Learning Math the Natural Way

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"Memory Tips for Math" by D. YatesLet’s be honest. Not every child is a natural mathematician. Encouragement and praise is great, but the help it provides can never substitute for real, hands-on, practical help that makes the mathematics learning experience effective. Many children try their best, yet their efforts leave them caught in a constant struggle to grasp the mathematical concepts. Their frustration is evident as they become tongue-tied with the heavy math jargon. How can a parent or teacher reach those children who are not natural logical or mathematical learners? How does one bring the best out of the kids who don’t naturally thrive on numbers and logic problems? In her book, “Memory Tips for Math, Memorization and Learning Styles: The Successful Way to Teach K-5 Math” Donnalyn Yates proposes a practical and creative solution that will take a lot of the “ouch” out of math class.

“Memory Tips for Math, Memorization and Learning Styles” recognizes that the three most common perceptual learning styles are visual, auditory and tactile/kinesthetic. Learning activities in the book focus on providing these categories of learners with stimulation that leads to effective learning. Acronyms, pictures, rhymes, and stories help students to develop vocabulary and retain mathematical procedures. For example, think about how you learned the relationship between the gallon, quart, pint and cup. Now imagine if you had discovered this relationship through a story of fantasy. Imagine the Kingdom of Gallon in which lived three queens of the family of Quart. Each Queen Quart lived in a castle with a young prince and princess – they’re the Pints. Prince and Princess Pint don’t have children but each of the Pints has 2 cats – the cats are the Cups. Imagine how much fun you might have had in Math class if you learned using the tools provided in “Memory Tips for Math, Memorization and Learning Styles: The Successful Way to Teach K-5 Math”. As you read the creative examples, don’t be surprised to find yourself conjuring up a few inspired examples of your own to help your child or student learn more effectively.

This book can be purchased at a discount of 30% for a limited period. Use coupon code FEBRUARYCART305USD at check out. The coupon expires on 19 February 2012.

 

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Questions and answers are simply mathematics

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If you find the study of mathematics dreadfully boring, it is time to play a little. In “Amusements in Mathematics” by Henry Ernest Dudeney (published by David Gaddy, Nov 2011),  plenty of mathematical fun is crammed into 640 pages. According to the author, this collection of puzzles and mathematical problems was created so that the user of the book could tap into the pleasure of “doing math”.

Henry Ernest Dudeney (1857-1930), an English mathematician, is best known as a master of logic puzzles. The author views mathematical puzzles as perplexing questions begging our answers. The reader is drawn into the hunt for solutions and answers to these questions. Asking and answering questions is a part of human life, and comes naturally to us all. When mathematics is viewed as the process of asking and answering questions, we allow ourselves to bypass any existing “number” prejudices and start to enjoy what comes naturally.

“Amusements in Mathematics” also includes a discussion on the psychology of puzzles and the application of math in our daily lives.  It is an excellent resource for mathematics teachers seeking a readily accessible collection of “questions” that will spice up a lesson. However, this puzzle book is just as useful to anyone seeking a little mental stimulation – after all, we can all answer questions and should not shy away from the challenge of doing so often. This extensive collection of puzzles and problem-solving exercises is now available from Lulu.com.  The book can be purchased at a saving of 20% until the end of February 2012 using the following coupon code: 20% off books – Enter code FEBBOOKS12 – Save up to $25 – Offer ends 2/29/12
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Are Puzzles Too Old Fashioned for Modern Kids?

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Puzzle building is a lost art, pushed aside by electronic gaming and dvd watching. Should you as a parent or teacher make any attempt to resurrect this lost art? Experts in the field of early learning tell us that young learners will benefit significantly from opening that puzzle box and putting the pieces together.

According to the article “Puzzles and Games for Preschoolers” by Alvin Poussaint, M.D. and Susan Linn, Ed.D., puzzles serve various educational functions in the development of young learners. Standing head and shoulders above the other advantages of playing with puzzles, is the fact that puzzle-building helps kids develop problem solving skills. And who doesn’t want a child who can think for herself and figure out solutions to every day problems?

Problem solving is a skill that goes well beyond the realms of mathematics and science. Without the ability to problem solve, relationships become dysfunctional and workplaces become a source of deadly stress. According to psychologist Dr. Jeffrey Bernstein in his article “Two Essential Skills for an Emotionally Healthy Life“, the ability to problem solve is critical for effective management our lives. Why then would anyone withhold opportunities for their children or students to develop this vital skill?

Poussaint and Linn suggest that trying to fit the puzzle pieces together helps children “learn the value of flexible thinking and persistence”. Moving and placing the pieces develops fine motor skills. Puzzle building also stimulates deductive reasoning and inference. The process of assembling a puzzle helps children understand that big things can usually be broken down into smaller parts. This realization is a critical element in successful problem solving.

Is it time for our children to put aside the gaming console for a little while and pick up an old fashioned box of puzzle pieces? To help young learners face life with well developed life skills, you cannot afford to procrastinate. Unpack that old jigsaw puzzle today.

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Can I make my own linear equation jigsaw puzzle?

