W06 journal

• In your opinion, what defines thinking and the culture of thinking in your area of STEM?

In mathematics thinking and the culture of thinking have to be closely related. Many times students come into our classrooms without the ability to think in different perspectives because they have been trained to view mathematics as a subject in which they write notes, memorize information and complete tons of practice problems, solely for the purpose of recreating these steps an a quiz or test and then  promptly forget it. It is a difficult situation to be in because in this subject area we are expected to cover so much and move so quickly that many teachers often fell they have no choice. I think it is important for teachers to take the time to establish a culture of thinking in their classrooms - a place where students are encouraged to look at situations, real world problems, even the vocabulary and rules in a way in which they are being analytical and discussing their thoughts about it. They need to be able to be open to other ways of viewing things and accepting the views of others - this way they can grow in their own thinking.

From the content of these videos, what can you infer about the following?

• What constitutes the essential elements of mathematical and scientific thinking?

These essential elements should include openness to discussion and logical thinking. SKills are taught in a progression throughout the school years and students are able to take the knowledge they have gained and build on it year after year. The students need to be able to think of situations and pull in skills that they have understand ( not just memorize!)  so that they can explain their thought process and ideas as the try to arrive to a conclusion.

• How are external representations related to the elements of mathematical and scientific thinking?

External representations are related to these elements because students can take the information that they have learned and apply them to other situations that they usually do not consider "oh! math is useful here!" In one of the videos we viewed, the speaker mentioned that even id students were able to solve problems, they were not understanding how the mathematics worked and the subject itself did not make sense, it was just something they had to remember how to do so they could do well in school.

• What defines the role for external representations in the knowing and learning of STEM?

External representations allow students to connect information, skills, formulas and vocabulary that they have learned in school and apply it to real world situations so that they may see how mathematics can be used in everyday life.