5. Students will represent mathematics in multiple ways. (tables, charts, graphs, pictures, symbols and The teacher models only one way to represent a concept. The teacher does not expect students to represent mathematical thinking and ideas. Students represent their mathematical thinking in the form of an answer only. The teacher models the use of multiple representations to teach concepts, but does not expect students to represent their work in multiple ways. Students represent their mathematical thinking symbolically. The teacher uses multiple representations not only to teach concepts and expects students to represent their work in multiple ways. Students represent their mathematical thinking in various ways when prompted. The teacher releases responsibility by providing opportunities for students to independently select and use various representations to organize, record, and communicate mathematical ideas. Students select and appropriate mathematical representations to solve problems, and explain and interpret the connections between those representations. 6. Students will make connections mathematical ideas and to other disciplines. ______ Mathematical skills and concepts are taught in isolation. Students do not connect new concepts to prior knowledge or other disciplines. The teacher connections between mathematical concepts and other disciplines. Students connect mathematical concepts to prior learning. The teacher makes connections between mathematical ideas and other content areas and supports students with connecting new concepts to those within previous strands or domains. Students mathematical concepts to prior knowledge and other disciplines when prompted. The teacher expects students to independently make connections without prompting. Students make connections between mathematical and other content areas and connect new concepts to those within previous strands or domains. Students understand how mathematical ideas interconnect and build on one another to produce a coherent whole. Students recognize and apply mathematics in contexts outside of the mathematics classroom. 7. Students will understand and use manipulatives appropriately. Manipulatives may not be visible in the classroom or Manipulatives are visible in the classroom, but not readily accessible to students. The teacher models the Decision-making process for choosing appropriate manipulatives to give meaning to abstract concepts. The teacher scaffolds students’ understanding so they become less reliant on manipulatives.
(e.g., tangrams, rods, pattern blocks, compasses, algebra tiles, graphing calculators, etc.) ______ accessible to teachers or students. The teacher does not model use of manipulatives and students do not use manipulatives. Students use manipulatives inappropriately. The teacher models use of manipulatives and directs student use of manipulatives. Students imitate use of manipulatives without reflection, exploration, or connection to symbols, pictures, and explanations. The teacher actively engages students in manipulatives to construct and give meaning to new concepts. Students independently select appropriate manipulatives to make connections from symbols, pictures, and explanations to concepts in order to problem solve and represent their understanding of mathematics. Students can demonstrate their knowledge of abstract relationships using symbols, pictures and explanations, but are no longer dependent on manipulatives. Some manipulatives, such as the graphing calculator, are appropriate for consistent use. Students have internalized use of manipulatives and can describe how manipulatives were used to develop an understanding of mathematical concepts.