Claims- Mathematics Instruction

• Information and models found in textbooks should be supplemented by authentic teacher-created models

Textbooks are important because students need to know how to problem solve using just a pencil and paper. However, during the learning proness, it may be difficult for students to conceptualize the word-problems. Therefore, meaningful real-world examples can be presented, and supplemented by manipulatives, in order to assist the students in completely understanding the concept. For example, when working with arrays, the students should be able to arrange and rearrange tiles in order to create their own arrays. According to Bloom’s Taxonomy, “creating” is the highest level of learning, when students are able to put information together in an innovative ways.

• Students should engage in meaningful “math-talk” in order to be able to explain their thinking in writing.

New math standards require students to write out their thinking, and explain “why” and “how” the math works out the way it does. In order to successful record their thinking on paper, students need to be able to verbally explain their thinking. They can practice doing so by frequently participating in “math-talk” with their peers. This can be done by working collaboratively on assignments, and even respectfully critiquing each other’s work. Students will become proficient in math-talk, as long as they are given ample opportunity to do so in the classroom.

• Students should not move to independent textbook until they have had opportunities to engage in cooperative learning and manipulatives.

Students who learn a new concept and move directly into independent work may not fully understand it yet, and, therefore, complete the work incorrectly. Cooperative learning allows students to collaborate and discuss strategies. Discussion, the use of manipulatives, gallery walks, etc. all give students plenty of meaningful practice that will transfer to their ability to working independently.