If metal balls are tipped down a big board filled with vertically-divided rows, they fall into a bell curve. At least that is what my granddaughter and I caused to happen when we participated in a discovery day at the University of Wisconsin. The effect reminded me of the statistics professor who brought our graduate class a large bowl of colored marbles and a scoop that had indentations we each filled with five marbles and then averaged the number of green marbles to demonstrate how sampling works.
At a middle school, a remedial math teacher brought in a Makey Makey circuit board, sewing kit, and 3Doodler pen. Students grouped themselves by interest to use each device. When students in a regular math class saw what the remedial math students were doing they voluntarily signed up to attend the math support class twice a week.
What were the remedial math students doing? They played a song on six bananas wired together and to the circuit board. Some students began seeing how they could make a circle in a football team's logo by embroidering an arrangement of the squares made by cross-stitch Xs, the same way pixels do on a computer screen. By using the 3Doodler pen to draw the same 2-dimensional design over and over again on top of each other, students learned how 3D printing is making a wide variety of products, including homes.
Finally, students in the regular math class saw how the remedial students purchased additional circuit boards and supplies for the sewing basket and 3Doodler pens by perfectly pricing and selling pencils.
Students everywhere in the world have creative juices. Invite them to illustrate the books they read, figure out how to move heavy rocks, use as little cushioning as possible to prevent an egg from breaking when dropped from different heights, dissect an old watch, not only a frog.
Showing posts with label math. Show all posts
Showing posts with label math. Show all posts
Wednesday, April 15, 2020
Monday, March 18, 2019
Why Kids Need Positive Relationships with Adults
Adult-child bonding achieves results. "Skin," the live action short film that won an Academy Award last month, featured a father proudly training his son to master a gun and hate black people. Through a plot twist and a bit of Hollywood magic, the father's skin turns black. His son shoots and kills him.
Research by the National Scientific Council on the Developing Child also found a lack of adult-child bonding in abusive environments and those with uncaring adults leads to kids with no motivation to learn, to explore, or to try new things. In a negative situation, kids can become fixated on fear, avoiding punishment, and the immediate danger of failure.
When children lack positive experiences with adults, they are apt to resist pressure to do things in a particular way, such as form cursive letters according to a prescribed method. Even guiding some children through mindfulness by requiring them to close eyes, sit up straight, and conform to other unnecessary procedures can undermine the positive benefits of mindfulness.
Teachers need to realize not all kids come into a room with a background of adult-child relationships that make them ready to answer an adult's question, volunteer an opinion, or ask for more information. A teacher needs to find ways to help students succeed, to feel a task is not impossible. It helps to lead into discussions with phrases like "I notice" and "I wonder." In other words, teachers need to give the impression all ideas are welcome and all subjects are worth exploring.
My mother was a math teacher who always tried to figure out what students were doing when they arrived at the wrong answer. She learned there were lots of things you could do with a column of numbers. "That's interesting," she would say, "I never thought of that." No matter how "crazy" a student's manipulation of numbers was, she'd caution other students not to laugh before they listened to and understood a classmate's reasoning.
Not every student is going to be good or poor at the same subject. Unless all kids begin to develop positive face-to-face interactions with adults, they may shut down and stop learning before they hit their strides. This goes for gifted and talented kids also. When an eight-year-old British boy, with Egyptian parents, perfect pitch, a knack for coding, and a sense of humor, told an international education conference, "(G)etting a few spelling words or facts wrong is not the end of the world," teachers needed to avoid taking offense. He also felt free to suggest learning to type on a keyboard saved trees and was more important in the digital age than learning cursive.
Research by the National Scientific Council on the Developing Child also found a lack of adult-child bonding in abusive environments and those with uncaring adults leads to kids with no motivation to learn, to explore, or to try new things. In a negative situation, kids can become fixated on fear, avoiding punishment, and the immediate danger of failure.
