## Setting Up Tiered Instruction

**Figure 1. Sample Student Tasks at Different Challenge Levels**

When Students Choose the Challenge - table

Lesson Topics | Green-level tasks (foundational) | Blue-level tasks (intermediate) | Black-level tasks (advanced) |
---|---|---|---|

Problem solving with linear equations | The difference in the ages of two people is 8 years. The older person is 3 times the age of the younger. How old is each? | The length of a rectangle is 3 less than half the width. if the perimeter is 18, find the length and width. | When asked for the time, a problem-posing professor said, “if from the present time, you subtract one-sixth of the time from now until noon tomorrow, you get exactly one-third of the time from noon until now.” What time was it? |

Understanding slope | Find the slope of the line passing through the following pair of points: (-4, 6) and (-3, 2). | Find a so that the line connecting the points (-2, -3) and (2, 5) is parallel to the line connecting the points (6,a) and (0, -4). | If a > 1, what must be true about b so that the line passing through the points (a, b) and (1, -3) has a negative slope? |

## The Power of Student Choice

*or*too easy would lead to less than ideal stress levels: Tasks that were just challenging enough would make learning interesting but not overwhelming.

- Students find choices motivating—often the key to achievement for middle schoolers.
- Students benefit from the opportunity to make decisions. Learning to reflect on personal learning and adjust tasks accordingly is a great skill for middle school students.
- Students can't conclude that a grouping decision made on their behalf is unfair or inappropriate.

My students consistently made appropriate choices and enthusiastically accepted this responsibility. One student, Ruth, wrote, Being asked to choose from three different levels of difficulty has given me more choices and opportunities to challenge myself. . . . I feel that I have more “say” in the level of math I am learning.

## How It Works in the Classroom

#### Figure 2. Tiered Work for a Lesson on Triangle Properties

## The Results

## Higher Achievement . . .

*increased*.

*A-*/

*B+*level of excellence no matter what assessment level they select. It follows, then, that if they are scoring at such a level on harder tests, their achievement has risen. By midway through the 2006–07 school year, teachers had asked 8th graders to make a total of 883 choices among levels of math assessments, and students most often chose harder-than-basic tests. Students selected green-level tests, which are similar to the whole-group assessments we used before introducing choice, only 33 percent of the time. They chose blue-level assessments (above the proficiency standard) 59 percent of the time, and black-level tests 8 percent of the time. Thus, students are now tackling greater challenges than in the past.

## . . . And Eager Learners

## Positive Perspectives

My students learn a lot about themselves as they grapple with questions about what is best for them and move forward with new insights. Student responses to the prompt “How did you select your challenge level? Are you satisfied with your choice?” are revealing. Vishali noted, [Blue-level work] is what I am comfortable with. I know I am capable of blue. I am satisfied with my choice because I learned and understood many new things. I know that if I had chosen black, then I would have been stuck in chaos. Tanisha commented, The three-choice color system helps improve learning because it gives you the feeling that no one is forcing you to do something that you might find too stressful. It also gives you a better idea of how to be independent and not have everything be decided for you.

Parents' reactions have also been very favorable. Parents of advanced students finally feel their children are being challenged in class, whereas the parent of a student at the other end of the readiness continuum remarked, “This is the first time my child feels successful in math.” Another mother enthused, This is making my daughter think about her learning and it gives her a chance to practice decision making. This is exactly what kids should be doing in middle school.

## A Work in Progress

*Making the Difference: Differentiation in International Schools*(Powell & Kusuma-Powell, 2007) or visit my blog at www.challengebychoice.wordpress.com/</FOOTNOTE>

*Challenging Problems in Algebra*and

*Challenging Problems in Geometry*, (Posamentier & Salkind, 1988).

*The MathCounts School Handbooks*, available at www.mathcounts.org.

*Balanced Assessments in Mathematics*, available at http://balancedassessment.concord.org</FOOTNOTE>

*A, B*, or

*C*on a task at any of the levels for any particular goal.