1 what does reading have to do with math? (everything!) amatyc conference 2008 amber rust november...
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What Does Reading Have What Does Reading Have To Do With Math?To Do With Math?
(Everything!) (Everything!)
AMATYC Conference 2008AMATYC Conference 2008Amber RustAmber Rust
November 22November 22ndnd - Saturday - Saturday12:00 – 12:5012:00 – 12:50
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AssumptionAssumption
When a student is not successful in math, When a student is not successful in math, teachers usually assume the difficulty is teachers usually assume the difficulty is with the studentwith the student’’s mathematical ability or s mathematical ability or possibly the studentpossibly the student’’s dislike of s dislike of mathematics, but the truth may more likely mathematics, but the truth may more likely lie with the studentlie with the student’’s poor ability to read s poor ability to read the mathematics textbook.the mathematics textbook.
(Draper, Smith, Hall, & Siebert, 2005; Kane, Byrne, & Hater, 1974; O(Draper, Smith, Hall, & Siebert, 2005; Kane, Byrne, & Hater, 1974; O’’Mara, 1982)Mara, 1982)
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StudentsStudents’’ Common Experiences Common Experiences In Math ClassroomsIn Math Classrooms
Students find math textbooks to be intimidating Students find math textbooks to be intimidating and confusing and therefore just skip past the and confusing and therefore just skip past the explanations. explanations. (Draper, 1997)(Draper, 1997)
Students expect the teacher to be the expert, Students expect the teacher to be the expert, do all the talking, and be the center of the do all the talking, and be the center of the classroom.classroom.
Students say the best means of learning math Students say the best means of learning math are are (Stodolsky, Salk, & Glaessner, 1991)(Stodolsky, Salk, & Glaessner, 1991)
1.1. ““hearing an explanationhearing an explanation””2.2. ““asking someoneasking someone””3.3. ““being told what to dobeing told what to do””
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TeachersTeachers’’ Common Experiences Common ExperiencesIn Math ClassroomsIn Math Classrooms
Teachers compensate for studentsTeachers compensate for students’’ lack of lack of reading ability by using the textbook as a reading ability by using the textbook as a resource for exercises only. resource for exercises only. (Draper, 2002; Porras, (Draper, 2002; Porras, 1994)1994)
Teachers Teachers ““telltell”” students all necessary students all necessary information therefore releasing students information therefore releasing students from needing to read the textbook. from needing to read the textbook. (Draper, (Draper, 2002; Porras, 1994)2002; Porras, 1994)
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Beyond CrossroadsBeyond CrossroadsStandards for Intellectual DevelopmentStandards for Intellectual Development
Communicating StandardCommunicating Standard: Students will : Students will acquire the ability to acquire the ability to readread, write, listen , write, listen to, and speak mathematics (p.5).to, and speak mathematics (p.5).
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Beyond CrossroadsBeyond CrossroadsStandards for PedagogyStandards for Pedagogy
Active and Interactive Learning StandardActive and Interactive Learning Standard: : Mathematics faculty will foster interactive Mathematics faculty will foster interactive learning through student writing, learning through student writing, readingreading, , speaking, and collaborative activities so speaking, and collaborative activities so that students can learn to work effectively that students can learn to work effectively in groups, communicate about math both in groups, communicate about math both orally and in writing (p.6).orally and in writing (p.6).
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Reading in MathReading in Math (Barton & Heidema, 2002)(Barton & Heidema, 2002)
Requires unique knowledge and skills not Requires unique knowledge and skills not taught in other content areas.taught in other content areas.
Math textbooks contain more concepts per Math textbooks contain more concepts per word, per sentence, and per paragraph word, per sentence, and per paragraph than any other text type or content area than any other text type or content area textbook.textbook.
Students need to be proficient at decoding Students need to be proficient at decoding words, numbers, and symbols.words, numbers, and symbols.
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Reading in Math Reading in Math (Barton & Heidema, 2002)(Barton & Heidema, 2002)
Writing style in math textbooks is compact Writing style in math textbooks is compact and succinct with little redundancy of text. and succinct with little redundancy of text.
Students often skip over the worded parts Students often skip over the worded parts looking for examples, graphics, or looking for examples, graphics, or exercises.exercises.
In K-12, math textbooks are often written In K-12, math textbooks are often written above grade level.above grade level.
Overlap between math and everyday Overlap between math and everyday English vocabulary can cause confusion.English vocabulary can cause confusion.
