Filter Cassette Test Procedure
Using Literacy Strategies to Help Students Transition to Math Application
Ann Wolf, Central New Mexico Highlands University Linda Russell, Minneapolis C & T College (ret.) Victoria Appatova, University of Cincinnati
CRLA Pre-Conference Institute Louisville, KY November 3, 2016
1
Disciplinary Literacy vs. Content Area Literacy
Disciplinary Discipline specific terms, genre, etc.
Content Area General reading strategies
Draw from the experts in the discipline
Study skill strategies Emphasize the reading to learn about the discipline 2
Disciplinary Literacy VS Content Area Literacy • Avoid a “false dichotomy”
(Brozo et al, 2013)
• Healthy discussion is needed about how to choose adequate courses in the context of your institution
3
Practices that Work in Most Disciplines • • • • •
Read with your students Discuss/debate ideas Analyze together Writing to respond Reading others’ writing (Moje, 2013)
4
Discipline–Specific Practices • • • •
Problem framing/question posing Gathering and working with data Working with multiple texts Summarizing and synthesizing (multiple main ideas from many passages) • Communicating knowledge (Moje, 2013)
5
What do you know about reading? • In English, we read right to left and top to bottom. • Space separates words, sentences, and paragraphs from each other. And perhaps footnotes. • Most academic reading is for learning information and concepts so we can remember them. • What else? 6
Let’s Compare Reading Tasks • Most “other” content • Text is read from top to bottom • Text is read from left to right
• The reader may have to decide when to read insets, boxed material, and graphics, relative to the main text. • There may be margin notes. • The purpose of the reading is to learn and remember concepts, facts, etc. Perhaps to use in writing or to answer test questions.
• Mathematics content • Text may be read from top to bottom, but not always. • Text may be read in varying directions; consider the Order of Operations. • Students read, move to the margin and do problems, look at the bottom for answers, resume reading display material. • The purpose of reading is to carry out mathematical operations.
What, exactly, constitutes “text” in Math? • • • • •
• • • •
Words Symbols (+, ≈, √) Abbreviations and Acronyms (LCD, in., mm; NASA) Numbers (especially when in equations, formulas, and working problems, as opposed to years, totals, percents) Logograms ($; the symbol stands for the whole word, dollar[s]) Photos Drawings and diagrams Graphs, tables, charts Arrows, braces, or other directional cues
Examples of “confusing little words” The (a specific thing, as opposed to “any”) Is (often refers to “equal”) A (a number can mean any or one or even several) Are (means more than just “exists”) Can (may refer to “allowed to according to the rules”) On (a physical place) Find (meaning solve) One(s) (place value, as opposed to “one item”) And (And vs Or) Or (exclusive or inclusive?) Number (has a definition) Numeral (write in numeral form, as opposed to in words) Many/How many/How (easily confused) What (might be a definition) Write or Rewrite (as in “Rewrite mixed numbers as improper fractions”) vs Right L meaning “right angle” (is there a “left angle”?)
It (refers to something) Each (important that it is a separation of things) All (not some, many, or most) Do (a question word or imperative?) Which (a contrastive term) Same (in terms of some mathematical concept) Here/there (relative to some location) Has/Have (possessing) Of versus Off (percent of vs percent off) Of (indicating multiplication, when following a fraction) Countable: many/few; more/fewer Uncountable (mass): much/little; more/less; greater/lesser
Density of language/concepts
• Density = many new terms + new meanings for known words + new concepts
10
How many times “a” appears When a letter can stand for various numbers, we call the letter a variable. A number or a letter that stands for just one number is called a constant. Let c = the speed of light. Then c is a constant. Let a = the speed of a car. Then a is a variable since the value of a can vary. 11
Let’s see some examples From Introductory Algebra
12
Textbook Samples: Intro Algebra Density of concepts and “economy of language” to describe them, which results in very brief explanations. The phrase “to make general statements about numbers in algebra…” is a very abstract way of describing why we would use variables.
13
There are four terms in this note box that might be new or bear reviewing: coefficient, variable, integer, reciprocal.
14
This problem solving hint has no examples. Abstractions like this force the students to imagine their own examples. And, if you use x + 2 for both even and odd integers, why even mention it?
15
The definition of “area” is almost out of reach because of the use of such unfamiliar terminology, such as “plane” and “geometric figure.”
16
The Caution box should explain more about distinguishing between “5 less a number” and “5 is less than a number.” A very common type of error.
17
This Caution box has no words! But it does have a period at the end of the expression, which may be confused with a decimal point. Math texts use punctuation in unexpected ways.
18
Long sentences, which include two expressions. Note the use of punctuation (commas) after the expressions. This is common in math texts. You’re supposed to read the whole thing like a sentence.
