Content Literacy Instructional Shifts for math

Report
CONTENT LITERACY
INSTRUCTIONAL
SHIFTS FOR
MATH
Facilitator
Auddie Mastroleo ҉ OCM BOCES Network Team
COMMON CORE SHIFTS
ELA & CONTENT LITERACY
Balancing Informational & Literary Texts (Grades PK-5)
Knowledge in the Disciplines (Grades 6-12)
Staircase of Complexity
Text-based Answers
Writing from Sources
Academic Vocabulary
BALANCING
INFORMATIONAL &
LITERARY TEXTS
Range of Text Types
Literature = Stories,
Dramas, Poetry
SHIFT 1
Grades
PK-5
Informational =
Literary Nonfiction,
Historical,
Scientific, &
Technical Texts
12th grade
8th grade
4th
grade
50% fiction
50%
nonfiction
40%
fiction
60%
nonfiction
20%
fiction
80%
nonfiction
Increase in
teaching
and learning
with nonfiction text
KNOWLEDGE IN THE
DISCIPLINES
Reading & Writing
Literacy
Standards
Depending on text
rather than
referring to it
• Complement,
not replace
content
standards
•Read a president’s
speech & write a
response
•Read scientific
papers & write an
analysis
SHIFT 2
Grades
6-12
Think sophisticated
non-fiction
•Analyze and
evaluate texts
within disciplines
•Gain knowledge
from texts that
convey complex
information through
diagrams, charts,
evidence, &
illustrations
Expectation of
rigorous domain
specific literacy
instruction
outside of ELA
PreCCLS Core
Text
SHIFT 1
Balancing
Informational
and Literary
Texts
SHIFT 2
Building
Knowledge in
the
Disciplines
PostCCLS Core
Texts
SHIFT 1
Balancing
Informational
and Literary
Texts
SHIFT 2
Building
Knowledge in
the
Disciplines
Paired Texts: The Golden Ratio
MATH PRE AND POST SHIFT NOTES
TURN AND TALK
With a partner…
Share your initial
thinking and
reactions
STAIRCASE OF
COMPLEXITY
Increase
in text
complexity
at each
grade
level
Qualitative
Levels of meaning
Structure
Clarity of language
Knowledge demands
Quantitative
Word length
Sentence length
Text cohesion
Reader &
Task
SHIFT 3
Motivation
Knowledge
Experience
Expectation of
proficiency and
independence in
reading grade
level text
Appendix B:
Text Exemplars
and Sample
Performance
Tasks
PRE-CCLS
A ratio compares two numbers by division.
The ratio of two numbers a and b can be
written as a to b, a:b, or a/b, where b=0. For
example, the rations 1 to 2, 1:2, and ½ all
represent the same comparison.
A proportion is an equation stating that two
ratios are equal. In the proportion a/b=c/d,
the values a and d are the extremes. The
values b and c are the means. When
proportion is written as a:b=c:d, the examples
are the first and last positions. The means are
in the two middle positions.
SHIFT 3
Staircase of
Complexity
POST-CCLS
In everyday life, we use the word ”proportion” either
for the comparative relation between parts of things with
respect to size or quantity or when we want to describe
harmonious relationship between different parts. In
mathematics, the term “proportion” is used to describe
equality of the type: nine is to three as six is to two.
The Golden Ratio has been used in [art,
architecture, design, and music] to achieve what we might
term as “visual (or audio) effectiveness.” One of the
properties contributing to such effectiveness is proportion –
the size and relationships of part to one another and to the
whole. The history of art shows that in the long search for
an elusive canon of “perfect” proportion, one would
somehow automatically confer aesthetically pleasing
qualities on all works of art, the Golden Ratio has proven to
be the most enduring.
SHIFT 3
Staircase
of
Complexity
TEXT-BASED ANSWERS
Questions tied
directly to the
text, but extend
beyond the
literal
Students must
cite text to
support
answers
Personal
opinions,
experiences,
and
connections to
the text are
minimized in
favor of what
the text
actually says or
doesn’t say
SHIFT 4
Questions are
purposefully
planned & direct
students to
closely examine
the text
PRE-CCLS
A ratio compares two numbers by division.
