Math Archives

Why Spelling is (Still) Important

June 10, 2014 Brad Hoffman

Spelling is a basic skill that has become neglected, but here is why spelling is still important, perhaps more than ever!

In recent years, electronic devices have become equipped with powerful spell check systems that automatically correct our spelling mistakes. In addition, we often use Google as our dictionary. Many highly-educated, successful, intelligent people have this trouble. Some say spelling stifles creativity by blocking the writer’s flow of ideas, while others argue that there is a stigma against people who do it poorly. Unfortunately, a bad speller can easily be mistaken for a bad student.

It is not merely stigma though, for young students, spelling may be the key to becoming successful readers and writers.

Spelling Improves Writing

Some students find spelling to be incredibly easy, noticing immediately when something does not look right. For others, words are unpredictable and confusing. The English language can seem daunting and filled with strange rules and inconsistencies. Students who struggle with spelling often feel insecure about writing anything. They may say “I hate writing” or “I have no good ideas.”

Often, these same students are creative thinkers who express themselves well verbally. What holds so many students back is the fear of not being able to spell. For these students an explicit reading program like Preventing Academic Failure (PAF) is vital. Through programs like these, students learn the English language’s rules and patterns and begin to read and spell words with ease.

Spelling Improves Reading

Spelling and reading are inextricably linked: learning how to spell is learning to read. Learning the way spelling works helps with decoding, which improves overall comprehension. The more a student understands these building blocks of language, the more fluent their reading becomes.

A Place for Inventive Spelling

Inventive spelling is the process of making words phonetically, which leads to unconventional examples of writing the same words. While exact instruction is helpful for students in first grade and above, inventive spelling does have its place.

Students in Pre-K or Kindergarten who are just learning how to form letters and words should be taught inventive spelling to learn sound and symbol correspondence.

They should practice pulling sounds in words apart and blending them together. Only as students gain experience writing, should they begin to learn spelling rules. Even as students advance through the upper grades, students should always have a place to journal without worrying about spelling. Even adults misspell words and there is always value in learning to proofread, edit and rewrite.

By Joanna Brown, Reading Specialist

What is the Reggio Emilia Philosophy?

May 16, 2014 Brad Hoffman

The Reggio Approach derives its name from its place of origin, the town of Reggio Emilia, located in northern Italy. Following World War II, Louis Malaguzzi, a teacher, along with a small group of parents, became interested in building a new school in Reggio Emilia where education would be viewed as a communal activity and sharing of culture would take place through joint exploration between children and adults. Malaguzzi’s approach focused on young children’s development in a setting where they would be encouraged to explore their environment and express themselves through multiple forms (movement, words, arts, dramatic play and music).

In the last several years, what is now known as the Reggio Approach, has become a popular model in the United States, particularly in early childhood education. Traditionally many preschools have employed pre-planned and theme-based curricula where the teachers choose the topics to teach and select activities to accompany them. In this model, the teacher presents only activities deemed age appropriate and plans monthly or weekly themes and lesson plans for an entire year before it even begins. The selection of themes is often based on the assumption that all children will benefit and be interested in the chosen subject. This traditional model lumps children into projects based on age rather than interests, capabilities and learning styles.

In contrast, a cornerstone of the Reggio philosophy is emergent curriculum. Emergent curriculum responds to children’s immediate interests rather than focusing on a narrow or calendar driven topic. As the name suggests, the study of a topic emerges from the interests and ideas of the children. The topics explored are gleaned from children’s discussions as well as interests demonstrated throughout different areas of the classroom. Once the topics of interest are identified, teachers act as co-collaborators, helping the children make decisions about the direction of inquiry and launch into in-depth studies of the concepts, ideas and interests that arise. The resulting investigations have no time limit and can span from several weeks to the whole school year.

The environment serves as a third teacher in the Reggio philosophy. The approach advocates that teachers play close attention to the myriad of ways that space can invite interaction. Small touches such as storing colorful objects in transparent containers can pique children’s curiosity and imagination. The design and use of space in a classroom encourages encounters, communication and relationships. Every corner of every space has an identity and purpose, rich in potential to engage. Spaces are valued and cared for by the children and teachers.

In the classroom, children should have the opportunity to explore and use many materials to discover and to communicate what they know, understand, wonder about, question, feel and imagine. In my classroom, there are an abundant variety of quality materials available to the children, beautifully organized and maintained by the adults and children together. In order to encourage young children to investigate their environments to the fullest, tools are placed carefully within the reach of the child so he or she explore, investigate, question and create. Through their ongoing explorations, children are then able to learn the qualities, possibilities and limitations of each material.

Written by: Editorial Team, My Learning Springboard, Inc.