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The Math Register and VocabularyThe Math Register and Vocabulary(Rubenstein, 2007)(Rubenstein, 2007)
Some words are…Some words are… found only in math (e.g., denominator, found only in math (e.g., denominator,
hypotenuse, polynomial, histogram)hypotenuse, polynomial, histogram) shared with science or other disciplines (e.g., shared with science or other disciplines (e.g.,
divide, radical, power, experiment)divide, radical, power, experiment) shared with everyday English, sometimes with shared with everyday English, sometimes with
different meanings, sometimes with different meanings, sometimes with comparable meanings in mathematics comparable meanings in mathematics (fraction, similar, variable, median)(fraction, similar, variable, median)
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The Math Register and VocabularyThe Math Register and Vocabulary(Rubenstein, 2007)(Rubenstein, 2007)
Some words…Some words… have multiple meanings in math (e.g., point, have multiple meanings in math (e.g., point,
cube, range)cube, range) Sound like other words (e.g., sum & some, Sound like other words (e.g., sum & some,
plane & plain, intercept & intersect, plane & plain, intercept & intersect, complement & compliment, hundreds & complement & compliment, hundreds & hundredths, pie & pi)hundredths, pie & pi)
are learned in pairs that often confuse are learned in pairs that often confuse students (e.g., complement & supplement, students (e.g., complement & supplement, combination & permutation, solve & simplify, combination & permutation, solve & simplify, at most & at least)at most & at least)
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Vocabulary - SymbolsVocabulary - Symbols
Symbols can also have…Symbols can also have… multiple meanings within mathmultiple meanings within math meanings in everyday Englishmeanings in everyday English meanings in other content areasmeanings in other content areas
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Symbol(s) Meanings/Placement
of, by, multiplication, a letter, a variable, an axis
: ratio, scale, colon, URLs
3 33 2
3, 3 , ,x xx
2, 2, x hyphen; can imply negation, subtraction, range
, , , , ab multiplication
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Content Area Reading StrategiesContent Area Reading Strategies
Reading strategies are NOT for students Reading strategies are NOT for students to to learn-to-readlearn-to-read the math textbook but to the math textbook but to read-to-learn read-to-learn from the math textbook.from the math textbook.
Reading Strategies are really Learning Reading Strategies are really Learning StrategiesStrategies Students can use strategies to help them Students can use strategies to help them
comprehend what is readcomprehend what is read Faculty can use strategies to check on Faculty can use strategies to check on
student comprehension of what is readstudent comprehension of what is read
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Easy Additions to InstructionEasy Additions to Instruction
Research shows…Research shows… explicit instruction in the physical presentation explicit instruction in the physical presentation
of the textbook and the textbook structure is of the textbook and the textbook structure is highly related to reading comprehensionhighly related to reading comprehension
connecting the new material to studentsconnecting the new material to students’’ prior prior knowledge increases understanding when knowledge increases understanding when reading the textbook.reading the textbook.
Prior knowledge, prior knowledge, and Prior knowledge, prior knowledge, and more prior knowledge!!more prior knowledge!!
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Example of a Vocabulary StrategyExample of a Vocabulary StrategyVerbal and Visual Word Association – Verbal and Visual Word Association – (Barton & Heidema, 2002)(Barton & Heidema, 2002)
Vocabulary Term(s) Visual Representation
Definition(s)Personal Association or a characteristic
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Example of a Vocabulary StrategyExample of a Vocabulary StrategyVerbal and Visual Word Association – Verbal and Visual Word Association – (Barton & Heidema, 2002)(Barton & Heidema, 2002)
Root, Zero, Factor, Solution, x-intercept
Each word can represent the answer to the function y=f(x) where f(a)=0 and a is a root, zero, factor, solution, and x-intercept
-Point (a,0) is the x-intercept of the graph of y=f(x)
-number a is a zero of the function f -number a is a solution of f(x)=0 -(x-a) is a factor of polynomial f(x) -Root is the function on the TI for this
x= -2 x= 3
x-ax
is
y-axisf(x)
Just find the answer to the function and that will be the zero. If I graph it, the zeros are where the function crosses the x-axis.
Special Note: this is just for real solutions.
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Example of a Vocabulary StrategyExample of a Vocabulary StrategyFrayer Model – (Barton & Heidema, 2002)Frayer Model – (Barton & Heidema, 2002)
Definition (in own words) Facts/Characteristics
Examples Non-ExamplesWORD or SYMBOL
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Example of a Vocabulary StrategyExample of a Vocabulary StrategyFrayer Model – (Barton & Heidema, 2002)Frayer Model – (Barton & Heidema, 2002)
Definition (in own words) Facts/Characteristics
Examples Non-ExamplesRADICAL
An expression in this form is called a radical, b is called the radicand and the n is called the index of the radical.
n b
44 81 3 3 81because 3 541 1 1 1 1
a is the positive square root of aa is the negative square root of a
0 0n 9 3 9 3
9 'can t do
3 2205Not a radical – this is a division sign
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Example of a Vocabulary StrategyExample of a Vocabulary StrategyFrayer Model – (Barton & Heidema, 2002)Frayer Model – (Barton & Heidema, 2002)
339 3 8 2 2 2 2
Definition (in your own words) Facts/Characteristics
Examples Non-Examples
These are radical signs . When no superscript number is in front (called the index) it means it is square root. With a “3” index it becomes a cube root and so on.
*there is never an index=1 *odd roots are always the same sign as the number under the radical.
