Similarities & Differences Math PowerPoint

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Identifying Similarities &
Differences
Research-Based Strategies for Increasing
Student Achievement
From
Classroom Instruction that Works
by
R. Marzano, D. Pickering, J. Pollock
Created by The School District of Lee County, CSDC
in conjunction with
Cindy Harrison, Adams 12 Five Star Schools
Participant Outcomes
Participants will:
• Understand the purpose and
importance of identifying similarities
and differences
• Determine ways to implement
identifying similarities and
differences in the classroom
• Review examples of identifying
similarities and differences activities
Categories in Instructional Strategies That Affect Student Achievement
Average
Effect
Percentile
Size (ES)
Gain
Identifying similarities and differences
1.61
45
31
Summarizing and note taking
1.00
34
179
Reinforcing effort and providing recognition
0.80
29
21
Homework and practice
0.77
28
134
Nonlinguistic representations
0.75
27
246
Cooperative learning
0.73
27
122
Setting objectives and providing feedback
0.61
23
408
Generating and testing hypotheses
0.61
23
63
Questions, cues and advance organizers
0.59
22
1,251
Category
No. of ESs
Identifying Similarities &
Differences
Fractions
Decimals
Research and Theory about
Identifying Similarities & Differences
Generalizations based on research:
1.
2.
3.
4.
Presenting explicit guidance in identifying
similarities & differences enhances ability to
understand and use knowledge.
Asking students to independently identify
similarities & differences enhances ability to
understand and use knowledge.
Representing similarities & differences in
graphic or symbolic form enhances ability to
understand and use knowledge.
Identification of similarities & differences can be
accomplished in a variety of ways.
Research and Theory about
Identifying Similarities & Differences
Generalization #1:
Presenting explicit guidance in identifying similarities &
differences enhances ability to understand and use
knowledge.
•
•
Teacher-directed
Directly present with steps and give the information to
compare
Generalization #2:
Asking students to independently identify similarities &
differences enhances ability to understand and use
knowledge.
•
•
•
Student-directed
Students identify topics for comparison
Stimulates divergent thinking
Research and Theory about
Identifying Similarities & Differences
Generalization #3:
Representing similarities & differences in graphic or symbolic form
enhances ability to understand and use knowledge.
•
•
Graphic/symbolic forms require students to deeply process information
Increases number of distinctions students find
Generalization #4:
Identification of similarities & differences can be accomplished in a
variety of ways.
•
•
4 ways to identify similarities and differences
Comparing, classifying, creating metaphors, and creating analogies
Recommendations for Classroom Practice on
Identifying Similarities & Differences
a. Use comparing, classifying,
creating metaphors, and
creating analogies
b. Give students a model
c. Use a familiar context to teach
steps
d. Use graphic organizers
e. Guide students
Recommendations for Classroom Practice on
Identifying Similarities & Differences
a. 4 basic processes should be taught
Comparing
The process of identifying and articulating
similarities & differences among items.
Classifying
The process of grouping things into
definable categories on the basis of their
attributes.
Creating
Metaphors
The process of identifying and articulating
the underlying theme or general pattern in
information.
Creating
Analogies
The process of identifying relationships
between pairs of concepts (e.g.,
relationships between relationships.
Recommendations for Classroom Practice on
Identifying Similarities & Differences
b. Give students models of the 4 processes
1. Select items want to compare
2. Select characteristics of the items on which
you want to base your comparison
3. Explain how the items are similar and
different with respect to the characteristics
you selected.
Example of Comparison
Square
Rectangle
1. Identify items
2. Describe key attributes of an important item
and identify other items with same
attributes
3. Create a category by specifying attribute
4. Select another item, describe key attributes,
identify other items with same attributes
5. Create 2nd category by specifying attribute
6. Repeat steps 4 and 5 until all classified
7. If necessary, combine or split categories
Example of Classification
Quadrilateral
Trapezoid
Parallelogram
Rectangle
Square
Rhombus
1. Identify important or basic elements.
2. Write basic information as a general
pattern by
•
Replacing works for specific things with
words for more general things
•
Summarizing info when possible.
3. Find new information/situation to
which the general pattern applies.
Example of Metaphor
Proportions are the Swiss
Army Knife of mathematics.
1. Identify how the 2 elements in the
first pair are related.
2. State the relationship in a general
way.
3. Identify another pair of elements
that share a similar relationship.
Example of Analogy
• 80 is to 8 as a dime is to a penny
• Circumference is to circle as
perimeter is to polygon
• Mean is to average as mode is to
most often
Recommendations for Classroom Practice on
Identifying Similarities & Differences
c. Use a familiar context to teach
steps
Example:Using the prefix tri, associate
it with a tricycle, triangle, and
trinomial.
Example: When discussing slope,
stairs have rises and runs.
Recommendations for Classroom Practice on
Identifying Similarities & Differences
d. Use graphic organizers
Examples: Venn Diagrams
Comparison Matrix
Classification Graphic
Organizers
Recommendations for Classroom Practice on
Identifying Similarities & Differences
e. Guide students as they engage
in this process. Gradually give less
structure and less guidance.
Think, Pair, and Share
What have you learned about
identifying similarities and
differences?
What thoughts,
questions, challenges,
or ideas do you have?
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