“Mathematical reasoning is essentially about development, justification and use of mathematical generalizations.” Jo Russell
Many teachers come to me for advice about teaching students to problem solve. I know that having a strategy is helpful for many students, but I also think it comes down to reasoning skills as well. I think mathematical reasoning is one of the biggest over looked skill taught in math. We need to start teaching more logic and reasoning in elementary schools so when the students start algebra, it makes more sense to them because they have a stronger background. This will eventually help students with problem solving as it will build critical thinking skills a vital 21st century skill.
There are two types of reasoning, deductive and inductive, that we need to teach. Many teachers don’t realize the importance of these math reasoning skills. Below I explain why!
Inductive reasoning involves going from a series of specific cases to a general statement. I like to relate inductive reasoning to a series of pictures and you have to figure out which on is the odd one out and why. We need to start teaching this type of reasoning in Kindergarten. Having the students look at four pictures and then asking them which picture does not belong, helps with inductive skills. In first, the teacher can do the same but this time asking the students what the ‘rule’ is about the pictures. Each year you add a different and harder element to inductive reasoning so by the time they are in the upper grades, they can figure out why a rectangle can not be a rhombus.
Deductive reasoning is a type of logic in which one goes from a general statement to a specific instance. I relate deductive reasoning to the game clue. When I am teaching reasoning, I like to start off teaching with Abbott and Castello Video- Who’s on First? (http://ow.ly/90Zhd) I have the students draw a picture of a baseball diamond in their notebooks, modeled after the one I have on the board. I then tell the students to just listen to the video, many of the students don’t even know who Abbott and Castello are so it is a great time to bring in a little history! After they listen to it once, I tell them to listen to it again and fill in the positions of the baseball team they are talking about. This is a great way to introduce reasoning and logic in grades 3 and up. The students don’t relate it to a math lesson right away because it doesn’t have numbers in it, yet they are still solving a problem.
You can find logic and reasoning throughout the Math Standards of Practice for the Common Core under….
#1. Make sense of problems and persevere in solving them.
#3. Construct viable arguments and critique the reasoning of others.
#6. Attend to precision.
#8. Look for and express regularity in repeated reasoning.
To view all the Math Standards of Practice (with more detail description) and the Math Common Core click here. http://www.corestandards.org