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Converting your “less than exciting” linear equation worksheet activities to puzzles is possible with a small investment in some supplies and a slightly larger investment in time. To get started, find some sturdy, colorful cardboard, a ruler, black marker, a pair of scissors, self-adhesive lamination plastic, an elastic band, and a set of solved linear equations. Dark colored card tends to be difficult to read equations from, so avoid dark colors unless you are working with white or silver metallic markers. While I prefer working with black markers, any colored pens that create contrast with the background card color will work.

Your puzzle can take any form, but simple shapes are the easiest to work with. For beginners, I recommend a square puzzle with no more than 9 pieces. Use the ruler to mark out a square on the card, and divide the square into a table with 3 equally spaced columns and 3 equally spaced rows. If you are feeling less ambitious, start with a 2×2 table. Make sure the lines and boundaries of the puzzle are drawn in bold ink. Neatly insert an equation along a side of a cell that has an adjacent cell. The solution to this equation is filled in across the boundary line in the neighboring cell. Try not to choose equations that will generate the same solution as this may cause confusion for learners who are new to this type of puzzle building. Duplicate solutions can be intentionally incorporated into more challenging puzzles, but should be avoided when first introducing these puzzles to a class or student. Complete the puzzle with equations and solutions, laminate the card for durability, and cut the puzzle into its individual pieces. Use the elastic band to keep the puzzle pieces together.

If you are new to putting the pieces back together, or want to know how to explain the process to your students, read “How to Solve a Linear Equation Jigsaw Puzzle“.

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How do I build a linear equation jigsaw puzzle?

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Unlike traditional “picture” jigsaw puzzles, linear equation jigsaw puzzles are largely blank. There are seldom patterns or background images to guide you as you put the pieces together. Although traditionally rectangular, some puzzles are designed to take on unexpected shapes when completed. However, these “shaped” puzzles are not usually sold with obvious clues that will allow the puzzle builder to construct the puzzle using only the goal of a particular shape. There are no short-cuts, cheat-sheets, or ways to avoid solving the equations. If you want to build the puzzle, you must first solve the equations printed on the puzzle pieces – they alone hold the keys to putting the puzzle together. If you are new to linear equation jigsaw puzzles, and need some help getting starting, read “How to Solve a Linear Equation Jigsaw Puzzle“.

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Are linear equation jigsaw puzzles only for classroom use?

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Puzzles are enjoyed by everyone from grandma to your toddler. Classrooms certainly don’t have exclusive rights over them. While perfect for building class spirit and developing team work skills within the classroom environment, linear equation jigsaw puzzles are even more useful at home.

If you home school your children, integrate the puzzles in your home school lesson plan to spice up traditional algebra lessons. Parents with children who show reluctance to do their algebra homework can encourage an interest in the subject by introducing these puzzles as part of a reward system. For example, for every 3 traditional equation worksheets completed, the child could earn the opportunity to complete a linear equation jigsaw puzzle instead of a worksheet.

Does your family enjoy building puzzles together? Take it to the next level by completing a linear equation jigsaw puzzle as a family. This type of family activity helps encourage an appreciation for mathematics, and teaches children that the topics they deal with “in school” are not for exclusive use in school.

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Solving Linear Equations is the Game to Play

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Linear Equation Jigsaw PuzzlesBad experiences with linear equations can brand algebra as the subject to hate. Many a middle-schooler has adopted this negative attitude during the early stages of exposure to algebra. As countless high school mathematics teachers will attest, changing this perception of algebra as being a “boring and difficult” subject is not easy. But solving linear equations need not be the doorway to mathematical doom and darkness. Repetition is certainly necessary to develop problem-solving skill, but the unexciting repetition that usually kills any interest in algebra can be presented as something fun and challenging. How this goal is achieved is limited only by the imagination of the teacher. A favorite for me is to present the activity of solving linear equations as a jigsaw puzzle. The puzzle may be offered as an individual or a team challenge, depending on the objectives of the teacher.

Linear equation jigsaw puzzles are the game-players’ alternative to solving pages of equations. These puzzles take advantage of all the skill-developing attributes of puzzle building, but do this on top of developing algebraic problem-solving skills. Before the second piece of the puzzle can be laid, a linear equation must be solved. While some students may be hesitant to embrace the challenge of a page of linear equations begging solutions, few will back down from the chance to build a puzzle.

The rate at which the puzzle can be built is primarily determined by the speed at which the student can solve the linear equations. The linear equation jigsaw puzzle therefore has the potential to serve as an informal speed test, but teachers should be cautioned against using these puzzles for formal tests. Since jigsaw puzzle building depends on the hand-eye co-ordination and the spatial perception of the students, timed test results may be indicative of more than just the student’s ability to solve linear equations.

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Stop blaming the parents and teachers for students’ choices.

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Peter Hilts, in his article  “Is it time to blame the students?”  addresses an issue that many educators feel uncomfortable expressing opinions on.  In this “politically correct” time that we live in, everyone is afraid to step on toes.  Responsibility is commonly shifted from one person to the next, so no-one has to feel too bad for too long.  Hilts boldly looks at that the statement “all students are all good all the time” and critically evaluates it from the perspective of the teacher.  If students are not just to acquire knowledge as they grow in years, but are also expected to “grow up“, shouldn’t they be taught to shoulder some responsibility for their learning?

