Using Tangrams To Explore Mathematical Concepts
Representations have always been a very important part of teaching mathematics. The visuals and hands on experiences help to aide the teachers by assisting them in relaying important topics and concepts to the students. By having a representation, the students are more likely to remember what they have learned, and recall the lesson when it comes time to take a test or do their homework.
Within mathematics, many different manipulatives are used to enhance learning. Among the most commonly used are tangrams. The seven pieces that make up a set of tangrams have value well beyond their small size. One of their most important values, other than providing educational entertainment to students, is the introduction of geometric properties and theorems.
When introducing the idea of using tangrams, it is good to tell the old Chinese folktale about how they came to be. The story goes as follows, “A young boy named Tan wished to give the emperor a beautiful tile. As he carries the tile to the palace, he accidentally drops it and it breaks it into seven pieces. Tan tries and tries to restore the tile to its original shape. In the process, he finds out that he can create all sorts of fascinating pictures with the seven pieces of his tile. The seven tile pieces are what are now called tangrams.” (Tackling Tangrams, 2000)
This story illustrates that tangrams can be used a method of discovery, as well as for enjoyment since many pictures can be formed. It also helps students to see why they are able to form a square, which is the main basis for the manipulative. It is beneficial to give the students some time to play and explore with the tangrams after the story is told so they can find different pictures.
By having the students use investigation, a teacher is able to establish a trusting classroom atmosphere as well as have the students see that abstract concepts are very meaningful. (Conundrum, 2001)
By definition, “a tangram is an ancient Chinese puzzle that provides another avenue for exploring rational number concepts.” (Teaching and Learning, 83) They are very useful to explore number concepts as well as in guided discovery. Tangrams are used for many things, including, understanding fractions, relating areas, discovering the Pyth...
... middle of paper ...
...om. Guided discovery through concrete materials will take over all math classes soon. As long as tangrams are among them, the students will learn a lot and retain the information for a lot longer.
Works Cited
“Areas of Tangram Pieces.” http://mathforum.org/trscavo/tangrams/area.html.
“Developing Geometric Understandings and Spatial Skills through Tangram Puzzles.” http://illuminations.nctm.org/index_d.aspx?id=168
Hatfield, Mary. “Use of Manipulative Devices: Elementary School Cooperating Teachers Report.” School Science and Mathematics. Volume 94, Issue 6. October 1994.
“More Tangram Activities.” http://mathforum.org/trscavo/tangrams/activities.html
Naylor, Michael. “Tangram Tricks.” Teaching Pre K-8. 32 no 8, 26-7. May 2002.
“The Pythagorean Theorem with Tangrams” http://www.math.wichita.edu/history/activities/geometry-act.html#pyth-tan.
Rigdon, Deanna. “Tackling Tangrams.” Teaching Children Mathematics. 6 no 5, 304-5.
January 2000.
Rubenstein. Teaching and Learning Middle Grades Mathematics. Key College Publishing. California. 2004
Thatcher, Debra. “The Tangram Conundrum.” Mathematics Teaching in the Middle School. 6 no 7, 397-9. March 2001.
With wonderful learning opportunities, a team of sharp and intelligent classmates and teachers, and specialized equipment, the Governor’s School at Innovation Park is the ultimate dream of all determined math/science devotees. With my natural curiosity for mathematics and science and eagerness to take on challenging ideas, I can collaborate with the team at Governor’s School to develop our wide spectrum of ideas and abilities into a highly sophisticated product.
teachers and students. It is true that students that this will help to increase their reasoning
The most common environmental, individual, and agent factors that increase the risk of this serious childhood health problem are obesity, exposure to secondhand smoke, and hospitalization with pneumonia. In the United States, “the prevalence of childhood asthma has increased from 3.5% in 1980 to 9.6% in 2009” and “according to a recent nationwide survey targeting 0-to 17-year-olds in the USA, nearly 25% and 13% were obese and diagnosed with asthma respectively” (Liu, Kieckhefer, & Gau, 2013). According to t...
3. Canoy D. et al (2004) Abdominal obesity and respiratory function in men and women in EPIC-Norfolk Study, U.K. Amer. J. Epidemiol, 2004;159 (12): 1140-1149.