The ratio of two numbers a and b can be
written as a to b, a:b, or a/b, where b=0. For
example, the rations 1 to 2, 1:2, and ½ all
represent the same comparison.
A proportion is an equation stating that two
ratios are equal. In the proportion a/b=c/d,
the values a and d are the extremes. The
values b and c are the means. When
proportion is written as a:b=c:d, the examples
are the first and last positions. The means are
in the two middle positions.
SHIFT 4
Text-based
Answers
Question:
The ratio of
the side
lengths of a
quadrilateral
is 2:3:5:7,
and its
perimeter is
85ft. What
is the length
of the
longest side?
POST-CCLS
In everyday life, we use the word ”proportion”
either for the comparative relation between parts of things
with respect to size or quantity or when we want to
describe harmonious relationship between different
parts. In mathematics, the term “proportion” is used to
describe equality of the type: nine is to three as six is to
two.
The Golden Ratio has been used in [nature, art,
architecture, design, and music] to achieve what we might
term as “visual (or audio) effectiveness.” One of the
properties contributing to such effectiveness is proportion
– the size and relationships of part to one another and to
the whole. The history of art shows that in the long search
for an elusive canon of “perfect” proportion, one would
somehow automatically confer aesthetically pleasing
qualities on all works of art, the Golden Ratio has proven
to be the most enduring.
SHIFT 4
Text-based
Answers
Question:
Describe
how the idea
of proportion
can be
applied to
mathematical
concepts as
well as life
and culture.
Use specific
examples
from the text
to support
your answer.
MATH PRE AND POST SHIFTS NOTES
TURN AND TALK
With a partner…
Share your initial
thinking and
reactions
WRITING FROM
SOURCES
Three
Text
Types
Argument
Informational/
Explanatory
Writing
Narrative
Writing
SHIFT 5
Supporting a claim
with sound
reasoning and
relevant evidence
Increase subject knowledge
Explain a process
Enhance comprehension
Conveys experience
i.e. fictional stories,
memoirs, anecdotes,
autobiographies
Argumentative
writing is
especially
prominent in
the CCLS
Appendix C:
Samples of
Student Writing
Pre-CCLS
1. Is the ratio 6:7 the same as 7:6? Why or
why not?
2. Susan wants to know if the fractions 3/7
and 12/18 are equivalent. Explain how she
can use the properties of proportions to find
out.
3. Copy and complete the graphic
organizer. In the boxes, write the definition
of a proportion, the properties of
proportions, and examples and nonexamples of a proportion.
SHIFT 5
Writing
from
Sources
Post-CCLS
Architect, mathematician, and engineer, Richard
Buckminster Fuller once said,
“When I am working on a problem, I never think
about beauty. I think only of how to solve the
problem. But when I have finished, if the solution is
not beautiful, I know it is wrong.”
Use your knowledge of proportions and the text, The
Golden Ratio to agree or disagree with this quote.
Define and
explain the
mystery of the
golden ratio.
Provide examples
of mathematical
and real life
applications of
the golden ratio.
Show the
mathematics of
the golden ratio
as it applies to
your examples.
SHIFT 5
Writing
from
Sources
ACADEMIC VOCABULARY
Tier One
Words
• Words of everyday speech
Tier Two
Words
• Not specific to any one
academic area
• Generally not well-defined
by context or explicitly
defined within a text
• Wide applicability to many
types of reading
Tier
Three
Words
• Domain specific
• Low-frequency
• Often explicitly defined
• Heavily scaffolded
SHIFT 6
Ramp up
instruction of
Tier Two
words
Pre-CCLS
ratio
SHIFT 6
proportion
extremes
means
Academic
Vocabulary
Post-CCLS
Tier 3
Words
Tier 2
Words
ratio
harmonious
proportion
intriguing
extremes
elusive
means
aesthetic
SHIFT 6
Academic
Vocabulary
MATH PRE AND POST SHIFTS NOTES
TURN AND TALK
With a partner…
Share your initial
thinking and
reactions
QUESTIONS? CONCERNS? NOTICES?

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