Literacy in Mathematics

1. Literacy in Mathematics Strategies to Support Mathematics Instruction for Students with Disabilities Chicago Public Schools Office of Specialized Services Instruction & School Support Winter 2008

2. What is Literacy? Literacy… • is the ability to read, understand, and use written information to communicate appropriately, in a range of contexts. • includes the recognition of specialized vocabulary, numbers, mathematical signs, and symbols within text. • involves the integration of speaking, listening, and critical thinking with reading and writing.

3. Mathematical Literacy Mathematical Literacy is… • An individual’s capacity to identify and to understand the role mathematics plays in the world. • An individual’s capacity to make well-founded mathematical judgments and to engage in mathematics in ways that meet the needs of that individual’s current and future life as a constructive, concerned, and reflective citizen. Program for International Student Assessment (PISA, 2000)

4. Students are expected to: read write interpret mathematical symbols and text Students need opportunities to demonstrate a variety of literacy skills in order to develop and communicate their: knowledge skills understanding of mathematics Literacy: Making Meaningful Connections through Language

5. Understanding Mathematical Symbols and Text Students are expected to: • recognize specialized vocabulary, numbers, mathematical signs, and symbols within text • locate specific information • understand concepts and procedures • interpret problems

6. Understanding Mathematical Symbols and Text Students need opportunities to: • talk to others about information in the text • re-read parts of the question or problem • make notes about key features • use diagrams which accompany the text • create diagrams to make sense of the text

7. Developing Mathematical Knowledge Students are expected to listen in order to gain information and follow instructions. Students need opportunities to: • ask questions to clarify meanings • make brief notes based on a spoken text • respond to alternative viewpoints

8. Students need opportunities to mark difficult text by: underlining, circling or highlighting words making notes, lists or drawing diagrams Students are expected to write when they are asked to answer mathematical questions. Students need opportunities to: consolidate understanding of what they have learned present proofs Developing Mathematical Knowledge

9. Students need opportunities to: work in small collaborative groups join in productive discussions communicate mathematical knowledge orally and in writing When conveying mathematical knowledge, students are expected to: discuss explain describe justify a particular point of view, by explaining a strategy for solving a problem Conveying Mathematical Knowledge

10. What is “Reading Mathematics?” Reading mathematics… • is the ability to make sense of everything that is presented mathematically: • worksheet • spreadsheet • computer screen • page in a textbook • journal • includes the ability to use resources to assist with learning and applying mathematics.

11. Teachers can help students assume their role as readers of mathematics. Teachers can establish a climate that is conducive to reading and learning mathematics. Teachers can introduce students to the role that text features play in comprehension. Teachers can equip students with strategies to learn new concepts and comprehend mathematical text content. Teaching Students to Comprehend Mathematical Text If students are to learn to read and construct meaning from mathematics text, how can teachers guide and support this process?

12. Three Interactive Elements of Reading Text Features Climate Reader Barton & Heidema, 2002

13. The Role of the Reader Comprehending mathematics is a constructive process. “In order to acquire mathematical expertise in a durable and useful form, students need to construct mathematical knowledge and create their own meaning from the mathematics they encounter.” Siegel & Borasia, 1992

14. The Role of the Climate Mathematics education should emphasize active, flexible, and resourceful problem solving. Mathematics education should place greater emphasis on the affective dimensions of learning mathematics. Learning is most likely to occur when students see value in what they are learning. Adapted from: National Research Council, 1989,1990; NCTM, 1989, 1991 2000.)

15. The Role Text Features Text Features Text Structure Vocabulary The Characteristics of Written Text Text features are those aspects of text content and presentation that influence comprehension.

16. Mathematics Strategies • Vocabulary Development • Concept Definition Mapping • Frayer Model • Informational Text • K-W-N-S (K-W-L for Word Problems) • Graphic Organizer • Reflection Strategy Learning Log Barton & Heidema, 2002

17. Concept Definition Mapping What is it? • Concept definition maps help students understand the essential attributes, qualities, or characteristics of a concept. • Students must describe what the concept is, make comparisons, tell what it is like (what properties it has), and cite examples of it. Schwartz, 1988

18. Concept Definition Mapping How could it be used in mathematics instruction? • To organize their understanding after students have completed several activities using a concept and/or reading about the concept. • To communicate understanding and to elaborate or make connections by citing examples from student’s own experiences.

19. What is it like? What is it? The Word > Closed Mathematical Shape Simple (curve does not intersect itself) Polygon Plane Figure (2 dimensional) Three or More Line Segments Octagon Pentagon No Dangling Parts Hexagon What are some examples? Schwartz & Raphael, 1985

20. Frayer Model What is it? • Word categorization activity that helps learners develop their understanding of concepts • Generally, students provide a definition, list characteristics or facts, and provide examples and non examples. Frayer, Fredrick, & Klausmeier, 1969

21. Frayer Model How could it be used in mathematics instruction? • Provides students with the opportunity to understand what a concept is and is not. • Gives students an opportunity to communicate their understanding and to make connections by providing examples and nonexamples from their own experience with the concept.

