Sunday, September 8, 2024

Why Is Geometry So Hard

Lack Of Understanding Of Geometry Concepts

Why is Math so HARD?!

Two Dutch researchers, Dina van Hiele-Geldof and Pierre van Hiele, suggest that students’ geometrical understanding progresses through various levels, which cannot be skipped. These levels are now known as van Hiele levels. Other research supports their theory and has found that most students enter high school geometry with a low Van Hiele level of understanding. Thus they cannot possibly understand the teaching, since writing formal proofs requires at least a van Hiele level 4.

The levels of van Hiele are :

This theory is not perfect but based on other research, it seems to model the progress of geometrical thinking. The important point is that a lot of the geometry taught before high school does NOT foster students into higher level of geometrical thinking. Many geometry problems in text books are mere calculations, such as, “Calculate the area/circumference/perimeter/radius of this figure.” Textbook problems concentrate too much on calculating and using formulas, and not enough on analyzing and investigating figures, and making conjectures about the properties of figures and testing them. More on this later.

Learning Difficulties & Disabilities

While teachers do a great job of bringing out the best in their students, the classroom isnt always the easiest learning environment for every child.

For children with learning difficulties or intellectual disabilities, its much harder to enjoy learning math without a teacher or teaching assistant who knows how to properly support them.

Also known as being neurodivergent, children with difficulties like dyslexia can find it challenging to read math questions or solve word problems. Other neurodivergent challenges like being on the autism or ADD/ADHD spectrums can also make it hard for your child to focus and comfortably participate in classroom math activities.

If you suspect your child is experiencing a learning difficulty and believe its affecting their performance in math, contact your childs teacher or school. Many schools offer special learning programs that will identify your childs difficulty and tailor a learning program designed to help them reach their full potential.

Top 7 Reasons Why Math Is So Hard

• Math is hard because you have a bad teacher. There are many reasons why you may end up with a bad teacher. Among others, the teacher was asked to teach a subject that he does not quite understand himself or the teacher does not know how to explain math concepts in a clear way.
• Math is hard because somebody told you that “math is hard” and you believed it.
• Math is hard because you are not a good reader. Many students struggle with math because of their inability to read critically the information in a math textbook.
• Math is hard because many concepts are abstract and therefore require more effort to understand them.
• Math is hard because you do not like math. May be you like music, sport, or language and that is ok. However, if you do not like something, you may not invest the time and effort that is needed to understand it.
• Math is hard because you do not get the support or the tutoring that you need on occasions. Some math concepts may be hard to understand, so you will need some extra help from time to time may be from a teacher, your parents, or a friend to understand something. A lack of adequate support when you need it the most can make math harder to understand.
• Math is hard because you may have some cognitive limitations. In that case, it is not just math that will be hard. You may struggle to learn anything.

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Get Other Professional Help

Challenges like math anxiety and learning difficulties shouldnt hold your child back from enjoying math. Getting professional help for your child, like sessions with a school counselor, can help your child develop coping strategies that will make them feel more confident with their math skills.

Make More Room For Data Science

Ninety percent of the data we have in the world right now was created in the past two years, Boaler said. Were at a point in this world where things are changing, and we need to help students navigate that new world.

Other countries act more quickly on that idea. Estonia students ranked first among European countries in mathematics, as well as reading and science, on the 2018 Programme for International Student Assessment. Many factors may have helped: The country offers high-quality early childhood education to all kids, class sizes are small, and there’s little high-stakes testing, leaving more time for instruction.

Unlike other countries, Estonia teaches computer programming at all grade levels a strategy started in the upper grades in the late ’90s and extended to elementary schools around 2012. The country is experimenting with adopting a new computer-based math curriculum.

Computer-based math:What it looks like, and why it’s important

In the USA, about 3,300 students this year in 15 Southern California school districts are taking a new Introduction to Data Science course that features data and statistics, real-life data collection and coding to analyze the data. The course was developed by the University of California-Los Angeles and the LA Unified School District, and it counts as a statistics credit.

Why Is Math So Hard

Why is math so hard ? Here are the top 10 reasons why you may end up believing that math is only for geniuses.

I came up with these 10 reasons based on my experience teaching mathematics in high school. First, see the top 7 reasons below. Then, keep reading to see my top 3 reasons why math is so hard.

Ongoing Math Support For Struggling Students

Learning math isnt always easy for some children, especially if they dont have the resources or support they deserve. At Prodigy, we know not every parent has the time or capacity to completely manage their childs math learning, even though they want the very best for their childs education.

