Help Kids Understand Math Problems: Take Away The Numbers And the Question!
It is important for teachers to provide ELLs with opportunities to learn and practice key vocabulary words. Help Kids Understand Math Problems: Take Away The Numbers And the Question! key words are very important, they are only part of the process. Understanding the language in word problems is critical for all students. They need to know the meaning of words.
But because words are often used differently and problems are set up differently, there are some cautionary messages. Here is an example of problem that uses “fewer than” to set up a subtraction equation. Maria has 24 marbles which is 8 fewer than Paolo has. How many marbles does Paolo have?
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If we were to only focus on using key words, “fewer than” is a signal to pick out the numbers and subtract. The student may immediately make the conclusion that the answer is 16, but that is not what the problem is asking, and the child would be wrong. What research has found is that if we ask students to only rely on knowing that certain key words signal specific operations, we can actually lead them away from trying to understand the problems. They will tend to look only for those words and whatever numbers are in the problem, even if they are not relevant to the answer.
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This will not help them be mathematically proficient later, even when they are proficient with English. Although the finding on key words was done with regular students, the consequences for ELL students of relying on them is the same. They would not be able to solve the problem above. Another good tool is to teach them to draw or model the problems. To illustrate the problem above, you could state: “Here’s Maria’s 24. The difference is between knowing the meaning of the words “fewer than” and using “fewer than” as a key to an operation. We want students to know the meaning of the words, but also to see them in the context of the whole problem.
How many students brought their homework today? How many more children brought their homework yesterday? We had 8 markers on the board, but now we only have 3. How many did we take away? How many animals are there in this magazine?
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Show students how easy it might be to misunderstand the problem. If possible, break up the problem into smaller segments. Allow students to act out the word problems to better comprehend what they are being asked to solve. Provide manipulatives to help students visualize the problem. Take field or walking trips to figure out distances, speed, area covered, etc. Ask students to do surveys, interviews, hands-on research in real-world situations to figure out percentages, differences, and higher-order math skills.
Allow students to make drawings or diagrams to help them understand problems. For more ideas that can be used to support math instruction in the ELL classroom, take a look at Math Instruction for English Language Learners. References Click the “References” link above to hide these references. Language and modeling word problems in mathematics among bilinguals.
Endnotes Click the “Endnotes” link above to hide these endnotes. Brenda Krick-Morales teaches at Reynolds Middle School in Lancaster, PA. She is currently teaching 6th grade communication arts and math. She has worked with ELLs at a beginners level as well as the intermediate level for the past 5 years. Brenda holds teaching certificates from Millersville University, and is currently pursuing a Master’s in teaching ESL through the University of Turabo, Puerto Rico. Endnotes Brenda Krick-Morales teaches at Reynolds Middle School in Lancaster, PA. Web page addresses and e-mail addresses turn into links automatically.
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Swearing Can Enhance Your Pain Tolerance! Kids Learn Math Easily When They Control Their Own Learning Math outside of school is fun, useful, and joyfully learned. Math is that school subject that we can’t BS our way through. That’s one thing that makes it so scary to so many. There are right and wrong answers to every question, no partial credit. It also seems to many people that math performance reflects basic intelligence. The first step in coming to grips with math is to knock it off its pedestal.
The real-life problems that are important to us are problems like these: Whom should I marry? Should gays be allowed to marry? What career should I go into and how should I prepare for it? If I invent gizmo X, will people buy it?
The second step in coming to grips with math is to realize that math is not particularly difficult. There is nothing magical about it. You do not need some natural gift beyond that of a normal human brain to do it. Nor does it require the thousands of hours of study that we try to force upon school children.
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The best evidence I know that math is not hard comes from the experiences of people involved in the unschooling movement and the Sudbury “nonschool” school movement. I have written about these movements in previous posts. Unschoolers are homeschooling families that do not provide a curriculum for their kids or evaluate their learning in any formal way. Several weeks ago I invited readers of this blog to send me stories about the self-directed learning of math. A total of 61 readers kindly responded, some with beautifully written pieces that could be stand-alone essays. I have found it convenient to organize the stories into four categories based on the primary motive that seemed to underlie the math learning that was described.
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I’ve chosen to start, most joyfully, with playful math. Playful math is what some call “pure math. It is what real mathematicians do, and it is also what 4-year-olds do. Playful math is to numbers what poetry is to words, or what music is to sounds, or what art is to visual perception. Four-year-olds have a knack for bringing the whole world around them into the realm of play. They play with words, so they are poets.
They play with sounds, so they are musicians. They play with crayons, paints, and clay, so they are artists. And they play with numbers, so they are pure mathematicians. I’ve noticed that students at Sudbury Valley, who are free of any imposed curriculum, don’t stop such play as they grow older. When he found out about connect-the-dot drawings, it started to click for him how numbers proceed in order. He started counting aloud all the time, when walking, when lying in bed, etc.
