An ASCD Study Guide for Literacy Strategies for Improving Mathematics Instruction

This ASCD Study Guide is designed to enhance your understanding and application of the information contained in Literacy Strategies for Improving Mathematics Instruction, an ASCD book written by Joan M. Kenney with Euthecia Hancewicz, Loretta Heuer, Diana Metsisto, and Cynthia L. Tuttle and published in October 2005.
You can use the study guide before or after you have read the book, or as you finish each chapter. The study questions provided are not meant to cover all aspects of the book, but, rather, to address specific ideas that might warrant further reflection.
Most of the questions contained in this study guide are ones you can think about on your own, but you might consider pairing with a colleague or forming a study group with others who have read (or are reading) Literacy Strategies for Improving Mathematics Instruction.

Preface and Chapter 1: Mathematics as Language

Joan M. Kenney

What are some of the demographic, historical and economic factors that have contributed to the change in our definition of an "educated person"?

When thinking and talking about mathematics, why is it important to maintain a distinction between mathematics content, and mathematics process? How does maintaining this distinction improve our ability to assess student performance?

Think about your own experience in learning mathematics vocabulary, and either the vocabulary of English or a new written or spoken language. What differences do you see?

Give examples of how the structure of the English language can impede mathematical understanding.

In addition to the items in Figure 1.1 on page 7, what other terms, formats and symbols have you found confusing for your students?

Chapter 2: Reading in the Mathematics Classroom

Diana Metsisto

Think about students reading in your mathematics class. What sorts of issues do they have with reading and interpreting their math text? reading math problems on standardized tests? Where do their difficulties lie?

What specific strategies have you tried in order to help students read and interpret mathematics problems in their texts? for standardized tests? How effective have those strategies been? What evidence do you have for their effectiveness?

What are some of the specific differences the author mentions between regular English text and mathematics text (pp. 11, 12)? How does regular reading instruction help students in reading mathematics text? Where does it fall short? What do you think of the author's assertion that mathematics teachers must help students become readers of mathematics text?

Think of some examples from your own experience where students have misinterpreted a word or phrase in math class due to its specialized mathematics use as opposed to everyday use (pp. 13, 14). What did you do to clear up the misinterpretation? What are some things you could do to help students identify this sort of roadblock themselves?

Think about a complex mathematics problem that you have solved recently, or find one to solve now. As you work through the problem talk aloud and write down what steps you use to figure out how to solve the problem: i.e. explicitly think about what you do to interpret and translate math text (p. 10). Doing this with colleagues will enrich your understanding of decoding strategies.

The author gives some specific tools for helping students to become strategic readers. Choose one and use it in one of your classes. Keep notes on how it works and what you'd like to change: i.e. become a research practitioner to ascertain what sorts of strategies help your students to become better readers and interpreters of mathematics text.

Chapter 3: Writing in the Mathematics Classroom

Cynthia L. Tuttle

What are some of the advantages of writing down your thoughts as you work through mathematical ideas and solve problems? What does the act of actually recording your thinking bring to your learning (pp. 24-25)?

From your experience, how important is mathematics success to reading and overall student achievement? What are some of the effects of placing students in lower level mathematics classes based on their reading and overall achievement (pp. 25-26)?

What are some recent changes in mathematics expectations for students? What are some of the changes in mathematics education for students (pp. 26-27)?

What criteria would you use to select a mathematics problem for written response? What might be an advantage of having a student try a mathematics problem alone before working with the group? What are the advantages of having students share their mathematics responses (pp. 27-20)?

Does writing down a correct answer show that the student understands the problem? What is sufficient indication that the mathematics has been learned (pp. 31-33)?

What is the role of vocabulary in mathematics? How do students learn vocabulary? Describe any writing supports (templates) that you find useful as you help students explain their thinking.

What should be the goals for ESL students in mathematics? What are some of the challenges for ESL students in mathematics (pp. 38-39)?

What are some appropriate mathematics expectations for special needs students? How does writing in mathematics help special needs students (pp. 44-47)?

What unique difficulties may students with weak reading and/or writing skills have in mathematics? How might technology support these students in their mathematics learning (pp. 48-49)?

What difficulties would you anticipate if you were introducing a mathematics program that emphasizes writing? What are some advantages to such a program?

