Are the parts similar in size, or is one larger than the other?
Once students are comfortable with one kind of diagram, they can think about how to relate it to a new situation.
An increase in nonlinguistic representations allows students to better recall knowledge and has a strong impact on student achievement (Marzano, et. In classic education research, Bruner (1961) identified three modes of learning: enactive (manipulating concrete objects), iconic (pictures or diagrams), and symbolic (formal equation).
The iconic stage, using pictures and diagrams, is an important bridge to abstracting mathematical ideas using the symbols of an equation.
They even practiced several model diagrams among themselves as no one had ever learned to use models with word problems. This time many students wrote the equation, 59 85 = ? As the class continued to do more word problems, the diagrams appeared to be a helpful step in scaffolding success with word problems.
Since part of their PLC work freed them up to observe lessons in each others' rooms, they decided they would watch Mr. Word problems require that students have the skills to read, understand, strategize, compute, and check their work. Following a consistent step-by-step approach-and providing explicit, guided instruction in the beginning - can help our students organize their thoughts and make the problem-solving task manageable.
Diagrams can capture the similarity students notice in addition/joining problems where both addends are known and the total or whole is the unknown.
Diagrams will also be useful for missing addend situations.
Given several missing addend situations, students may eventually generalize that these will be subtractive situations, solvable by either a subtraction or adding on equation.
The work of Bruner, Dienes and Skemp informed the development of computation diagrams in some elementary mathematics curriculum materials in the United States.