Literacy Link Using Literacy Strategies in Nelson Mathematics Literacy is integral to mathematics. Using effective literacy strategies to support reasoning (thinking), problem solving, communicating, representing, and making connections can result in more effective learning in mathematics. Why Reading Mathematics Text is Challenging Researchers have identified several reasons why mathematical text is challenging and why students can benefit from knowing how to read it strategically: Mathematics text usually has a high concept load it features more concepts per page than any other text. The vocabulary is often unfamiliar to students. The organizational structure is unfamiliar or invisible to students. Students do not have a strategic plan for reading mathematics text. Students must often read text in an unfamiliar manner, (for example, from right to left as well as left to right, and diagonally). There is usually very little repetition or redundancy in math texts. Ideas build on earlier ideas, and students must grasp the underlying logic of an idea before proceeding to the next step. Word problems may contain a substantial amount of prose. Students must be able to identify the question and categorize the rest of the information as useful or not useful. Math texts require the student to decipher both words and symbolic language. (Barton and Heidema, 2002, pages iii v) Before, During, and After Reading Reading is a process of constructing meaning in which readers interact with the text using prior knowledge and experience to make connections, generate hypotheses, and make sense of what they read. Reading mathematics involves comprehending mathematical text that is constructed of numbers, symbols, graphs, illustrations, and prose. Skilled readers use strategies to help them construct meaning from text before they read, during their reading, and after reading. Students can increase their understanding of text and become more effective at using reading strategies through explicit instruction. 70 Nelson Mathematics 8: Overview
Before Reading Students need to access prior knowledge, make predictions about the text, have a clear purpose for reading, and preview the text to form a strategic plan for reading based on type of text and purpose of reading. Teachers need to employ instructional strategies that provide a focus for learning, help students to access, clarify, revise, and extend their knowledge, and introduce and review vocabulary and concepts. During Reading Students need to focus their attention on the reading, anticipate and predict, use the structures of text to help them construct meaning, use strategies to gain and regain meaning (ask questions, visualize, identify main idea, make connections, make inferences, reread, use context clues, and so on) and integrate new information with what they already know. Teachers need to employ instructional strategies that support students in using their prior knowledge as a framework to build new understanding, to help students understand the structure of the text, and to explicitly teach those strategies that will allow students to acquire independence when reading text. After Reading Students need to reflect on what they have read, confirm predictions, make connections to their background knowledge, and clarify their understanding. They also need to reflect on their reading strategies and the way in which they approached both the text and the task. Teachers need to employ instructional strategies that support students in clarifying their understanding, in making connections between new knowledge and prior knowledge, in considering how this learning applies in new situations, and in reflecting on their skills as a learner. Strategies for Before Reading Pre-reading strategies are designed to give students a kind of roadmap for the lesson. If they preview what is to be covered, they are more likely to build their understanding through logical steps and stages. Setting a purpose for reading Setting a purpose for reading means recognizing (though not yet understanding) the main idea of the lesson recognizing (though not yet understanding) the key terms for the lesson A purpose for reading can be set by reviewing the Chapter or Lesson Goals and taking note of the bolded vocabulary terms. Literacy 71
Introducing Vocabulary Students are required to know and use the vocabulary of mathematics. There are many activities that teachers can use to ensure students are familiar with the vocabulary that they will encounter in their reading. The following is one example of a pre-reading instructional strategy that focuses on new vocabulary: Word Splash Purpose: Introduce new vocabulary Activate prior knowledge Assess students prior understanding of a concept/topic Help students make predictions Directions: Preview the text and identify important terms and vocabulary. Write each word on a card and display on the board. Individually have students select three words and write each in a sentence that conveys its meaning. Invite students to read their sentences. Ask students to identify the main topic. Ask students to organize the words in a specific way and to explain their organization. Ask if others have a different way of organizing. Have students read the text to compare their understanding of the terms. Ask them to revise, add to, or change their sentences based on new information. Have students share their sentences in a small group and post three collective sentences. Example: Chapter 4, Lesson 2 table of values scatter plot pattern ordered pair term general term algebraic expression Fibonacci sequence variable 72 Nelson Mathematics 8: Overview
Accessing Prior Knowledge/Making Connections Suggestions for helping students connect new learning to prior knowledge are found in the Introduction teaching notes for each lesson. Making a concept map is a strategy that can be used instead for many lessons. Making a Concept Map Purpose: Access prior knowledge Make connections Organize thinking Categorize, make comparisons, identify attributes, name examples Directions: Identify the key concept that the students will encounter in their reading. Using sticky notes or small squares of paper, have students either individually or in small groups, brainstorm what they know about this concept/topic. Ask students to write one idea on each sticky note. Have students cluster like ideas together and give each cluster a name. Students could physically connect ideas into some form of hierarchy or use lines to show the connection among ideas. Share some of the organizational structures. After reading, have students revise their concept map using new information. Example: Chapter 1, Lesson 4 composite number prime number prime factorization number relationships power least common multiple greatest common factor Literacy 73