Chapter 4: Graphic Representation in the Mathematics Classroom

Loretta Heuer

In your own mathematics classroom what "little words" (prepositions, articles, and conjunctions) tend to confuse students (p. 51)? Create a list of these as a reference for your own lesson planning.

As you read though "Reading Graphics" (pp. 53-61) consider the various forms of representation that students in your class need to interpret: pictures, icons (stylized graphics such as dots or circles that substitute for the items in a problem), geometric figures, charts, tables, and graphs. At what level of abstraction do your students get "stuck"? How might you help them interpret more abstract representations of their mathematics?

In the "Reading Graphics" section, students bring both intellectual misconceptions and visual misperceptions to word problems. What similar errors in prior "knowledge" do your students exhibit? How can you use graphic representations to expose students' erroneous thinking? How can you help students "unlearn" incorrect concepts by pressing for new interpretations of familiar graphic representations?

In common parlance, the word "even" is used in several ways. Think of how you use the term, what evenness may "look like," how students have heard the word used in mathematics lessons, and the context in which it is being used in Scenario #4 (p. 57). Consult a dictionary to see how many definitions the word "even" has. Create a list of other terms whose rich definitions may be causing confusion in your students' thinking.

Consider the students in Scenario #6, "The Wordsmiths" (p. 60) who were inventing terminology to articulate emerging understanding. Listen for "naïve" words, phrases, and expressions that your own students use as they try to talk about partially formed concepts. How can you move these student-generated terms toward greater mathematical precision?

Scenario #10 (p. 66) begins with an adult rewording of a problem in the student text. Work the "Nona's Restaurant" problem yourself, complete with hand-drawn diagrams and paper and pencil calculations. What issues arise as you become the "student"? Does doing the mathematics on your own help clarify the difference between "count nouns" and "mass nouns"?

Choose one of the ten Scenarios. Work with a colleague to "unpack" student confusion using the coach/practitioner questions listed at the Scenario's end. What do you discover?

Read through the list of suggestions offered by teachers (pp. 69-71) and select one to use as an intervention in your classroom. Treat this as a practitioner research project by writing up: a) what you hoped to change, b) what intervention you chose, and c) how the student(s) responded.

Chapter 5: Discourse in the Mathematics Classroom

Euthecia Hancewicz

Many ideas in Chapter 5, Discourse in the Mathematics Classroom, flow from the idea that "discussion and argumentation improve conceptual understanding" (p. 72). What does this mean to you? To your colleagues?

Consider the definitions of traditional, probing, and discourse-rich classroom conversations (p. 73). What images come to mind for each? How does the author define each? Cite examples from your own experience.

On page 74, the author states, "Discourse is more than a teaching technique; it is a framework on which to build effective mathematics lessons." What did this mean to you when you read it for the first time? Keep this statement in mind as you read the rest of Chapter 5.

In the section "Creating Discourse-Friendly Classrooms" (pp. 74-80), there are three bulleted lists of strategies that help teachers foster discourse:

Small but significant changes

Ways to let student ideas lead

Pisauro's tips

Which of these strategies have you tried? What impact on student learning did you see? What other strategies might you try?

Practitioners argue about whether or not computation skills can be learned through investigative lessons. Read the section "Discourse and Computation" (pp. 80-82). Have you seen similar evidence that discourse enhances computation learning? Write up an illustrative example.

Concept maps are not widely used in mathematics classes. Have you used any? How? After reading the section, "Using Concept Maps to Foster Discourse" (p. 83) write a set of directions for using a familiar concept map, and try it with students.

Create a short action research project –alone or with a colleague. Use an existing lesson plan; embed within that plan some strategies from this chapter. As you teach the lesson, be conscious of student discourse; perhaps a colleague might observe and record evidence. Create a written reflection of your observations.

Chapter 6 and Appendices: Creating Mathematical Metis

Joan M. Kenney

How might some of the characteristics that contribute to metis (p. 88) evidence themselves in the mathematics classroom?

In what ways can high-stakes testing contribute to a decrease in metis in the classroom? What steps can a teacher take to diminish this negative effect?

How can action research contribute to a synthesis of content and process in classroom practice? Is there a particular topic that you, as an educator, would like to research?

Which of the four abilities listed under "What Students Need to Know" (p. 92) do you think is the least developed in our mathematics students today? What steps can we take to remediate this deficiency?

In which literacy area (reading, writing, representation, discourse) do you feel you need more information? Consult the citations in the Resource Bibliography (pp. 99-104) for additional references.

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