Reflections: Algebra tiles microteaching

The major insights I gained from this 15-minute experience  and how these might impact on my actual teaching are:

1.   The time factor can be an all-consuming goal for teachers.  We try to cover as much material as mandated by the curriculum by a target date, with little regard to whether the students have the prerequisite knowlege base.  This can lead to impatience when getting a wrong answer or to subconsciously asking  leading questions as a guise for discovery learning.  We look for shortcuts (instrumental vs relational) to buy  time.

2.   The more planning time you spend on a lesson, the better it gets as you incorporate small adjustments as you review a previous plan.  The first tendency for new teachers is to want to do just about everything they've learned in education school.  You must temper your eagerness with the practicality of your actions.

3.   Teaching is not about you impressing the students of what you know.  Rather, the focus should always be on how best the students learn.  It is sometimes hard to rein back on all the complex  mathematical concepts that we know.  But we should be clear on one thing;  as math teachers, we naturally like doing math; it is the exact opposite for the great majority of our students (and non-math teachers as well).  We need to go down to their level, talk their language, address their anxiety, and access their personal mathematical experience.

4.   Judicious use of technology, without doubt, greatly enhances mathematical learning.   Multi-media, multi-modal presenattions complement traditional teaching startegies, and  build on a more wholistic, integral understanding of mathematical concepts. The dynamic representations of changes in variables permit connections that might otherwise be lost on traditonal paper-pencil algorithms.

5   Manipulatives are a great way to concretize abstarct math concepts.  They appeal to visual/spatial and kinesthetic learners who want to move things around.  They provide a solid link to the physical world and hence appeals to the practical student.  Algebra, especially geometry should do well capitalizing on its benefits.

6.   Working through your chosen examples for class discussion is important as errors might undermine students confidence in you. 

7.   Good questioning  stimulates critical thinking and maximizes students' engagement.  This is both an art and a science that should improve through time.

Overall feedback on our group's micro-teaching:

1.   The overwhelming majority found the topic interesting as they they have no previous experience on algebra tiles.  Further, many did not make the connection between product - area and factoring - dimensions of a rectangle prior to the presentation.
2.   Majority commented on the well-planned presentation, as well as different approaches used.
3.   Time manangement was the chief must-improve item, as they felt that I talked too fast, without giving students time to ponder on questions.

Self-assessment:

1.   The decision to try algebra tiles as a micro-teaching topic stemmed from a comment of  a veteran math teacher in one of the biggest schools in the lower mainland, that the use of manipulatives, although strongly recommended by the Education Ministry, might have little practical use in a classrom setting.  I think a carefully planned lesson build around these tiles can bring math concepts more tangible, accessible and palatable to many students.  Solving equations, even systems of equations with algebra tiles is another must-try activity.

2.   Apart from the usual content questions (including pre and posttest), we included a learning log question and an evaluative question at the end of the students' worksheet.  The former forces the student to state what he has learned today; the latter asks the student if he found  "value" in the whole exercise.  We found both to be a useful imput in assessing the overall effectiveness of the lesson.