Algebra Out Loud: Learning Mathematics Through Reading and Writing Activities

Overview

Algebra Out Loud is a unique resource designed for mathematics instructors who are teaching algebra I and II. This easy-to-use resource is filled with illustrative examples, strategies, activities, and lessons that will help students more easily understand mathematical text and learn the skills they need to effectively communicate mathematical concepts.

Algebra Out Loud's strategies and activities will give students the edge in learning how to summarize, analyze, present, ...

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Overview

Algebra Out Loud is a unique resource designed for mathematics instructors who are teaching algebra I and II. This easy-to-use resource is filled with illustrative examples, strategies, activities, and lessons that will help students more easily understand mathematical text and learn the skills they need to effectively communicate mathematical concepts.

Algebra Out Loud's strategies and activities will give students the edge in learning how to summarize, analyze, present, utilize and retain mathematical content. The book offers proven writing activities that will engage the students in writing about algebraic vocabulary, processes, theorems, definitions, and graphs. Algebra Out Loud gives teachers the tools they need to help their students learn how to communicate about math ideas between student and teacher, student and peers, and student and the wider world. For quick access and easy use, the activities are printed in a big 8 1/2" x 11"format for photocopyin g and are organized into eight chapters.

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Product Details

  • ISBN-13: 9780787968984
  • Publisher: Wiley
  • Publication date: 10/31/2003
  • Edition number: 1
  • Pages: 244
  • Sales rank: 786,910
  • Product dimensions: 8.28 (w) x 11.06 (h) x 0.68 (d)

Meet the Author

Pat Mower, Ph.D., is an associate professor in the Department of Mathematics and Statistics at Washburn University in Topeka, Kansas. Dr. Mower prepares preservice teachers to teach mathematics in elementary, middle, and secondary schools. Her interests include reading and writing in mathematics, and alternative methods for the teaching and learning of mathematics.

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Table of Contents

Introduction.

Algebra Time Line.

PART ONE: Reading to Learn Algebra.

1. Prereading Strategies and Activities.

Prelude.

Review/Preview Process.

Knowledge Ratings.

Anticipation Guides.

PreP.

Problem-Solving Prep.

Wordsmithing.

2. Reading and Vocabulary-Building Strategies and Activities.

Prelude.

Magic Square Activity.

Concept Circles.

K-W-L.

Semantic Feature Analysis.

Graphic Organizers.

Reading Math Symbols.

Proof Reading.

Semantic Word Maps.

3. Postreading Strategies and Activities.

Prelude.

Group Speak.

Concept Cards.

Frayer Model.

Question–Answer Relationship (QAR).

Comparison and Contrast Matrix.

4. Readings in Algebra.

Prelude.

The Secret Society of Pythagoreans: An Ancient Cult.

Ancient Egyptian Multiplication.

Marathon Math.

True Prime.

PART TWO: Writing to Learn Algebra.

5. Writing to Understand Algebra.

Prelude.

In Your Own Words: A Paraphrasing Activity.

MO (Method of Operation).

Graph Description Activity.

Crib Sheets.

Math Story Activity.

Math Ads.

The Writing Is on the Wall.

Creating a Math Mnemonic.

Creation of Written Problems (or Fat Men in Pink Leotards).

Math Concept Paragraphs.

Math Biographies.

Experimenting-to-Learn-Algebra Reports.

Concept Math.

Learning Logs.

6. Writing to Communicate Algebra.

Prelude.

Writing Across Campus.

Group Exposition.

Guided Math Poetry.

Math Letters.

Math Profiling.

Math Journals.

Mathematical Investigator.

7. Writing as Authentic Assessment.

Prelude.

Muddiest Point.

Math Analogies.

One-Minute Summary.

Math Is a Four-Letter Word.

E-Writing.

Math Similes, Metaphors, and Analogies.

Targeted Problem-Solving Assessments.

Self-Portrait as a Learner of Algebra.

8. Writing for Assessment.

Prelude.

Math Portfolios.

Math Essays.

Write Questions.

Math Posters.

References.

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First Chapter

Algebra Out Loud

Learning Mathematics Through Reading and Writing Activities
By Pat Mower

John Wiley & Sons

ISBN: 0-7879-6898-6


Chapter One

Prereading Strategies and Activities

Prelude

Mathematics students will readily admit they often skip over the mathematical text and go right to the problem section of a lesson in the text. As teachers, we attempt to remedy the situation by cajoling and coaxing the students to open the book and read. However, we suspect that many of our students pay little attention to this, for they know that they will learn the important content from our presentation of the content in class or can refer back to examples in the text for help with assigned problems. What appears to be missing is the students' willingness to read and learn from the text. So if willingness is the key, how do we instill this in our students?