When children lack positive experiences with adults, they are apt to resist pressure to do things in a particular way, such as form cursive letters according to a prescribed method. Even guiding some children through mindfulness by requiring them to close eyes, sit up straight, and conform to other unnecessary procedures can undermine the positive benefits of mindfulness.
Teachers need to realize not all kids come into a room with a background of adult-child relationships that make them ready to answer an adult's question, volunteer an opinion, or ask for more information. A teacher needs to find ways to help students succeed, to feel a task is not impossible. It helps to lead into discussions with phrases like "I notice" and "I wonder." In other words, teachers need to give the impression all ideas are welcome and all subjects are worth exploring.
My mother was a math teacher who always tried to figure out what students were doing when they arrived at the wrong answer. She learned there were lots of things you could do with a column of numbers. "That's interesting," she would say, "I never thought of that." No matter how "crazy" a student's manipulation of numbers was, she'd caution other students not to laugh before they listened to and understood a classmate's reasoning.
Not every student is going to be good or poor at the same subject. Unless all kids begin to develop positive face-to-face interactions with adults, they may shut down and stop learning before they hit their strides. This goes for gifted and talented kids also. When an eight-year-old British boy, with Egyptian parents, perfect pitch, a knack for coding, and a sense of humor, told an international education conference, "(G)etting a few spelling words or facts wrong is not the end of the world," teachers needed to avoid taking offense. He also felt free to suggest learning to type on a keyboard saved trees and was more important in the digital age than learning cursive.
Monday, August 29, 2016
Back to School with a New Perspective
Preparing for a new school year probably doesn't require the purchase of a harmonica, paint brush, and Thesaurus. Yet Einstein played the violin, Samuel Morse painted portraits, and Galileo wrote poems.
Study after study shows the value of the arts. Playing music asks the brain to coordinate the notes eyes see and two hands play, to listen, and to recognize rhythms. Add dance and the whole body gets involved. In the process of drawing, painting, sculpturing, and writing stories, essays, and poems, students tap into their creative juices, express emotions, and discover their individual identities. Mistakes are made and corrected just as they are in every subject and life.
Music, art, and literature connect students to each other, their communities, and the world. One study, for example, found that children who participated in a dance group for eight weeks were less prone to anxiety and aggression compared to a control group. At the same time, the arts promote the creativity and innovation needed to deal with a rapidly changing global economy.
Consider how one kindergartner used an art project to discover there were two ways to find the total five. While one student had shown five by taking a photo of two red scissors and three blue scissors, another saw five, because the direction of four scissors pointed left and one pointed right. Math and science thrive on the same unexpected discoveries and strategies celebrated in the arts. Is there another way to do something is a question that has produced a Salvador Dali and a Thomas Edison.
Study after study shows the value of the arts. Playing music asks the brain to coordinate the notes eyes see and two hands play, to listen, and to recognize rhythms. Add dance and the whole body gets involved. In the process of drawing, painting, sculpturing, and writing stories, essays, and poems, students tap into their creative juices, express emotions, and discover their individual identities. Mistakes are made and corrected just as they are in every subject and life.
Music, art, and literature connect students to each other, their communities, and the world. One study, for example, found that children who participated in a dance group for eight weeks were less prone to anxiety and aggression compared to a control group. At the same time, the arts promote the creativity and innovation needed to deal with a rapidly changing global economy.
Consider how one kindergartner used an art project to discover there were two ways to find the total five. While one student had shown five by taking a photo of two red scissors and three blue scissors, another saw five, because the direction of four scissors pointed left and one pointed right. Math and science thrive on the same unexpected discoveries and strategies celebrated in the arts. Is there another way to do something is a question that has produced a Salvador Dali and a Thomas Edison.
Saturday, February 27, 2016
Make Spatial Relationships
When estimating the number of casualties planes flying into the World Trade Center's towers would cause, Osama bin Laden believed burning jet fuel only would weaken the steel above the plane crashes. According to Lawrence Wright's book, The Looming Tower, bin Laden thought higher floors would collapse, but lower ones would remain standing.
