Similarities differences math

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


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?