History of Geometry

I decided to take a look at the history of geometry. Geometry is used in numerous professions related to engineering, architecture and space exploration. It was used by Greeks and Egyptians in building their pyramids and monuments. Geometry, by definition, is a branch of mathematics concerned with properties of shapes and space. Egyptians, specifically Egyptian priests, have been noted to invent the science of studying shapes and space around 580 B.C. Beginning in 300 B.C., the first of 12 books were written by Euclid, who collected the elementary truths of Geometry and many were used in schools. The Euclidean thought of Geometry then became well known and respected. Euclid’s first book included information such as shapes occur in the real world, parallel lines never meet, and the angels in a triangle always add up to 180 degrees.

One quote I found interesting was from Thomas Hill in 1855. He wrote in the preface of the book, First Lessons of Geometry, “I have addressed the child’s imagination rather than his reason, because I wished to teach him to conceive of forms. The child's powers of sensation are developed before his powers of conception, and these before his reasoning powers. This is, therefore, the true order of education.”

Maybe we should be introducing Geometry at an early age.

When should Geometry be Taught?

I think that Geometry should be taught in 9th grade. I think that Pre-algebra should be taught in 8th grade to all students, then Geometry in 9th grade and Alg. 1 in 10th and Alg. 2 in 11th. I think this is a logical order for the maths to be taught in and it introduces the Algebra to all students in middle school so they are not struggling but not falling behind either. Also, I think this is young enough in high school that they have plenty of time to understand it and aren't struggling to understand it in elementary school or middle school. Yes, I think the idea of shapes and measurement like length, width, area, perimeter can start to be introduced in elementary school, however should not be a major topic until 9th grade. I took Geometry in 10th grade in high school and did not feel behind and actually even though math has always been a struggle for me, I understood geometry at that age and grade and after taking Alg. 1. I think Geometry should be required for all as it can be useful in knowing how to build or measure something in our every day life even if we do not use it in our jobs. I just don't think it should be introduced as an entire subject or unit in Elementary School as I think it would be too difficult at that age for most students.

When to Teach... Geomentry?

When to introduce geometry into the classroom? Well, I remember back when I was in Elementary and High school math was the subject that my school seemed to be behind in. I am from a small town up north that maybe didn’t get the best funding or books or supplies for school. So, my math class was always a year or two behind the others. I actually never learn geometry until I was in 10th grade and took geometry. Yes, we were introduced to it a little here and there throughout other years of school but we never really studied geometry until 10th grade. I personally liked that I didn’t learn it until I was older because I feel that I better understood it than maybe others would at a younger age. I always remember talking with my cousins who lived in the cities about the subject we were learning. I remember one cousin of mine was taking geometry in the 8th grade. Wow! Now thinking back over that I would have never understood geometry at that age. So, when to introduce geometry, I say we give them the proper background in geometry throughout elementary but don’t fully teach it until late middle school or early high school level.

Anybody can learn Geometry

I read the article "Geometry is supposed to be easy" http://abcnews.go.com/Technology/story?id=1537045 . What I got from it more than anything is that Geometry is all around us and we develop thoughts and ideas about it weather it is taught or not. We see patterns and make connections about how objects belong or don't belong. It really isn't a subject that we need to wait to introduce children to, from an early age they are seeing the differences in the shapes in their toys, it is never too early to start teaching children the names of these objects and telling them how they are the same and how they are different. The more they know the better prepared they will be to understand new concepts. Some Geometry could be introduced into all math so they can see how they relate and have some familiarty with it. Angles are everywhere, on a clock, a ramp, they are used everywhere in sports just being aware of them and how they work can be very useful.

Manipulatives in Geometry

Using manipulative's to teach any type of math makes since, they really give the students the opportunity to see how to solve the problems. The manipulative's help break down the problems for the children, and make them to remember later on. I think that manipulative's will help all ages to do, and remember all sorts of problems. Using them for geometry is a great idea. I used the NLVM (http://nlvm.usu.edu/en/nav/topic_t_3.html) (National library virtual manipulative's) web site to check out different manipulative's for geometry, and found it to be very helpful. They have different manipulative's for different age groups, and they are all virtual so the children get the hands on practice needed for them to remember how/what they are doing.

How young is too young for geometry?

When I think of geometry, I usually think of my eighth grade math teacher. He was a pretty funny and dry humored guy. But I was 14 in eighth grade. We begin various geometry lessons from the time we can first visualize an item. As babies we had a variety of multiple toys that were played with of all sorts of shapes and sizes. As toddlers and preschoolers we begin to learn the correct naming of all of these fun looking shapes. (Square, triangle, circle, rectangle..etc) Geometry is all around us from the time we are born. We may not know we are learning it but we are. I found an article called The Geometric World of Young Children. The article reminded me of all the fun projects and ideas I had as a preschool teacher. My hope, some day, is to teach a younger elementary grade level. I may not have to get in depth with all of the evasive equations like in our chapter 10 homework, but the teachers who teach in the younger elementary set a guideline for the future of their students. If a student doesn't know a hexagon has six sides they may struggle in future geometry classes. One of the most interesting points I found in the article was, they gave a, sort of, scenario about taking a 4-year-old on a walk to the grocery store. If a parent were to take their child on a walk to the grocery store turning in multiple directions the child, when asked, will be able to point out which direction the grocery store is in when they arrived home. I have witnessed many parents amazement when their 3-year-old can tell them where to turn on their way to preschool. Children at such young ages are using math through multiple everyday experiences and they don't even realize it. I don't know if any age is too young to teach geometry as children are learning it way before we, as future teachers, begin to teach it.

The Wonderful World of Geometry

I think Geometry can start at a very young age and that is just by learning shapes. The world has so many fascinating shapes and once children see those geometric shapes it opens up a whole new world. When working with children in the preschool, I found that they loved finding shapes in their classroom and outside in the playground. For example, they get to see and touch everyday shapes like, blocks, party hats, stop signs, balls, clocks,etc. For some students when they discovered a "Shape" they would get so excited, it was as if they discovered "Gold"!

When children get older, they can learn about "patterns" and that numbers and objects repeat in predictable ways. Also, in the third grade they get to draw and cut out patterns to see the relationships. I think manipulatives to teach geometry, especially in the early years is important. Instead of looking at a book and learning a shape from a page in the books, kids can touch and see the shape. When subbing for the third grade teacher, the students had to cut out their shapes and then colored the shapes when they halved them into sections. This cutout was used to solve their math geometry problems. This helped all learners, from struggling to high achievers, which is why manipulatives is so important.

I think that geometry is so important for students to learn and understand for their future because there are times when we need to know how to figure out how much carpet we need for our floor or proportionally what size furniture pieces will fit in our living room and the list could go on. Everyone, will have a chance to build or create at some time in their life and will need to understand geometry. However, I think we should teach geometry so students learn it well. In our country, we try to teach so many new concepts and formulas that students have a hard time remembering it the next year. As we have learned it's better to "dig deep" than only scratch surface!!