# data[].attributes.headline
"The van Hiele Model of Geometric Thinking"

# data[].attributes.subject
"The van Hiele Model of Geometric Thinking"

# data[].attributes.body
Taking each of the four levels of geometric thinking hierarchy, this informational piece breaks down what each level means for students as well as what that might look like in practice.

# data[].attributes.body
Museum Shapes: Metropolitan Museum of Art (2005); Using artwork from masters such as Matisse and Warhol, you can challenge students to look for particular shapes in paintings through an "I spy" approach. This can be extended to postcards of artwork from local museums or act as a catalyst for building "mathematical artists in the classroom.

# data[].attributes.body
Utah State University has created an amazing online resources called the National Library of Virtual Manipulatives. We have linked their geometry section that provides the public with free when you download Java or the NLVM app. It provides resources for K-2, 3-5, 6-8, and 9-12

# data[].attributes.body
Geometric concepts are those that are formed from the analyzation of not only shapes, but the components that create them as well. Understanding how points, surfaces, curves, & lines exist in harmony to make classifyable shapes helps us understand more complex geometric systems, which may be instrumental in resolving real-world problems.

# data[].attributes.body
In this activity students will be given four descriptors, and be asked to draw or create a shape that fits the description. Students will be put into breakout rooms and work with their small group to brainstorm different shapes and what properties they have. After working with their small groups, everyone will come back together for a large group discussion. Then, we will have each group explain why they picked what they did, and if they can think of any other shapes that they could have added as well.

https://docs.google.com/presentation/d/1N70d2NWQTGGMU5WEyy8RFGSl6on2oQUtvxcJAXULmgs/edit?usp=sharing

# data[].attributes.body
These wordless books contain photographs of geometric shapes in the environment. Using digital cameras to create hoban like books allow students to seek and identify two- and three- dimensional shapes in the world around them. Send the books home for students to share with families or have students in upper grades make books for younger students.

# data[].attributes.body
Mathigon provides an amazing free online resource for many math subjects however we have linked to the geometry section. It allows its users to create and manipulate polygons, tangrams, polyominoes, geometry utensils and so much more. This is also a resources that can be adapted to any age level depending on whether it is used for instructional input, guided practice, or independent practice.

# data[].attributes.body
This video includes a 4 minute song explaining 5 different 3D shapes. The video was created for kindergarten - 3rd grade and we all really enjoyed the way this video introduces the shapes. It provides multiple real life examples of a given shape and constantly reiterates all the shapes being covered in the video. Overall it is a super cute and engaging video that students could benefit from being exposed to.

# data[].attributes.attachment_link.title
3D Shapes Song For Kids | Spheres, Cylinders, Pyramids, Cubes, & Cones

# data[].attributes.headline
Geometry for Elementary Students: Beyond Just Shapes

# data[].attributes.subject
Geometry for Elementary Students: Beyond Just Shapes

# data[].attributes.body
This website is an awesome way to help you as a teacher solidify how we can approach geometry in the classroom. It connects you with a 7 minute video explaining how we should introduce geometry in the classroom and to help our students really grasp the concepts as well as a transcript of the video. It also links a pinterest board/website that provides some activities that are in line with everything previously discussed.

# data[].attributes.attachment_link.readable_text
Geometry in elementary school tends to be a lot about just shapes. Today, I want to talk about why we need to take a look at teaching geometry for elementary students beyond just shapes.

Here are links to products/activities mentioned in this vlog. (Some may be affiliate links which just means that if you do purchase using my link, the company you purchased from sends me some money. Find more info HERE about that.)

Now the first thing I want to direct your attention to is the van Hiele levels. These levels are one of the main research that we have around geometric thinking. And there's a lot of people who don't know about them. I'm going to give you a brief overview. And, if you want to know more, here's a link to a great site by Nrich that you can go to to get a little bit more info about these levels.

But basically, kids in elementary school are typically in Level 0 and 1, and some a little bit in Level 2 in the upper grades of elementary. The research of Van Hiele showed that Level 0 is known as Visualization. This is where kids see visuals and it looks like something. So this is where you see kids who will say that a ball is a circle because it looks like a circle. They aren't looking at attributes, knowing that it's three-dimensional, and that makes it a different shape. They just say it looks like whatever. An ice cream cone looks like a triangle to them because of the shape. It's got a point. And that's all that they're noticing.

