What is Literacy?

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## What is Literacy?

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**What is Literacy?**• Literacy is the ability to identify, understand, interpret, create, communicate and compute, using printed and written materials associated with varying contexts. Literacy involves a continuum of learning in enabling individuals to achieve their goals, to develop their knowledge and potential, and to participate fully in their community and wider society. • United Nations Educational, Scientific, and Cultural Organization (UNESCO)**Problems and Problem Solving**“Most, if not all, important mathematics concepts and procedures can best be taught through problem solving.” --John Van de Walle**What is Problem Solving?**• “Problem solving means engaging in a task for which the solution method is not known in advance.” --Principles and Standards for School Mathematics • It encompasses exploring, reasoning, strategizing, estimating, conjecturing, testing, explaining, and proving.**What is a Problem?**• A problem is a task that requires the learner to reason through a situation that will be challenging but not impossible. • Most often, the learner is working with a group of other students to meet the challenge.**Problem or Exercise?**• An exercise is a set of number sentences intended for practice in the development of a skill. • A problem is what we commonly refer to as a “word problem.” • But beware! Problems can become exercises!!**Common Characteristics of a Good Problem**• It should be challenging to the learner. • It should hold the learner’s interest. • The learner should be able to connect the problem to her life and/or to other math problems or subjects. • It should contain a range of challenges. • It should be able to be solved in several ways.**What Does It Mean to Be Successful at Problem Solving?**• Having success means that the child has discovered a way of thinking about mathematics that he had not experienced before he came upon this problem. • Success will involve the process of problem solving as well as understanding the content presented.**Success with “How Many Rectangles”**• Do the students resolve the question about whether to include the squares in their count of rectangles? • Do they understand that squares meet all the criteria to be considered a rectangle? • Do they recognize that there are many different sizes of rectangles in the drawing?**Success with “How Many Rectangles” (continued)**• Have the students devised a way of counting the rectangles they find? • Do they find patterns in the number of different-sized rectangles? • Do they think about the concepts embedded in the problem differently than before?**The Teacher’s Role in Problem Solving**“The more regularly that teachers make it part of the curriculum, the more opportunities students will have to become successful problem solvers.” --Children Are Mathematical Problem Solvers**Choosing Problem-Solving Tasks**• The problem must be meaningful to the students. • The teacher must sometimes adapt the problem to make it more meaningful. • The teacher must work the problem to anticipate mathematical ideas and possible questions that problem might raise.**Presenting the Problem**• It must be interesting and engaging. • It must be presented so that all children believe that it’s possible to solve the problem, but that they will be challenged. • The teacher has to decide whether students will work individually or in groups.**Group Work or Individual Work?**• In groups, students don’t give up as quickly. • Students have greater confidence in their abilities to solve problems when working in groups. • When in a group, students hear a broad range of strategies from others. • Kids enjoy working in groups! • Students remember what they learn better when they assist each other. • If students are less productive, arrangements can be made for them to work alone. • There will be a heightened noise level—but conversation is an important part of the learning process.**Once the Kids Are Working…**• Allow students to “wrestle” with the problem without just telling them the answer! • If we are just telling them what to do, the students are not engaged in the process. • Finally, teachers have to determine how to assess what the students are learning and what they need to learn next. • There are several ways to do this…**Assessing Understanding**• Listen to and record the students’ conversations as they solve the problem. • Have students explain their solutions in writing. • Give them another problem that requires them to use what they learned in the first problem.**Learning Mathematics through Problem Solving**• Students learn to apply the mathematics as they are learning it. • They can make connections within mathematics and to other areas of the curriculum. • Students can understand what they have learned.**Expressions and Problem Solving**“Math Expressions was developed to meet the national need for a balanced program that could expand the types of word problems to those solved by other countries and use an algebraic approach to word problem solving.”**In Kindergarten…**• Students act out family experiences about meals they might eat at home. • “Tom sets the table. He puts down 3 plates and then 1 more. How many plates are on the table?” • Using paper plates, each child can act successfully solve a story problem.**In First Grade…**• Students might solve the following problem and then explain their solutions at the board: • “I took 4 rides on the roller coaster. My sister took 5 rides. How many roller coaster rides did we take in all?” • Students could use any way that makes sense to them to solve this problem.**In Second Grade…**• Using Solve and Discuss, students might solve the following problem: • “Last year our school had 5 computers in the library. They bought some more over the summer. Now there are 12. How many computers did they buy over the summer?” • Two or three children might show their solutions on the board. Students at their desks should be encouraged to ask questions:**5 + 7 = 12**C buy now • How did you get 7 more? • Why did you start with 5? • How did you know 7 was a partner? • How did you know 12 was the total? • Where did you get 5 + 2? 5 + 5 + 2 = 12 C buy now xxxxx xxxxxxx 12 5c 7 buy now**In Third Grade…**• Students might solve the following problem and record their answers in several ways: • “Chris picked 8 apples. His mother picked 6 more. How many apples do they have now?” • Children might show their solutions in several ways:**Math Mountain:**Count All: 14 now xxxxxxxx xxxxxx Chris Mom now T 14 8 6 P P Chris Mom Count On: Equation: 8 + 6 = 14 P P T 8 xxxxxx 14 had count on now 6 more**In Fourth Grade…**• As the problem become more complex, students may rely less on pictures and more on ways to represent the steps in the problem: • “In the morning, 19 students were working on a science project. In the afternoon, 3 students left and 7 more students came to work on the project. How many students were working on the project at the end of the day?” • Manipulatives and drawing paper should still be available for those students who would like to use it. Following are abstract ways to represent this problem:**Tommy’s Method**Write an equation for each step. Lucy’s Method Write an equation for the whole problem. Find the total number of students who worked on the project. 19 + 7 = 26 Subtract the number of students who left in the afternoon. 26 – 3 = 23 Let n = the number of students working on the project at the end of the day. Students who left Students who arrived in the afternoon. in the afternoon. 19 – 3 + 7 = n 23 = n**In Fifth Grade…**• Students are still encouraged to solve problems any way that works for them. • “A right triangle has sides of 4 feet, 5 feet, and 1 yard. What is its perimeter in inches?” • In this case, students may well want to draw a picture to assist them in solving this problem.**Expressions: Inquiry + Fluency**• Using Expressions, students balance deep understanding with essential skills and problem solving. • Students invent, question, discover, learn, and practice important math strategies. • Students explain their methods daily.**Sources**• Children Are Mathematical Problem Solvers • by Lynae E. Sakshaug, Melfried Olson, and Judith Olson • Math Expressions • developed by The Children’s Math Worlds Research Project; Dr. Karen C. Fuson, Project Director and Author