Not a radical – this is a division sign
n nx x
3 2205
nor
0 0n
339 3 8 2 2 2 2 9 3
9 3
33 8 2 2 2 2
1 1n
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As you read the textbook page, As you read the textbook page, think about these questions…think about these questions…
What vocabulary difficulties could students What vocabulary difficulties could students have?have?
What do you think they may find confusing?What do you think they may find confusing? Are the explanations well written?Are the explanations well written? What is left unexplained?What is left unexplained? Do you only read from left-to-right and from top-Do you only read from left-to-right and from top-
to-bottom?to-bottom? What isnWhat isn’’t defined that you think should be?t defined that you think should be? Do they know how to read the graph and how to Do they know how to read the graph and how to
connect it to the other information given?connect it to the other information given?
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Guide-O-RamaGuide-O-Rama(Daniels & Zemelman, 2004)(Daniels & Zemelman, 2004)
A written guide (A written guide (notnot an outline) given to students an outline) given to students to show them the way through the textbook to show them the way through the textbook reading selection.reading selection.
It lets you informally coach, support, and chat It lets you informally coach, support, and chat with your students as they read the textbook with your students as they read the textbook outside of class.outside of class.
It activates prior knowledge and sets a purpose It activates prior knowledge and sets a purpose for the reading.for the reading.
It guides the students through the words, charts, It guides the students through the words, charts, diagrams, graphs, tables, pictures, equations, diagrams, graphs, tables, pictures, equations, symbols, notation, examples, etc. in the textbook.symbols, notation, examples, etc. in the textbook.
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Use Jigsaw to Encourage ReadingUse Jigsaw to Encourage Reading When teaching quadratic solution methods…When teaching quadratic solution methods…
divide students into groups; each group reads divide students into groups; each group reads the textbook to become the expert on the textbook to become the expert on oneone method,method,
next, make up new groups with at least one next, make up new groups with at least one expert for each method, expert for each method,
then, each expert in the group explains their then, each expert in the group explains their method to the others,method to the others,
after the explanations, the group makes a list of after the explanations, the group makes a list of the pros and cons of each method and when the pros and cons of each method and when use each method can be useduse each method can be used
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Advantages to Help StudentsAdvantages to Help Students Read Math Read Math (DeLong & Winter, 2002)(DeLong & Winter, 2002)
Offers students another way to learn math.Offers students another way to learn math. Teachers will have more class time to cover Teachers will have more class time to cover
content in appropriate depth.content in appropriate depth. Some studies have shown that reading is better Some studies have shown that reading is better
than lecture for retention.than lecture for retention. Offers another approach to teaching that can Offers another approach to teaching that can
accommodate different learning styles.accommodate different learning styles. Most vocabulary can be easily acquired through Most vocabulary can be easily acquired through
reading, leaving class time for clarification, reading, leaving class time for clarification, extension, and reinforcement of the material.extension, and reinforcement of the material.
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Textbook UseTextbook Use(Daniels & Zemelman, 2004)(Daniels & Zemelman, 2004)
DonDon’’t teach as if they have never had or never will t teach as if they have never had or never will have the opportunity to read the material!have the opportunity to read the material!
Have empathy, remember you are the expert and Have empathy, remember you are the expert and it really may be Greek to them.it really may be Greek to them.
DonDon’’t leave the students to decipher the textbook t leave the students to decipher the textbook alone.alone.
Front-load your teaching before they read – point Front-load your teaching before they read – point out possible difficulties they may encounter.out possible difficulties they may encounter.
Choose wisely what is to be read; every page is Choose wisely what is to be read; every page is not needed.not needed.
Supplement richly with websites, newspapers, Supplement richly with websites, newspapers, trade books, magazines, and environmental print.trade books, magazines, and environmental print.
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Textbook UseTextbook Use (Daniels & Zemelman, 2004)(Daniels & Zemelman, 2004)
Remind the students about what they Remind the students about what they already know – prior knowledge.already know – prior knowledge.
Research shows that students find it very Research shows that students find it very difficult to learn from the math textbook with difficult to learn from the math textbook with little or no support from their teacher.little or no support from their teacher.
Research shows a strong connection Research shows a strong connection between vocabulary knowledge and the between vocabulary knowledge and the ability to understand what is read.ability to understand what is read.
Be explicit about the what, why, and how for Be explicit about the what, why, and how for each strategy shown to your students.each strategy shown to your students.
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Final ThoughtsFinal Thoughts
““A mathematics education that assumes to A mathematics education that assumes to prepare students without providing them prepare students without providing them with ways to access the text falls short of with ways to access the text falls short of truly educating studentstruly educating students”” (Draper, 2002).(Draper, 2002).
““The priority of instructing for reading The priority of instructing for reading comprehension must be balanced with the comprehension must be balanced with the priority of teaching the content area itselfpriority of teaching the content area itself”” (RAND, 2002, p. 30).(RAND, 2002, p. 30).
