2. Abstract means “to draw away”
Students are expected to break
away from concrete thinking and
toward abstract thinking in around 3rd
grade
They can accomplish this by
climbing the abstraction ladder
3. We will start with Bessie the cow, all we know
about Bessie is that she is a cow. We don’t know
any specific details about her.
We know that a cow is a member of the group
livestock but other animals fit into this category
too (chickens, pigs, goats) we ignore the
differences by calling them all livestock.
4. The next level is farm assets. Now we are
grouping animals with other things on my farm
that I can sell or make money off of.
Assets is the next level on the ladder. This will
now include anything that I personally own along
with the farm assets that are worth something.
** Note that Bessie is still included in all of this
The last rung on the ladder would be wealth we
have now connected Bessie to wealth.
6. Reading
• As we read stories, the author goes up and down the
ladder-referring to objects, ideas, specifics, and
generalities.
Math
• With each grade level math becomes more abstract.
Numbers and operational signs are symbolic but soon
will be replaced with x and y.
7. Science
• A hypothesis is formed based on observations, by
continually checking the hypothesis against concrete
facts the scientist is moving up and down the ladder.
Social Studies
• The abstractions are the social systems (democracy,
socialism, monarchy) and the ideals (justice, civil rights).
Specifics are the leaders, events, court cases.
8. Third grade teacher, Mrs. Francis divided her
class into 5 groups. Four are heterogeneous, one
was made up of advanced students.
Each heterogeneous group did activities to get
students working with maps and the advanced
group worked at a more abstract level.
The learning stations were set up as shown in
Figure 5.1
9. Mrs. Francis did a few other enrichment activities
to help students work toward thinking more
abstractly
◦ Maps and manipulatives-construct a 3D map.
◦ Maps and movies-make a map that represents where
your favorite movie takes place.
◦ Maps and animals-show where various breeds of dogs or
cats originate from.
◦ Maps and biography-use maps to tell the life story of an
interesting person.
10. Mrs. Francis found that some of her students had
deficiencies in their map skills. She grouped
these students and worked with them on the
basics.
11. Mrs. Lee, a fifth grade math teacher uses different
math journals in her classroom.
◦ The Writer’s Math Journal
◦ The Engineer’s Math Journal
◦ The Designer’s Math Journal
12. The Writer’s Math Journal-for students whose
verbal skills outweigh their math skills
◦ Vocabulary-keep a list of math terms, use them in
sentences
◦ Sentence Starters-write 3-5 sentences each day starting
with “I don’t understand”, “I know why”, “I check my
answer by”
◦ From numbers to words-write out the process of doing a
problem (theno words-write , after that, first, second,
third)
13. The Engineer’s Math Journal-for students who are
precise
◦ Vocabulary-for each term make a labeled diagram
◦ Construction Site-take a few problems and show how
they could be used to build something
◦ Encoding-pretend that a problem is the key to a secret
hidden treasure, express the problem using a code of
symbols instead of numbers
14. The Designer’s Math Journal-for students who
have good art skills
◦ Vocabulary-draw designs and figures that bring clusters
of terms together
◦ Three-dimensional design-show what math problems
would look like in 3D
◦ Color-use color to show your understanding of a math
problem
15. To assess the journals Mrs. Lee looks at the
journals once a week and writes short sentences
to help students expand on their answers.
◦ “What else?”, “Can you think of other examples?”, “What
do you mean?”, “This is great. Can I show this to the
class?”
◦ Then students are allowed to go back and work on the
problem again
16. We differentiate instruction for abstract thinking by
perceiving students’ readiness, giving tiered
assignments, using concept maps and graphic
organizers, and gradually moving along the
ladder.
17. Concept mapping is a way of showing
connections, making associations, linking one
idea to another.
New information can be processed only if it can
stick to old information
The more you know, the more you can learn
Knowledge builds capacity
18. 1. Prewriting-brainstorming and organizational
◦ Brainstorming-use a cluster map, representing possible
ideas and sub-ideas
◦ Organizational-use a cluster diagram, the writer
decides on main ideas, details, transitional expression,
keywords
19. 2. Expressing hierarchy-hierarchy maps show
pyramidal organizations, looking for more
generalities and specifics (i.e. branches of
government)
3. Part-to-whole relationships-used mostly for math
and science also how words are built onto roots
through prefixes and suffixes, mostly seen as pie
charts and bar graphs
4. Memorizing-auditory modes and rhythm and
sometimes visual, information will have more
meaning if the learner can find rhyme and reason.
20. 5. Class Participation-gives students think-time and
confidence when called upon
6. Understanding of systems and sequence-
translate verbal understanding into a picture
(storyboard representing the process of long
division)
7. Rules and applications-helps with spelling and
grammar exceptions
8. Make sense of readings-after reading concept
maps help us recall, reinforce, and organize
what we read
21. Accuracy of relationships
Correct use of terminology
Detail and specificity
Overall organizational plan
22. Use colors, clusters, arrows, shading ,and
branches to show relationships
Maps should be drawn quickly, provide lots of
space and freedom
Put nouns in circles and verbs in connecting lines,
cluster adjectives around nouns
Think in terms of who? What? When? Where?
Why?
Think of it as a work in progress, revisit it to add
new ideas
Use unlined paper
23. Add examples
Add synonyms and antonyms (use a different
color)
Make the map three-dimensional
Work on symmetry, eye appeal,
background/foreground
Progressively develop maps
Include venn diagrams
24. Inductive Reasoning-process of making
generalizations based on particulars when
students are given the chance to reason
inductively, they are doing field research-they
discover truths for themselves rather than being
told what is true (Figure 6.1)
Deductive Reasoning-reverse of inductive, begin
with generalization, we generate specifics “This is
true of most cases. Therefore, it probably applies
to this specific case.” (i.e. If/Then) Figure 6.2
25. Students can complete it as a whole or in parts
Students can supply the specifics on vertical axis
Students and get to a point where they create
their own matrices for a subject area
Matrices can form the basis for written work
Example 1, example 2, example 3, example 4
26. Concept maps encourage nonlinear thinking in all
subject areas. It is a tool of differentiated
instruction because it allows students to think
freely and use a variety of responses. Students
can use single words rather than sentences and it
can be done individually, with pairs or teams , or
as a whole class activity.
