Chapters

When it comes to teaching and learning geometry, many students and sometimes even teachers struggle.

Geometry translates the structural world around us into mathematical concepts, but not everyone can do this seamlessly.

Therefore, many students in Atlanta, New York, and other parts of the US turn to geometry tutoring services for assistance. Read on to discover how you can excel at this all-important subject, too!

## Van Haile's Thoughts On Geometry

**An abundance of established evidence illustrates the significance of geometry in the international school curriculum. **

One of the primary researches was conducted by a couple in the Netherlands.

This academic couple, Pierre and Dina Van Heile, developed a theory proving the importance of geometry.

According to them, some deliberate instructions are required to push children through their comfort zones, which only comes from studying geometry.

However, most youngsters are not inclined to think at a deductive level. Hence, they end up memorizing geometrical formulae like 'rules' and 'fact.'

Furthermore, they are always confused about the relationships between these geometrical ideas.

Given the situation, it is vital to learn geometry from someone who uses the right approach. To this end, Van Hiele puts forward three levels of geometric schooling.

### Level 1: Visual Understanding

The primary level or level 1 is where it starts. Also called nonverbal thinking, shapes are generally seen as 'whole,' and their appearance defines them.

Even though most children start using names of different shapes, they can rarely associate those shapes with familiar objects.

For instance, a kid might say, "This is square because it looks like a box." That is because children can identify some words by their literal definition before grasping the contextual meanings they carry.

### Level 2: Descriptive Understanding

At this level, kids can identify properties and the components of shapes. For instance, a kid can differentiate an equilateral triangle from other triangles because it has equal sides, symmetries, and angles.

That said, at this level, children cannot establish a language that goes with their freshly developed concepts.

Understandably, most kids in this stage cannot comprehend the different relationships between seemingly unrelated properties.

For instance, they might be able to identify an equilateral triangle, but they won't be able to tell that it has equal sides and angles.

### Level 3: Understanding Informal Deduction

Students at this level can see how one shape's property proceeds from another's. Consequently, this knowledge helps them accumulate increasingly complex geometric skills.

Moreover, it makes them understand the complex relationships between shapes.

By the end of level 3, students should have learned the basics. Then, after learning informal deduction, a student can begin establishing the foundations of formal deduction.

However, this is not always the case. In fact, many students would still be unable to comprehend the role of axioms, theorems, and their relationships.

## Developing the Geometric Thinking

Since the fundamentals of geometry are not sufficient to fully understand geometry, Van Heile's theory has also introduced five additional phases of activities.

These phases are designed based on children's previously acquired knowledge and level of understanding.

Wondering what they are? Let's delve in!

### Phase 1: Inquiry

Learning starts with playing!

That is right. You cannot instill something in children's heads unless they mentally open themselves to it. After all, the best way to open children's minds is to play with them.

Thus, teachers should create different games that allow children to play with shapes and explore their potential.

**Playing also offers teachers an opportunity to observe students' language and comprehension.**

So use relevant toys that can cultivate students' grasp of geometry. Alternatively, you can ask students to draw various shapes and share their thoughts about them.

Although these activities are academic, students must not feel that they are being given assignments and evaluation tests.

### Phase 2: The Direct Orientation

In this phase, children engage in activities that help them identify the particular characteristics of shapes.

Teachers can ask their students about the shapes that combined form a complex structure. Furthermore, teachers can ask students to choose between the shapes and name their properties.

These activities will help children garner more understanding regarding different shapes. Moreover, they will encourage young students to notice properties they had not observed earlier.

**Lastly, the fun activities will help them see how different angles can fit together.**

### Phase 3: The Explication Part

In this phase, games and fun tasks are specifically developed to advance a specialized vocabulary in geometry. These ideas are predominantly created to help comprehend the features of varied shapes.

The teacher is expected to clarify some terms that children are already using, adding complexity to them.

As expected, this explication phase involves vocabulary. Hence, students should be encouraged to write and talk about their experiences.

Here are a few questions that a teacher can ask students in this phase:

- Name the shapes that have right angles or match them up.
- How many types of triangles are there?
- What is one feature shared among all triangles?
- Which shapes have parallel sides?

Irrespective of the chosen questions and the type of exercises teachers conduct, they must ensure they are engaging.

