Note: This blog post is part 3 of a three part series discussing the Van Hiele model which has significantly influenced the geometry strand of the Standards published by the National Council of Teachers of Mathematics (NCTM) and the new proposed Common Core Standards. Our math game called “Sunken Shapes” also follows this model to help kids learn geometry for Pre-K, Kindergarten and Grade 1. The game will be launched in the App store in the next few weeks. Please don’t forget to give us your feedback. Part 1 of the series can be found here. Part 2 of the series can be found here.

Level 2: Abstraction

At level 2, the objects of thought are the geometric properties of shapes and the relationships between those properties. So, kids start understanding that if one set of properties is true for a shape, then this may imply another property to be true. They understand necessary and sufficient properties. Because of their deeper understanding of the properties of the shapes, they can start recognizing that a square is also a rectangle. At this level of understanding of geometric shapes, kids can logically reason and answer simple “what if” scenarios. What if I stretch a square from the two opposite sides? Kids at level 2 are, however, not ready to understand or apply formal geometric proofs.

Kids at level 2 gain experience by identifying and experimenting with the “necessary” and “sufficient” properties of shapes. Initially they will list all the properties that they associate with a shape as necessary and sufficient. But with guidance, they will minimize them.

Note: This blog post is part 2 of a three part series discussing the Van Hiele model which has significantly influenced the geometry strand of the Standards published by the National Council of Teachers of Mathematics (NCTM) and the new proposed Common Core Standards. Our math game called “Sunken Shapes” also follows this model to help kids learn geometry for Pre-K, Kindergarten and Grade 1. The game will be launched in the App store in the next few weeks. Please don’t forget to give us your feedback. Part 1 of the series can be found here

Level 1: Analysis

At level 1, the objects of thought are classes of shapes rather than individual shapes. They start recognizing that these classes of shapes have certain properties. For example, any square (not just “this” square) has “4 equal sides, 4 equal angles, parallel opposite sides, etc.” At this level, they also start recognizing that for identifying shapes, features like size and orientation are irrelevant. However, they may still not to understand the concept of overlap in categories – to them, a square is not a rectangle, and a rectangle is not a parallelogram. A significant difference between level 0 and level 1 is that kids start to see specific shapes or drawings as representatives of classes of shapes based on the properties-match that they can find in the drawings.

Kids at level 1 gain initial experience by working on one class of shapes at a time. They can be given 5 different rectangle shapes, for example, and then they can list down the common properties they see in all those shapes. After some experience, they can start categorizing those properties under headings like sides, angles, diagonals, symmetries etc. At an advanced stage of this level, kids will be able to group and differentiate shapes based on multiple properties. And they will understand that if a property applies to a few shapes available, then it will apply to all shapes in the category.

Continue reading: Part 3 of the series

Note: This blog post is part 1 of a three part series discussing the Van Hiele model which has significantly influenced the geometry strand of the Standards published by the National Council of Teachers of Mathematics (NCTM) and the new proposed Common Core Standards. Our math game called “Sunken Shapes” also follows this model to help kids learn geometry for Pre-K, Kindergarten and Grade 1. The game will be launched in the App store in the next few weeks. Please don’t forget to give us your feedback.

Introduction

We all think about geometry slightly differently. However, we are all capable of thinking and reasoning in geometric contexts. There are five levels in which kids learn to reason in geometry. These levels do not tell us how much knowledge of geometry we have. Instead, they describe how we think and what types of geometric ideas we think about. Kids start at the lowest level (0), and with experience and instruction, progress to higher levels of sophistication. A well experienced elementary school student can reach up to level 2. However, without such experiences, even an adult will remain only in level 1. With our focus on elementary math education, we will only discuss the first three levels (Level 0 to Level 2).

Level 0 (Visualization)

At this visualization level, kids’ focus is on the overall appearance of the shape, with little or no attention to the properties of the shape. A square is a square because it matches with the “square prototype” that the kid has in mind. So, to the kid’s mind, a square that has been rotated at a 45-degree angle will not be a square anymore. It may become a diamond, or an unrecognizable shape. For kids in this level, the shapes can be changed by rotation or rearrangement. The goal at this level is to explore how shapes are alike and different and to use these ideas to create categories of shapes, like squares, triangles, circles, cylinders, etc. The kids may start by grouping a triangle and a square together (they both have corners). But with more experience, they will start recognizing the differences between the more pointy corners of a triangle and the right angle corners of the square.