We know that children learn to read after they have demonstrated a readiness to learn. We can surmise that when our students are ready to read mathematical text, they will do so. So our role seems clear: facilitate this readiness. The key components for readiness to learn are interest, competence, and confidence. First, the text must capture the attention of the reader by containing content that is both interesting and relevant. Also, students must possess the skills that allow them to read efficiently and know that they either possess these skills or will soon have them. Competence in readingmathematical text includes understanding the vocabulary and the background or fundamentals of the concepts in the reading. To foster confidence, Vacca and Vacca (1999) suggest that we arouse curiosity, elicit predictions, and urge our students to ask questions about the new content. The prereading strategies and activities presented in this chapter are designed to promote and encourage student readiness and willingness to read mathematical text and content.

As teachers of mathematics, we are often limited by time constraints and the amount of content we are obliged to cover. Some of us may feel that teaching reading is not a priority. However, if we overlook this part of our instruction, we limit the amount of mathematics and diversity of mathematical processes that students might learn. Moreover, if we address the reading of mathematical content initially, we stand a chance of turning out students who are effective readers and, ultimately, successful communicators of mathematics.

Chapter One begins with the review/preview process, which later strategies and activities refer back to. The following prereading strategies and activities are explored in this chapter:

Review/preview process

Knowledge ratings

Anticipation guides

PreP (prereading plan)

Problem-solving prep

Wordsmithing

Review/Preview Process

WHAT? Description

The review/preview process takes place prior to the students' reading of the text. There are two parts to the process: (1) teachers present a review of the prerequisite or background material needed to understand the new content and (2) students preview the new content.

To review the background content, teachers should do one or more of the following:

Summarize background material.

Pose a problem from the background material.

Share a historical anecdote regarding the new concepts.

Present an interesting problem to be solved after students read and learn the new content.

To preview the assigned reading, students should complete the following tasks:

Note the title.

Note all subtitles.

Note all boxed or highlighted definitions and theorems.

Note all pictures and graphics.

Note all other boxed or highlighted special sections, such as biographies of mathematicians or special applications.

WHY? Objectives

The review process allows the mathematics student to:

Recall necessary mathematical concepts and processes.

Connect previously learned concepts with new concepts.

Approach the new content with curiosity and interest.

Previewing allows the mathematics student to:

Obtain an overview of the reading.

Pose questions regarding new concepts and anticipate the answers to these questions.

Delineate or categorize different methods or concepts regarding the main topics from the text.

HOW? Worksheet

The lesson that follows gives a review/preview worksheet that students may use to assist in the review/preview process.

Review/Preview Process

NAME _______________________________ DATE ________________________

ASSIGNMENT: Briefly answer the following questions as you preview the section on _______________________________ on pages __________________________

List all titles and subtitles from the new content.

What background concept do I need to know?

What new concept and processes do I anticipate learning?

What questions do I have regarding the new content?

Knowledge Ratings

WHAT? Description

Charts that ask the student to assess their prior knowledge are called knowledge ratings (Blachowicz, 1986). The teacher presents students with a list of concepts or topics and surveys their knowledge on these topics. The survey headings for Knowledge Rating charts may take various forms, as the examples that follow show.

WHY? Objectives

Completing the knowledge ratings chart will allow the mathematics student to:

Self-assess prior knowledge of topics to be studied.

Target problem areas and make study plans.

Point out to the teacher personal problem areas.

Reviewing the completed knowledge ratings charts will allow the teacher to:

Observe problem areas and gaps in learning for students.

Plan content focus and time allotment for particular topics.

Find and assign other readings or assignments on problem subjects.

HOW? Example

The following example is from a unit on functions in advanced algebra.

Knowledge Rating for a Unit on Functions

How much do you know about the terms listed in the table? Place an X in the spaces that signal your knowledge.

A lot! Some Not much Function

Domain

Range

x intercept

y intercept

Vertical line test

Horizontal line test

Knowledge Ratings: Rating for a College Algebra Course

NAME _____________________________ DATE _______________________________

How much do you know about the equations listed below? Place an X in the spaces that signal your knowledge.

Can define Can give an Can sketch Am totally Example basis graph lost

Linear equation

Identity equation

Constant equation

Quadratic equation

Polynomial equation

Rational equation

Logarithmic equation

Exponential equation

My learning goals for this part of the semester are the following:

1. I will _______________________________________________________

2. In terms of studying, I will spend _____________ each _______________ on studying and homework.

3. I will earn at a(n) _____________ on this unit.

___________________________ _____________________________ signature date

Knowledge Rating for a Unit on Graphing Rational Functions

NAME _________________________ DATE __________________________

Place an X in the spaces for which you agree.

I can define I can give an I can graph or I can graph or Example of find on the find on the graph graph using my graphing calculator

Rational function

x intercept

y intercept

Vertical asymptote

Horizontal asymptote

Extrema

Knowledge Ratings: Template

NAME _____________________________ DATE _______________________________

Topics A lot! Some Not much

Anticipation Guides

WHAT? Description

Anticipation guides (Herber, 1978) are lists of statements that challenge students to explore their knowledge of concepts prior to reading the text and to discover through reading the text's explanation of these concepts.

