Thinking Inside and Outside the Geometrical Box

Geometry is something we’ve all heard of and many of us have taken. If you’re an architect, drafter, mechanical engineer, urban planner or surveyor, you and geometry and probably really good buddies. For the rest of us, geometry was something we took in school – and whether we realize it, it was something that helped us develop our thinking into new and even more expansive mathematical concepts. To review, geometry is a branch of mathematics that deals with measurement, properties, lines, angles, surfaces, solids and their relationship to one another. Think of it as math applied in shapes and pictures. For some people, geometry is more of a creative endeavor than hard math, because it’s sometimes thought to have been less analytical. However, as creative as you may think it might be, algebra’s involvement in geometry definitely makes it math.

The crux we run into with geometry and teaching kids is that sometimes the leap between algebra and geometry isn’t so obvious. Algebra is very analytical and if students are accustomed to only putting on their analytical thinking cap when it comes to math, the spatial and logical skills used to do geometry can require a reroute in thinking. To be more specific, here three major reasons we see kids struggle with geometry:

1. They don’t recognize all the pieces that go into making up a geometry problem. If kids don’t have great visual and spatial reasoning, it can be hard to “see” this, so to say. 
2. They don’t comprehend what all of the geometry specific vocabulary means. Remember us talking about the language of math? Well, when kids don’t understand geometry specific terms, they can’t decode problems. 
3. They don’t have a great algebra basis. Algebra is really the backbone of geometry, so if kids don’t retain algebra skills, they will not understand a lot of geometry. 

With this said, let’s elaborate more on some of these issues, to help you understand more.

They don’t recognize all the pieces that go into making up a geometry problem.

This struggle sometimes comes from impatience. A picture in a problem can contain multiple steps before you get to a final answer. While the problem may call for the value of one angle, students often must figure out the rest of the values before they solve the problem. The entire picture must be taken into consideration, instead of ignoring what doesn’t seem important. There’s a reason the picture is there in its entirety and geometry works as a progression. You find one piece of information that leads to another that leads to another, and so on and so forth until you have the answer the problem is asking for. Once students know how to start the problem, working their way to the end may take them solving 5 or 6 other pieces. They must be patient in understanding thatall of these pieces are necessary to get to the end.  

They don’t comprehend what all of the geometry specific vocabulary means. 

Most geometry problems look like pictures. Sometimes there is an x or y axis, which borrows from algebra terms, but you’re generally trying to solve in form of shapes. Typically when geometry is first introduced to students, it’s the first time in their math classes that the problem isn’t written out for them and doesn’t always involve numerals, variables, expressions, fractions, actions (like *, ÷, -, +,  /,  >,  <, tan, sin, cos, sec) or Latin or Greek alphabet letters. Generally with geometry, the information is all given in the picture for them to solve the problem, but if they don’t recognize it as useful and/or they don’t pick up on how to translate algebra language they know into a picture, they won’t be able to solve geometry problems. Learning geometry terms like bisector, vertex, parallelogram, ray, point etc. is critical to their geometry future. 

They don’t have a great algebra basis.

Opposite of not understanding geometry specific vocabulary because they are used to algebra, is not actually understanding algebra well enough. When students first enter geometry classes, they might think they are getting away from the abstract and analytical numbers and concepts algebra deals with. Then they find out the inevitable: algebra is the basis of geometry and necessary in truly understanding it. Because geometry classes often start with the beginning of a new school year, summer slide in algebra can be a huge problem when trying to move forward. We address summer slide and give tips for how to help prevent it as the summer months start to approach, but teachers often have to spend up to a month reteaching concepts already taught in the previous year to address the learning loss that occurs over the summer for kids. Algebra is no exception, as it’s really crucial for success in geometry. 

Geometry is one that might be hard to help with at home, unless you use it as an adult on a regular basis. That’s not to say you can’t try, if your child is needing help in it, but if you find that your child is needing a lot of help with geometry and the algebra which is needed it for it, give us a call at Mathnasium of Littleton. We are happy to do assessments for your child to find out exactly what they’re needing to be successful and have confidence moving forward in geometry and beyond!