logical-mathematical knowledge – Early Math Counts https://earlymathcounts.org Laying the foundation for a lifetime of achievement Mon, 01 Jun 2020 17:57:03 +0000 en-US hourly 1 183791774 Trash or Treasure? https://earlymathcounts.org/trash-or-treasure/ https://earlymathcounts.org/trash-or-treasure/#comments Mon, 01 Jun 2020 18:00:39 +0000 https://mathathome.org/?p=12256   “Can we go to the park today?” asks three-year-old Benjamin. We are actually in the park when this comment is made. We spend many of our days at the park. It takes me a second to understand that he is asking if we can leave the “forest” section of the park and head to […]]]>

 

“Can we go to the park today?” asks three-year-old Benjamin.

We are actually in the park when this comment is made. We spend many of our days at the park. It takes me a second to understand that he is asking if we can leave the “forest” section of the park and head to the playground.  As often as we head to the park, we very rarely make it to the actual playgrounds. We tend to be the “forest gang,” but today we follow his lead.

“Yes, let’s head to the playground!” I reply. Six little friends scream with delight and dash up the 60-foot hill to the slides and swings.

When we arrive at the playground, we discover a newly fallen tree with bark and branches scattered everywhere. I hear Ave call to her friends, “Who wants to make a creation?” But her friends are more interested in the playground equipment. I see the look in Ave’s eye. The tree is her playground today—her own personal treasure box. Her brain is on fire, and her creative juices are flowing. Ave quickly falls into a play buzz all her own. She starts collecting sticks, acorns, walnuts, rocks and large pieces of bark. She makes small piles and then settles in to start her “creation.” The blank sidewalk canvas is calling to this child. She begins to design, create and investigate, oblivious to her noisy friends on the playground.

Whenever I see a play buzz like this one blossoming, I offer my services.

“What do you need, Ave?” I ask.

“Bark, sticks, acorns, rocks…treasures!” she responds. “I need more treasures!”

Her “treasures” turn out to be discarded water bottle caps. Ha! I am sure that my brain is working as hard as Ava’s as I try to decipher her request. She never looks up and never stops to show me what she means. She is that deep into her play buzz. She has tuned out the world around her—and she is engaged in deep learning. This is the educational foundation that we strive for.

“Do you want STEAM? [Science, Technology, Engineering, Art and Math learning] I’ll show you STEAM,” I think to myself as this child creates her own curriculum. This is not teacher-directed learning. She owns this.

 

This nine-foot-long “creation” took our four-year-old friend 40 minutes of intense focus, determination and math and science investigation as she tried different pieces in different places before determining exactly where each piece belonged. She worked with an intensity that would make any early childhood educator dance with joy!

There are math and science benchmarks galore in this nine-foot work of art! Deep, brain-enriching, neuron-firing play. We have art, we have math, we have science and we have beauty. We have it all in this masterpiece from the hands of a four-year-old who used to worry me because I feared that she wouldn’t be able to sit for long periods of time once kindergarten began. Ave is a mover, a creator, an explorer, an investigator. She has been a hands-on learner from her earliest days.

Can Ave recognize her numbers from 1-20? She can’t. Can she count to 100? I don’t honestly know. I haven’t worked on these things with her. She hasn’t shown an interest in these benchmarks yet.

Do I struggle with that? Yes, I do. I am well aware of what that first week of “testing” in kindergarten will say about her “readiness.” Then I remind myself that Ave’s brain may not yet be ready for number recognition and counting, but her brain is ready for this! This estimation, this dimension-building and this logical, mathematical-thinking MAGIC that is happening before my eyes.

These interactions based on experience are truly the best way to lay the foundation for early math and science learning. These are the puzzle pieces that inspire children to keep learning. Ave has created shapes, worked with non-standard units of measurement, created sets and hit spatial reasoning out of the ballpark.

Math and science benchmarks are everywhere in this nine-foot work of ephemeral art! What exactly is ephemeral art? It’s art that is temporary and never expected to last. This masterpiece, in a city park where vandalism (sadly) is rampant, will be destroyed in a matter of hours. I feel a slight twinge in my heart.

