach mathematics. Even if they do take a course on teaching methods for mathematics it lacks value if the participants have serious gaps in their knowledge and understanding of mathematical concepts. It is like a course on how to coach basketball if you have no knowledge of the game and the skills involved.

The student, totally unprepared to teach mathematics, now enters the teaching profession and the cycle continues.

The dilemma facing educational leaders, politicians, and society in general is figuring where and how to break the cycle.

One possible solution, which could address the problem fairly quickly, would be to have a series of courses addressing both mathematical understanding, and teaching methods for specific topics or strands of the curriculum. On successful completion of each course participants would be given a certificate to say they had been trained in that topic and were qualified to teach that topic. Over time teachers would become fully qualified to teach mathematics.

This, like most solutions to problems in education, would require financial commitment by governments, education authorities, faculties of education, and a time commitment from teachers.

At the same time the mathematics requirements for entry to teacher education programs could be made more stringent to ensure that students entering these programs will have greater mathematical understanding thus ensuring that methods courses in mathematics will be more relevant and useful.

Until we improve the entrance requirements and the qualifications of potential mathematics teachers, mathematics will be poorly taught, too many students will not achieve the numeracy skills necessary to function in today’s society, and the work done by teachers will not be given the respect it deserves.


College and the Mathematics Prodigy – What Career Should You Take?

There are many super up and coming math student in our time, for some reason, perhaps due to increased population, we are discovering more and more anomalies. And yet, we need so many more. It’s great to have the super-stars of humanity and these unbelievable mathematical prodigies, but we are going to need more to run our ever increasing complex and technologically advanced society.

If you are good at math, you should work to excel and see where it leads, as there are excellent jobs and careers available if you go for it. What sorts of jobs could you take? Well, many of the very most important jobs and career paths that our nation relies on include math. For instance; There is a whole lot of math that goes into a Missile Defense Shield system.

Oh speaking of math and careers, why don’t we also mention “Computer Science” as a potential academic choice, if this interests you maybe you should set your sites on a technology school – Virginia Tech, MIT, Cal Tech, Stanford, Carnegie Mellon, they have AI, VR, Robotics, Computer science degrees, perhaps with your name it. Don’t give up on math and science, we need you for America’s future.

If you are gifted in math, or love the subject we need you and you can enjoy a good career in the area of mathematics. Everything in the world we know is made up of math, without it, everything would fall apart. Why not be part of that master plan, and help us use this knowledge to write the next chapter in human evolution. Please consider this.


Remember the Simple Mathematics of Pay Per Click

Some have the PPC experience of a geriatric turtle whilst many are only just starting out with testing PPC campaigns, landing pages, ad-copy, and fine-tuning all of these factors as a means of maximising profit. With this in mind, one thing that never fails to amaze me is the frequency of which I speak to affiliates who have not thought through the raw figures of the campaign they are spending their hard-earned wonga on.

Let me give you an example.

I recently spoke to an affiliate who was using PPC to promote a videogame store on a sales campaign. The store paid out 5% commission and he had been told that the average order value was £26. So, it doesn’t take ‘Arnold Cleverbugger’ to calculate that every successful conversion will be worth, on average £1.30 in commission to him.

Now, videogames retailers have more competition than the Olympic Games, so there is a fair chance that conversion rates (unique visitors/number of sales) wil be no higher than, let’s be really generous, 3%. (TOP TIP: this is the conversion rate to PPC traffic, not other types of traffic that may have higher conversion rates and distort the figures.)

So, following our example, every 100 clicks purchased will yield £3.90 in affiliate commission.It follows then that the affiliate must be buying clicks for less than 3.9p per click to be showing an operating profit.

Can this be done? Possibly, but the affiliate I was speaking to had his maximum bids (all of them, as he hadn’t heard of keyword tracking/identification) set to 10p per click, paying on average 9p per click. So, for every 9p he spent, he would earn, on average, 3.9p.

Now that is a very quick way to fall out of love wth PPC, not to mention your bank manager who wants his pound of flesh and your new lady-friend who has her eye on those new Jimmy Choo footwarmers.

So, the moral is to look at the simple mathematics first and select campaigns from there. Then, with split-testing, accurate tracking, and ongoing optimisation, the rest will follow.

It really is all just very simple mathematics.


