He is an excellent communicator and very easy to understand.
Tuesday, 29 September 2015
Video tips for new maths teachers @misterwootube
Monday, 28 September 2015
How to find the area under a curve and why you would want to
In many situations we may want to find the area under a curve. For example on a velocity-time graph, the area under the curve represents the distance travelled.
Source: BBC
As the concept is developed, the following GeoGebra Worksheets (by gdix) will be beneficial:
1. Area under a curve by rectangles under and then rectangles above: https://tube.geogebra.org/m/254255
2. Area under a curve using Trapeziums (Trapezoidal Rule): https://tube.geogebra.org/m/254381
3. Area under a curve using Simpson's Rule: https://tube.geogebra.org/m/254405
Reflecting on Teacher Education - have we got it right?
Today, I have the privilege of taking a tutorial in the Mathematics Methodology subject at Macquarie University. Whilst there are not the 50 students studying Mathematics when I went through but rather there are around a dozen students.
In preparing for the first session, it is interesting the time spent in teacher education on content and preparation of lessons is somewhat different from what I have actually engaged in as a teacher in the classroom. Some might expect that I would argue for a complete overhaul for the course, but I think there is a place for both.
Unless you first go through the university method, you can't progress to the school model where corners will be cut, not every lesson will be the best lesson ever and there are competing pressures from students, parents, the school, etc.
Given a typical school day for a teacher, there may be 5 teaching periods of 50-55 minutes. The time required by a teacher to prepare for each of these (let's estimate at 15 minutes), plus time for marking, writing test papers, etc. is simply not manageable. This has only allocated 15 minutes to preparing the lesson, rather than the 1-2 hours that uni students would spend creating the 'ideal lesson'.
Students should walk out of uni with a number of excellent pre-prepared lessons. When approaching teaching, I strongly recommend that teacher's plan 'units of work'. I used my holiday time to prepare each of the units for each of my classes, which meant that I could spend just a few minutes the day before refreshing myself and adding any bells and whistles that I could.
For the unit of Integration (2 unit), I would develop the ideas from areas of rectangles, trapezoidal rule, Simpson's rule, integration and then integration rules.
To answer the question, the current mode of teacher education does have a place, but it can't be the only thing that develops a teacher and gives them the skills required to plan lessons to have students in their classes who are taught exceptionally within a caring professional relationship.
In preparing for the first session, it is interesting the time spent in teacher education on content and preparation of lessons is somewhat different from what I have actually engaged in as a teacher in the classroom. Some might expect that I would argue for a complete overhaul for the course, but I think there is a place for both.
Unless you first go through the university method, you can't progress to the school model where corners will be cut, not every lesson will be the best lesson ever and there are competing pressures from students, parents, the school, etc.
Given a typical school day for a teacher, there may be 5 teaching periods of 50-55 minutes. The time required by a teacher to prepare for each of these (let's estimate at 15 minutes), plus time for marking, writing test papers, etc. is simply not manageable. This has only allocated 15 minutes to preparing the lesson, rather than the 1-2 hours that uni students would spend creating the 'ideal lesson'.
Students should walk out of uni with a number of excellent pre-prepared lessons. When approaching teaching, I strongly recommend that teacher's plan 'units of work'. I used my holiday time to prepare each of the units for each of my classes, which meant that I could spend just a few minutes the day before refreshing myself and adding any bells and whistles that I could.
For the unit of Integration (2 unit), I would develop the ideas from areas of rectangles, trapezoidal rule, Simpson's rule, integration and then integration rules.
To answer the question, the current mode of teacher education does have a place, but it can't be the only thing that develops a teacher and gives them the skills required to plan lessons to have students in their classes who are taught exceptionally within a caring professional relationship.
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