A Level 1 is when they start to get into the Analysis, or what's known as the Description level. This is where kids will start to notice some properties about something. And they use those properties. But they aren't starting to see connections between properties. So, they might notice and say how a square is a square, because it has all the same sides, but they don't know how a square is connected to a rectangle. They don't see those connections.

That starts to happen in Level 2, where they are able to use properties, they're able to justify thinking about shapes, they're able to analyze a little bit, and kind of get informal proofs. This is the stage that's known as Informal Deduction. And that's about where elementary kiddos stop.

There are Levels 3 and 4, as kids progress through their understanding of geometry, into middle school, high school, and beyond. And this is where kids start giving formal proofs, they start doing very abstract geometry. We're not going to go into those levels here. But I wanted you to understand those three levels that most of your students will progress through, throughout elementary school.

We tend to focus a lot on shapes because that's a lot of the description that happens in those Van Hiele levels. I want to give you three things that will help kids progress through those Van Hiele levels, that isn't necessarily about describing and identifying shapes.

Our first one is to use lots and lots of visuals. Now, in geometry, geometry is very visual. And I was a kid, growing up, that I did wonderful in mathematics, until I was in high school, and did geometry. And it was because it was so visual and I had to prove things. And to me, I was like, just give me the procedure and tell me how to do it. I wanted the abstract numbers and the equations to do. I wasn't used to doing visual things. Yet there were other groups of kids who struggled in mathematics, but then they finally flourished when they got into geometry because it was so visual. So, the first recommendation is to include lots of visuals that aren't just shapes.

You guys hear a lot from me around number sense, about how we need to build a sense of numbers. That three isn't just the digit 3, it is three things. And giving kids those visuals in all areas of mathematics will help kids as they're developing that Level 0, and moving into Level 1.

Now, a thing that will help with Level 1 is our second recommendation here, which is to let kids draw. Not just in geometry, but in all of mathematics. You guys know I'm a big fan of the C-R-A model, which is Concrete, Representational, to Abstract. Kids need to start out with concrete manipulatives. But oftentimes we jump from those concrete manipulatives to the abstract symbol. So they're seeing three, and then we're attaching the digit 3 to it.

The in-between phase is a representation. They need to draw three things. Or draw a model of three. Because we all know there is a whole lot that goes into drawing something versus just seeing it, and saying, "Oh yeah, that's three." When you have to sit there and draw three squares, or three rectangles, something is starting to build in that kid about what they start to notice about shapes, that they don't do if they just see three cubes. So get kids to draw, and that will help kids in that Level 1.

Get Kids Explaining & Proving

Alright, my third recommendation is to get kids explaining their thinking and proving their thoughts. Ask them, "Why is this correct?" It's not just in geometry. But if they figured out 7 + 8 is 15, having them explain it and prove their thinking isn't just to be mean but to get them to explain why they think that is the answer.

And there comes a point that, yes, we just let kids say, "7 + 8 is 15." But having them explain their thinking will start to build other ideas. It's not just about getting to the answer. Remember that it's not just about creating calculators. It's about building their math minds and getting kids explaining their thinking. And justifying why they're right.

Plus, It's not just about building their math minds, guys, it's about just common things that we need kids to be able to do in life, right. Not just proving why they're right about an answer in mathematics, but proving why they think something is correct out there in life. It's a habit that we want to help develop in all aspects of our children. But mathematics, when we do it in there, it also helps start to build them into Level 2, and get them to start having informal deductions.

So, you can focus on shapes in geometry. But, I want to encourage you to provide lots of visuals outside of shapes and geometry, get kids drawing, and get them explaining and proving their thinking. All of that goes into helping your kiddos progress through the Van Hiele levels and build their geometric thinking.

Alright, I hope that this helped you build your math mind, so you can go build those math minds, and not just create calculators.

# data[].attributes.attachment_link.title
Geometry For Elementary Students Beyond Just Shapes - The Recovering Traditionalist

# data[].attributes.attachment_link.description
Geometry in elementary school tends to be a lot about just shapes. Today, I want to talk about why we need to take a look at teaching geometry for elementary students beyond just shapes. Here are links to products/activities mentioned in this vlog.