On Mathematical Proofs,Problems and Impossibility

Geometric constructions captivate one and all and is one of the areas of mathematics that is highly preferred by a high school student. Although easy to comprehend and fun to do, a few geometric constructions defy completion with a ruler and a compass. This article takes a look at the confusion in the mindset of many people regarding these ‘impossible’ constructions.
The following are the most famous of the impossible constructions with a ruler and a compass:
Trisecting an angle
Doubling the volume of a cube
Constructing a square equal to the area of a circle

A Proof:
What is a proof? For those of you who are wondering about that, here is the definition for a proof:
‘A proof is that which has convinced and now convinces the intelligent reader’ Who is an intelligent reader? In this context, those people who are known to be mathematicians by the society are the intelligent people.
Also a major requirement for a proof is that,a proof should be in complete harmony with another proven fact.

The ‘Impossibilty of a Problem’:
One often confuses the impossibility of a problem with an unsolved problem. A few problems are unsolved, that is, they have not been solved as of yet, whereas some other problems are insoluble,that is, they cannot be solved.The problem is proved to be impossible to solve. There is no question of anyone coming up with a construction for trisecting an angle because it has been proved mathematically that no one can trisect an angle.Whereas if someone were to claim that he/she (no discrimination) has found a proof of the Riemann’s hypothesis or the Goldbach Conjecture ( famous problems that have not yet been solved but have not been proved to be impossible either), mathematicians shall look into the claim. However for those of you who are itching for a claim to fame by solving one of the unsolved problems, let me remind you the path to success is not a bed of roses.


Easy and Fun Mathematics Or Why Can’t You Do Math in Your Head?

How many times have you been cheated simply because you did not had time to calculate the sum of what you bought? How many times have you trusted the seller but got cheated?

How many times have you suffered and felt shame just because you could never understand all the romance behind the numbers? If none, congratulations – you are a lucky person. If several or many times, welcome to the club! – you must know that there is a cure, actually more than one.

A traditional, but a difficult method – you could simply study all the mathematic books again. Does not sound lucrative? Not, I agree! That’s why I would like to share with you The Easy Way out of this problem. This is especially important nowadays when each cent counts.

Knowing these simple secrets you will be able to calculate faster in your head than most of us with a calculator. Wouldn’t that be exciting? Many people, just like you and, me have taught these important but extremely simple math secrets and they are shocked and keep asking themselves: “Why no one taught me this when I went to school? Why were I not given these amazing tools?” I like to compare it this way – you were taught to walk up the street backwards, now it’s time to walk forwards.

If you are going in school now – this is your shortcut to Fast Math calculations giving you an advantage over the others.If you are an adult – missing these simple secrets is the reason why you can be easily cheated.

The secret of Fast and Easy Mathematics was rediscovered after 3000 years !!! Todays methods taught at school are not simple, in fact they are blocking your potential not releasing it.

How simple is this multiplication 43 by 38? Do you need a calculator? Wrong – all you need is simple knowledge and you will be able to multiply these and other number faster that you could type them on your calculator. What about adding and subtracting fractions in seconds? All those tests what they give to pupils at school are just taking them further and further away from the simplest truth there is – mathematics is simple if you have the right tools.


Tips for Setting Up a Special Education Classroom

When dealing with special needs children, setting up the classroom may be one of the most important things you can do to make your year successful. Many special needs children regardless of their diagnosis have similar things they find difficult. Below are many ideas to help the teacher arrange and get the classroom ready for the year to begin.

1. Make a visual schedule for students to follow each day.

2. Put tennis balls on the bottom of the chairs to decrease the sound in the room.

3. Be very aware of sensory issues. If a child is overwhelmed by sensory stimuli in the classroom this is going to distract them making it impossible for them to concentrate.

4. Prompt students when they get off task. Sometimes this may be just walking over to the student and putting a hand on their back.

5. Use things like visual supports however make sure the visual supports aren’t so cluttered the child becomes overwhelmed by it.

6. Teach organization. This can be a notebook with all their information in one place.

7. Have open communication with parents so they can follow through and there is a consistent way of doing things.

8. Model appropriate behaviors.

9. Many children have problems with memory, help make flashcards so they can find what they are looking for and help them study.

10. Seek out and understand success as much as possible.

11. Break tasks into smaller tasks. Don’t give them a huge task or a list of assignments and expect them to follow through. They are much more successful when its broken down.

