1 What Does Reading Have To Do With Math? (Everything!) AMATYC Conference 2008 Amber Rust November 22 nd - Saturday 12:00 – 12:50

2 Assumption When a student is not successful in math, teachers usually assume the difficulty is with the student’s mathematical ability or possibly the student’s dislike of mathematics, but the truth may more likely lie with the student’s poor ability to read the mathematics textbook. When a student is not successful in math, teachers usually assume the difficulty is with the student’s mathematical ability or possibly the student’s dislike of mathematics, but the truth may more likely lie with the student’s poor ability to read the mathematics textbook. (Draper, Smith, Hall, & Siebert, 2005; Kane, Byrne, & Hater, 1974; O’Mara, 1982)

3 Students’ Common Experiences In Math Classrooms  Students find math textbooks to be intimidating and confusing and therefore just skip past the explanations. (Draper, 1997)  Students expect the teacher to be the expert, do all the talking, and be the center of the classroom.  Students say the best means of learning math are (Stodolsky, Salk, & Glaessner, 1991) 1. “hearing an explanation” 2. “asking someone” 3. “being told what to do”

4 Teachers’ Common Experiences In Math Classrooms  Teachers compensate for students’ lack of reading ability by using the textbook as a resource for exercises only. (Draper, 2002; Porras, 1994)  Teachers “tell” students all necessary information therefore releasing students from needing to read the textbook. (Draper, 2002; Porras, 1994)

5 Beyond Crossroads Standards for Intellectual Development Communicating Standard: Students will acquire the ability to read, write, listen to, and speak mathematics (p.5).

6 Beyond Crossroads Standards for Pedagogy Active and Interactive Learning Standard: Mathematics faculty will foster interactive learning through student writing, reading, speaking, and collaborative activities so that students can learn to work effectively in groups, communicate about math both orally and in writing (p.6).

7 Reading in Math (Barton & Heidema, 2002)  Requires unique knowledge and skills not taught in other content areas.  Math textbooks contain more concepts per word, per sentence, and per paragraph than any other text type or content area textbook.  Students need to be proficient at decoding words, numbers, and symbols.

8 Reading in Math (Barton & Heidema, 2002)  Writing style in math textbooks is compact and succinct with little redundancy of text.  Students often skip over the worded parts looking for examples, graphics, or exercises.  In K-12, math textbooks are often written above grade level.  Overlap between math and everyday English vocabulary can cause confusion.

9 The Math Register and Vocabulary (Rubenstein, 2007)  Some words are… found only in math (e.g., denominator, hypotenuse, polynomial, histogram) found only in math (e.g., denominator, hypotenuse, polynomial, histogram) shared with science or other disciplines (e.g., divide, radical, power, experiment) shared with science or other disciplines (e.g., divide, radical, power, experiment) shared with everyday English, sometimes with different meanings, sometimes with comparable meanings in mathematics (fraction, similar, variable, median) shared with everyday English, sometimes with different meanings, sometimes with comparable meanings in mathematics (fraction, similar, variable, median)

10 The Math Register and Vocabulary (Rubenstein, 2007)  Some words… have multiple meanings in math (e.g., point, cube, range) have multiple meanings in math (e.g., point, cube, range) Sound like other words (e.g., sum & some, plane & plain, intercept & intersect, complement & compliment, hundreds & hundredths, pie & pi) Sound like other words (e.g., sum & some, plane & plain, intercept & intersect, complement & compliment, hundreds & hundredths, pie & pi) are learned in pairs that often confuse students (e.g., complement & supplement, combination & permutation, solve & simplify, at most & at least) are learned in pairs that often confuse students (e.g., complement & supplement, combination & permutation, solve & simplify, at most & at least)

11 Vocabulary - Symbols  Symbols can also have… multiple meanings within math multiple meanings within math meanings in everyday English meanings in everyday English meanings in other content areas meanings in other content areas

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13 Content Area Reading Strategies  Reading strategies are NOT for students to learn-to-read the math textbook but to read-to-learn from the math textbook.  Reading Strategies are really Learning Strategies Students can use strategies to help them comprehend what is read Students can use strategies to help them comprehend what is read Faculty can use strategies to check on student comprehension of what is read Faculty can use strategies to check on student comprehension of what is read

14 Easy Additions to Instruction  Research shows… explicit instruction in the physical presentation of the textbook and the textbook structure is highly related to reading comprehension explicit instruction in the physical presentation of the textbook and the textbook structure is highly related to reading comprehension connecting the new material to students’ prior knowledge increases understanding when reading the textbook. connecting the new material to students’ prior knowledge increases understanding when reading the textbook. Prior knowledge, prior knowledge, and more prior knowledge!! Prior knowledge, prior knowledge, and more prior knowledge!!