Strategies for During Reading It is important to stress that reading is an active, not a passive, process. As students read, they should be trying to make sense of the text by connecting what is being said to what they already know, and by seeking answers to the questions that are forming as they read. Think Aloud One strategy for developing active reading is for you to read a section of text and model a Think Aloud while students read the passage silently to themselves. During the Think Aloud, you can focus on verbalizing your thoughts, reactions, and questions calling up old knowledge when it connects to the text drawing attention to something you understand by saying, Oh yes, that s because remarking on things that are not quite clear to you or things you think you should check This kind of talking your way through the reading can familiarize students with the differences between effective (active) and non-effective (passive) reading. Students can practise this strategy in pairs using passages from Nelson Mathematics that you select. Visualizing Encouraging students to visualize concepts, relationships, and problems while they are reading is another useful strategy. Visualizing means creating a mental image of an idea. Students can sketch their images on paper or use concrete objects as representations. Pairs Reading Pairs reading involves two students taking turns reading to each other. One student reads and the other follows up by summarizing the main idea and supporting ideas and asking the reader questions to clarify meaning. Students then reverse roles. Students can reverse roles after each paragraph until they come to the end of a difficult passage of the text. Developing Vocabulary Students may find math vocabulary challenging to master. There are a number of ways to represent math terms and their definitions graphically, which can help support comprehension. Some of these graphic organizers extend the explanation of terms to characteristics, properties, and examples (and even non-examples). 74 Nelson Mathematics 8: Overview
Concept maps Concept maps (see p.73) can be used during reading, as well as before reading. Students can create concept maps after they have read about an idea or have completed several activities based on an idea. They should place the main term in the inner circle and use spokes to connect the main idea to other circles that describe what the idea is (category), what is can be compared to (comparisons), what its properties are (properties), and examples of the idea. Math Word Wall In the Teacher s Resource for every Chapter Opener in Nelson Mathematics, suggestions are made for words that can be incorporated in a Math Word Wall. One possible framework for building the word wall follows: Students can also use this structure to create their own math glossary. Word Diagram Definition Synonym or or Analogy Representation Using the supporting text features Students should be made aware of how new vocabulary is treated in Nelson Mathematics. Related features will have been identified if you complete the Book Walk with students before using the Student Book (see p.77). New vocabulary is bold-faced and highlighted in yellow; it is defined in the margin where it first appears (often with an accompanying illustration), and appears in the Glossary. Students should also be aware of the section of the Glossary devoted to Instructional Words. Supporting Comprehension of Word Problems Word problems often contain a large amount of prose, as well as mathematical ideas for decoding. Some students say that problems give them the most trouble because they get lost in all the words. Students need to be able to identify the question in the word problem (for example, what they are being asked to do), along with the key facts and the less relevant information. Two simple tips for students to remember are as follows: The key facts usually involve numbers. The question, or task, usually comes at the end of the problem. The KNWHL Chart (Literacy Master 1) helps students identify what they know, what information in the problem is not relevant, what the problem is asking them to do, and what strategy they can use to solve the problem. Students can begin using this strategy in small groups, discussing how they know what information to put in the columns. However, make sure they have lots of opportunities to use the chart and the other problem comprehension strategies independently. Literacy 75
Using a KNWHL Chart Purpose: Identify main ideas Identify irrelevant information Decode information Ask questions Select strategies Synthesize information Draw conclusions Directions: Distribute the five-column worksheet (similar to KWL for prose text). Work collaboratively using a problem from the Student Book. Model how to fill in the columns, explaining not just the what but the how of your thinking. In the K column, have students identify the information they know after reading the problem. In the N column, have students enter the information they read that is not needed to solve the problem-irrelevant information. In the W column, have students answer what the problem asks them to find out. In the H column, have students suggest a strategy they could use to solve the problem. Have students attempt to solve the problem, then fill in the last column. The L column asks students to reflect on each of the columns and determine how well they read the problem, identified the key ideas, and how well the strategy they selected worked for them. Have students select a word problem from the Student Book and use the KNWHL Chart in pairs. Have students select a word problem from the Student Book and use the KNWHL Chart independently. Strategies for After Reading Post-reading strategies allow students to go back over the material covered and test their understanding. Some ideas for re-reading include returning to the Setting the Purpose questions (see p.71) and attempting to answer them, taking notes about the key points, reviewing vocabulary aids, or devising test questions on the material for a partner or for a student-generated class test. You can also have students complete Literacy Master 2: Understanding What I Read, which reviews vocabulary, and Literacy Master 3: Thinking About Reading Math, which helps students review their use of reading strategies. Using Text Structures and Text Features to Read Good readers know text structures and use them to comprehend more effectively. For many young readers, the only text structure that they have embedded in their mental schema is the narrative text structure. These students approach reading non-fiction the same way in which they 76 Nelson Mathematics 8: Overview
