Some Tools for Teaching Mathematical Literacy

Transcription

1 Some Tools for Teaching Mathematical Literac Julie Learned, Universit of Michigan Januar 200. Reading Mathematical Word Problems 2. Fraer Model of Concept Development 3. Building Mathematical Vocabular Word Wall Word Card Word Sort 4. Summarizing Mathematics Tets with GIST (Generating Interactions Between Schemata and Tet)

2 . Reading Mathematical Word Problems Reading word problems can present a host of challenges for students. This organizer helps students read and unpack world problems b identifing the main question, listing the important information, answering the problem, justifing their approach, and asking clarifing questions. Teachers can assess at what step(s) in the word-problem-process students demonstrate understanding and/or confusion. What is the word problem asking; what is the main question? List an words or concepts ou do not understand. Get an eplanation or definition (teachers establish a protocol for doing this). List all of the relevant, important information for this question. Answer the question using the relevant information. Show all of our thinking. You ma use words, numbers, smbols, pictures, graphs, charts, and tables. Justif the mathematical approach ou took to solve this problem. Write down an questions or confusion ou still have about the problem. 2

3 2. Fraer Model of Concept Development Students use a variet of methods and modes (oral, visual, written) to develop an in-depth understanding of mathematical concepts and terms. The Fraer Model is a strateg designed to help students understand and internalize concepts. This strateg uses a graphic organizer to help students understand a concept using definitions, characteristics, eamples and non-eamples to clarif meaning. Definition in our own words Characteristics Eamples CONCEPT Non-eamples Adapted from Fraer, Federick, & Klausmeier, 969 3

4 Fraer Model Eamples Definition in our own words A simple closed curve made up of three or more line segments Characteristics Closed Simple (curve does not intersect itself) 2 dimensional 3 or more line segments Square Triangle Rectangle Trapezoid Heagon Eamples POLYGON Circle Cone Ra Pramid Non-eamples Definition in our own words A number that can be epressed as a fraction or ratio Characteristics Can be positive or negative As a decimal, the number must terminate or repeat Eamples 8, /2,.56,.999. RATIONAL NUMBER π, 2, 7, e Non-eamples 4

5 3. Building Mathematical Vocabular Students encounter new mathematical vocabular in ever unit. There are several teaching tools available to help students learn and be able to use new words and concepts. The goals are to move from rote memorization to conceptualization, to build connections to new learning, and to build background knowledge needed for reading comprehension.. Word Wall: Word walls are an organized collection of words displaed in large letters on a classroom wall. Post vocabular words with everda, et precise definitions. Students can help generate definitions. To be effective, teachers must reference the word wall often during instruction. The word wall can become a resource to students during independent and group work time (Fisher & Fre, 2008, Word Wise and Content Rich). 2. Word Cards: Word cards can help build deeper conceptual understandings than definitions alone. On one side, students write the word. On the other side, the write the dictionar/tetbook definition, write an everda definition, write what the word is not, and draw a diagram, illustration, or picture. Students can use cards to practice with peers, teachers, and famil members. For triangle, the following word card could be created. Dictionar/Tetbook Definition A three-sided polgon Diagram, Picture, or Illustration Everda Definition The shape of a ield sign What the word is NOT Circle, rectangle, square 3. Word Sort: Teachers provide students with a vocabular list at the beginning or in the middle of a unit of stud. Students sort the words b familiarit. This can be used as pre-assessment and/or formative assessments throughout the unit. I learned this in elementar Sum Multiplication Subtraction Dividend Divisor I ve heard this word Equation Epression Solution Algebra I have no clue Function Linear equation Quadratic equation Adapted from the Michigan Department of Education, Writing Across the Curriculum,

6 4. Summarizing Mathematics Tets with GIST (Generating Interactions Between Schemata and Tet) GIST is a step-b-step process for summarizing tet material. It is particularl helpful when students have difficult putting what the read into their own words. Students restate main ideas from mathematics tets (Cunningham, 982). Read a portion of tet, and write down important ideas in phrases. Using important ideas, write a summar in 5 words or less. Continue portion b portion for longer pieces of tet. Write a short summar for the entire tet selection. GIST Eample Tet Passage: Ratios epress how one number is related to another. It ma be written as a/b, a:b, or as a phrase, a to b. For eample, the ratio of :8 is read as to 8, and means that the second number is eight times as large as the first. A proportion is a statement of equivalenc for two or more proportions. Given the proportion of a:b = 3:8 and asked to find b if a = 2, follow these steps:. First substitute 2 in the proportion for a, 2:b = 3:8; or 2/b = 3/8 2. Then use cross products, 3 b = Solve the equation 3b = 96, b = Therefore, if the ratio of a to b is 3:8 and a = 2, then b = 32. Important Ideas: How numbers relate Can be written different was a:b is 3:8 and a=2 The proportion is 2:b = 3:8 3 b = 2 8 which is 3b =96 96 / 3 = 32 b = 32 Summar: Ratios epress how numbers relate and if the ratio is 3:8 and a = 2, then b = 32. 6

7 Multiple Representations in Mathematics What s the connection? Linear Functions Represented Four Was Graph that when graphed on a Cartesian coordinate sstem fall on a Euclidean line Formula that can be epressed as the set {(, ), and Y, such that = a + b } where a equals the constant ratio 2 and b is the -value 2 associated with =0 whose slope (tangent of the angle with the horizontal ais) equals the constant 2 ratio 2 Linear Functions are particular kinds of correspondences between two numerical magnitudes X and Y Table that when displaed in tables such as X Y Problem that model application problems such as transforming measures due to a change of a measurement scale (e.g., the transformation between temperatures in degrees Fahrenheit and those in degrees Celsius). verif that 4 3 = for an pair of associated values 7

8 Eercise : Reading Mathematical Tets Directions: Mathematical literac involves the abilit to translate across multiple forms of representation. The representations below make use of smbol sstems commonl seen in mathematics, and the can be considered mathematical tets. Read each of the tets and list the specific knowledge, was of knowing, and was of reading (e.g., What aspects of the representation to look at first? In what order do ou read the information?) that ou put to use to understand what ou read. ) 4( X + ) = Y 6 2) X Y=f() ) Mora discovers that she walk 60 meters in 22 seconds in gm class. When she gets home from school, she times her little sister, Yvette, who walks 20 meters in 4 seconds. Yvette challenges her big sister to a walking race but wants a head start. How much of a head start would Yvette need in order to win? 4) 8

9 Eercise 2: Role Pla Directions: Role pla with a partner; teach our partner how to make sense of the particular wa in which each of those tets represents a linear function. Include eplanations of how ou read each tet. Articulate the different things ou had to do as a reader to interpret and make meaning of each tet. Adapted from the Michigan Department of Education, Writing Across the Curriculum,