Students don't come to us as blank slates. Our job as teachers is to anticipate when faulty mental models are likely to be in play when a student is having trouble and to help them correct the misconceptions they have built in their minds around academic concepts.
For example, coin size is related to coin value, right? As a 2nd grade teacher, I encounter this mental model in the minds of some of my students every year. In their world, bigger has usually meant more, and now we are telling them that the dime in front of them is more than the larger nickel sitting next to it? But, they may still pull out that same familiar model when learning the concept of coins and their values and attempt to make it apply.
Don't get me wrong! I'm not saying that they haven't been taught in kindergarten and 1st grade the value of coins, but this is a difficult concept to change. Some students hold onto these notions despite all of our lessons and activities.
A mental model is a representation, or picture, seen in the mind when thinking abstractly.
The picture you see in your mind when you think about a year divided into months is a good example of a mental model. What do YOU see in your mind when you think about it? Is it a row of months? A circle? A calendar? What I see could be described as a Ferris wheel turning counter-clockwise.
You might be surprised to know that everyone has a slightly different mental model of a calendar year. What I perceive may not be what you do, but both models will be sufficient for us to use for problem solving and planning. If they aren't, our minds will attempt to fix the error.
When our students encounter an error in their own mental models, it causes a conflict in their thinking and sometimes our students fight to keep their "logical" model. However, it's that conflict that helps to make the necessary changes to their mental models.
Counting change, telling time, adding ten to a number, working with a number grid, thinking about calendar time, and measuring distance: all of these are topics in which students will be accessing their own mental models (either mostly correct or full of errors and misconceptions) in the classroom. Understanding that we are not working with a blank slate will help us to help our students.
By the end of 2nd grade, my students need to have a good understanding of coins, their value, and how to make change. This can be a real challenge because these are very abstract concepts.
We use dots on coins, each of which represent five cents, for some of my students. One dot on the nickel, two on the dime, etc. This was an idea that someone suggested to me that works with many of my struggling coin counters.
We play coin exchange games where the roll of the die means the addition of more pennies that can be exchanged for nickels, which can be exchanged for dimes, etc.
We learn how to use decimal points and practice figuring how much money we should get back (by subtracting) during simulated purchases.
Once the basics are learned, I'm about out of games, and my students stare blankly at me when I demonstrate how to count back change. No mental models come with most of my 2nd graders that will help them with this abstract concept! They need their teacher to come to their rescue by creating a model that they can use to help them learn this skill.
The Counting Change to $1.00 Model that I developed has helped my students understand what is happening when they are counting money up to a dollar. I love seeing the lights come on when they realize that they understand what's happening with this mysterious concept! I'm hoping that my students will put the model to use in the future as part of their mental model repertoire.
Click the images below to download the graphic and instructions.
Mental Models and Social Studies
Social Studies is another subject where mental models help us with map reading, locations on a globe or map, time lines, and understanding past and future. I begin building mental models around maps very early in the year. Maps are mental models that will continue to develop, change, and help them plan and problem solve for the rest of their lives.
We have all had our mental models challenged at one time or another. An example would be when we read a book and form our own ideas of the appearance of characters and locations in the story. Our mental models are shaken when we see a movie, based on that same book, and the mental model of the director is completely different from ours. Our students can probably relate to that example, also!
Measuring distance can be a real problem for my students when they don't understand what a mile is. I begin by choosing neighborhood landmarks that my class is sure to know. The convenience store on the corner near the school is an easy choice. One mile to the west of the convenience store is an intersection with a large grocery store and a slew of fast food restaurants that they have all visited. We visualize the trip from one to the other, naming places we would pass if we were walking the distance. We follow the mile-long stretch of road on Google Earth and they point out more landmarks they notice on the map.
Online map programs help students make more accurate mental models (maps) of their world. We look at our school and the area around it. We take several field trips by bus during the year. I point out landmarks that we look for, when we are back in the classroom, by looking at Google Maps and Google Earth.
We also make six weekly trips to the YMCA for swimming lessons in the spring. It's the perfect opportunity to see the neighborhood for real. Those six trips become very teachable moments that I get as much out of as possible. The students enjoy following the route on Google Maps and testing themselves on the next trip.
Every year, we read Me on the Map and find our own places on earth in a special project using maps. The work we have done on our way to field trips during the year provides my class with a good perspective of where we are "on the map."
Look for a future post on time, time lines, and other mental models!
How do you help your students develop and correct the mental models they need in order to think in abstract terms?