“If attendance, effort, and integrity are part of the problem in education, it isn’t fair to hold teachers, parents, reformers, unions, politicians, or the tooth fairy responsible,” says Hilts.  He is to be commended for making such a bold stand on a sensitive educational issue.   “Students who give partial or no effort to classwork, exams and standardized tests are mostly or exclusively responsible for their behavior.  When a student who can attend skips instead, that student is responsible.”  Certainly any education system has some disinterested teachers, or teachers who simply hate the work they do but refuse to leave it.  Every society has some parents who actively discourage the educational growth of their children, or who simply don’t care enough to encourage it.  But is it always the teachers and the parents fault when children don’t succeed at school?

As Hilts so insightfully points out, “responsibility has two faces”, and this is as true in the classroom as it is anywhere else.  When a teenage student is offered the opportunity to learn and CHOOSES not to, shouldn’t they be the ones to accept responsibility for that choice?

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Parents are the reason that students cannot hack the Math in Physics?

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High school kids cannot use fractions.“Another physics teacher told me that students cannot hack the math in physics,” says Stewart Brekke in his article entitled, “Urgent Math Crisis in our Nation: Basic Math Deficits Affect Student Performance in High School Physics and Chemistry“.  Is this an unusual observation for a Physics teacher?  Brekke estimates that the USA “may now have over 100,000 high-school students who do not know fractions and decimals well enough to do high-school physics and chemistry successfully, let alone go on to college and pass a physics or chemistry course.”

There is clearly a problem on our hands – many teens cannot do basic mathematics.  Where do we find the source of this problem?

Stewart Brekke speculates that part of the problem may be attributed to the elementary schools placing too much emphasis on reading skills and not nearly enough on basic arithmetic skills. Japanese elementary school students typically spend two to three times as much time on developing mathematical skills as their American counterparts. The result of this shift in priorities is evident.  Stewart also believes that the “lack of a proper foundation at home” is also a significant contributor to the poor arithmetic skills observed in high school students. Sadly, many children enter first grade without being able to count to ten, and their progress in arithmetic skill development is severely hampered.

“It is not that parents do not care, for, on the whole, I have seen them show deep concern about their children’s education, but that many of these parents do not take the time to teach their children number facts nor reading skills. These parents must be informed early that their child’s success in school means that they must start educating their children before they enter kindergarten,” says Brekke.

Education systems all over the world invest vast sums of money into remediation of high school students struggling with poor basic skills. Yet high school Physics and Chemistry classes continue to shrink in size as teenagers avoid confronting the issues that stand in their way of understanding these subjects.  Are we trying to solve a problem instead of preventing it?  What would happen if more of the national or state education investment was used for programs aimed at educating the PARENTS of pre-school children, thus effectively equipping them to help their children develop the basic skills needed for future success at school? 

 Can parents make a difference at home?  All indications are that if parents do not participate in the education process BEFORE their child enters the school system, they may in fact be contributing to their child’s future scholastic failure.

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Does withholding knowledge stimulate or stunt learning?

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Does refusing to share knowledge truly stimulate learning? I love to learn new things, and am constantly on some mission of discovery.  Over the years, I have tried to share my enthusiasm for learning with my students, and anyone else who will allow me to indulge my love of learning.  I have just as eagerly shared what I have learned as I have shared my enthusiasm for learning.  One of my greatest thrills as a teacher is to see curiosity light up the eyes of a student, and watch them begin their own journey of discovery. I don’t believe we are ever too old to learn new things.  I do believe that as soon as we choose to give up the quest for knowledge and understanding we limit our relevance to society.

Earlier today, I interacted with an intelligent, interesting individual who often writes some thought-provoking articles.  A recent article of his stimulated some study on my part and raised some questions, so I addressed those questions to the author, in the hope that he would help me understand his thought process better.  He responded in a rather unexpected way.  He indicated that he did indeed have the answers to my questions, but felt that sharing what he knew would discourage me from thinking independently and stunt my ability to aquire or generate knowledge.  If he answered my questions, that would somehow make him guilty of spoon-feeding me. 

How often has an intelligent, educated, and seemingly-wise teacher with a vast and valuable knowledge- and understanding-base quenched the desire that a student may have to learn simply by not embracing a desire to share?  How often is the learning process retarded, because those who have the knowledge will not share it with those who do not have it?  I have, at times, experienced this “what is mine is mine, and I will not share” attitude in the highly competitive research environment where it is believed by some that withholding knowledge grants power, and sharing knowledge weakens your position to dominate as a researcher.  How often does this attitude seep down into the classroom environment where the goal should be to encourage everyone to learn as much as they can?

Are there teachers who withhold answers just to ensure that the students do not grow to know more than they do?  Is this restricted sharing environment comforting for the teacher, and effective in stimulating the students to seek their knowledge elsewhere?  Are there teachers who are not motivated to take up the torch of lifelong learning?  Do our formal learning environments still accommodate teachers who have no interest in growing and developing, so they always have something new to share with their students?

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