From one method of solving is right or best...
To multiple ways of solving (and maybe multiple answers) are planned and valued
Closely related to shift 3, this shift helps us remember that there may be multiple productive pathways to explore in any given situation. We want to create classrooms where students follow multiple routes to solving problems or answering questions.
When only one method is considered right or best, several problems can arise:
1. Students avoid creative thinking and lose flexibility; they become rigid; they cannot see outside the box.
2. When given a problem to solve, students often jump quickly into a memorized algorithm. They don’t stop to get the big picture; they often don’t pause long enough to ask, “Do I understand the question?” or “What might a reasonable answer look like?” This can lead to answers that don’t make sense.
3. If students try the only “acceptable” method and get stuck, they have no recourse and may give up.
4. They may come to view the subject as an established or finished set of rules or methods determined by experts; the student’s job is to accept these rules and memorize them.
5. They see a concept from a single viewpoint, which results in understanding that lacks depth.
By contrast, when students are routinely exposed to multiple methods…
1. They develop confidence to be creative and flexible.
2. They learn to pause before jumping into problem-solving mode; they take time to make sense of the question, think about multiple approaches, and get a feel for what a reasonable answer might look like.
3. When they get stuck, students might consider multiple approaches, possibly even creating their own method. They might first start with a comprehensible (though inefficient) strategy to make sense of the problem before using a more sophisticated or efficient strategy. Having made sense of the problem themselves, they are often primed to hear about and understand different ideas and approaches.
4. They view the subject as a frontier to be explored; it is a way of figuring out, not a set of static facts or rules.
5. They see a concept from multiple viewpoints, begin to discover connections/relationships with other concepts, and engage multiple parts of their brain.
A classroom centered in the practices can naturally create opportunities for students to experience varied approaches.
Planning for multiple approaches
Pose open-ended questions/tasks that allow space for divergent thinking and invite input at various levels. This could include multiple entry points, multiple solution pathways, different ways to investigate, different possible explanations, etc.
Develop flexible lesson plans that give up some control and allow the class to move in somewhat unexpected directions. It is helpful to anticipate possible student strategies or mistakes in order to plan ways to respond, but also be open to following the kids when they get going in a certain direction.
When choosing or creating problems to solve or questions or phenomena to investigate, avoid telling students how to solve the problem, what approach to take, or what tools to use. The goal is to have students begin to plan (with support) their own investigations, solution paths, and explanations.
Setting a Culture for Supporting Multiple Approaches
Make explicit new expectations regarding multiple methods by using statements such as, “I am interested in the different ways you think about this”, “I expect to learn something new about this topic today after hearing your ideas.”
Have students discuss their answers with one another before asking for class comments. When students share their answers or strategies ask, “Who has another idea?”, “Who thought about it in a different way?” in order to continually reinforce that you value and expect different ways of thinking.
Ask students questions about their ideas and ideas of others as this can help them make sense of and see the relevance of different strategies and points of view.
1. "What does he/she mean by…?"
2. "Where do you see that?"
3. "Can anyone add/respond to that?"
4. "Why does that make sense?"
5. "Draw a diagram to represent what’s going on."
Listen to students differently – listen for the connections students are making to the content and indicators of student thinking.
The way in which a student expresses his/her thinking may not initially make sense, so asking, “What do you mean by that?” or “Could you draw a picture to show your thinking?” can help a teacher understand student thinking.
Even with our best efforts, we may not understand every thought. It is okay to ask other students “Who can see what ‘so-and-so’ is saying?” or to leave it on the “back burner”.
Discussing student work with colleagues can also help teachers gain insight into student thinking. Try keeping brief notes about different approaches and ideas that come up. This can be great fodder for discussions about student thinking with your colleagues.
Asking for comparisons can help students make connections to and see relationships between prior and related content or ideas. Following student thinking in this way not only deepens understanding, but also shows students the value in divergent thinking. Asking the following types of questions can reveal conceptual building blocks and patterns that may help students generalize their thinking and deepen their understanding of big ideas.
1. "How are they the same, different?"
2. "What does that look like in Carl’s strategy?"
3. "Why does it make sense that these are equivalent?"
4. "When would Amy’s strategy be most helpful?"
5. "What else have we done or learned that could be of help here?"