''Eduardo has 12 posters in his room. Manuela has one-third as many posters as Eduardo. How many posters does Eduardo have?'' asked Bush Elementary School third-grade teacher Mary Neumann-Ceminilli to her students. ''That's the comparison word problem you had to solve. Anthony, can you come up and show us your methods and strategies for solving the problem?''
Anthony Melendez-Cortez went to the front of the room, showed his proof drawing and explained how he came up with his answer, four, using a pointer. He then asked his fellow students if they had any questions.
"Can you explain your thinking on how you knew to put three boxes on your whiteboard to solve the problem?'' asked one student.
Bush Elementary School third-grader Anthony Melendez-Cortez explains his strategies for solving a word problem during Math Talk.
''I knew to put three boxes because of the one-third in the problem and to keep my problem organized and separate,'' said Anthony, who took more questions from his peers and then finished his presentation.
''I solved the math problem. I used my proof drawing. I explained my strategies. I asked questions and I justified my answer,'' he said.
''Thank you, Anthony. Can you tell me what strategy helped you solve your problem?'' asked Mrs. Neumann-Ceminilli.
''Creating mental images!''
''That's correct. I'm proud of all of you for solving a complicated problem. You had to use division, fractions, multiplication and addition all in one word problem. Good job!''
Mrs. Neumann-Ceminilli's class was participating in Math Talk, a component of the district's Math Expressions curriculum. Math Talk emphasizes the need for students to discuss their mathematical thinking as a way to increase understanding. The teacher moves from traditional teacher-focused instruction to productive student-to-student discussion monitored and supported by the teacher. The important ''Solve, Explain, Question and Justify'' classroom activity allows students to learn from each other with no class learning time lost. In other approaches, when students are sent to the board to draw their work, the rest of the class remains at seats doing nothing. In Math Expressions, the students at their desks are just as involved as the student-leader.
''I am only a facilitator in the process. But I am also supporting an environment where everyone is a teacher and a learner,'' said Mrs. Neumann-Ceminilli. ''By creating a nurturing and secure base for learning, Math Talk enhances everyone's mathematical understanding, competence and confidence. My parents have been so supportive of the new program and I've the response has been great as to the benefits to their children.''
Math Expressions uses verbal communication and math drawings, where students can show a variety of ways to demonstrate the situation in a word problem. For example, Mrs. Neumann-Ceminilli's class all solved the word problem above but some students drew 12 small posters, some used stick figures to represent Manual and Eduardo and others used numbers. The math drawings help everyone, including the teacher, understand the student's math thought process.
Math Expressions is done every day within Mrs. Neumann-Ceminilli's class. In addition, math workstations are set up two to three times a week to supplement and give extra practice to the work done in Math Expressions.
Jamestown teachers had extensive training in the new Math Expressions program, which provides learning paths that move all students forward. These research-based accessible strategies are taught so everyone has an effective method to demonstrate understanding.
''I love math and because we all learn different ways, I can learn from my friends how they did the problem and maybe find a new way to do it,'' said Bush School student Rebecca Freeman. ''Learning this way with the group and teaching each other helps me remember the math steps so when I take a test I can think through the problem step-by-step.''