All children learn differently and teachers, especially those who teach mathematics, have to accommodate for all children’s different capacities for learning information. When teaching mathematics, a teacher has to be able to use various methods of presenting the information in order to help the students understand the concepts they are being taught.
The relationship between obesity and health has been a major factor in drawing national attention to the growing prevalence of obesity. As the second leading cause of preventable deaths in the United States, obesity claims approximately 300,000 lives each year (Salinsky & Scott, 2003). Obesity is strongly associated with multiple chronic conditions, such as high blood pressure, high cholesterol, heart disease, stroke, type 2diabetes, and with some forms of cancer, such as uterine, gall bladder, breast, colon, and kidney. Other conditions, such as sleep apnea, asthma, arthritis, reproductive complications, and psychological disorders such as depression, can be attributed to obesity as well. Obese individuals have a 50 percent to 100 percent increased risk of death from all causes, compared with normal-weight individuals. Most of the increased risk is due to cardiovascular issues.
Obesity is a severe public health problem which can threaten our health. This is because obesity is a factor that can develop into certain chronic diseases later life, for examples diabetes, cancers and cardiovascular disease (L. Cai, J. He, Y. Song, K. Zhao, W. Cui, 2013). Obese persons have higher risk of many health conditions, such as sleep apnea, mental health conditions, stroke and osteoarthritis(CDC, 2011). Cardiovascular diseases can be caused by obesity and they were the top cause of death in 2008. BMI 25.0 to 29.9 has higher risk of co morbidities and BMI more than 30 has moderate to serious risk of co morbidities. Underweight less to cause dea...
Recent studies have shown that these increases in extreme obesity rates are not specific to a certain population, but are rather an integral part of the weight distribution in the USA, and the more extreme the obesity, the higher the rate of growth [4]. Thus, the public health concerns associated with this growth are of extreme importance given that those who are obese in any form are much more likely to suffer from obesity comorbidities including type 2 diabetes, cardiovascular disease, hypertension, hyperlipidemia, asthma, sleep apnea, and stroke. (Ginny Garcia, Ph.D. & Thankam S. Sunil, Ph.D. & Pedro
However, technology should never substitute the fundamental learning in our educational systems. Specifically, in primary school, building a firm fundamental education is crucial. Seeing children still using fingers to do simple math in second grade is not a good sign of academic improvement. Though the students may easily figure out the answers by using a calculator, before letting the children get any closer to these technical gadgets, they have to first learn to figure out the answers themselves.... ... middle of paper ... ...
Skemp, R (2002). Mathematics in the Primary School. 2nd ed. London: Taylor and Francis .
Mathematics teachers teach their students a wide range of content strands – geometry, algebra, statistics, and trigonometry – while also teaching their students mathematical skills – logical thinking, formal process, numerical reasoning, and problem solving. In teaching my students, I need to aspire to Skemp’s (1976) description of a “relational understanding” of mathematics (p. 4). Skemp describes two types of understanding: relational understanding and instrumental understanding. In an instrumental understanding, students know how to follow steps and sequential procedures without a true understanding of the mathematical reasons for the processe...
...nd make similar problem situations, and then, they provided the students with a little bit of practice because practice makes perfect! After that, teachers may put the students on the situation given just now.
Posing questions on materials covered and the quality of materials selected can create the desired environment for students to thrive. I want to inspire my students to think outside the box and to ask questions. Society needs thinkers not robots. The classroom plays an important part in aiding the growth of an individual. It is my duty as a teacher to impart knowledge because ideas have a way of changing lives. Examining and discussing ideas with students allows them to move to a new level of understanding, so that ultimately, they may be transformed.
Imagine you are on vacation on a cruise having a great time. You look around and see the ocean is covered with garbage. According to Discovermagazine.com, there are patches of garbage present in the middle of the oceans. If you collect all garbage in the oceans, it would be double in height to Mount Everest. According to climatechange.com, if we do not act immediately, not recycling is going to affect our environment. Refusing to recycle the waste materials would poison the food and water we use, leading to our death. Recycling affects the earth more than we can imagine. We’ve got be more aggressive towards reducing and reusing the waste material, as there is an increase in the amount of garbage production.
Martin, D. J. (2000). Elementary Science Methods: A Constructivist Approach( 2nd Ed.). Belmont, Ca: Wadsworth.