Math development often has the expectation that at a specific age a student “should” be at a specific level. It is tempting to conclude mathematical potential either by comparing skills with materials marked by grades or by comparing their skills against another student’s abilities. Visual arts development is often judged by the student’s interest level or how his or her work compares to someone who is viewed as talented. Another conclusion is made by how their work lines up with realism. Unfortunately, students are often judged as to whether they are adept at math and or art or not at a young age. The success or failure mindset sticks with them. In my work as an adult beginning art instructor, it is common to have a first time student make a comment such as, “So-and-so is the artist in our family.” They gave up years ago when someone else in the family filled the shoes of the artist in the family. Let us be cautious about labeling a student as not being mathematical, artistic or unable in any subject. Instead, I encourage you to discover ways to build skills in sequential order and at the student’s individual pace. The goal is to assist the student to develop basic skills and learn how to learn. Potential comes in all shapes and size
This is where it gets very interesting. In my 30 years of mentoring and learning from parents as a Demme Learning consultant and an art instructor, I have observed that most students, unless there is an extremely serious learning delay, have potential to be proficient in both math and art. Artsy student can develop confidence in math and “mathy” students can develop art confidence. Not only that, intentional development of art and math will result in a stronger ability to combine both naturally as the student moves into upper level math, professional art and ultimately into the job market. In both mediums the creative strategic thinking, problem-solving, and self-expression developed will set your student up for success for whatever their plans and goals may be. Both subjects correlate directly with science and language expressions as well. To me art is the glue that connects all of the above.
Art and Math Parallels
Concept Parallels
In my personal art, I am continually considering angle, proportion, perspective, balance, grids, quadrants, slope-intercept and probably more math concepts that I do not even realize. Other artists I have asked about the connections between math and art indicate they use measurement, weight, and even trigonometry.
Tools Parallel
All you have to do is take a look at the tools both artists and math professionals use and you will actually see the strong parallels.
A special note here: In art especially, using tools is not cheating or a sign of being “less than.” Even the great masters used tools; in fact, they developed many of them. While there are likely a few artists who have developed their skills being a purist, most of us have at least a few favorite tools.
Story and Vision
The most profound way I see this connection between math and art is that both involve telling a story, expressing a vision, working though a strategic process, or yes, sometimes evoking an emotion. The lightbulb in my math/art connection came on when I studied Algebra 1. When preparing to certify to support Math-U-See Algebra 1, the most exciting “aha” moment was the realization that the same learning process I enjoy in my art development provided success in Algebra 1 as well. The skills and concepts I had developed in art began to correlate with the math I was learning. Because Math-U-See focuses on the importance of “seeing” math concepts, I was able to visualize and ultimately find new success in math. Now those formulas that I could not even begin to understand or memorize when I failed Algebra 1 in school were relevant. The same processing I use to develop my art supports my ability to find success in math.
In both math and art a story is being communicated, a vision being processed that you may have seen or wish to create. Students, even if they’re not particularly artsy, benefit from working through art skills, as it promotes strategy processing skills which will ultimately enhance the ability to apply and excel in other subjects. I assure you basic art skills can be developed by all learners. Beginning at any age systematic development of art will encourage creative thinking. In the job market your child will be competing in, being able to be creative and having the skills to communicate creativity in math, visual art and language will be a valuable
Let’s Get Practical
Ok, this is a blog post right? Not a book, so let me prioritize and narrow this down to five things as an art instructor that I would suggest as a starting point.
1) Tension Control / Awareness / Trial and Error
The ability to control tension when creating is something that is both vital and difficult to reteach. By the time the student ends up in my class reworking muscle memory, this is often the number one hill to climb. When the habit is to apply too much pressure to the pencil, it makes it difficult to erase. Consequently, the art student feels they have no choice but to get it right the first time. Learning to draw lightly until you get it right evokes a mindset that promotes trial runs and changes as part of the process, not failure or a sign that you are not capable. When watching even most professional artist sketch, you will notice them making small, light marks to begin their composition. They start out getting a feel for what they are envisioning. They now can see their options and know where to put their hard line or use it as a light line to guide them if they are painting. Because they drew lightly, they can erase all the other lines and have a clean area with which to continue. Here we can learn the incredible value of trial and error. An additional bonus will be as the student begins to work through multi-step math concepts. The skill and mindset that they can find the error and erase without making a big mess on the paper or having to start over can be key to building confidence and lowering the frustration level. Additionally, you, the viewer, will produce something much more enjoyable to look at, lowering your frustration level as well. Teach your budding artists and mathematicians to love erasers and view “failures” as opportunity to grow
2) Thinking Outside of the Lines
Going outside the lines can be quite risky. In the end, just getting those worksheets completed with a specific percent correct will not be what best serves your student.
