As with chapter 4, this chapter focuses on a different "lens"of differentiating math, which is flexibility. The authors state that flexibility in the differentiated math classroom means that something is adaptable and/or able to be modified.
Before discussing flexibility, the authors identify what is not flexible – the five strands of math proficiency identified by the National Research Council’s 2001 publication, Adding It Up:
When differentiating math lessons and activities, these five strands must be addressed - no flexibility there!
The first area of flexibility that the authors address is grouping, and they describe several types of grouping:
Random groups - to create a new interactive environment. The authors describe the use of partner seating (starting at the beginning of school year), which allows for easy think-pair-share partnering. The partnering is random and changes every two weeks. The authors use random card draws to pair the partners (cards might match vocab and definition; match fraction and decimal or percent; match simple computation question and answer, etc) The pairs are also grouped with another pair, resulting in a heterogeneous group of four, readily grouped for an activity.
Readiness groups – used to provide appropriate challenge and support. Can be a short grouping (10 min) when the teacher notices a small group that needs a minilesson.
Heterogeneous groups – to represent a broad range of styles, intelligences, and abilities.
The next aspect of flexibility discussed is time. Because students can work at such different paces, the authors believe that anchor activities are a “major strategy” in accommodating for those paces and maintaining the flexible use of class time. The anchor activities were mentioned in chapter 2 as options for students when they have completed assigned tasks before the class is ready to come back together; they include things like math challenges, activities, games, centers, or books. It seems that the anchor activities can really be anything, so long as they have a purpose, are challenging, are engaging, and build math knowledge. (So, I have a lot of planning and organizing to do to get these ready!)
Content flexibility is a third area the authors address. All students need to be able to access the content, but the way in which it is presented can be adapted. Content flexibility is closely related to student readiness, and tiered lessons/activities are helpful in meeting student needs within the study of a particular topic.
Process flexibility refers to the ways in which students work through math – paper and pencil, manipulatives, calculator, mental math; strategies such as using models, guess and check, looking for a pattern, and solving a simpler problem. Allowing students to choose a particular process is a motivator for the students, though students should be encouraged to expand their process choices.
Product flexibility allows students some choice in what product they might produce when working on a project .
Assessment flexibility – the authors discuss the fact that assessment can be formal or informal, but that in math, assessments are often “casual,” as teachers are always observing students as they work through concepts. The authors offer a partial list of about 30 assessment tools, including: tests, rubrics, skill performance, pop quizzes, exit slips, checklists, partner quizzes, and logs.
The authors discuss rubrics, their purpose as tools to guide assignments and their evaluations, and the flexibility in the variety of rubrics that can be used – scoring rubrics, instructional rubrics, and student self-evaluation rubrics. Rubrics that are created by students and teachers together can be more effective because students are more vested. Self-reflection rubrics help students to focus less on a score and more on the types of mistakes they may have made, as well as on the math that they showed an understanding of. For example, when a unit test was returned, a teacher gave a self-assessment rubric listing the math concepts and the problems that addressed each concept. Students had to look over their test, look at teacher corrections, and analyze their own performance, to determine if they “did not meet,” “partially met,” or “met” each standard. These self-reflections help guide teacher instruction and grouping.
While I am using flexibility in some of these areas, I do need to increase my flexibility in others (more planning and creating needed!)