I get down on one knee and say, as kindly as I can, “Ave, I am going to take pictures of your creation because I am worried that the wind or the raccoons or someone walking at night might accidentally break it. It is so beautiful, and I am sorry that it might get broken, but I promise to share a photo of your masterpiece with your family ….”

But, before I can finish my sentence, Ave stands up and says, “Oh, I know. Can we go back now? I am starving!”

This is a child who understands nature and ephemeral art. She engages in scientific exploration and mathematical investigation. The benchmarks for number recognition, when that part of her brain is ready, will come quickly and without effort. There is no doubt that her benchmarks in other areas of math are beyond her years. You can’t teach children what their brains aren’t developmentally ready to learn. Discover each child’s passion and learning style, and the benchmarks will take care of themselves.

Time has flown since Ave made her ephemeral art in the park—and she has just turned seven. As I write this, we are in the final days of the 2020 school year—a school year that has been disrupted by a global pandemic that has brought online learning into Ave’s life. It is not going well. Ave’s mother just texted me to say that online learning is not her daughter’s forte, nor is it hers. This is not how Ave learns, and it is straining their relationship and causing stress in the family. Ave is in tears, her mom is in tears and now her former preschool teacher is in tears.

Maybe it’s time for all of us to pause during this pandemic to take a good, hard look at what education could look like in America—without screens, without testing, without walls. It could be the treasure box that we give to this next generation of young minds. Another silver lining of the pandemic.

Oh, and Ave’s art creation in the park? It was left untouched for more than two weeks. I guess the raccoons and the would-be vandals appreciated it, too. So share the love and share the foundation of education through play! Trust me, it’s STEAM learning at its finest!  Stay safe, my friends. 

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Tool-Time Math https://earlymathcounts.org/tool-time-math/ https://earlymathcounts.org/tool-time-math/#comments Fri, 15 May 2020 10:59:47 +0000 https://mathathome.org/?p=12066 “Miss Diann, I need a hammer! Look! Look! See? I need a hammer!”

Three-year-old fix-it man Jonathan is pointing to a loose wagon screw that needs his immediate attention. We turn the wagon on its side to take a closer look at the wheel. Yes! We definitely have a loose screw.

“You need a hammer to pound it in?” I ask.

“Yes!” exclaims Jonathan.

I return with a hammer and Jonathan immediately recognizes that I have made a huge mistake. “No, not that one! I need a hammer! Look, it has a line. I need a hammer to fit in there to make it tight.”

This was not Jonathan’s first rodeo. He knew his way around a tool bench, just not by name.

“Oh, let me look again,” I reply.

I return with three tools.  “Jonathan, I have a hammer, a screwdriver and a wrench. Will one of these work?”

Jonathan’s eyes light up.  “Yes, I need a screwdriver!” He jumps with joy and gets straight to work.

My little friend is a math machine. This is logical mathematical thinking!  We have deductive reasoning and problem-solving at a three-year-old pace. Having the vocabulary to explain that he needed a tool that would fit in that “line”  demonstrated that he could imagine the type of tool that he needed.

Early scenarios like this will deepen Jonathan’s understanding of how objects fit together. This is exploring spatial relationships. This is fine-motor skill development, relationship building and spatial reasoning—all at the same time.

Jonathan’s spark of excitement ignites the interest of his friend, Harrison, who joins in. Harrison is also in need of a screwdriver because he has decided that the screws on every bicycle and wagon in the yard need a good tightening.

As Harrison and Jonathan discuss their actions, their understanding of spatial relationships and attributes about shapes, size and measurement deepens. High-quality hands-on experiences like these provide opportunities for children to develop a richer vocabulary as they reason out loud: “My screwdriver isn’t working. No, you need to turn it this way! Look, it’s going down!”

Children learn to understand and use information when they have direct contact with materials. Drawing a line from a hammer to a nail on a worksheet does not give our children the same educational benefits as an actual hands-on learning experience.

