Mason's article - entrance slip

In his article, Mason looks at what types of questions are asked in a math classroom.  He argues that there is a certain way of asking questions which invites students to deepen their understanding of mathematics in an authentic way.  Asking questions in a way which does not presume that there is one, concrete answer which the teacher already has in mind, fosters a way of approaching mathematics which is more inquiry-based.  If students feel that the teacher is authentic when he/she asks for the students' help in solving a problem, they will feel more inclined to develop an original approach to arrive at the desired solution.  If the students don't feel constrained by the narrowness of a question, they may feel free to take a broader, more inquiry-based, approach to solving the problem.

During my long practicum, I must be careful not to give students very narrow questions which I already have pre-determined answers to.  I must try believe more in the students' ability for original and creative thought.  Hence, I must take an approach, like Mason's, to ask students broader questions, questions which allow for a multitude of answers, and questions which can ultimately foster the understanding of the students.

Micro-teaching exit slip - a reflection

Deeya, Ying Ting and I did a microteaching on the ambiguous case of the Sine Law.  Our presentation began with a brief summary of the Sine Law, followed by an inquiry-based lesson whereby students constructed triangles which show-cased the ambiguous cases of the Sine Law.
Overall, I think that we were weak when it came to time considerations.  Also, I thought that the presentation seemed quite disorganized because I do not think that we gave students enough information to be able to understand the inquiry-based part of our presentation - making triangles out of skewers.
Teaching inquiry-based lessons, I have learned, can be quite challenging, especially if time is short.  I felt that when we divided the class into three smaller groups, we lost the attention of a lot of the students, because they were no longer focused only on one presenter but on three.  If I were to teach this in a classroom, I would definitely spend more time showing the students what they are trying to discover, scaffolding their understanding so that they don't get confused later on.
We also lacked an appropriate hook.  Keeping students focused during the entire presentation requires that they be on-track right from the beginning.  Also, although this is not crucial, we lacked an appropriate conclusion because of time considerations.  We should have tried to include this regardless.