Overcoming Your Fear of Math

April 29, 2014 Brad Hoffman

Math is everywhere. From the buildings, streets, and parks you see around you that were built using math; to the cars and trains you ride in that are run using complicated equations; to the decisions at the grocery store and in restaurants that we make on a daily basis, math surrounds us. Why is it such a scary subject in schools? Why do so many students have a fear of math?

When I was in high school, I was a part of the Math Team…yes, I was that girl. But, really, I was also terrified of it! Joining this team was my way of overcoming that fear of math.

Why do so many students have a fear of math?

In a Washington Post blogpost entitled, “Why is math so hard for so many?,” Valerie Strauss summarizes a few plausible explanations. In trying to answer this questions, she refers to cognitive scientist Daniel Willingham, who in turn refers to work done by David Geary, also a cognitive psychologist at the University of Missouri. In Dr. Geary’s work, the issues of learning it may be:

a) a problem with approximating quantities
b) problems associating mathematical symbols
or
c) problems with understanding logical relationships between numbers.

Dr. Willingham further suggests that mathematical ability may not be a “natural” human activity, suggesting that it became a human necessity faster than the population could acquire the ability through evolution.

So if math is not “natural” why do we teach it?

In our current and evolving world, mathematical skills are essential to many job opportunities that garner what is considered a good salary. Higher-paying jobs such as lawyers, doctors, engineers, and financiers require a strong foundation of math, demonstrated by college grades and admission exams that test this special ability.

But there are good jobs that don’t require math skills…

Those who work in the humanities and arts, as well as countless other jobs don’t typically require terrific grades (though kudos if you have them!) as they may rely upon other cognitive abilities such as creativity, verbal articulation, and visuo-spatial reasoning.

So why–again–should we learn math?

Math, like science, is not so much about the answers as it is about the process. It requires students to understand that there is a set of rules that governs a set of tasks. It helps you to understand that if you want to alter a system, you need to learn its structure and organization well in order to find the “loop-hole” exception. You can either be an appreciator of that structure or you can be the renegade who tries to prove its flaws. Math helps you see that the intricate and technical details matter in determining the outcome even if you understand “the big picture”. It can help you design the object you have always dreamed about or help predict the future in terms of risks, benefits, or likelihoods.

Even human behavior has mathematical implications: John Nash Jr., a mathematician and winner of the Nobel Prize in Economics in 1994, developed game theory: a type of math that provides a mathematical framework to understand human behavior in a particular situation.

How do I succeed in math when I find it so challenging?

As with anything in life that is challenging, one has to confront their fears. While I don’t expect all students to go out and join the math club, I do hope that students can find an appreciation for the art and science of math. Tutoring and mindful teaching can help every student succeed in mathematics.

By Dr. Kathy Aligene, Private Tutor

Thinking about Math Differently

April 14, 2014 Brad Hoffman

$math tutoring$ There’s something about being naturally good at math that makes people believe you’re exceptionally intelligent. There’s a mystique about math; the idea that only a few gifted people are able to do it. Conversely, I’ve lost count of the number of parents who have warned me that they have no ‘math brain’ and that their son or daughter has inherited this lack of ability.

The truth is that there is no such thing as a ‘math brain’. We’ve all got the same human brain, the same raw material. The difference between those who ‘can’ and those who ‘can’t’ is nothing more than how we use the brain: do we use it in the way that the brain finds easy, or in a way that it finds difficult?

Math is a language, and like any language, it’s only easy if you understand what it means. But most people don’t actually learn to make sense of what the math symbols are actually saying. Rather, they try to learn a set of rules in order to determine what to do. Their experience with math becomes a mundane litany of “do this, do this, do this, then do this”–of course this kind of learning is tedious, boring, and utterly forgettable. By contrast, the minority of people who appreciate what the math-symbols actually mean find that they learn how to solve math problems simply because it makes sense. And things which make sense seem obvious and easy to learn.

One of my favorite examples of this concept is in learning how to add fractions. How do you calculate the sum ⅝ + ⅔? Most of the students I meet have learned a series of steps to determine the answer, which goes something like this: “multiply the denominators–8 and 3, making 24; then multiply the bottom number of one fraction with the top number of the other fraction–8 with 2, making 16, and 5 with 3 making 15; we now have the sum 16∕₂₄+ 15∕₂₄and now we have add together the two numbers on the top–16 + 15, making 31; but not add the two numbers on the bottom (!) and so we end up with an answer of 31∕₂₄… which can then be turned into a mixed fraction, but that’s a different problem we don’t need to worry about here.” The student who is taught this way then finds themselves trying to memorize these very abstract steps. No wonder they get confused.