This is crucial because children are unlikely to take an interest unless asked to explain and demonstrate.

**Disinterest will make students treat these exercises just like other tasks. Consequently, they will rely upon rote learning rather than engaging with the content. **

### Phase 4: Free Orientation

As the name implies, in phase 4, children have the liberty to engage in any problem-solving activity.

Thus, a curriculum or geometry teacher is required to offer activities that can be completed in multiple ways.

**The chief objective of these exercises is to push students and help them utilize everything they have learned so far. **

To further help you understand, here is a list of questions that are ideal for this stage:

- How many ways are there to make a square?
- Draw or complete this square.
- Examine the given pieces concerning the provided grid and enlarge every detail.

### Phase 5: The Integration

The integration phase gives students different opportunities to pull together everything they know and reflect on the shape as a whole. After this phase, they should be able to summarize their knowledge.

For instance, teachers can divide their class into small groups, assigning different activities to each. For example, one of the groups can be asked to write about different shapes or make a chart about them.

See math class here on Superprof.

## What Are The Outcomes Of Five Phase Activities?

Since all activities mentioned above are curated to engage students, most can discuss shape properties by the end of these five phases.

Most pupils recognize the shapes and discuss their geometric properties if these phases are executed accurately.

Furthermore, they can make comparisons between the shapes. To put it in other words, the knowledge that a student has gained while moving from level 1 to level 2 will assist them with understanding geometry.

With that being said, students' knowledge regarding geometry should not be confined to the knowledge provided by these levels and phases.

Hence, tutors and teachers should offer more activities and experiences to develop geometric thinking among their students. You'll find geometry tutors in LA to be exceptionally open to this new way of teaching.

## What Careers Require Geometrical Skills?

Now that you know all the fundamental levels and phases of geometry, you might be wondering, "Why should I teach or learn this complicated stuff when they do not offer any jobs?"

Well, we have some good news!

Like every academic subject out there, geometry can also pave the way for a glorious career. Thus, if you are a student who relishes studying or practicing geometry, here is a list of some career options for you!

See online math courses here on Superprof.

### Graphic Designing

From making small animation clips to creating mind-blowing movies and artworks, graphic designing can open a world of career options for imaginative youngsters.

Since graphic designing animation involves the extensive use of 3-D images, it heavily depends on geometry.

Although computer programs can help make these geometrical shapes, human expertise is still needed to make those shapes into art.

Hence, if you want to create abstract imaging and understand graphic designing in detail, you should familiarize yourself with geometrical shapes.

### Robotics

Another common profession enabled by geometry is robotics. Creating different motions for robots or robotic equipment requires exceptional geometric skills.

**The ability to control the motion of robots could not have been possible without geometric skills.**

That is because one cannot determine different arcs and angles of robotic equipment unless they are capable of geometrical computation.

Not to mention, geometry is crucial in designing robotic equipment and its motion manipulation.

### Medical Imagining

Whether radiology, sonography, or MRI, medical imagining is one field that never runs out of demand. Plus, these fields can help an individual make quick cash.

**Aside from anatomy and physics, medical imagining also requires an adequate understanding of geometry. **

Once the medical imaging specialist takes a human body's scan, they must make a 3D reconstruction of internal human organs.

If the scan detects a tumor, the radiographer or practitioner must construct a three-dimensional reconstruction of it.

Otherwise, the tumor's shape, size, and density will remain obscure. Similarly, geometrical skills are applied to reconstruct bones, tissues, vessels, or other items in the human body.

### Construction

Structural geometry is another fascinating subject that marries structural understanding, building construction, and architecture.

Determining the stability of different structures and understanding their construction components requires solid geometric understanding.

Therefore, studying geometry can also open many fields of real estate development for you.

## Learn Geometry with Absolute Satisfaction

Learning geometry in Houston, Atlanta, and other parts of the US does more than just sharpen your mind. It can seriously help you build a lucrative career.

Therefore, you should stop seeing geometry as an uninteresting subject of strange shapes.

Hiring a private geometry tutor is highly beneficial since one cannot understand geometry unless it is taught correctly. Luckily, Superprof offers exceptionally qualified geometry online teachers in most US states, including Atlanta and Chicago!

So, it is time to put the confusion at bay and get on board with Superprof without further delay!

The platform that connects tutors and students