# data[].attributes.headline
Cubes, Cones, Cylinders, and Spheres by Tana Hoban (2000)

# data[].attributes.subject
Cubes, Cones, Cylinders, and Spheres by Tana Hoban (2000)

# data[].attributes.body
Textless book, photographs of shapes from everyday life

# data[].attributes.headline
Shapes, Shapes, Shapes by Tana Hoban (1996)

# data[].attributes.subject
Shapes, Shapes, Shapes by Tana Hoban (1996)

# data[].attributes.body
This is a wordless book that shows children that geometric shapes are all around us.

# data[].attributes.headline
So Many Circles so Many Squares by Tana Hoban (1998)

# data[].attributes.subject
So Many Circles so Many Squares by Tana Hoban (1998)

# data[].attributes.body
Helps students look at the world differently. They begin to see that squares and circles are all around them.

# data[].attributes.headline
The National Council of Teachers of Mathematics 

# data[].attributes.subject
The National Council of Teachers of Mathematics 

# data[].attributes.body
This infographic offers a clear & concise understanding of the van Hiele model.

# data[].attributes.body
This tune introduces terminology relating to shape formation through comparison to everyday objects, such as "parallel" & "congruent" alongside relevant educational visuals.

# data[].attributes.attachment_link.title
Geometry: Lines & Angles Songs For Kids | 3rd Grade - 5th Grade

# data[].attributes.body
This pictoral & descriptive lesson demonstrates step-by-step components which result in the formation of shapes!

# data[].attributes.attachment_link.readable_text
Below are some of the key concepts and terms you will need to know in order to begin your study of geometry.

Points

In geometry, we use points to specify exact locations. They are generally denoted by a number or letter. Because points specify a single, exact location, they are zero-dimensional. In other words, points have no length, width, or height. It may be helpful to think of a point as a miniscule "dot" on a piece of paper.

Points A, B, and C

Lines

Lines in geometry may be thought of as a "straight" line that can be drawn on paper with a pencil and ruler. However, instead of this line being bounded by the dimensions of the paper, a line extends infinitely in both directions. A line is one-dimensional, having length, but no width or height. Lines are uniquely determined by two points. Thus, we denote the name of a line passing through the points A andB as , where the two-headed arrow signifies that the line passes through those unique points and extends infinitely in both directions.

Line Segments

Consider the task of drawing a "straight" line on a piece of paper (as we've done when thinking about lines). What you've actually done is create a line segment. Because our piece of paper has defined dimensions and we cannot draw a line infinitely in any direction, we have constructed a segment that begins somewhere and ends somewhere. We write the name of a line segment with endpoints A and B as . Note that the notation for lines and line segments differ because a line segment has a defined length, whereas a line does not.

Rays

A ray is a "straight" line that begins at a certain point and extends infinitely in one direction. A ray has one endpoint, which marks the position from where it begins. A ray beginning at the point A that passes through point B is denoted as . This notation shows that the ray begins at pointA and extends infinitely in the direction of point B.

Endpoints

Endpoints mark the beginning or end of a line segment or ray. Line segments have two endpoints, giving them defined lengths, whereas rays only have one endpoint, so the length of a ray cannot be measured.

Midpoints

The midpoint of a line segment marks the point at which the segment is divided into two equal segments. In other words, the lengths of the segments from either endpoint to the midpoint are equal. For instance, if M is the midpoint of the segment , then . Note that neither lines nor rays can have midpoints because they extend infinitely in at least one direction. It would be impossible to find the middle of a line or ray that never ends!

Intersection

When we have lines, line segments, or rays that meet, or cross at a certain point, we call it an intersection point. In other words, those figures intersect somewhere.

Parallel

Two lines that will never intersect are called parallel lines. In the case of line segments and rays, we must consider the lines that they lie in. In other words, we must consider the case that the line segments or rays were actually lines that extend infinitely in both directions. If the lines they lie on never intersect, they are called parallel. For instance, the statement " is parallel to ," is expressed mathematically as .

If extended infinitely, the lines above will never meet.

Transversal

A transversal is a type of line that intersects at least two other lines. The lines that a transversal crosses may or may not be parallel.

In both figures, the red line is a transversal.

Planes

A plane can be thought of as a two-dimensional flat surface, having length and width, but no height. A plane extends indefinitely on all sides and is composed of an infinite number of points and lines. One way to think about a plane is as a sheet of paper with infinite length and width.

Space

Space is the set of all possible points on an infinite number of planes. Thus, space covers all three dimensions - length, width, and height.

# data[].attributes.attachment_link.description
Below are some of the key concepts and terms you will need to know in order to begin your study of geometry. In geometry, we use points to specify exact locations. They are generally denoted by a number or letter. Because points specify a single, exact location, they are zero-dimensional.