In regards to art development there will be more obvious ways to think outside the box and color outside the line…keep it simple. One of my favorite ways is through photography. Next time you and your student are sitting somewhere waiting, hand your student the phone and say, “Okay let’s snap a few shots.” Do not just take pictures of people or buildings. Find some texture, interesting colors, and surprising scenes. Play “Who Can Take the Most Unusual Photo in Four Shots.” Later you can teach them about cropping. How do you make it look better? How do things look better if you crop it this way, or that way? Be ready to print two or three of them monthly to mat and frame for your gallery wall at home. Maybe rotate them and put the previous one in an album. We miss so much in life by not really seeing our surroundings. Learning to “see” what is really there is definitely a math/art connection
3) Limit Time for Intense Instruction
When I teach children’s classes I typically figure in 10-15 minutes of formal instruction mixed in with a remaining experience of free play. It is often better to leave the project unfinished, move to free play and come back for multiple additional brief sessions either during the session at another time. I have learned from experience that students start out doing great and all of a sudden trash it because they need a break from that level of concentration. A mature artist knows breaks are vital for a quality result. My best works often involve a break at 80% finished or sooner. I then leave the work out so that it is somewhere where my peripheral vision will keep working on it during my day. Our brain is so amazing that it will continue to create when we do not realize it. Often out of nowhere I will know exactly how to finish it with the “edge” I want it to have. I encourage you to be aware of this and build the habit of knowing and honoring when it is time to “step away from the art work”. It is the same with math. Try 10-15 minutes of math when learning something new, then walk away for a spell and re-approach with fresh eyes.
4) Free Play and Exploration
I get it…not everyone enjoys messy art as much as I do. I am one of those glitter grandmas. If the kids come over, we usually end up with glitter, paint, and glue somewhere. However, I cannot stress enough the value of your student experiencing both inside and outside the box creative discovery. This is where they learn to understand when and where both are appropriate. A balance of messy art at the level you can handle, brief sessions of formal skill instruction, and frequent habits of drawing, photographing, or taking note of what you see in your daily surroundings is important. The same goes for math. The student who insists on getting the answer “their way” will be well served by learning to balance that wonderful ability by simultaneously being required to solve at least some of the problems as instructed. Another thing to keep in mind is that while some need complete order to function, others of us need things at least a little messy.
5) Think Intentionally
Likely, you plan with intent as to the best fit for your student’s math. What makes Math-U-See a well-rounded program is that we teach to master concrete understanding, not only at the student’s individual pace, but we also provide potential development of all learning preferences. While your student may have a favorite way to learn, do not underestimate the value of strengthening the other preferences. If you are using Math-U-See currently and find your student “block resistant,” be sure to require that they use the blocks until they can teach the lesson back to you while using them. Even if they can get answers correct without doing this, you will be connecting to the valuable creative thinking and promote deeper mathematical creativity. If you need support as to how this might work in your individual classroom…call for a consult for some ideas as how to do this without either of you becoming frustrated
Art needs intentionality as well. There are tons of purchase choices out there. If you as a parent are not confident as to what to do or where to start, post in the comments and tell us more. Also tell us about how art and creativity already happen or do not happen in your family. I learn so much from the parents and students I have the privilege to walk along side. Hearing from you will help me know what to include in my next blog post. The key here is let’s keep it simple…but in some way intentional.
Saturday, July 30, 2022
Analysis of Pythagorean Theorem
Pythagorean Theorem is one of the most fundamental theorems in mathematics and it defines the relationship between the three sides of a right-angled triangle. You are already aware of the definition and properties of a right-angled triangle. It is the triangle with one of its angles as a right angle, that is, 90 degrees. The side that is opposite to the 90-degree angle is known as the hypotenuse. The other two sides that are adjacent to the right angle are called legs of the triangle.
The Pythagoras theorem, also known as the Pythagorean theorem, states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle. Or, the sum of the squares of the two legs of a right triangle is equal to the square of its hypotenuse.
In a right-angled triangle, the total sum of the individual squares of the base and altitude would be equal to the square of the length of the hypotenuse.
Let us denote the base of the right-angled triangle as letter ‘b’, the altitude of the triangle as ‘a’ and hypotenuse of the same triangle as the letter ‘h’, then as per the Pythagoras theorem
h2 = b2 + a2
The numerical triplets which would satisfy this formula are termed as Pythagorean triples. The numerical triplets like (3, 4, 5), (5, 12, 13), (7, 24, 25), (8, 15, 17), etc. comes under the category of Pythagorean triplets. The multiples of these basic triplets also behave like a normal triplet, and if considered (a, b, c) as a basic Pythagorean triplet then the multiple of these triplets (ka, kb, kc) also comes under the category of the Pythagorean triplet. It should be noted that the constant ‘k’ in this context is a non-negative integer.
Application of Pythagoras Theorem in Real Life
The following are the applications of the Pythagoras theorem:
Pythagoras theorem is used to check if a given triangle is a right-angled triangle or not.
Aerospace scientists and meteorologists find the range and sound source using the Pythagoras theorem.
It is used by oceanographers to determine the speed of sound in water
What is the use of Pythagoras Theorem?
The Pythagoras theorem, also known as Pythagorean theorem is used to find the sides of a right-angled triangle. This theorem is mostly used in Trigonometry, where we use trigonometric ratios such as sine, cos, tan to find the length of the sides of the right triangle.
What is the real-life application of Pythagoras Theorem Formula?
