soliphp.blogg.se - Pictorial representation math

#PICTORIAL REPRESENTATION MATH SERIES#

Helping students discern the two different addends by color.

Allowing students to touch each counter, and keep track while counting.

Providing a scaffold for 1:1 correspondence.

Manipulatives are playing an important role here! They are supporting students in SO MANY ways: They work to count the two different colors and then determine how many counters are there in total. Students take a handful of counters from the container on the table. Let’s take a closer look at an example, shall we? (I always learn best when given examples and visuals.) In this example, let’s imagine that our students are learning about addition, and we have selected double-sided counters as our manipulative.

Exploring Cuisenaire rods to talk about addend pairs.

Utilizing Geoboards to learn about partitioning shapes.

Working with Unifix cubes to understand the commutative property of addition.

Using base-ten blocks to show the relationship between different place values as they relate to base-ten.

We are helping students make meaning of abstract concepts by giving them a visual of that concept to manipulate. So, when students are working with manipulatives, this is the representation we are focusing on. Okay, let’s dive into Concrete Representation! Concrete representation is when a math concept is introduced with manipulatives.

#PICTORIAL REPRESENTATION MATH SERIES#

(Again, don’t worry! I promise to talk more about these and Lesh’s Translation Model, which you can begin to understand in the title image, as we go through the series too!) Concrete Representation While Concrete, Pictorial, and Abstract are three very important forms of representation, there are others to consider. The second problem with this model is that I feel it leaves out some very important ways that we represent mathematical thinking. Why is this a problem? Well, the magic of mathematical representations is not when they are created in isolation, but when we make connections BETWEEN them! (Don’t worry, I promise to talk about this magic more as we go through this series.) Problem #2 Unfortunately, folks then begin to also view these as “stages” and look at the representations in isolation. This leads them to believe that there is a starting point and an end point. Problem #1įirst, people often misinterpret this model as linear. Now, while I agree with the representations shown in this model, it’s not my favorite for two reasons.

$pictorial representation math$

I learned Piaget’s stages of cognitive development and the importance of moving from pre-operational to concrete-operational thinking, and how that applied to teaching math with manipulatives. This is the model I was taught in college. Many folks are familiar with the Concrete-Pictorial-Abstract model of representation (seen below), or at least the idea behind it. The one we will be discussing today is likely a familiar one: Concret Representation. Representations are how our brain communicates mathematical thoughts and concepts. I know I often talk about different math topics and skills, but today I want to enter into a discussion about how we represent those skills.