Kids at level 0 gain most experience by evaluating common shapes and discussing interesting features that they see in the shapes. They can later compare two shapes and discuss features in the shapes that are alike and that are different. A kid at an advanced stage of this level should be able to sort multiple shapes based on a feature based sorting mechanism chosen by the kid, and should start noticing some traditional geometric properties.

Continue reading: Part 2 of the series

Note: The following is a post sent to us by a mother who has been trying MathZee games with her daughter. We put customers’ posts on our blog without any modification. Any opinion here is not necessarily ours. If you also want to send us a blog post, please send it by email to admin@mathzee.com .

Nothing is more permanent than change. I am certain many of you would agree. When I was in school, computers did not exist and research for homework was done the good old fashioned way — by going to the library. Most children today (at least the ones who are from well-to-do families) spend a significant portion of their time in front of computers and know how to operate the Blackberries and iPhones of the world by the time they are 5. Today’s generation has never seen life without all these gadgets. Entertainment through computers and smart phones is very natural to them. I think we are doing a disservice to these children by not utilizing this new media, that they are so familiar with, for education. Why not channel this interest into something fruitful? When education becomes fun, the child does not see studying as a forced task. Learning math through online games is a great way for a child to enhance her math skills while having fun. That’s why I am keen to see how my daughter will use Mathzee, and learn on her own.

I recently heard on radio that to keep students’s interest, a school teacher in a public school performs a song and dance routine while teaching math. What a brave feat! I doubt that I can dance or sing well enough (yet to keep my daughters interest in math. So, for now, I’ll just go with the easier solution — MathZee.

A new report released by Wheelock College’s Aspire Institute says that students will have more success in math and science if they are exposed to the subjects as early as pre-kindergarten. The report came from a study with the help of Boston area colleges and community groups. We at MathZee completely agree with the analysis. This is one of the main reasons why we decided to launch MathZee for Pre-K to Kindergarten students first.

According to the latest statistics from The Broad Foundation (a foundation to transform the public education system from K-12), out of 30 developed countries, US ranks 25th in math education. Moreover, by the time the US students complete 8th grade, their math education level is 2 years behind that of students from most other countries. More details can be found here

Note: The following is a post sent to us by an aunt. We put customers’ posts on our blog without any modification. Any opinion here is not necessarily ours. If you also want to send us a blog post, please send it by email to admin@mathzee.com .

As an aunt with six niece and nephews in the age range of 3-12 years, I now see the importance of education through the “oh so” magnificent computer! I started learning to work on the computer in my early 20’s. Today’s generation is clearly so far ahead. My niece and nephews at age 4 already know what I learned at such a later stage. Talk about a generation gap! Whenever I call my sisters in New York and I hear no screaming and yelling in the background, I know where the kids are. My sisters consider the time when the kids are huddled around the computers, playing games or discovering new stuff on the internet, quality learning time. “That is the only time I actually see them wanting to learn anything on their own, ever!” That makes me wonder how much happier my sisters would be if they could send their kids to a place where they could verify that the kids were truly learning something concrete. This way, the mischief makers would think they are just playing on the computer, but they would also be getting supplimentary education on what is taught at school.

This is why I am excited about Mathzee. I don’t know about you, but I find most of the online educational math game sites confusing, not easy on the eyes and, well, just random. Let’s face it; many of us were scared of math when we were kids. Who knows, if we had something like MathZee growing up, numbers could be my friends!

Recently, President Obama urged efforts to enhance Math and Science education. I am glad that powerful and inspiring people like him are trying to encourage people to take more interest in Math and Science. If you are not aware of the story, here is a quick summary:

The White House has launched a campaign to improve math and science education in the United States. President Barack Obama said, “It is about the ability to understand our world, to harness and train that human capacity to solve problems and think critically – a set of skills that informs the decisions we make throughout our lives. The initial commitment of the private sector to this campaign is more than $260 million.” Later, he said that students from many other countries are outperforming the United States, and his goal is to put America back on top within a decade.

As I mentioned before, I am glad that someone as powerful and inspiring as him is taking the education efforts seriously. However, I do want to highlight two questions:

1. $260 million doesn’t sound like a lot of money in the world of trillion dollar bailouts, defense expenditures and health-care costs. With all the cuts that schools are facing due to poor financial situation of most states (Look at the cost-cutting taking place in California), how much relief will this $260 million bring? I hope the private sector will increase its involvement many folds in the next few years.

2. Why is Mr. President trying to make education in Math and Science seem like a competition with other countries? In my personal opinion, he should stay with highlighting the benefits that education brings to an individual and her society. We should encourage our children to learn for their own benefit, not so that United States can outperform other countries.