I hear this story often: Your child did extremely well last year in Algebra I, but suddenly he or she is struggling in Geometry— and it’s starting to take a toll on their self-esteem. First of all, understand that this is normal— geometry requires a completely new way of thinking than algebra, and it comes less naturally to most children. Beyond that, geometry introduces a new type of problem called “Proofs” where students need to make statements that lead sequentially toward a certain conclusion. This is significantly more challenging than the arithmetic and algebra that students have seen before, because they have to create their own path to the desired conclusion, and this requires higher levels of critical thinking and reasoning skills.
1. Act out new, abstract geometry topics with real-life objects. Just yesterday I used two pencils pointing in opposite directions and clearly not on the same plane to explain the meaning of “skew.” I also poked a pencil through a piece of paper to illustrate how when a line intersects a plane, the only piece of intersection is a point. If you’re not sure of the concepts yourself, search for online videos that demonstrate these concepts using visuals.
2. When writing proofs, work backwards. Have your child should look first at what needs to be proven; from there, they can brainstorm out loud what needs to come first in order to lead to that conclusion. For example, if you are trying to prove two base angles of a triangle equal, perhaps you could prove the two corresponding legs equal, which would make the triangle isosceles and would logically lead you to your desired outcome. This is essentially working backwards—figure out where your proof is going, and work from that outcome toward the information you already have.
3. Know that there might be several ways to complete a proof. As long as you are using mathematically correct theorems and conclusions, you can solve proofs in a variety of different ways. After your child has completed a proof one way, you may ask them to go back and see if they can find a second way to solve the same proof. This challenge will help your child think outside the box and have a deeper understanding of the content at hand.
4. Practice, practice, practice! If your child completed a few problems for homework and struggled with them, give them additional similar problems from the same chapter to complete in order to improve their understanding. They might groan for a moment, but they will be grateful when they confidently face their math tests.
As always, we’re here to help. Good luck, Geometry students! We will be thinking of you and wishing you luck over here at Madison Tutoring.
Head Math Tutor