19
Some skills needed for success in Math courses • COMPREHENSION OF THE LANGUAGE OF MATHEMICS (LECTURES, BOOK INFORMATION, TESTS) • NOTE-TAKING • TIME MANAGEMENT • TEST ANXIETY MANAGEMENT 20
Integrating literacy and communication skills in Math • WRITTEN COMMUNICATION – Reading (receiving a message: reading texts, ppt, handouts, assignments, tests) – Writing (sending a message: writing journals, reflection essays, final reports)
• ORAL COMMUNICATION – Listening (receiving a message: oral instruction in classroom and online ) – Speaking (sending a message: peer teaching)
21
Not understanding LANGUAGE OF MATH: Difficulties related to both oral and written representations Phonetic o professors’ accents, pronunciation of unusual vocabulary (incl. terms); homophones Morphological o Greek and Latin roots, prefixes, and suffixes; compound words Lexical o Unknown semantics of lexical units (words and phrases) Syntactical o Sophisticated sentence structure Discourse o Logical structure of the whole lecture; connections with text, notes, ppts, other lectures; other applications 22
Vocabulary Development • • • • • •
In-depth vocabulary work (linguistic cards) say, write, read, define words visualize words and concepts discuss words play with words differences and similarities between confusing words (Moje, 2013) 23
From Vocabulary to Syntax to Discourse 24
3 Steps to Reading a Word problem • 1st Reading: number-blind; look for key words; devise a formula; draw a picture • 2nd Reading: exclude unnecessary details; convert units; assign a variable • 3rd Reading: evaluate the answer; are all questions answered? 25
Recommended activities to develop writing and speaking skills in Math: • Journal writing and formative self-assessment • Journal portfolio and summative selfassessment • Peer teaching sessions – Classroom teaching – Reflective essay • Final projects – Written reports – Oral presentations 26
Peer Teaching: Triad Teaching • Directions: • Get into groups of three (randomly chosen groups) • Each person will teach the other two people one Example problem from Chapter X, p. X-Y. – Example X will be taught by____________________ – Example X will be taught by____________________ – Example X will be taught by____________________
•
Include in your teaching the following: – Give an overview of the learning outcome for the lesson. – Lead your classmates through the steps to solve the problem. – Figure out a good method for checking to see if they do it correctly. – Check their work. Analyze any errors and provide correct feedback.
• When all three are finished teaching, answer the questions below.
27
Reflection on Triad Teaching • What were the challenges for you as the “teacher” for the group? Please describe in what way(s) it was challenging. • Did your “students” follow your directions appropriately? If not, explain. • Did your “students” get everything correct? If not, describe their errors. • Describe your experience being the “student.”
28
Habits of Mind for Math • Accurate reading of every word. Correct representation of words, numbers, etc. No “looseness.” Pronunciation needs to be correct too. (Commutative has nothing to do with Communication.) • Precision reading, which involves accuracy, but goes beyond, to exactness in all things. (8.0, 8 and 8.000 are not the same if rounding is involved.) • Meticulousness in terms of having a systematic process. This dovetails nicely with the problem solving steps that math texts always include, as well as for following other important steps, like order of operations. This is where I plan to teach the word “protocol.” • Persistence. Reading a sentence or paragraph several times if it doesn’t make sense. • Valuing all of the above traits and habits. This can be a tough sell, but it is really important to change attitudes.
Literacy Strategies Frayer Model and Visual Word Association (VVWA)– Vocabulary Builder Think Aloud – using Metacognition and Comprehension skills Anticipation Guide – Support Prior Knowledge and Comprehension 30
Vocabulary Builders
31
Another Frayer Model Example
32
Think Aloud • Literacy strategy designed to help students monitor comprehension and direct their thinking as they work through the problem solving process. • With teacher modeling, students are “talked through” the thinking process. • Share with students exactly what the instructor is thinking as he/she solves many, many types of problems 33
Anticipation Guide • Reading comprehension tool to scaffold text comprehension • Activates student prior/background knowledge
• Created with a list of statements about the topic of the reading or problems, some statement are true and accurate and others are incorrect or based on misconceptions 34
35
36
Answers are in blue.
37
“Politics is the art of the possible, the attainable — the art of the next best” Otto von Bismarck (1815-1898)
READ 1006 – Effective Reading for Mathematics Paired with ALL Developmental Math courses 38
Focus on Metacognition and Learning Strategies: • text annotation • note-taking systems (Cornell, SQ3R, HIT, etc.) • vocabulary development • concept mapping • summarizing • outlining • oral presentations
• test development (factual and conceptual questions) • reading and creating visuals: charts, pictures, graphs • online reading strategies • learning with technology; etc.
