Differentiating curriculum to involve reasoning and reflection means having students:

• explain not only their conclusions but also the reasoning that led them to these conclusions, and
• describe the metacognitive aspects of their thinking throughout the process (planning, monitoring and evaluating).

These practices ask students to access and share their reasoning. Students can be asked to describe

• their planning before beginning an activity involving reasoning learning experience,
• their reasoning and monitoring during learning and
• their evaluations of the development of their new understandings after it is concluded.

This should be the case whether their thinking is correct or incorrect.

Students learn different reasoning processes from other students when the activity involves sharing explanations, descriptions of reasoning with one or more classmates. Students benefit from examining their own thinking and that of their peers, especially those who think differently or in slightly more sophisticated ways. Reflective activities also give teachers insight on students’ thinking for assessment purposes.

Examples

Reasoning tasks

Sample activities involving reasoning include:

• Planning and budgeting for a fun school event-perhaps a science fair or fund-raiser.
• Preparing a case (prosecution or defense) for a “mock trial.” Peter Rabbit has been charged with trespassing.
• Taking and justifying one’s position on an environmental issue. For example, “Is nuclear energy safe?”
• Taking a stand on a moral or ethical dilemma. For example, is it right or wrong for the media to publish or broadcast confidential government documents?
• Designing an amusement park ride that takes riders through the human circulatory system as a blood cell.
• Preparing students with a difficult math problem and a solution. Students must provide the path to the solution

Strategies for nurturing reasoning and reflection:

• Three-Minute Pause
• Think-Pair-Share

Reflection

When reflection is a goal of an activity, one-quarter to one-third of the time allowed for an activity should be reserved for it. The activity must involve rich, complex reasoning or problem-solving or there will be nothing to reflect on. Sample activities involving reasoning and reflection include:

• Provide students with a problem and three solutions. Ask students to decide which is best and to describe the steps in their decision-making. Were their steps effective? How could they be improved?
• Recounting and evaluating one’s attempts to solve a difficult problem, including unsuccessful attempts.

Metacognitive awareness is a prerequisite to effective reflective activities such as those described above. Highly capable learners are not necessarily aware of their reasoning or able to articulate it. Zuckerman^[72] created an activity, “My Mind Works in Different Ways,” to scaffold her students’ ability to access and describe their reasoning process with classmates (click here for the lesson plan).

Water Jug Problems, like those in the box, are classic problems. This set increases in difficulty. Controlling the pace by feeding them to students one at a time on separate slips of paper allows the teacher to create a time between problems for students to ponder, share and reflect on their reasoning. Students can be asked to identify what the problems have in common and what is changing as they move from problem to problem. How can they use what they learned from the previous problem to solve the next?

Water Jug Problems^[73]

1. A mother sends her boy to the river in order to measure out 3 quarts of water. The mother gives her son a 7-quart bucket and a 4-quart bucket. How can the son measure out exactly 3 quarts of water using nothing but thee two buckets and not guessing as to the amount of water that he brings home?
2. A circus owner sends one of his clowns to bring back from a nearby river 7 gallons of water to give to the elephants. He gives the clown a 5-gallon bucket and a 3-gallon bucket and tells him to bring back exactly 7 gallons of water. How can the clown measure out exactly 7 gallons of water using nothing but these two buckets and not guessing the amount?
3. A cook needs 1 gram of salt to season a special meat he is cooking. When he opens the drawing to get a measuring spoon, he finds out that he has only an 11-gram measuring spoon and a 4-gram measuring spoon. How can the cook measure out exactly 1 gram of salt using nothing but these two spoons and not guessing at the amount?
4. With a 5-minute hourglass and a 9-minute hourglass, what is the quickest way to time a 13-minute steak?
5. * You have three jugs — A, B, and C. Jug A has a capacity of 8 quarts. Jug B has a capacity of 5 quarts and Jug C has a capacity of 3 quarts. Initially, Jug A is full, but the two smaller jugs are empty. How can you divide the contents of the largest jug evenly between the largest and middle-sized jugs — that is, between Jugs A and B?