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.

Micro-Teaching for Nov 30 - the Sine Law

Title: Learning the different cases of the Sine Law
Date: November 30, 2015
Grade Level: Pre-Calculus 11
Prescribed Learning Outcomes: B3. Solve problems, using the cosine law and sine law, including the ambiguous case.
General Purpose: This class will look at how the Sine Law can be used to find the unknown length of the side of a triangle given one angle and the lengths of the other two sides.  We will look at three cases: 1) where there is no solution, 2) where there is one solution, 2) where there are two solutions.
SWBAT: 3.5 Sketch a diagram and solve a problem, using the sine law. 3.6 Describe and explain situations in which a problem may have no solution, one solution or two solutions.
Probing of previous knowledge: We are assuming that in the class previous to the one we are teaching, students learned about the Sine Law and about how to prove it.  They also know basic properties of triangles, like how all the angles add up to 180 degrees.
Objective	Time	Activity	Materials
Introduction/hook	1 minute	Give students a little background information about the use of trigonometry - how it has been used early on as a way of measuring long distances, by calculating angles and smaller distances, and using perspective to approximate the longer distances.
Summary	2  minutes	Review the concept of the Sine Law (presented from a previous class).  Ask the students whether they think they can find an unknown side length of a triangle given the other two lengths and an angle.  Is this always possible?	·
Inquiry project	3x3 = 9 minutes	Illustrate the three different cases for Sine Law (whether one, two or no solutions) by dividing group in three, and having one instructor (Ying Ting, Deeya and Etienne) assigned to each group.  Each instructor will present a different case.  They will give students sets of three sticks, with which they have to make as many different triangles as they can.  Once they have come up with an answer, they have to explain why their solution is correct.  The instructor will help guide the students, writing the problem on the board and explaining why there is indeed only one, two, or no solution. The instructors will spend 3 minutes with each group, and then rotate, for a total of 9 minutes.	Measured sticks with which to make triangles.  Multiple sets for each case.  Three cases.
Handout+ summary	3 minute	Give students the handout on the Sine Law cases.  Go over the handout briefly.  Use it to show students that the three different cases necessarily have one, two or no solutions.  Illustrate this on the board, clearly.  Show the implications of this for when solving the Sine Law.
Summative Evaluation: By having students use the sticks to make up different triangles, students will illustrate their knowledge of the different number of triangles that can be made given certain lengths.

2-column math problem - work and thoughts

 

 

Hewitt Movie Class reflection - exit slip

I liked watching the movie today on a math teacher (Mr. Hewitt) not just talking about educating kids (as we have been doing for most of our BEd courses now), but on actually educating them.  I appreciated the techniques that he used - it allowed me to compare my own techniques to his, and to ask myself whether I would have done things the same or differently in his place.  I liked his use of repetition.  I also liked the way the he went around the class and made things more interactive for the kids.  I might have changed what he did slightly by writing more on the board the things I was saying.  But other than that, I thought that he demonstrated a good model for the way I would like to teach.

Hewitt Article - Entrance Slip

Those things which do not have to be the way they are, are called arbitrary.  Those things which must necessarily be as they are, are called "necessary".  The names we attribute to things, definitions we give to certain words, these are arbitrary.  A square does not have to be called a square.  It could be called a triangle.
There are others things, however, which cannot change.  The three angles of a triangle add up to a half turn - this is a fact which is not merely based upon convention, but upon reality.  The sum of the squares of two sides of a right triangle is equal to the sum of the square of the hypotenuse.  This also is true in every instance, no matter what name we give to certain terms.
In my math class, I would try to allow my students time to work out those things which are necessary.  Necessary things can be arrived at through intuition and through working out problems by oneself.  Those things which are arbitrary, that need to be told to students, I would try not to spend as much time on.  These things should be supplied as tools to the students, so that the students can proceed to work on those parts of mathematics which are not arbitrary, but necessary.

MOA Math Fair - exit slip

I just attended the Math Fair at the Museum of Anthropology. The students from West Point Academy were there, presenting mathematical problems in pairs of two.

I was very impressed by the presentations made by the young people. They were professional, and evidently very proud of their work. I was amazed by their eagerness in presenting their problems to us (the "grown-ups"). I felt they had put so much work into it, and were happy to show off the fruit of their labours. The students were cooperating very well together, and took turns presenting. They helped us with hints and clues as we tried solving the problems. They looked proud when we told them how well they did.

This experience of the Math Fair really encouraged me. From the way the students responded to this project, I would say that it was very successful. It would be worth doing in the schools.