39
Q&A For additional information, email: • Ann Wolf at [email protected] • Linda Russell at [email protected] • Victoria Appatova at [email protected] 40
Ann Wolf, Central New Mexico Highlands University Linda Russell, Minneapolis C & T College (ret.) Victoria Appatova, University of Cincinnati
CRLA Pre-Conference Institute Louisville, KY November 3, 2016
1
Disciplinary Literacy vs. Content Area Literacy
Disciplinary Discipline specific terms, genre, etc.
Content Area General reading strategies
Draw from the experts in the discipline
Study skill strategies Emphasize the reading to learn about the discipline 2
Disciplinary Literacy VS Content Area Literacy • Avoid a “false dichotomy”
(Brozo et al, 2013)
• Healthy discussion is needed about how to choose adequate courses in the context of your institution
3
Practices that Work in Most Disciplines • • • • •
Read with your students Discuss/debate ideas Analyze together Writing to respond Reading others’ writing (Moje, 2013)
4
Discipline–Specific Practices • • • •
Problem framing/question posing Gathering and working with data Working with multiple texts Summarizing and synthesizing (multiple main ideas from many passages) • Communicating knowledge (Moje, 2013)
5
What do you know about reading? • In English, we read right to left and top to bottom. • Space separates words, sentences, and paragraphs from each other. And perhaps footnotes. • Most academic reading is for learning information and concepts so we can remember them. • What else? 6
Let’s Compare Reading Tasks • Most “other” content • Text is read from top to bottom • Text is read from left to right
• The reader may have to decide when to read insets, boxed material, and graphics, relative to the main text. • There may be margin notes. • The purpose of the reading is to learn and remember concepts, facts, etc. Perhaps to use in writing or to answer test questions.
• Mathematics content • Text may be read from top to bottom, but not always. • Text may be read in varying directions; consider the Order of Operations. • Students read, move to the margin and do problems, look at the bottom for answers, resume reading display material. • The purpose of reading is to carry out mathematical operations.
What, exactly, constitutes “text” in Math? • • • • •
• • • •
Words Symbols (+, ≈, √) Abbreviations and Acronyms (LCD, in., mm; NASA) Numbers (especially when in equations, formulas, and working problems, as opposed to years, totals, percents) Logograms ($; the symbol stands for the whole word, dollar[s]) Photos Drawings and diagrams Graphs, tables, charts Arrows, braces, or other directional cues
Examples of “confusing little words” The (a specific thing, as opposed to “any”) Is (often refers to “equal”) A (a number can mean any or one or even several) Are (means more than just “exists”) Can (may refer to “allowed to according to the rules”) On (a physical place) Find (meaning solve) One(s) (place value, as opposed to “one item”) And (And vs Or) Or (exclusive or inclusive?) Number (has a definition) Numeral (write in numeral form, as opposed to in words) Many/How many/How (easily confused) What (might be a definition) Write or Rewrite (as in “Rewrite mixed numbers as improper fractions”) vs Right L meaning “right angle” (is there a “left angle”?)
It (refers to something) Each (important that it is a separation of things) All (not some, many, or most) Do (a question word or imperative?) Which (a contrastive term) Same (in terms of some mathematical concept) Here/there (relative to some location) Has/Have (possessing) Of versus Off (percent of vs percent off) Of (indicating multiplication, when following a fraction) Countable: many/few; more/fewer Uncountable (mass): much/little; more/less; greater/lesser
Density of language/concepts
• Density = many new terms + new meanings for known words + new concepts
10
How many times “a” appears When a letter can stand for various numbers, we call the letter a variable. A number or a letter that stands for just one number is called a constant. Let c = the speed of light. Then c is a constant. Let a = the speed of a car. Then a is a variable since the value of a can vary. 11
Let’s see some examples From Introductory Algebra
12
Textbook Samples: Intro Algebra Density of concepts and “economy of language” to describe them, which results in very brief explanations. The phrase “to make general statements about numbers in algebra…” is a very abstract way of describing why we would use variables.
13
There are four terms in this note box that might be new or bear reviewing: coefficient, variable, integer, reciprocal.
14
This problem solving hint has no examples. Abstractions like this force the students to imagine their own examples. And, if you use x + 2 for both even and odd integers, why even mention it?
15
The definition of “area” is almost out of reach because of the use of such unfamiliar terminology, such as “plane” and “geometric figure.”
16
The Caution box should explain more about distinguishing between “5 less a number” and “5 is less than a number.” A very common type of error.
17
This Caution box has no words! But it does have a period at the end of the expression, which may be confused with a decimal point. Math texts use punctuation in unexpected ways.
18
Long sentences, which include two expressions. Note the use of punctuation (commas) after the expressions. This is common in math texts. You’re supposed to read the whole thing like a sentence.