A mathematical anticipation guide usually contains four to five statements, each with two parts. First, the student is asked to agree or disagree with each statement. Then the student reads the text and determines whether the text or author agrees with each statement.

WHY? Objectives

Anticipation guides allow and motivate mathematics students to:

Explore their opinions and prior knowledge of mathematical concepts.

Read closely to find evidence to support their claims or discover the text's view.

Uncover and identify any misconceptions regarding these concepts.

HOW? Example

Here is an example of an anticipation guide for a section on linear equations in two variables.

Anticipation Guides: Selection on Linear Equations in Two Variables

Directions: In the column labeled ME, place a check next to any statement with which you agree. After reading the section, consider the column labeled TEXT, and place a check next to any statement with which the text agrees.

Me Text

_______ _______ 1. The solution set for any linear equation in x and y is exactly one ordered pair.

_______ _______ 2. The graph of a linear equation is a line.

________ _______ 3. The slope of a vertical line is zero.

________ _______ 4. Slope-intercept form looks like: y = mx + b.

_______ _______ 5. Two parallel lines have equal slopes.

Anticipation Guides: Solving Quadratic Equations in One Variable

NAME ___________________________ DATE _________________________

Select the chapter or section in any Algebra II text that discusses solving quadratic equations in one variable. Follow the directions in the anticipation guide below.

Directions: In the column labeled ME, place a check next to any statement with which you agree. After reading the section, consider the column labeled TEXT, and place a check next to any statement with which the text agrees.

Me Text

_______ _______ 1. Quadratic equations have at most two solutions.

_______ _______ 2. The quadratic formula can be used to solve any quadratic equation.

_______ _______ 3. If x2 = 25, then the solution set for x is {5}.

_______ _______ 4. Completing the square is a valid method for solving quadratic equations.

_______ _______ 5. When using the factoring method to solve a quadratic equation, you must set the equation equal to zero before you factor.

Anticipation Guides: Measures of Central Tendency

NAME ____________________________ DATE __________________________

Directions: In the column labeled ME, place a check next to any statement with which you agree. After reading the section, consider the column labeled TEXT, and place a check next to any statement with which the text agrees.

Me Text

_______ _______ 1. The median is the middle-most value of a data set.

_______ _______ 2. The mean = median = mode of every data set.

_______ _______ 3. The mode is the most recurring number in a data set.

_______ _______ 4. If the median is more than the mean, then the data set is skewed to the left.

________ _______ 5. If a set contains an even number of data, then the median will be equal to the mean of the two numbers in the middle of the data set.

PreP

WHAT? Description

The Prereading Plan (PreP) (Langer, 1981) is a large-group brainstorming activity. The teacher guides students in activating, sharing, and fine-tuning prior knowledge. Initially, the teacher chooses one of the key concepts of the reading or lesson and then guides the students in the brainstorming of this concept. Langer suggests that the teacher follow a three-step process to guide the students' collective thoughts:

1. Initial associations. The teacher asks, "What comes to mind when you hear ________?" The teacher wrtes student responses on board.

2. Secondary reflections. The teacher asks individual students regarding their responses, "What made you think of ______________?" The teacher writes the student reflections under appropriate initial responses on board.

3. Refining knowledge. The teacher asks, "Do you have any new ideas or thoughts after hearing your peers' ideas?" The teacher writes new ideas on board.

WHY? Objectives

The PreP allows mathematics students to:

Activate prior knowledge.

Hear and reflect on peers' ideas.

Clarify, refine, and enlarge knowledge.

HOW? Example

The teacher presents the new concept of rational numbers and uses the three-step process in this way:

1. Initial associations Fraction Whole number Not a square root Not pi

2. Secondary reflections Fraction-fraction of integers Whole number-integers

Not a square root. Could be square root of perfect square.

Not pi. Pi is a decimal, approximately 3.14, where the decimal digits go on forever and ever with no pattern.

3. Refining knowledge A rational number is a fraction of integer over integer.

Rational numbers are decimals that terminate or have a repeating pattern.

Problem-Solving Prep

The National Council of Supervisors of Mathematics (1988) says that the principal reason for studying mathematics is to learn to solve problems.

WHAT? Description

Problem solving is the process of resolving the confusion or mystery of an unfamiliar situation. The twentieth-century mathematician George Polya devoted his life to helping students become good problem solvers. In his famous book How to Solve It (1973), he outlines a four-step process for solving problems:

1. Understand the problem, which means read, reread, make a guess, restate the problem, and/or rewrite the question.

2.

Continues...


Excerpted from Algebra Out Loud by Pat Mower Excerpted by permission.
All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
Excerpts are provided by Dial-A-Book Inc. solely for the personal use of visitors to this web site.

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