Spatial relationships are important for architects and engineers who design buildings and cars and for dentists who need to know how upper and lower teeth should fit together, but being able to make accurate calculations about spatial relationships is a skill needed by people everywhere in the world. Check how the skill is used in the following examples:
Spatial relationships are important for architects and engineers who design buildings and cars and for dentists who need to know how upper and lower teeth should fit together, but being able to make accurate calculations about spatial relationships is a skill needed by people everywhere in the world. Check how the skill is used in the following examples:
- Knowing where to sit at a sporting event or play so the view isn't obstructed by a pole,
- Figuring how many cars can be parked in a lot,
- Assembling furniture by looking at instructions,
- Visualizing how atoms are arranged in a molecule,
- Deciding how many pans are needed to bake five dozen cookies for a bake sale.
Recent studies suggest ways to help children develop spatial visualization skills. Engineering professor Sheryl A. Sorby recommends playing with blocks, using two-dimension instructions to build with LEGOs, holding objects and sketching them when turned in different positions. She also suggests introducing girls to the toys sold by Goldie Blox (goldieblox.com). Other teachers have had students draw maps, design 3-D treehouses, build robots, knit, play chess, and use 3-D modeling software SketchUp. Theater classes are a natural place to learn blocking, i.e. positioning and spacing actors so that everyone in the audience can see what is happening on stage. Art classes model with clay and learn techniques to create the illusion of space on a two-dimension surface.
The connection that seems to exist among spatial reasoning, math skills, creativity, and the arts is reason enough to get kids up and doing things all around the world.
Wednesday, January 6, 2016
How Can Girls and Boys Discover Their Worth?
I was in the elevator with a girl of 4 or 5 years old who asked her mother, "Why is that there?" She was referring to a little board book, about 4" x 4", that I could barely see in the folds of her younger sister's stroller. (Her mother said she forgot to put the book away before they left.)
This incident reminded me how we all have different strengths and talents. What can help a child in any country, who speaks any language, learn what she or he can contribute to the world probably better than anyone else? Consider the kindergarten teacher who helped her students learn numbers and addition by asking each child to draw a number and either draw or find pictures that made a combination of objects that equaled that number. When the number pictures were hung on the wall in numerical order, the children sat on the floor and talked about what they saw. While one student observed two red scissors and three blue scissors had been used to illustrate the number five, another said the handles of four of the scissors pointed left and the handle of the other scissors pointed right. These keen observers (and future mathematicians) had discovered five could be the sum of 2 + 3 or 4 + 1. Parents can see if their children are keen observers who can add up the number of items that go into a salad, their lunch bags, or a grocery basket at the market.
Teachers discover keen observers (and students with writing talent), when they ask their classes to write mini-memoirs about significant moments in their pasts. Directing young people to focus on the influences on their lives is a technique that can lead to valuable insights about their personal interests and their future career options.
(An earlier blog post, "Resolve to Help Kids Observe Their World," suggests some of the observations future scientists might make.)
This incident reminded me how we all have different strengths and talents. What can help a child in any country, who speaks any language, learn what she or he can contribute to the world probably better than anyone else? Consider the kindergarten teacher who helped her students learn numbers and addition by asking each child to draw a number and either draw or find pictures that made a combination of objects that equaled that number. When the number pictures were hung on the wall in numerical order, the children sat on the floor and talked about what they saw. While one student observed two red scissors and three blue scissors had been used to illustrate the number five, another said the handles of four of the scissors pointed left and the handle of the other scissors pointed right. These keen observers (and future mathematicians) had discovered five could be the sum of 2 + 3 or 4 + 1. Parents can see if their children are keen observers who can add up the number of items that go into a salad, their lunch bags, or a grocery basket at the market.
Teachers discover keen observers (and students with writing talent), when they ask their classes to write mini-memoirs about significant moments in their pasts. Directing young people to focus on the influences on their lives is a technique that can lead to valuable insights about their personal interests and their future career options.
(An earlier blog post, "Resolve to Help Kids Observe Their World," suggests some of the observations future scientists might make.)
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