Lucy, in the UK, wrote about her son who has just turned 5: “He counted to one hundred once just for the fun of it whilst getting dressed. It was the first time I realized he could do that! He loves to line up number magnets and get me to tell him what the number is, particularly when the number goes into the millions! He can work out what a number is into the thousands from playing with fridge magnets.
Kathy wrote: “Our oldest son, who is 6, has always been fascinated by numbers. He could count to 199 before the age of 4. He loved to count, and to have me count, and to do rhythmic things with his body. He would jump while I counted, or bounce on the couch. He started on math when he wanted to know how many things he would have if he doubled them.
We went through a doubling phase! In their continued math play, young children often discover the basic concepts of adding, subtracting, multiplying, dividing, and more. Once they have the concepts, the actual ways of performing these operations come easily. Janet wrote, of her young daughter: “She developed counting skills as most toddlers do, using fingers, food and toys, and game pieces and spaces on game boards and computer games. That naturally led to adding and subtracting with fingers and objects, and then doing that in her head. Does four plus ten equal fourteen?
Then does five plus ten equal fifteen and seven plus ten equal seventeen? Unschooling mom Lori wrote: “One thing just happened two minutes ago. What is 4 plus 4 plus 4 plus 4? What is 2 plus 2 plus 2′ and he got exactly the right number of 2’s to go to 16. A-L wrote of her young son: “When he was 3 or 4, one day he went into our living room where we have a large window and noticed that there were four rows of seven panes. I count to seven four times then it’s 28. I don’t think we’d ever talked about multiplication at that point, but he’d essentially figured out how it worked and how to do it on his own from looking at the arrangement of squares.
And Barbara wrote this about her unschooled young daughter: “She had just been telling me what games she and her friend had been playing, and then we were both quiet for several minutes. She then proceeded to explain that when you have a whole of something and you want to break it up into some number of equal parts, that’s division. Aurore wrote of her son: “One evening, at age 7, he had brought home a pack of Skittles. Like many kids, he likes to put them on a plate, sort them by color and play with them. On this day he had nine left and arranged them into three rows of three. I told him that’s what it’s called, a square number, and that he could also make a square with four rows of four. Some readers are no doubt thinking, “Well, a good teacher can use these sorts of demonstrations to teach math and thereby help children learn more quickly and efficiently than they could through self-discovery.
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But the problem with such reasoning is that every child is different and no teacher, no matter how brilliant, can get into every child’s mind and come up with just the trick that will engage that mind at that exact time. Most of the math stories sent to me included at least some account of learning math as a tool in daily living. Amy, a homeschooling mother of seven, wrote: “They all know how to divide and multiply, calculate percentages, add and subtract, just by handling money and cooking. I’m sure it helps that they have to share limited amounts of yummy snacks not only among the 7 of them but with various friends who are always around.
Food and money teach kids a LOT of math, and it highly motivates them. Anne wrote: “All five kids learned to read recipes, measurements, how to divide and how to double or triple a recipe’s ingredients. They read maps and figured out the mileage. Vincente, a staff member at a Sudbury school, sent me this cute story: “Somehow we always end up with a lot of loose change, which needs to be rolled to be deposited. One of our very young students chose to do this . We make stacks of five and count to fifty, stack and roll.
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A week later I’m dodging vampires. Another of our mega-young invites me to play in one of the first role-playing adventures he’s running. And this, from Jennifer: “Three years ago, my son was diagnosed with Type 1 Diabetes. We calculate total carbohydrates from nutritional labels, total carbs for a meal, carb to insulin ratios by time of day, correction factors, percentages, etc. Now he NEEDS to know math to stay alive. He still hates memorizing times tables. If I asked him, “What is 3×6?
I just got a blank stare. But it’s not just food and money. Beatrice wrote: “Playing the piano, my daughter told me she was doing math. She was encountering fractions–half notes, quarter notes, eighth notes, sixteenth notes, all in musical notation as well as in patterns and rhythm. Many of the stories sent to me about instrumental math had to do with games. H wrote: “I have 3 kids attending a democratic free school with no imposed curriculum.
My kids have spent a lot of time playing online games. Real games, not those stupid educational ones. If I want to buy this helmet for this amount, how many hours do I have to play making this amount per hour in order to buy the helmet? Gillian wrote: “My 10 year old and 5 year old are unschooled and there is no way to avoid them being exposed to math if they live a stimulating life. In particular, the computer and PS3 games that my son plays — World of Warcraft, Second Life, Uncharted, City of Heroes — have math concepts built into them in a completely natural way. I do not particularly like games that are deliberately ‘educational’ and my children have never liked them. It’s a strategy game that uses addition and subtraction.