12. Go for quality rather than quantity with classwork and homework. Keep in mind, many children with special needs take medication and remember that the medications are wearing off by the end of the day. Before assigning homework is it really necessary?

13. Make consequences logical and reward often. Come up with a reward system so the children are getting positive reinforcement on a continuous basis.

14. Use privacy boards when there are things going on around the room.

15. Move student’s desk to where there are fewer distractions. Most of the time that will be beside the teacher, up front or beside a quite child.


4 Difficulties With Stay Put Placement in Special Education Due Process Hearings

Are you the parent of a child receiving special education services that is considering filing for a due process hearing? Have you already filed for a due process hearing due to a dispute with special education staff? Would you like to know what issues can arise with a stay put placement? This article will give you information on what difficulties may arise when you ask for a stay put placement.

Stay put is the last agreed upon placement between parents and school districts; the placement that the child is in when the parent files for a due process hearing.

Below are some difficulties that may arise when determining stay put!

Difficulty 1:  If a child is transitioning from preschool to Kindergarten or from middle school to high school stay put can be difficult to determine. If a child is transitioning from preschool what is stay put-preschool or kindergarten. Some hearing officers have ruled that in this situation the child would stay in preschool until the due process was finished.

Difficulty 2: If your child is currently in a private placement at public expense and will be changing districts from elementary and high school, a dispute on stay put may develop. This actually happened to a friend of mine, and the decision was that stay put is the child’s private school placement at public expense. The high school was angered that they had to pay for a private school placement that they disagreed with, until the due process was finished.

Difficulty 3: A difficulty would arise if a parent had a settlement agreement with their school district waiving stay put as the private school at public expense. Be extremely careful when signing settlement agreements to ensure that you are not giving up IDEA rights in the future!

Difficulty 4: A difficulty would arise if a school district wanted to change a child’s placement because they thought the child was dangerous. Case law has held that the school district cannot unilaterally change the placement of a child for behavior that is caused by their disability. The exception is if the child had drugs at school, a dangerous weapon at school, or caused serious bodily injury to another child or school district employee. The school district could then remove the child for 45 days to a Interim Alternative Educational Setting.

By understanding what the difficulties could be in a stay put placement will allow you to advocate for your child.


Why Participate in Kids Sports?

Sitting idle and looking dull is not a healthy sign for kids. When there are a lot of kid’s sports activities, it makes no sense to be idle. Taking a regular part in child’s sports not only keeps the youngsters fit, but also enriches their intelligence. In addition, participating in sport events also brings out the talent in youngsters and provides them with a lot of learning experiences, which remains useful for them throughout their entire lives. It helps them learn how to set a goal and act accordingly to achieve that goal. Therefore, child’s sports activities are the essence of the educational infrastructure in the modern age. Children who want to join extra-curricular activities can find the following discussion quite handy and interesting.

With the wide ranges of sport activities, you have a lot of things to do throughout the year. The first thing to do is to be placed in a similar age group and schedule routine practice hours for every day. This is the first step that makes them value the time they are spending. Then discuss the rules of the game that you are going to play. It is advisable to include initial training and free-hand exercise to warm them up.

After finishing with the rules and practices, they can be allotted into different teams who will compete with each other. It allows them to know their contributions to the team and help them to perform in a united way. The best contributors can be rewarded with trophies and mementos. This boosts up the confidence of the kids and helps them to perform their responsibilities to the team.

Playing softball is one such game that kids can participate in during nice weather. This game is enjoyed by all ages by both boys and girls. One of the more popular and effective games for youngsters is golf, which can improve their patience and attentiveness. In addition, soccer heads the list when it comes to kid’s sports. It needs a lot of practice and energy to play the game. Also, you need to be familiar with the various rules governing the game. Playing soccer tests your skills to a great extent. The team who crosses the nets of the opponent scores a goal. At the end of the game, the team with the highest score is declared as the winner.

If you are energetic and physically sturdy, then track and field is the best sport for you. This sport activity involves long jumps, gymnastics, pole vaulting etc. If you want to enjoy sports during the winter, then you can try snowboarding and skiing. This requires a lot of balancing acts and techniques. Once you grab these requisites, you may become an integral part of your adventure team. During winter, you cannot skip ice hockey practice. The knowledge of ice skating helps you to participate actively in ice hockey. Presently, ice hockey has become one of the popular games played during the winter.

