## Sunday

### The Differentiated Math Classroom: Chapter 7: Lessons as Lenses (part 4)

In the fourth lesson presented in Chapter 7, the differentiation is for readiness and learning styles. This fraction lesson, dealing with the concept of half, was designed for second grade. The class used tangram puzzles and triangle grid paper (duplicates of the small tangram triangles).

The launch part of the lesson was a discussion of the tangram pieces and the goal of the lesson was shared: to show one half using the tangram pieces. An example, with discussion, was shared using the overhead projector.

During the exploration, students worked individually, with their own tangram sets. The students’ task was to represent a tangram shape on the triangle grid paper, and shade in the halves of the shape using two different colors. They were then to cut their shapes out and glue them to a class poster.

During the summary, students spent time digesting what was on the poster. Each student had to go to the poster, point to a shape that was showing one half, and explain how they knew it was one half. They also identified shapes they were unsure of.

The open-endedness of this lesson provided differentiation  - students were able to explore at different levels of understanding and then show those different levels through explanation.

Open-ended problems offer differentiation because they may have multiple solutions and approaches; they encourage “…students to be personally involved in extending their knowledge and understanding.”

In reflecting on the lessons presented in this chapter, the authors refer to Tomlinson’s principles of a differentiated classroom:
1. Teacher is clear about what matters in subject matter.
2. Teacher understands, appreciates, and builds on student differences.
3. Assessment and instruction are inseparable.
4. Teacher adjusts content, process, and product in response to readiness, interests, and learning profiles of students.
5. Students participate in respectful work.
6. Students and teachers are collaborators in learning.
7. Goals are maximum growth and individual success.
8. Flexibility is the hallmark of a differentiated classroom.

Additional differentiation formats that the authors mention are stations/centers, which work well with flexible grouping. One design for differentiation found in Tomlinson’s book is called ThinkDots, which is to be used after students have gained essential knowledge of a concept. ThinkDots consists of sets of six cards. Each card has a task on one side and one to six dots on the other side. The cards can be used for individuals or groups, to assign specific tasks to specific students, or can be chosen by rolling a die to determine the assignment.

 Basic idea of Pathway Plan checklist
Another strategy the authors mention is called Pathway Plans (from Heacox, 2002). This strategy includes a checklist of skills for a unit, with a list of independent tasks, activities, or projects. This is used as a planning document for students, and the skills are checked off when they are completed (or they are crossed off if students already had them mastered at the beginning of the unit.) Using this strategy, the teacher works with small groups while the remainder of the students work on their activities. In order to be sure that students needs are being addressed, a preassessment should be given.

Finally done with Chapter 7:)