Guess what: most students can’t remember what to do, and that’s no fault of theirs. Our brains are not designed to deal with this kind of abstract nonsense. As a result, pupils are made to practice endless examples until the problem becomes an automatic robotic program. Even if it doesn’t make complete sense to them, students will answer correctly, by pure rote memorization. They haven’t really been educated in any meaningful way, but everyone’s happy because they get the right answer, which is all the system cares about.

Now compare that complicated, abstract approach, to adding fractions with the following explanation of the same problem: ⅝ + ⅔. The first thing to do is read it properly. It says “5 eighths plus 2 thirds.” This is like saying 5 cushions plus 2 windows: you’re being asked to add two completely different types of things together, which you can’t do. You can only add things of exactly the same type together: windows go with windows, cushions go with cushions. So the problem we have is that we are trying to add different types of things together. What’s the solution to this? Make them the same. We have to turn eighths and thirds in something that they have in common, and that would be twenty-fourths.

However, by the time the student is learning how to add fractions, they will already have learned about equivalent fractions: they will have already learned that ⅝ is the same as 15∕₂₄, and that ⅔ is the same as 16∕₂₄. So we realize that the original sum ⅝ + ⅔ is identical to the sum 15∕₂₄+ 16∕₂₄. We now no longer have the problem of trying to add different types of number (eighths and thirds); we now have the same type of number (twenty-fourths). So we’re asking: “what is 15 twenty-fourths plus 16 twenty-fourths?” which is like asking: “15 doors plus 16 doors is 31 doors”. Thus our sum has a total of 31 twenty-fourths, or 31∕₂₄.

We will end up with the same answer whichever route we take. However, one of these approaches connects the dots, explains why each step makes sense and makes use of previously learned knowledge.

Math is a lot easier than it looks and is easier than a lot of people would expect. Math is a language. If you learn to speak the language in a way that is meaningful and makes sense then it will be meaningful and will make sense. If you never learn to speak the language, then it will always seem foreign and difficult. When you or your child think that you don’t have any talent for math, you need to know that this just means you haven’t yet learned how to read math in such a way that it make sense. Math is not just a language: it is the most reliable, logical and sensible system that exists. All you need is to find the person, friend, teacher, tutor who can talk about it not as a robotic system of rules, but as a living, breathing, human, meaningful piece of common sense.

By Nick Thomas, Private Tutor

Happy Poetry Month: All About the Fibonacci Poem

April 7, 2014 Brad Hoffman

April is National Poetry Month! One of our favorite forms of poetry is the “Fib” Poem, which integrates poetry and math using the Fibonacci sequence. This mathematical sequence follows the following integer pattern:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, …

By definition, the first two numbers in the Fibonacci sequence are 1 and 1, or 0 and 1, depending on the chosen starting point of the sequence. The next number in the sequence represents the sum of the previous two numbers. What we know as the Fibonacci sequence was founded by Leonardo Pisano (known as Fibonacci) in 1202. Leonardo Pisano theorized the growth of a rabbit population to discover the sequence in his book Liber Abaci.

How fast could rabbits breed in ideal circumstances, he wondered. Suppose a newly-born pair of rabbits, one male, one female, are put in a field. Rabbits are able to mate at the age of one month, so that at the end of its second month, a female can produce another pair of rabbits. Suppose that our rabbits never die and that the female always produces one new pair (one male, one female) every month from the second month on. The puzzle that Fibonacci posed was: how many pairs will there be in one year?

At the end of the first month, they mate, but there is still only 1 pair.
At the end of the second month the female produces a new pair, so now there are 2 pairs of rabbits.
At the end of the third month, the original female produces a second pair, making 3 pairs in all.
At the end of the fourth month, the original female has produced yet another new pair, the female born two months ago produced her first pair also, making 5 pairs (from Plus Magazine)

This is how we get the sequence of Fibonacci numbers: if we continue to add to the quantity of rabbit population, after twelve months, there will be two hundred and thirty three rabbits.

Fib poetry is similar to the haiku, the famous Japanese poetry form, because both forms of poetry have strict rules for the amount of syllables that are used in each line of the poem. In haiku, the first line of the poem must be 5 syllables, then the second line must be 7 syllables, and the third and last line must be 5 syllables again. Haiku also typically describes something beautiful in nature. Here is an example of haiku:

The wren
Earns his living
Noiselessly.
– Issa

In fib poetry, the number of syllables per line are based on each number in the Fibonacci sequence. Most fib poems are made up of six lines with twenty syllables that correspond to the first six numbers in the Fibonacci sequence. Here is an example of a fib poem:

One
Small,
Precise,
Poetic,
Spiraling mixture:
Math plus poetry yields the Fib.

Gregory K. Pincus, “Fibonacci Poems Multiply on the Web After Blog’s Invitation”

Can you try to write a Fibonacci poem?