The length of diagonal connecting two buildings can be calculated using this formula.
Also, we use this formula along with trigonometry concept, to find the angle of elevation if a person seeing an object kept at top of the building with respect to the horizontal line. The angle of depression is calculated when the object is kept below the line of sight of the person..
Wednesday, March 10, 2021
Audio-Visual aids
learning is modification of behavior through experience. The basic learning experiences have to be received by the pupil through his senses; as the gateways of knowledge. Most of such experiences enter through one’s eyes and ears. Materials that help to make learning experience clear and vivid by appealing to the senses are called audio-visual aids.
FUNCTIONS OF AUDIO – VISUAL AIDS It help learning at the scenery level They develops deeper understanding It arouses curiosity and stimulates self activity. It motivates pupils It provides direct and representative experience It make children feel freedom It provides clarity to learning. Provide variety in methods of teaching and learning. They offer reality of learning experience. CLASIFICATION OF AUDIO VISUAL AIDS Audio Visual Aids can be classified into three categories. They are projected aids, Nonprojected aids, Activity aids. Project aids Non Projected Aids Activity Aids Slides Graphic aid Field trips Slide projector Audio aids Museum Film projector 3-D aids Exhibition LCD Display board Demonstration
PROJECTED AIDS A projected aid is one in which items to be observed are projected on a screen using mechanical devices. The various aids under this category have been listed in the above table. Films and film projector
A single picture itself is an effective aid, but a sequence of pictures presented continuously have a cumulative effect. That is why films in the form of motion picture is considered to be a valuable aid. Film projector is a device used to project the film on a screen at a convenient place so that every student can clearly observe the presentation and at the same time attend to the related sounds.
SLIDES AND SLIDE PROJECTOR
Any picture or diagram which will take a long time to be drawn on black board in the course of a class period can be developed as a slides. A slide projector is an instrument equipped with a powerful light source and a carrier for holding slides of suitable sizes.
LCD
An LCD project is device for giving presentation generated on computer and it is a type of video projector for displaying video images or computer date on a screen or other flat surface.
Advantages
It can be used in dark room as well as in light room
It makes teaching- learning process more interesting, easy, impressive.
Reaches a mass audience.
Multimedia presentation
No need of special screen for the projection . any white projection surface can be used.
NON PROJETED AIDS
Non projected aids can classified in to :-
1. Graphic aids
2. Display boards
3. 3-D aids
4. Audio aids
Graphic aids
Graphic aids are visual aids such as graphs, diagrams, chart, posters, maps, cartoons, etc…
Display Board
Black board, peg board, flannel board, magnetic board, bulletin board, marker board, hook and
loop board, plastigraph board are goes under this category.
Uses of the black board
The teacher can illustrate the lesson on the black board and draw the attention of the
class to the salient features in the lesson.
The lesson can be phased and summarized in the right manner
The teacher can erase writing and drawing and a start afresh
It provides a lot of space for decorative and creative work
Pupil’s interest in class work can be stimulated by black board writings and drawing.
Abstract ideas can be clarified in the exposition stage and summery containing important
points can be given in the recapitulatory stage.
3-D aids
Models, objects, specimen, Moke-ups ,puppets, diorama are examples of three dimensional aids.
Models are concrete representation of object. They may be static or working models. Specimen may be representative of class or group of similar object. When we talk about flowers in general and represent all flowers by a typical flower is a specimen . A moke up is an operative model usually of a process designed to be worked with directly by the Lerner for specific analysis.Puppet is used to stimulate reality, to entertains, and to pass knowledge .
Audio Aids
Radio, recordings, tape recorder public address system are belonged this category. Radio is a powerful medium for mass communication. Programmers mean for teachers as well as student are available . tape recorders is used to record sound which can be reproduced at will as many times as required it is vary effective aid for class room instruction. the recorded tapes consisting of lessons and handled by eminent teachers on any subject can be played in the class. It is impressive because by novelty and expertise used in its preparation and the possibility for repeated presentation.
ACTIVITY AIDS
Field trips and Excursion , Exhibition , Demonstration, Museum, Dramatization, Vivarium planetarium are examples of activity aids. Excursion usually involve a tour by a person or a group of persons to some selected pales. Exhibition are effective models of mass communication if it is ordained by the pupils them selves, they get opportunity for self activity. Demonstration is a technique which is often used by all teachers. Ideas, skills, attitude, and process can be demonstrated. Museums are wonderful media for public education they are institutions that collect and preserve original objects and specimen and use them for research and educational displays. Museums are depositories with an array of educative materials including rare specimen
on verity of subjects arranged in a logical order. Dramatization is reality and concentrate to
learning situation it also gives opportunities for self expression. It can be successfully utilized for
the learning of various subjects. It gives new life to the dead facts deposited in the text books.
Vivarium is a live corner arranged in school or at home where creatures living in the air are
grown. A planetarium consists essentially of a dome usually mounted on the ceiling of a hall to
represents sky. A special projected is used to display images of the celestial beady on the dome.
The viewers who are seated below can see the projected image that will appear to be very realistic. Taped narration and sound effects as adds to the effectiveness of the presentation
