Differentiating Instruction Without Lowering Rigor

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Although differentiated instruction is popular, a common criticism is that by meeting the needs of students at their level, teachers lower their expectations and decrease the level of rigor, especially for students who are struggling. In these situations, we are not even allowing students the opportunity to learn at higher levels.

That is why we need to address the role of rigor in the differentiated classroom. If the goal of differentiation is to help students learn and grow, then we cannot lower the bar just because it is easier for them. In Rigor Is NOT a Four-Letter Word, I define rigor as creating an environment in which:

  • Each student is expected to learn at high levels;

  • Each student is supported so he or she can learn at high levels; and

  • Each student demonstrates learning at high levels.

To ensure that a differentiated classroom is truly rigorous, we can blend famous author and differentiation expert Carol Ann Tomlinson’s differentiation concepts with the definition of rigor together into a new framework.

Sample Differentiated Math Lesson

In the following example, let’s assume you want to ensure high expectations for everyone, and you would like the final result to be the same assignment for all students. In the sample lesson below, which includes both the standard version and a revised version, the teacher ultimately differentiates by using a variety of support structures and activities.

Standard Tiered Lesson

Perhaps you are teaching proper fractions and mixed numbers in your math classroom. Your objective is that students understand and apply mixed numbers. A typical lesson might begin with a review of proper fractions, such as 2/3, then continue with a discussion of improper fractions and mixed numbers with examples of each. Next, students practice identifying the two types with a partner; then they complete a worksheet for homework.

Let’s adjust this to a basic lesson tiered by the level of challenge. After the review, discussion and guided practice, students work on tiered tasks, either alone, with a partner or in small groups. Note that the tiers listed are not the same as tiers described in the commonly used program for special education students,  Response to Intervention.

 

Tier One

Tier Two

Tier Three

Tier Four

 

Given lists of fractions, students circle the improper fractions.

 

Given a list of improper fractions, change them to mixed numbers.

 

Students solve a real-world problem that includes the use of mixed numbers.

 

 

Students create a real-world problem using mixed numbers.

 

 

As we consider the tiered activities through the lens of rigor, you’ll notice that, although they may appear to increase in complexity, students are actually identifying a type of number, following a formula or basic instructions, or computing a simple algorithm. If you are familiar with Webb’s Depth of Knowledge, a commonly used framework which defines levels of depth and complexity, you know that none of those are rigorous activities. In the top tier, you may think that, since students are creating word problems, that is more rigorous, especially since asking students to “create” is at a higher level of Bloom’s.  However, writing a word problem that includes mixed numbers is basic application. I am simply writing a new algorithm, just with words. In this lesson, although we have differentiated by level of challenge and/or complexity, none of our tiers included rigorous tasks. Let’s turn our attention to a tiered lesson that is rigorous.

Rigorous Tiered Lesson

In our revised lesson, the teacher starts with activating prior knowledge and a review of proper fractions, such as 2/3, then continues with a discussion of mixed numbers (1 1/3) with examples of each type of fraction. Next, students briefly practice identifying the two types by circling mixed numbers given a list of fractions. Some students work alone, others work with a partner, and the teacher may pull a small group for extra instruction. After they have completed this activity, students generate a T-chart of proper fractions and mixed numbers. Some students are given a list of fractions to categorize on the chart; others generate their own. Although these are low-level activities, they are likely necessary for students to move forward. Minimal tiering was used in this part of the lesson.

The teacher then shifts to solving problems using both proper fractions and mixed numbers. The teacher follows a process similar to the one described above. Next, students are provided structured tiered tasks, building to rigorous tasks in the second activity.

 

Tier One

Tier Two

Tier Three

 

Teacher works with small group to review whole class instruction, then students are guided through the process of generating their own mixed numbers and solving simple algorithms.

With guidance, students solve one simple word problem that uses proper fractions and mixed numbers.

 

 

Students work in pairs to apply the information by creating new algorithms using proper fractions and mixed numbers. They switch problems with a second pair and solve the problems.

Next, each pair chooses an algorithm and uses it to create a word problem.

 

Students create word problems using proper fractions and mixed numbers. Problems must include multiple steps and require solving at least two algorithms.

They switch problems with another person or pair and solve the problem.

 

With guidance, students are given two simple word problems that include proper fractions and mixed numbers. The problems include the solution. They identify which of the two word problems is not solved correctly and why.

The small group is divided into two groups. With guidance from the teacher, each group creates its own set of two problems, one of which is not correct. They swap sets with the other group, which must follow the same process as above.  

 

Students are provided a set of three word problems that include proper fractions and mixed numbers which have been solved. They are told that one of the problems is incorrect. They are asked to identify which of the word problems is not solved correctly, then to solve the problem correctly; then they explain why the original problem was not correct, as well as describing their solution and why it is accurate.

Next, students create their own set of two problems, one of which is not correct. They swap sets with another student, who must follow the same process as above.

 

 

Students are provided a set of four word problems that include proper fractions and mixed numbers which have been solved. They are told that some of the problems are incorrect, but the number is not specified. They are asked to identify which of the word problems is not solved correctly, solve the problem correctly, explain why the original problem was not correct, as well as providing a written description of their solution and why it is accurate.

Next, students create their own set of four problems, two of which are not correct. They swap sets with another student, who must follow the same process as above.

 

Notice that in the second round of tiering, all students working at a rigorous level by “recognizing and explaining misconceptions,” a Level 3 expectation in Webb’s Depth of Knowledge. That is exemplified in different ways, but they all finish at Level 3.

A Final Note

Providing differentiated instruction to meet the needs of all learners is at the heart of teaching. To ensure achievement for all students, we must create learning opportunities that help each child succeed. However, in the process of differentiating instruction, we must be certain that we do not lower the rigor for students who are struggling. By using different supports—in terms of resources and scaffolding strategies—we can hold students to high expectations, and students can demonstrate their learning in rigorous ways.

References

Blackburn, B. (2018). Rigor and Differentiation in the Classroom. New York: Routledge.

Blackburn, B. (2018). Rigor Is NOT a Four-Letter Word (third edition). New York: Routledge.


For more information on Webb’s Depth of Knowledge:  www.webbalign.org 

For more information on Carol Ann Tomlinson:  http://www.ascd.org/Publications/ascd-authors/carol-ann-tomlinson.aspx

For more information on Response to Intervention (RTI):  http://www.rtinetwork.org/learn