Thats why Prodigy is here to help you and your child. Prodigy is an online math game that immerses your child into a safe, fun and engaging game-based learning environment. All our math questions are made by teachers for students in 1st grade all the way to 8th grade.

• Work on the areas they find hardest Thanks to our nifty algorithm!
• Practice math activities Specifically designed for your childs curriculum.
• Learn in a fun and safe space Complete with cute pets, engaging math battles and plenty of exciting quests.

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How Hard Is Geometry

Geometry is the study of shapes, as well as their sizes, angles, and dimensions. Typically, in high school geometry courses, students are introduced to formal proofs, in which they must demonstrate logical reasoning through application of math laws. Through a series of logical deductions, students will have to write out statements and reasons in order to prove or disprove a given statement, usually relating to geometric shapes.

Many students list proofs as some of the more difficult aspects of geometry in high school, but there are other complicated subjects that geometry classes cover. The SAT also places importance on a strong grasp of geometry in both of the Math sections. Topics like congruency and similar triangles, angle rules, and shapes areas appear very often within the SAT, so its important to have a good understanding of basic geometry rules and formulas before taking the exam. If a student is unfamiliar with the core concepts of Geometry they might need SAT tutoring.

If a student is struggling with their geometry class in high school, we recommend looking up some cheat sheets with a general outline of extremely common core concepts. SoFlo Tutors has a great school resource page students should explore.

Ancient Geometry: Practical And Empirical

Why is Math So Hard?

The origin of geometry lies in the concerns of everyday life. The traditional account, preserved in Herodotuss History , credits the Egyptians with inventing surveying in order to reestablish property values after the annual flood of the Nile. Similarly, eagerness to know the volumes of solid figures derived from the need to evaluate tribute, store oil and grain, and build dams and pyramids. Even the three abstruse geometrical problems of ancient timesto double a cube, trisect an angle, and square a circle, all of which will be discussed laterprobably arose from practical matters, from religious ritual, timekeeping, and construction, respectively, in pre-Greek societies of the Mediterranean. And the main subject of later Greek geometry, the theory of conic sections, owed its general importance, and perhaps also its origin, to its application to optics and astronomy.

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Why Do Kids Struggle With Geometry

Why do kids struggle with Geometry?

Geometry is the branch of mathematics that deals with the properties, measurement, and relations of points, lines, angles, surfaces, and solids. In laymans terms it is math applied to pictures. Many people say it is creative rather than analytical, and students often have trouble making the leap between Algebra and Geometry. They are required to use their spatial and logical skills instead of the analytical skills they were accustomed to using in Algebra.

There are 3 major reasons students struggle with Geometry:

1. They dont understand and cant apply the vocabulary to decode the problem.

2. They cant see or recognize all of the pieces that go into making up the Geometry problem.

3. They struggle with the Algebra skills involved in doing Geometry, which means they didnt retain some of their skills from last year.

Most Geometry problems are given in terms of pictures. It is probably one of the first times in a students Mathematical career that the problem hasnt been completely spelled out for them. If they dont pick up on the subtle clues given in the picture, they arent able to decode the problem. The information they need is all there, they just dont recognize it as useful. Vocabulary plays a critical role in this process. If you dont know what a bisector is and what it does, how are you going to be able to solve a problem involving one?

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Change The Way Elementary Teachers Think About Math

Improving the math aptitude of older students in the USA is connected to messages students hear about why math is important and who’s good at it when they’re younger.

Those messages often come from their elementary school teachers, many of whom didnt like math as students themselves.

“Math phobia is real. Math anxiety is real,” said DeAnn Huinker, a professor of mathematics education at the University of Wisconsin-Milwaukee who teaches future elementary and middle school teachers.

New research suggests that when teachers improve their attitude toward math, it can help to raise student test scores. At Stanford, Boaler and her team designed an online course for teachers featuring research showing anyone can learn math with enough practice, intelligence isnt fixed and math is connected to all sorts of everyday activities.

They recruited fifth grade teachers from a county in central California to take and discuss the course. Within a year, the participating teachers’ students posted significantly higher state math scores compared with previous years. The jumps were particularly significant for girls and low-income students, Boaler said.

They thought they had to teach procedures, and then realized they could teach in this open, visual, creative way,” Boaler said. “A lot of research studies suggest that it takes a long time for changes to come about. In this one, it was quick.