read fiction which actually interferes with their ability to make meaning from the text. To read and comprehend math text, students need to have a mental structure for this particular type of non-fiction text. Knowledge of text structure can be a valuable predictive cue the reader spends less time trying to figure out the structure and more time focused on meaning. In other words, students who are knowledgeable about text organization comprehend more of what they read. Research shows that students who are skilled at working with text organization are better able to: locate key information identify what is important and unimportant synthesize information that appears in different locations within a text connect new information with what is known restructure schema to account for new learning Explicit instruction in the organization of the text can make the structure visible for students and act as an aid in reading comprehension. When underlying structures and/or text features recur in predictable patterns, they help the reader make predictions, find information, and make connections. Nelson Mathematics uses consistent structures and features to support students in their reading. Walking students through the Student Book and the two-page lesson format to show the organizational structure, assists students in understanding how the book works (see Literacy Masters 4 and 5 for a sample Book Walk). Book Walk Purpose: Introduce the structure of the Student Book Identify and understand text features Directions: Remind students that their math book is a non-fiction text. Ask them what they know about the organization of a non-fiction book and have them record their ideas. Ask them what they expect to find in a mathematics Student Book and have them record their ideas. As students take the Book Walk, they can note which of their expectations were met. Students go on the Book Walk in pairs or small groups. Each group should complete one of the tables on the Book Walk Record Sheets (Literacy Masters 4 and 5). Have students share their results. Ask a few general questions, such as: Where are the Reflecting, Checking, and Practising sections? How is colour used in the book? Where do you find the goal? What is its purpose? Another activity that will assist students to identify text features is included in Look It Over (Literacy Master 6). This strategy supports students in identifying text features, but goes beyond that, to helping students understand how text features help them become more competent readers. Text features include things such as: headings, diagrams, photos, illustrations, bolded words, graphs, charts, boxed features, captions, table of contents, and glossary. Literacy 77
Talking and Writing About Math Reflection is an important metacognitive process for clarifying thinking and consolidating understanding. Students reflections offer a window into their thinking. In Nelson Mathematics, students have numerous opportunities to think about their learning and the role of math in their lives: the Reflecting questions in each lesson are excellent examples. Students should be encouraged to respond to these questions orally and in writing. Before students attempt to reflect in writing, they will benefit from hearing the thinking of others. Their reflections will become more articulate as they develop their ability to self-monitor, self-direct, and self-assess. Over time, student will become more able to respond in writing to many prompts in a variety of situations. Throughout the year, frequent prompts encourage them to combine diagrams, numbers, and words to describe math concepts and relationships. When students approach any writing task, it is important for them to have an opportunity to talk about their ideas before writing. Conversation can take place with the whole class, a small group, a partner, or with you, depending on the lesson; but organizing ideas orally first helps students learn to record their math thinking. Equally important is sharing their writing when it is finished. This allows students to compare their own work with their classmates, and to think about ways to clarify and expand their writing. Math Journals I used... to calculate because... Something I ve learned about solving problems is... What surprised me about the math in this chapter is... Something that is improbable tomorrow is... My survey told m I know my answer is r Representing int counters and wit Having individual reflective journals encourages students to write frequently about math. They can use their journals to write about their work in math make predictions and generalizations, express their thoughts about the processes of math that they are experiencing and about what they have learned. Including visual representations such as diagrams, graphs, and charts with their writing enhances journal entries, and leads students to combine methods of recording math. It may be helpful to begin the year with a collaborative journal where students describe their thinking orally, and you or a student record it on chart paper. As skills and confidence develop, students can gradually take over the writing. Eventually they write independently in personal journals. Or, you might provide personal journals from the beginning. You can use chart paper to model possible responses for the class before the students start to write on their own. On some occasions, students find it beneficial to work in pairs or a small group to write a journal entry on chart paper, combining their ideas. Reflecting questions are a natural prompt for journal entries. Journal suggestions are also made in the teaching notes (for instance with the Chapter Opener and the Chapter Review). Other prompts will flow naturally from lessons and the discussions that arise. 78 Nelson Mathematics 8: Overview