2008-04-21 09:28:00

*Analysis 1 - Didactics* is one of the larger projects that the first year's students have to tackle. There are ten reports to be made, some of them rather largeish. To us the project is known as *Analyse 1 - Didactiek - Rekenen is complex*. Analysis in this case is the dutch name for what is know in the english speaking world as *Calculus*.

In short, this course focusses on the learning of arithmetic and math. We'll take close looks at the various algorithms that children need to learn and we'll even try and re-learn calculus ourselves by doing it all in Base-8 (octal). I found this class particularly challenging, mostly due to the pressure of having to hammer out these reports so quickly. All in all I did well though, since I managed to score a 90% at the end of the term :)

Students are asked to re-learn arithmetic by doing it all in Base-8, instead of in Base-10. This way we would be forced to study addition, subtraction, multiplication and division like we were twelve year olds again. This was great fun! We also examined multiple methods to do multiplication.

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All of us are studying to become math teachers in high school, so it's only natural for us to focus on maths for teenagers. However, it is also a very interesting exercise to examine mathematics education in pre- and middle school. Using reports made by CITO called the *PPON* (*Periodieke Peiling Onderwijs Niveau*, more information here), we are asked to investigate the level of math knowledge at the end of preschool (K8 in the USA). We are also asked to search for any problem areas that our teenagers may have encountered in their education.

This document is available as a .PDF document and can be downloaded here.

One of the (comparatively) recent trends in mathematics education is *realistic calculation* (*realistisch rekenen*). The proponents of this method reason that students don't benefit from simply repeating algorithms all day. Instead, they'd like assignments to relate to reality by way of providing a context. That ought to keep students motivated, while also keeping maths "tangible" for them.

For this report, students are asked to investigate the pros and cons of realistic maths.

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This assignment is kind of similar to the first report: we will be re-learning various methods for division and for determining the square root of a number.

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Remedial teaching is an important part of education. Not every child will immediately grasp the concepts that you are explaining and some will have a downright hard time understanding the materials. As teachers we will need to understand why students make the mistakes they do and we'll need to know how to address these problems.

For this assignment we'll be talking with kids, after taking a look at some of the mistakes they've made in their calculations. For my report I spoke with a few kids who'd recently done a test on coordinates.

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Continuing the research into thinking mistakes, the student is given five separate situations to analyse. In each, people have made mistakes in their assumptions or calculations and it's up to the students to find and explain them.

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The students are asked to do some book research on learning disabilities and disorders that may affect kids in learning mathematics.

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For this assignment students will treat the high school math education as a black box. We will be comparing the output of pre school with the output of high school to determine the process that takes place -in- high school. As input for our research we will be using the final exams of preschool and the final exams of maths education in the VMBO part of high school.

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We continue our research of *realistic math* by researching contexts used to teach about negative numbers. This is one of the notorious subjects in teaching high school maths.

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For our final report, we are asked to do a *didactical analysis* (*didactische analyse*) of the way that fractions, percentages and decimals are taught in high school. This starts off with some book research and ends with us pouring through books for the first three years of maths ed in high school. Nice :)

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