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Why Is Geometry So Important

Geometry is defined as the area of mathematics dealing with points, lines, shapes and space. Geometry is important because the world is made up of different shapes and spaces. Geometry helps comprehend the measurements and relationships of lines, angles, surfaces and solids found in the everyday world.

Reasons Why Geometry Can Be A Hard Class

In geometry, you will be finding the lengths of the sides of shapes, finding the sizes of angles and doing things such as finding perpendicular lines. There will also be some algebra involved as will. However, the algebra can be made easier by the more visual elements in geometry.

Geometry can be a difficult class for some students for a number of reasons.

The first reason is struggling with algebra. If you had a hard time with algebra, it would help to take the time now to brush up on it since it will help you to do better in geometry. It will also likely be very important for any later mathematics classes that you take.

The best way to improve your algebra for geometry would be to watch a geometry playlist and to make sure to take the time to understand the algebra as you go. I will provide you with some materials to use at the end of this post.

The second reason why students can have a hard time in geometry is that geometry involves proving things such as the size of an angle or the length of a side. These proofs can be difficult for many students who are not used to them. However, they are basic proofs and it will be possible for you to learn how to do them by studying.

Why Cant I Do Geometry

Students are often faced with many doubts like Why is geometry so hard?Is geometry hard?Why can’t I do geometry?Why learn geometry?How hard is geometry and Geometry is hard. And thus, discussing this is integral in clearing these conceptions to the point they thinking Geometry is easy!.

Children often have this fear in their minds that geometry is hard and ask why I can’t do geometry. Removing this fear of geometry is hard is the first step that should be taken by you as a parent. It’s possible that children are not vocal about it, and you may have to identify this difficulty for them. Observe if they are:

Why Is Learning Modern Algebraic Geometry So Complicated

Many students – myself included – have a lot of problems in learning scheme theory. I don’t think that the obstacle is the extreme abstraction of the subject, on the contrary, this is really the strong point of modern algebraic geometry. I’m reading many books such those written by Hartshorne, Gortz & Wedhorn, Liu, Vakil , Gathmann , Shafarevich, Perrin and Milne and in my humble opinion the learning problems arise from the following considerations:

• In mathematics when two object are isomorphic, it is a common practise to “identify” them. Basically if \$A\cong B\$ but \$A\$ has a simple description we write \$A\$ instead of \$B\$, but formally we are thinking of \$B\$. This procedure is used very often in algebraic geometry, but in some cases without explaining the isomorphisms and in other cases the two objects in question are considered “really the same” even if this can provoke formal problems . This “abuse of identifications” often makes one lose sight of the essence of what one is studying and once again the “stupid student”, exhausted, tends to simply memorize things. I point again that the problem is not the abstraction, but the fact that the excessive tendency to simplify notation, often leads to inconsistencies.

• In summary, because of the above issues , rigorous mathematical statements, incredibly seem to be informal dissertations at the eyes of the student that is eager for formalism.

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Math As A Cumulative Discipline

Math know-how is cumulative, which means it works much like a stack of building blocks. You have to gain understanding in one area before you can effectively go on to build upon another area. Our first mathematical building blocks are established in primary school when we learn rules for addition and multiplication, and those first concepts comprise our foundation.

The next building blocks come in middle school when students first learn about formulas and operations. This information has to sink in and become firm before students can move on to enlarge this framework of knowledge.

The big problem starts to appear sometime between middle school and high school because students very often move on to a new grade or new subject before theyre really ready. Students who earn a C in middle school have absorbed and understood about half of what they should, but they move on anyway. They move on or are moved on, because

• They think a C is good enough.
• Parents dont realize that moving on without a full understanding poses a big problem for high school and college.
• Teachers dont have time and energy enough to ensure that every single student understands every single concept.
• So students move to the next level with a really shaky foundation. The outcome of any shaky foundation is that there will be a serious limitation when it comes to building and real potential for complete failure at some point.

Concentration And Attention Difficulties

Why math is so hard for some students

When your child is trying to solve a math problem, they need to concentrate and carefully follow each step. If they lose concentration or are distracted at any point in this process, theyre much more likely to make a mistake and will have to start over until they get the right answer.

Over time, making the same mistakes repeatedly can lower your childs confidence and interest when solving math problems, especially if they feel like theyre falling behind their classmates.

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Why Do You Need Trigonometry

As one of the most important fields of mathematics, particularly for careers that are built around calculating angles, a working knowledge of trigonometry and its uses is important for students of all ages. With consistent study, students can master all aspects of trigonometry and improve their mathematical skills.