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This is a Summmary of the article** ” Learning to Think and Thinking to Learn”** By Kate Kline

Three questions to better understand about this article:

- How do teachers create a classroom environment where mathematical thinking is the focus?
- How do teachers help students who are having difficulty in explaining their thinking or making sense of task hand?
- What are positive impacts of learning environment by focusing on thinking?

This article discusses issues to consider when establishing a tone that encourages children to think during whole-group discussions, including addressing children’s diversity of thinking approaches and using their incorrect solutions. Besides it, this article gives examples of exchanges that may occur as teacher interact with students at work and suggest ways in which these interactions impact children’s developing notions of what it means to do mathematics.

**Facilitating Whole-Group Discussion**

A productive classroom environment can happen during whole-group discussions where students can be encouraged to share their solution methods, listen and ask questions, grapple with misconceptions, and probe and extend their thinking.

*Addressing diversity of thinking*

How students process information will be different between extroverts and introverts. Extroverts tend to process and think while they are talking. On the other hand, introverts must think carefully before speaking. This is often why introverts have difficulty participating in group discussion. Just when they are ready to contribute, the discussion may have move on. Cognitive processing certainly has ramifications for facilitating whole-group discussion and providing opportunities for voice to be heard. One technique to deal with this diversity is to encourage the class to work collaboratively. Hence, it’s expected that all students whether they are extroverts or introverts can share their solution method or idea.

*Using incorrect solutions*

Accepting incorrect answer or ideas as a natural part of doing mathematics and pursuing them in the same ways as correct solution can give powerful impact on young children’s thinking. The key is to use the same discussion techniques regardless of student’s response, so whether a student offers a correct or an incorrect solution, the responsibility for determining correctness then falls on the students. In this article is given example about how the teacher began the discussion with incorrect solution to encourage students to think more deeply about the problem’s meaning.

*Questioning one another’s solutions*

The most productive discussions around mathematical ideas seem to happen in classrooms where questioning is an almost spontaneous part of the way students talk to one another about their work. In this article is given an example where the students have been encouraged to develop their own procedures for computing. The teacher can make discussion by questioning students each time they have a solution method and asked other students if they have additional questions.

Then, discusses about the value of this questioning will helps everyone more deeply understand one another’s method.

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**Engaging with Children at Work**

Keeping goal of the learning environment where thinking is placed at a premium can capitalize on moments to extent thinking when engaging with students while they work.

*Suggesting a strategy*

When trying to assist struggling students, many of the teachers attempt to alleviate their frustration over a puzzling solution by suggesting a previously discussed efficient strategy. However, this approach may have some negative ramifications on the learning environment. To overcome this matter, a teacher can encourage students to develop procedures for computing that make sense to them rather than first learning the standard algorithm involving borrowing across place value. This will give opportunity for students to learn from one another and exchange their way of thinking to find the correct solution.

*Allowing time to develop understanding*

Young children can’t always directly find the right solution in some situations. One of things that make them can’t do it is they haven’t had enough knowledge about it. In this case, teachers can encourage them and guide them to the right solution using questions. By allowing time for them to think, they might develop their understanding of the problems types and solutions. In addition, students also can develop notions of what it means to do mathematics and emerge their ideas.

*Reflect and Discuss*

Reflective teaching is a process of self-observation and self-evaluation. The author gives questions related to “Learning to Think and Think to Learn” as suggested prompt to aid teachers in reflecting on the article and on how the author’s idea might benefit for practicing in their own class.

**Concluding Remarks**

In the conclusion, the author gives some points how learning environment is implemented through center children’s instruction on thinking for themselves, use their struggles, encourage ownership of their learning, and embrace their natural inquisitiveness. Presented ideas for facilitating whole-group discussion and engaging with children work while they work help establish conditions where thinking is valued as the avenue toward learning. Maintaining a consistent focus on thinking is not easy. It requires formal, deliberate reflection on the impact of specific instructional moves. However, by combining such analysis with a commitment to learning through thinking gives positive impacts like children are willing to take risks and think their way through whatever challenges they encounter.

Read the complete article here * *Learning to Think and Thinking to Learn