Understanding How Mental Representations Foster Understanding and Remembering New Concepts
Grade
K-2
3-5
6-8
9-12
Construct/Component
Higher Order Cognition - Mental Representations
Subject
Area
Math
Objectives
Estimated Time Needed
One 90-minute session
Teacher
Preparation
Story of King Midas Variety of objects that could be used to illustrate fractions (sheets of paper, apples, Halloween candy, playing cards, popsicle sticks).
Materials
Lesson Procedure
1. Have students explain what a given word means to them. They will be asked to describe it in words and with pictures. The word will be “beach.”
2. Discuss with them the many pictures that came to mind and how the mind worked like a camera shooting pictures inside their heads.
3. Present the word “avarice”. Ask them what this word makes them think of. (The expectation is that most of the students will not know the meaning of the word). Have them reflect on the fact that no picture appears inside their heads.
4. Explain to them that they will listen to a story about a king who acted with avarice. Tell them that they must pay attention to the actions of the king and think about how his actions show avarice.
5. Read them the story of King Midas.
6. Discuss what they now think that the word avarice means.
7. Have them make a drawing to help them remember what the word means.
8. Discuss what they might do if, later on, they forget the meaning of the word – think about what happened in the story of King Midas and have that image help them remember the meaning of the word.
9. Ask them what a “fraction” is.
10. Tell them that they will now have different experiences with fractions to help them make pictures in their minds of what fractions are and how they are formed.
11. Write each of the fractions on the board –1/2, 1/3, 1/4, - and with each one illustrate the fraction with different objects and groups of objects.
12. Have them reflect on what is being done with the objects.
13. Create a definition of what a fraction is – “A fraction is what we get when we take an object and break it into equal parts or we take a group of objects and break them into equal groups.”
14. Have them demonstrate given fractions with different objects. Make sure to include fractions with different numerators (2/3, 2/4, 3/3, etc.)
15. Have each student give the definition of what a fraction is.
16. Have each student describe the object that he/she will “bring to mind” to help him/her remember what a fraction is in real life. It is important that they have 2 examples – one with a single object and one with a group of objects.
17. Discuss how making a picture in our minds helps us remember and understand things better.
Debrief (checking for understanding)
Extension/Going Further
Comments/Instructor's Note
The students I will be working with are in a small private school that serves only students who have been unable to adapt to a regular school setting. Most of them have significant problems with attention and temporal-sequential ordering. Some of them have significant language problems. Class size is 8 students. It is important for the lesson to be as engaging and as clear as possible. Care must also be taken to help individual students put into words the given concept.
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