With a lot more options behind, you need to pick the best sport that you will best suits you and gives you the most enjoyment. If you love the game and improve your performance, then in the future, you can choose this as a part of your professional career. Therefore, participating in child’s sports provides a lot of space for your physical and mental growth.

Speech and language

Home Based Speech and Language Services for Children

Has your child suffered from multiple ear infections? Do you have a feeling that your child’s speech is not developing as quickly as it should? Is your child’s speech not clear to you? Are his/her words flip flopped?

Maybe it is time that your child not matter what his/her age is be seen by a home based speech and language therapist. Having an evaluation is such good piece of mind. Children’s Hospital has a great evaluation department or you can request that your child be evaluated at home. Getting on the internet and looking up No Child Left Behind programs, Easter Seals, and Head Start programs in your area are great resources. There are private speech and language therapist’s like myself that have all of the testing materials for evaluations and home based speech services.

Being at home for speech therapy is very rewarding to the therapist, child, and caregiver. The caregiver is able to see how therapy can be done in the home. The speech therapist provides great ideas for using the “home” as everyday therapy. There are so many ideas in the home that aid in therapy: siblings, parents, all of the rooms in the house even outside, all the child’s toys and books. Even therapy is conducted at the park down the street from you.

So if you are thinking of home based therapy for your child no matter what his/her age from toddlers to teens. Try home based speech therapy.

Speech and language

What is Speech and Language Therapy?

A Speech and Language Therapist (SALT) is qualified to work with children, young people and adults who have some form of communication disorder. It is often thought that a Speech and Language Therapist is only able to help with actual speech production problems, but in fact the range of services is much wider.

What does a Speech and Language Therapist do?

A therapist working with children and young people will initially assess both comprehension (understanding of language) and expressive language (how language is used).


The Therapist will look at various areas where difficulties might occur including:

* Vocabulary – types of words such as nouns (naming words), verbs (actions) and prepositions (in, on, under etc.)

* Understanding language structures such as following instructions – eg. “brush dolly’s hair”, “give me the yellow pencil”

Expressive Language

Spoken language may be assessed for the following:

* Speech sounds – often termed phonology. The child or young person may not have certain speech sounds in their vocabulary, or may use them inappropriately eg. “dog” becomes “dod” (termed fronting) or “glove” becomes “glub” (termed stopping)

* Articulation difficulties – the production of speech sounds may be difficult, possibly due to a physical problem such as cleft lip/palate or poor dentition or even a co-orindation problem – Dyspraxia

* Fluency – is there any evidence of dysfluency (stammering) or general hesitancy in speech

What can be done if the child/young person has little or no speech?

Language is not only the spoken word but can include communicating by various alternative methods. Some of the more common ways are:

* Symbol systems – a simple line drawing is used to represent an object or concept eg. Makaton, Rebus, Mayer Johnson

* Pictures/photo systems – actual pictures or photos are used to indicate objects, activities etc.

* Signing systems – include British Sign Language (BSL) and Makaton. These systems use manual signs to convey meaning

* Eye pointing – by using a special board with symbols or pictures, it is possible for a parent or carer to interpret what the child/young person wants to communicate by following their eye gaze until it stops at the item they want. This can be useful for children or young people who have physical difficulties and no speech.

* Communication aids – these can range from simple picture boards to complex computers with voice synthesizers

What other aspects of communication are assessed?

Other areas which Speech and Language Therapists might look at and which underpin communication are:

Listening and attention skills/concentration – can the child or young person attend to a task? Not to be confused with a hearing impairment – the child or young person may hear what is said but cannot concentrate sufficiently to process the information

Play and imagination – can the child play alone, alongside others (parallel play) or take part in group play? Is imaginative play present ? eg. putting doll to bed, pretend tea parties

Social communication – can the child or young person interact with others? Do they understand the rules of conversation, such as turn taking, repairing conversations, keeping on topic and appropriate greetings?

Functional use of language – can the child/young person use whatever system of communication is appropriate to them to make choices, comment on events, question or refuse?

Behaviour – an inability to communicate can be very frustrating for the child/young person and may result in agitated or challenging behaviour patterns.

How does the Speech and Language Therapist carry out the assessment?

The Speech and Language Therapist will look at all areas in which the child/young person is experiencing difficulty.

* This may include observation or direct working with them in various settings, such as the home, school or college.

* Liaison with people who come into frequent contact with the child/young person is also very important. As well as parents, teachers, carers, other health professionals etc. may be consulted.