19
Some skills needed for success in Math courses • COMPREHENSION OF THE LANGUAGE OF MATHEMICS (LECTURES, BOOK INFORMATION, TESTS) • NOTE-TAKING • TIME MANAGEMENT • TEST ANXIETY MANAGEMENT 20
Integrating literacy and communication skills in Math • WRITTEN COMMUNICATION – Reading (receiving a message: reading texts, ppt, handouts, assignments, tests) – Writing (sending a message: writing journals, reflection essays, final reports)
• ORAL COMMUNICATION – Listening (receiving a message: oral instruction in classroom and online ) – Speaking (sending a message: peer teaching)
21
Not understanding LANGUAGE OF MATH: Difficulties related to both oral and written representations Phonetic o professors’ accents, pronunciation of unusual vocabulary (incl. terms); homophones Morphological o Greek and Latin roots, prefixes, and suffixes; compound words Lexical o Unknown semantics of lexical units (words and phrases) Syntactical o Sophisticated sentence structure Discourse o Logical structure of the whole lecture; connections with text, notes, ppts, other lectures; other applications 22
Vocabulary Development • • • • • •
In-depth vocabulary work (linguistic cards) say, write, read, define words visualize words and concepts discuss words play with words differences and similarities between confusing words (Moje, 2013) 23
From Vocabulary to Syntax to Discourse 24
3 Steps to Reading a Word problem • 1st Reading: number-blind; look for key words; devise a formula; draw a picture • 2nd Reading: exclude unnecessary details; convert units; assign a variable • 3rd Reading: evaluate the answer; are all questions answered? 25
Recommended activities to develop writing and speaking skills in Math: • Journal writing and formative self-assessment • Journal portfolio and summative selfassessment • Peer teaching sessions – Classroom teaching – Reflective essay • Final projects – Written reports – Oral presentations 26
Peer Teaching: Triad Teaching • Directions: • Get into groups of three (randomly chosen groups) • Each person will teach the other two people one Example problem from Chapter X, p. X-Y. – Example X will be taught by____________________ – Example X will be taught by____________________ – Example X will be taught by____________________
•
Include in your teaching the following: – Give an overview of the learning outcome for the lesson. – Lead your classmates through the steps to solve the problem. – Figure out a good method for checking to see if they do it correctly. – Check their work. Analyze any errors and provide correct feedback.
• When all three are finished teaching, answer the questions below.
27
Reflection on Triad Teaching • What were the challenges for you as the “teacher” for the group? Please describe in what way(s) it was challenging. • Did your “students” follow your directions appropriately? If not, explain. • Did your “students” get everything correct? If not, describe their errors. • Describe your experience being the “student.”
28
Habits of Mind for Math • Accurate reading of every word. Correct representation of words, numbers, etc. No “looseness.” Pronunciation needs to be correct too. (Commutative has nothing to do with Communication.) • Precision reading, which involves accuracy, but goes beyond, to exactness in all things. (8.0, 8 and 8.000 are not the same if rounding is involved.) • Meticulousness in terms of having a systematic process. This dovetails nicely with the problem solving steps that math texts always include, as well as for following other important steps, like order of operations. This is where I plan to teach the word “protocol.” • Persistence. Reading a sentence or paragraph several times if it doesn’t make sense. • Valuing all of the above traits and habits. This can be a tough sell, but it is really important to change attitudes.
Literacy Strategies Frayer Model and Visual Word Association (VVWA)– Vocabulary Builder Think Aloud – using Metacognition and Comprehension skills Anticipation Guide – Support Prior Knowledge and Comprehension 30
Vocabulary Builders
31
Another Frayer Model Example
32
Think Aloud • Literacy strategy designed to help students monitor comprehension and direct their thinking as they work through the problem solving process. • With teacher modeling, students are “talked through” the thinking process. • Share with students exactly what the instructor is thinking as he/she solves many, many types of problems 33
Anticipation Guide • Reading comprehension tool to scaffold text comprehension • Activates student prior/background knowledge
• Created with a list of statements about the topic of the reading or problems, some statement are true and accurate and others are incorrect or based on misconceptions 34
35
36
Answers are in blue.
37
“Politics is the art of the possible, the attainable — the art of the next best” Otto von Bismarck (1815-1898)
READ 1006 – Effective Reading for Mathematics Paired with ALL Developmental Math courses 38
Focus on Metacognition and Learning Strategies: • text annotation • note-taking systems (Cornell, SQ3R, HIT, etc.) • vocabulary development • concept mapping • summarizing • outlining • oral presentations
• test development (factual and conceptual questions) • reading and creating visuals: charts, pictures, graphs • online reading strategies • learning with technology; etc.
39
Q&A For additional information, email: • Ann Wolf at [email protected] • Linda Russell at [email protected] • Victoria Appatova at [email protected] 40
