Success In Algebra
September 5, 2013
Leitchfield, KY
Facilitated by the P12 Math and Science Outreach Unit of PIMSER, UK
Funding provided by Council on Post Secondary Ed
Gathering
• Chart #1
–What SIA activities I’ve done already
this year…
• Chart #2
–Now that I know my classes, these are
my concerns…
Vocabulary
Why Teach Vocabulary
• Learning is fundamentally and profoundly
dependent on vocabulary knowledge.
• Vocabulary knowledge is highly correlated with
overall reading achievement.
• Vocabulary knowledge affects a student’s
ability to participate fully in both social and
academic activities.
Access Center, Improving Outcomes for All Students K-8
4
Why Teach Vocabulary
• Significant disparities exist in word
knowledge among students.
• Vocabulary deficiencies are a primary cause
of academic failure in Grades 3–12.
vocabulary: reading O2: breathing
Access Center, Improving Outcomes for All Students K-8
5
The Matthew Effect
(Stanovich, 1986)
Their limited
comprehension
contributes to
reading failure.
Children
who fail at early
reading, begin to
dislike reading.
Their limited
vocabularies
interfere
with their
comprehension.
They read less
than their peers
who are stronger
readers.
They do not
expand their
vocabularies
and
background
knowledge.
6
Vocabulary Acquisition
• At age 5-6 children typically have 2,500-5,000
words in their oral vocabulary.
• 3,000 words per year are added during their
early school years. (average 8 words/day)
• 25-50% of annual vocabulary growth is
incidental.
• Typical vocabulary lessons focus on 10-20
words per week.
7
Why Students Struggle With Vocabulary
Meaningful Differences (Hart & Risley, 1995)
Words
Heard
per
Hour
Words
Heard in a
100-Hour
Week
Words
Heard in a
5,200 Hour
Year
Words
Heard
in 4
Years
Welfare
616
62,000
3 million
13
million
Working
Class
1,251
125,000
6 million
26
million
Professional
2,153
215,000
11 million
45
million
8
Vocabulary Development
Generate interest in new
words
Relate new words to
children’s personal
experiences
Help children make
connections and attach
meanings to new words and
concepts that go beyond a
label or definition
9
Vocabulary Research
• Researchers have named vocabulary
knowledge as the most important factor in
reading comprehension. (White, Sowell, & Yanagihara, 1989)
• Effective vocabulary instruction requires active
and positive student participation. (Carr & Wixson,
1986)
• Personal engagement with a new word can
lead to deep processing of meaning. (Dole, Sloan &
Trathen, 1995)
10
National Reading Panel Report, 2000
• Vocabulary instruction leads to gains in
comprehension, but the methods must be
appropriate to the age and ability of the
reader.
• Vocabulary should be taught both directly
and indirectly.
• Teaching vocabulary before reading has
significant effects on vocabulary
development.
11
National Reading Panel Report, 2000
• Repetition and multiple exposures to vocabulary items
are important.
• Learning in rich contexts, incidental learning, and the
use of computer technology all enhance the
acquisition of vocabulary.
• Direct instruction should include task restructuring and
should engage the student.
• Dependence on a single vocabulary instruction method
will not result in optimal learning.
12
National Reading Panel Report, 2000
• Repetition and multiple exposures to vocabulary items
are important.
• Learning in rich contexts, incidental learning, and the
use of computer technology all enhance the
acquisition of vocabulary.
• Direct instruction should include task restructuring and
should engage the student.
• Dependence on a single vocabulary instruction method
will not result in optimal learning.
13
Reading Math Texts
vs. Fiction
FICTION
Dorothy lived in the midst of the great Kansas prairies,
with Uncle Henry, who was a farmer, and Aunt Em, who
was the farmer's wife. Their house was small, for the
lumber to build it had to be carried by wagon many miles.
Baum, L. F. p.1
----------------------------------------------MATH TEXT
Based on the pattern, how could you figure out the
number of small squares in any figure number? Write an
equation to find the number of squares in Figure n.
What differences do you notice?
© EDC, 2012
14
Conceptual Density of Mathematics Text
“One reason students struggle with reading
mathematics is the sheer number of
concepts packed into the text. According
to Schell, math text presents more
concepts per word, sentence, and
paragraph than any other content-area
text.”
Source: Barton, M. and Heidema, C. (2002) p.14
© EDC, 2012
15
What’s different about reading math
texts?
• Not just left to right -- need to read in different
directions
• Not just words – also tables, graphs diagrams, and
symbols
• The process of decoding symbols is different from
decoding words. Symbols are like “sight words.”
• One challenge is that different symbols are used
to describe the same process.
– Multiplication *, x, (), ●
© EDC, 2012
16
Multiple exposures to a word
shape word meaning for the
student.
6-10 Exposures (Marzano)
17
Multiple Exposures
•
•
•
•
Extensive reading/wide variety of texts
Discussion in the classroom
Discussions at home
Explicit vocabulary instruction in the
classroom
18
Word Recognition
The cognitive level of a student is a factor in the
number of exposures required for word recognition.
120-129………………..…….... 20
110-119……………..……….....30
90-109………………………......35
89- 80……………………………40
79- 70……………………….…..45
69- 60……………………..…….55
Dr. Bonnie
Armbruster
University of Illinois
Urbana-Champaign
19
Levels of
Language
Selecting
Words
Tier 1
High
Frequency
Words
Tier 2
Vocabulary
Tier 3
Specialized
Vocabulary
Beck, McKeown, and Kucan, 200220
Tier 1 Language
• Most commonly used words that should be
learned by sight.
• Once the core of the basic sight words has been
committed to memory, children generally go on
to master phonics rules and generalizations
more easily and efficiently.
• Sight Word Lists:
– Dolch List
– Fry List
21
Tier 2 Language
• Sophisticated words (e.g., absurd, commotion,
reluctant)
• Frequently occurring words across a variety of domains
• Building rich representations and connections with
words in a variety of ways
• High frequency for mature language users
22
Tier 3 Language
• Specialized Vocabulary
• Examples: evaporation, asymmetrical,
peninsula
• Specialized words typically associated with
a content area or topic
23
Guidelines for Selecting Tier 3 Words
Less is More
• Teach terms that are central to the unit or theme of
study
• Teach terms that address key concepts or ideas
• Teach terms that will be used repeatedly throughout
the term, semester, or year
24
Guidelines for Selecting Tier 3 Words
Levels of
Language
Selecting Words
Tier I
High Frequency
Words
Tier III
Tier II
Vocabulary
Specialized
Vocabulary
AVOID Choosing Words:
•
•
•
•
•
•
Just because they are highlighted
Just because they appear in a list at the end of the chapter
With little utility once the student has passed the test
You cannot define
In large quantities
Which students will rarely encounter again
25
1.
Teacher provides description, explanation, or
example of new term.
2.
Students restate explanation of the term in their
own words.
3.
Students create nonlinguistic representation of term.
4.
Students periodically do activities that help them
add to their knowledge of vocabulary terms.
5.
Periodically, students are asked to discuss terms
with one another.
6.
Periodically, students are involved in games that
allow them to play with the terms.
26
Math Practice Standards
1. Make sense of problems and persevere in solving
them
2. Reason abstractly and quantitatively
3. Construct viable arguments and critique the
reasoning of others
4. Model with mathematics
5. Use appropriate tools strategically
6. Attend to precision
7. Look for and make use of structure
8. Look for and express regularity in repeated reasoning
Lunch
Telephone
Revisit Fractional Workers
Effective Discussion
Closing
• Homework
–Vocabulary Homework Menu