When children explore the different ways that they can manipulate materials—by rotating them, cutting them in half or transforming them into different shapes by composing or decomposing them—they are learning how materials relate to one another and the space around them. Working with real tools and materials is critical to fostering children’s understanding of spatial relationships. This is math. This is our foundation.  I think you should check your wagon and see if that left wheel “needs tightening.”  Don’t forget to document and check this off of your list of learning standards! Take your young friends outdoors. The math curriculum? It’s already “pre-loaded” into the activity!

 

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Puzzles and Howard Gardner https://earlymathcounts.org/puzzles-and-howard-gardner/ https://earlymathcounts.org/puzzles-and-howard-gardner/#comments Mon, 25 Mar 2013 11:00:13 +0000 http://www.mathathome.org/blog1/?p=1421 MI ChartDo you think some people are good at solving puzzles and others are not?  Is puzzle-solving a skill you are born with or can everyone eventually learn how to solve puzzles?  Are you a puzzle solver?

Howard Gardner of Harvard University argues that we all have various intelligences that manifest themselves in varying amounts and degrees and reveal themselves over time.  He calls these the Multiple Intelligences (MI).

The 9 Multiple Intelligences are as follows:

Visual-Spatial
Think in terms of physical space, as do architects and sailors. Very aware of their environments. They like to draw, do jigsaw puzzles, read maps, daydream. They can be taught through drawings, verbal and physical imagery. Tools include models, graphics, charts, photographs, drawings, 3-D modeling, video, videoconferencing, television, multimedia, texts with pictures/charts/graphs.
Bodily-kinesthetic
Use the body effectively, like a dancer or a surgeon. Keen sense of body awareness. They like movement, making things, touching. They communicate well through body language and be taught through physical activity, hands-on learning, acting out, role playing. Tools include equipment and real objects.
Musical
Show sensitivity to rhythm and sound. They love music, but they are also sensitive to sounds in their environments. They may study better with music in the background. They can be taught by turning lessons into lyrics, speaking rhythmically, tapping out time. Tools include musical instruments, music, radio, stereo, CD-ROM, multimedia.
Interpersonal
Understanding, interacting with others. These students learn through interaction. They have many friends, empathy for others, street smarts. They can be taught through group activities, seminars, dialogues. Tools include the telephone, audio conferencing, time and attention from the instructor, video conferencing, writing, computer conferencing, E-mail.
Intrapersonal
Understanding one’s own interests, goals. These learners tend to shy away from others. They’re in tune with their inner feelings; they have wisdom, intuition and motivation, as well as a strong will, confidence and opinions. They can be taught through independent study and introspection. Tools include books, creative materials, diaries, privacy and time. They are the most independent of the learners.
Verbal/Linguistic
Using words effectively. These learners have highly developed auditory skills and often think in words. They like reading, playing word games, making up poetry or stories. They can be taught by encouraging them to say and see words, read books together. Tools include computers, games, multimedia, books, tape recorders, and lecture.
Logical -Mathematical
Reasoning, calculating. Think conceptually, abstractly and are able to see and explore patterns and relationships. They like to experiment, solve puzzles, ask cosmic questions. They can be taught through logic games, investigations, mysteries. They need to learn and form concepts before they can deal with details.
Naturalist Intelligence (“Nature Smart”)
Designates the human ability to discriminate among living things (plants, animals) as well as sensitivity to other features of the natural world (clouds, rock configurations). This ability was clearly of value in our evolutionary past as hunters, gatherers, and farmers; it continues to be central in such roles as botanist or chef. It is also speculated that much of our consumer society exploits the naturalist intelligences, which can be mobilized in the discrimination among cars, sneakers, kinds of makeup, and the like.
Existential Intelligence
Sensitivity and capacity to tackle deep questions about human existence, such as the meaning of life, why do we die, and how did we get here.

So, people who have Visual/Spatial Intelligence or Logical/Mathematical Intelligence are probably more drawn to puzzles- and may be better at solving them.  Have you ever met a child who could complete a puzzle that was clearly far too advanced for his age?  Chances are, that child has a strong leaning toward one or both of those Intelligences.

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