15 Example of a Vocabulary Strategy Verbal and Visual Word Association – (Barton & Heidema, 2002) Vocabulary Term(s) Visual Representation Definition(s) Personal Association or a characteristic

16 Example of a Vocabulary Strategy Verbal and Visual Word Association – (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-axis y-axis f(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.

17 Example of a Vocabulary Strategy Frayer Model – (Barton & Heidema, 2002) Definition (in own words) Facts/Characteristics Examples Non-Examples WORD or SYMBOL

18 Example of a Vocabulary Strategy Frayer Model – (Barton & Heidema, 2002) Definition (in own words) Facts/Characteristics Examples Non-Examples RADICAL An expression in this form is called a radical, b is called the radicand and the n is called the index of the radical. is the positive square root of a is the negative square root of a

19 Example of a Vocabulary Strategy Frayer Model – (Barton & Heidema, 2002) 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 or

20 As you read the textbook page, think about these questions…  What vocabulary difficulties could students have?  What do you think they may find confusing?  Are the explanations well written?  What is left unexplained?  Do you only read from left-to-right and from top- to-bottom?  What isn’t defined that you think should be?  Do they know how to read the graph and how to connect it to the other information given?

21 Guide-O-Rama (Daniels & Zemelman, 2004)  A written guide (not an outline) given to students to show them the way through the textbook reading selection.  It lets you informally coach, support, and chat with your students as they read the textbook outside of class.  It activates prior knowledge and sets a purpose for the reading.  It guides the students through the words, charts, diagrams, graphs, tables, pictures, equations, symbols, notation, examples, etc. in the textbook.

22 Use Jigsaw to Encourage Reading  When teaching quadratic solution methods… divide students into groups; each group reads the textbook to become the expert on one method, divide students into groups; each group reads the textbook to become the expert on one method, next, make up new groups with at least one expert for each method, next, make up new groups with at least one expert for each method, then, each expert in the group explains their method to the others, then, each expert in the group explains their method to the others, after the explanations, the group makes a list of the pros and cons of each method and when use each method can be used after the explanations, the group makes a list of the pros and cons of each method and when use each method can be used

23 Advantages to Help Students Read Math (DeLong & Winter, 2002)  Offers students another way to learn math.  Teachers will have more class time to cover content in appropriate depth.  Some studies have shown that reading is better than lecture for retention.  Offers another approach to teaching that can accommodate different learning styles.  Most vocabulary can be easily acquired through reading, leaving class time for clarification, extension, and reinforcement of the material.

24 Textbook Use (Daniels & Zemelman, 2004)  Don’t teach as if they have never had or never will have the opportunity to read the material!  Have empathy, remember you are the expert and it really may be Greek to them.  Don’t leave the students to decipher the textbook alone.  Front-load your teaching before they read – point out possible difficulties they may encounter.  Choose wisely what is to be read; every page is not needed.  Supplement richly with websites, newspapers, trade books, magazines, and environmental print.

25 Textbook Use (Daniels & Zemelman, 2004)  Remind the students about what they already know – prior knowledge.  Research shows that students find it very difficult to learn from the math textbook with little or no support from their teacher.  Research shows a strong connection between vocabulary knowledge and the ability to understand what is read.  Be explicit about the what, why, and how for each strategy shown to your students.

26 Final Thoughts  “A mathematics education that assumes to prepare students without providing them with ways to access the text falls short of truly educating students” (Draper, 2002).  “The priority of instructing for reading comprehension must be balanced with the priority of teaching the content area itself” (RAND, 2002, p. 30).

27 Any Questions?   OR 