22. Frayer Model • Characteristics • 2 is the only even prime number. • 0 and 1 are not prime. • Every whole number can be written as a product of primes. Definition (in own words) A whole number with exactly two divisors (factors). Prime Examples 2, 3, 5, 7, 11, 13,... Non-Examples 0, 1, 4, 6, 8, 9, 10,… Frayer, Fredrick, & Klausmeier, 1969

23. K-W-N-S[K-W-L for Word Problems) What is it? • Students use a worksheet to analyze and plan how to approach solving a word problem. • Students answer what facts they KNOW, WHAT the problem asks them to find, what information is NOT relevant, and what STRATEGY they can use to solve the problem. Barton & Heidema, 2002

24. K-W-N-S(K-W-L for Word Problems) How could it be used in mathematics instruction? • Engages students in exploration of word problems as they decode the given information, determine the question, and select an appropriate solution method. • Provides the teacher with the opportunity to evaluate students’ understanding and check for misconceptions. Barton & Heidema, 2002

25. K-W-N-S(K-W-L for Word Problems) Problem: The ends of a rope are tied to 2 trees, 500 feet apart. Every 10 feet an 8-foot post is set 2 feet into the ground to support the rope. How many support posts are needed? For this problem make sure you: — show all your work in solving the problem, — clearly label your answer, — tell in words how you solved the problem, — tell in words why you did the steps you did to solve the problem, and write as clearly as you can. Barton & Heidema, 2002

26. K-W-N-S(K-W-L for Word Problems) What strategy operations/tools will I use to solve the problem? What facts do I know from the information in the problem? Which information do I not need? What does the problem ask me to find? Draw a model to understand how to place posts. Solve the problem with the trees closer and find a pattern. There are 50 (500 ÷10) 10-foot intervals between the trees. Trees are 500 feet apart. Posts are placed at 10-foot intervals between the trees. The posts are 8 feet tall. The posts are set 2 feet into the ground. How many support posts are needed? Barton & Heidema, 2002

27. Graphic Organizer What is it? • Webs, maps, charts, diagrams • Visual representation of key concepts and related terms, helping students see how ideas link together. • Effective tool for thinking, note taking, and learning. • Represents abstract ideas in concrete form.

28. Graphic Organizer How could it be used in mathematics instruction? • Incorporated throughout a lesson or unit. • Used to engage students by having them share what they know about a topic. • Make connections, explain relationships, elaborate on what they have learned. • Used to evaluate students’ understanding and check for misconceptions.

29. Generalization/Principal Diagram

30. Learning Log What is it? • Effective means of writing-to-learn. • Can foster reflection on reading processes and hands-on activities to increase students’ understanding. • A writing focus on content covered in class, rather than personal or private feelings. • A way to have students write down their thinking processes.

31. Learning Log How could it be used in mathematics instruction? • It can be incorporated across mathematics lessons. • Students can examine a concept more closely as they collect data or work with examples. • Students can formulate explanations through writing. • It helps students know if they really understand a concept. • It helps students self-evaluate as they reflect on what they have learned

32. Learning Log Before Learning:activate and access prior knowledge Example: How is multiplication similar to addition? During Learning:help students identify how well they understand what is being covered in class Example: Draw three pictures that demonstrate the concept of multiplication. After the lesson:help students reflect on their learning Example: Write a note to a student who was absent from class and explain what was learned today about multiplication. Adapted from Brudnak, 1998

33. Present advance organizers. Preview prerequisite skills and concepts before introducing a new skill. Model procedures enough times for clarity. Use step by step procedures. Provide sufficient guided and independent practice. Teach the skill of generalization specifically and directly. Developing a Strategic Classroom Environment • Use real life and meaningful examples. • Focus on essential ideas for ideas, • connections and foundations. • Use mnemonic devices. • Teach self-questioning and self monitoring. • Teach and practice the use of visual aides. • Use cooperative learning groups. • Teach gradually from the concrete to the • abstract.

34. References • Barton, M. L., & Heidema, C. (2002). Teaching reading in mathematics (2nd ed.). Aurora, CO: Mid-Continent Research for Education and Learning. • Barton, M. L., Heidema, C., & Jordan, D. (2002, November). Teaching reading in mathematics and science. Educational Leadership, 60(3), 24–28 • Brudnak, K.A. (1998, January/February). What Works in Math: Math Communication. Learning, 26(4). 38-49. • Frayer, D., Frederick, W. C., and Klausmeier, H. J. (1969). A Schema for Testing the Level of Cognitive Mastery. Madison, WI: Wisconsin Center for Education Research. • National Council of Teachers of Mathematics. (2000.) Principals and Standards for Mathematics. Reston, VA: Author. • Schwartz, R. M., & Raphael, T. E. (1985). Concept of definition: A key to improving students' vocabulary. Reading Teacher, 39(2), 198-205. • Schwartz, Robert. "Learning to Learn Vocabulary in Content Area Textbooks." Journal of Reading. (November 1988):108-118. • Siegel, Marjorie, and Raffaella Borasia. 1992. Toward a new integration of reading in mathematics instruction. Focus on Learning Problems in Mathematics 14, no. 2: 18–36.