This sketch, while excellent for demonstration purposes, is ideally put into the hands of students so they can manipulate the variables and see how their actions impact the graph and the action.
Download the sketch!
Showing posts with label nonlinguistic. Show all posts
Showing posts with label nonlinguistic. Show all posts
Thursday, February 24, 2011
Representing Stories Graphically
The Geometer's Sketchpad can do so much more than build polygons! Use this sketch to help your 7th graders build their connections between graphic representations and real-world situations.
This sketch, while excellent for demonstration purposes, is ideally put into the hands of students so they can manipulate the variables and see how their actions impact the graph and the action.
Download the sketch!
This sketch, while excellent for demonstration purposes, is ideally put into the hands of students so they can manipulate the variables and see how their actions impact the graph and the action.
Download the sketch!
Friday, October 8, 2010
Making Sense of Division
When solving division problems, students are often able to produce a quotient without realizing what that quotient represents. For example:
The bag has 695 pieces of candy corn, and Alyssa wants to put them into bags of 50. How many bags will she need?
Students may be able to mechanically produce the quotient 13. But do they fully understand the referential meaning of "13"? And let's not even get started about what the remainder represents!
Explicitly teaching students, with a model, that there are two ways to think about division can help them develop powerful mental structures for analyzing their results. I'm going to suggest Cuisenaire Rods as an excellent model for representing division.
Sharing (partitive) division is the situation your students are most comfortable with because it can be solved by dealing out. In sharing division, we know the total and we know the number of groups. The unknown is the number of items in each group. We can solve this by dealing out, or sharing, all of our items one at a time until there are no more to be distributed.
Sarah has 10 puppies and 2 doghouses. How many puppies can be grouped evenly in each doghouse?
In the second division situation, the action to solve the problem is making groups. This is called measurement division, and lends itself well to the idea of repeated subtraction - repeatedly removing groups of a particular quantity until there are no more to be removed.
The bag has 695 pieces of candy corn, and Alyssa wants to put them into bags of 50. How many bags will she need?
Students may be able to mechanically produce the quotient 13. But do they fully understand the referential meaning of "13"? And let's not even get started about what the remainder represents!
Explicitly teaching students, with a model, that there are two ways to think about division can help them develop powerful mental structures for analyzing their results. I'm going to suggest Cuisenaire Rods as an excellent model for representing division.
Sharing (partitive) division is the situation your students are most comfortable with because it can be solved by dealing out. In sharing division, we know the total and we know the number of groups. The unknown is the number of items in each group. We can solve this by dealing out, or sharing, all of our items one at a time until there are no more to be distributed.
Sarah has 10 puppies and 2 doghouses. How many puppies can be grouped evenly in each doghouse?
 |
| The Cuisenaire Rods offer a nonlinguistic representation of the situation. We have a given total divided into 2 groups. We must find the number in each group. |
 |
| There will be 5 puppies in each doghouse. |
Friday, September 17, 2010
Non Linguistically Speaking
When students struggle to interpret story problems into a mathematical statement they can tackle and solve, a nonlinguistic representation may lead to success. Explicitly engaging students in the creation of lonlinquistic representations increases activity in the brain (Gerlic & Jausovec, 1999)
Language challenged 3rd graders might find this problem difficult to navigate:
Riverside School had 517 students last year. This year, 60 students moved away before school started. How many students does the school have now?
A nonlinguistic representation to help students create a mental picture of, and organize, the essential information.
Substituting the information from the problem, our representation becomes:
Using this representation, it is perhaps clearer to students that they are looking for the difference between 60 and 517. They could then solve the problem in one of two ways: by counting on from 60, or by subtracting 60 from 517.
Language challenged 3rd graders might find this problem difficult to navigate:
Riverside School had 517 students last year. This year, 60 students moved away before school started. How many students does the school have now?
A nonlinguistic representation to help students create a mental picture of, and organize, the essential information.
| TOTAL | |
| Part | Part |
Substituting the information from the problem, our representation becomes:
| 517 students (Total) | |
| 60 students (Part) | Part |
Using this representation, it is perhaps clearer to students that they are looking for the difference between 60 and 517. They could then solve the problem in one of two ways: by counting on from 60, or by subtracting 60 from 517.
Subscribe to:
Posts (Atom)