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> Maths teaching

All my term papers for History 2 (Geschiedenis 2 - Vakgedeelte)

2008-06-19 21:37:00

One of the few second year's courses that I got out of the way in my first year at college is History 2, ie Geschiedenis 2 - Vakgedeelte. I'd planned on leaving the didactical part of the course until the next year.

The workload for this course isn't that high and it mostly depends on the students reading a whole book on the history of mathematics. Starting at the arithmetic of the Egyptians and Babylonians we proceed through India, Arabia, the middle ages and the Renaissance to discover how maths evolved through the ages. Surprisingly most of the really interesting stuff starts around the seventeenth century. -Astoundingly-, over 90% of the maths we know was invented after 1900. o_O



Biography of Euclid

As part of the preparations for our exam, each student was asked to write a two page biography of a famous mathematician. I was assigned Euclid (Euclides in dutch).

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



Summary of "Math through the ages"

This course relies on a syllabus made by the Hogeschool and the Math through the ages book by Berlinghoff and Gouvea (Amazon.com). Since the book's rather voluminous I reckoned I'd write a summary of the whole thing, with some stuff from the syllabus thrown in.

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



Assignments 7.3 through 7.6

One of the minor assignments we were given was to work out a few ancient, dutch math assignments. Well, ancient? Sixteenth, seventeenth century like-stuff. It was actually fun to try and decypher the instructions given in the original texts.

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


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All of my term papers for Analysis 1 (Analyse 1 - Didactiek)

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 :)



Dossieropdracht 1

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.

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



Dossieropdracht 2

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.



Dossieropdracht 3

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.

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



Dossieropdracht 4

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.

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



Dossieropdracht 5

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.

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



Dossieropdracht 6

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.

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



Dossieropdracht 7

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

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



Dossieropdracht 8

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.

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



Dossieropdracht 9

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.

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



Dossieropdracht 10

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 :)

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




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All my term papers for Student Care 1 (Project Zorgverbreding)

2008-04-21 09:01:00

In my third semester I only took one class, because I'd fallen behind in my work a little bit. Luckily, the semester's project Student Care (project zorgverbreding) wasn't very complicated.

In this course, students will explore the care for students with learning and personality disorders. ADHD, ADD, Asperger, Tourettes, Anorexia... You name it, we've got it. The assignment for each project team was to pick a number of disorders, each of which was to be studied on an individual basis. Each team member would report on the specifics of his chosen disorder, including information such as:

My chosen disorders (I accidentally picked two, instead of one) were anxiety (angststoornis) and mood disorders (stemmingstoornis, depression et al). Below you'll find my big report on the subject, two summary sheets and a flyer.



Individueel verslag

Each of the team's members was to compile a document on his chosen disorder. Mine covers anxieties and mood disorders.

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



Informational flyer

The docent offered extra credit to each team for making additional, informational products. I took the time to create flyers for each of our disorders, based on the reports everyone'd written. My flyer is a compilation of the two summary sheets below.

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



Summaries

In the course of our project, we were to hold a small presentation for other project teams. As a basis for this presentation, each group member wrote a summary of his materials.

These documents are available as a .PDF document and can be downloaded here and here.



Mind maps

In order to keep my research for this project organised, I've worked with so-called mind maps.

These mind maps are available as .PNG files and can be downloaded here and here.


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A summary of "Identiteitsontwikkeling en leerlingbegeleiding"

2008-02-16 21:05:00

As I've said, one of the killer first year's courses is Kijk op leerlingen en leren. Aside from a number of term papers and research that need to be done, there's also a big exam.

This exam presents the students with a number of cases that they need to assess using the experience they've gained throughout the course. During the exam, students are allowed to refer to the course book, Identiteitsontwikkeling en leerlingbegeleiding by van der Wal, de Mooij and de Wilde.

Below, you'll find my summary of four of the book's chapters. I didn't have time to tackle the chapter on the development of intelligence.

My summary is compiled as a 50+ .PDF document. You can download my summary here.


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All my term papers on Student Identity Development

2008-02-16 20:52:00

One of the killer courses in the first year of the teachers education at Hogeschool Utrecht is Kijk op leerlingen en leren. This course has a twofold focus and is tested in three seperate ways. The two main subjects of this course are identity development in students and a new approach to teaching known as The New Learning (Het Nieuwe Leren).

Testing is done as follows:

  1. An exam on identity development in teens.
  2. Five term papers on identity development.
  3. A group project on Het Nieuwe Leren, with a bunch of papers as output.

To help prepare for the test, I've written a summary of the book that we used in class. The book in question is Identiteitsontwikkeling en leerlingbegeleiding by van der Wal, de Mooij and de Wilde. Here's the summary.

The page you're currently browsing features all of my term papers on identity development and all of the papers I wrote for the group project.



Dossier opdracht 1

As an introduction to this course all students are asked to look back at their own teenage years. They're asked to speak candidly about their days in high school, their sexual development and their identity as a teenager.

Since this document contains a lot of stuff that hits a bit too close to home, I won't be putting it up on my website.



Dossier opdracht 2

This paper contains a few assignments about chapter 2 from the course book. The chapter covers basic identity development, including the various influences that work on a teenager.

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



Dossier opdracht 3

This paper contains a few assignments about chapter 3 from the course book. The chapter covers the development of intelligence and learning processes.

I haven't done this one yet ^_^



Dossier opdracht 4

This paper contains a few assignments about chapter 4 from the course book. The chapter covers the sexual identity of teenagers and how they cope with the changes their body and mind go through.

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



Dossier opdracht 5

This paper contains a few assignments about chapter 5 from the course book. This chapter covers student guidance and counseling. It explains what to do with students who have learning problems, or various disabilities.

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


Group project on The New Learning

The second, huge part of this project involved research into The New Learning, or Het Nieuwe Leren as it is known in the Netherlands. These "new" (or actually "reinvented") teaching methods have led to a lot of changes to the dutch educational system and as you can imagine it has led to a lot of fighting as well.

Our group of four was asked to investigate various parts of Het Nieuwe Leren, including the didactical and historical backgrounds. We produced a number of documents, but you'll only find my own documents on this site.

The following documents are available for download:


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LPI-101 summary

2008-01-01 00:00:00

In 2007 I got my LPI-1 certification. This certificate requires one to take two exams: LPI-101 and LPI-102. I've studied hard for both exams and created summaries of all of the stuff I had to learn. I thought I'd share my summaries with all of the other LPI students. I hope they are useful to you!


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SCNA summary

2008-01-01 00:00:00

Back in 2004, when I originally studied for my SCNA certification, I wrote a big summary based on the course books. I thought I'd share this summary with the rest of this world's students. Even though it was meant for the Solaris 8 SCNA exam, it should still be useful.


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LPI-102 summary

2008-01-01 00:00:00

In 2007 I got my LPI-1 certification. This certificate requires one to take two exams: LPI-101 and LPI-102. I've studied hard for both exams and created summaries of all of the stuff I had to learn. I thought I'd share my summaries with all of the other LPI students. I hope they are useful to you!


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SANE 2006 conference notes

2008-01-01 00:00:00

In May of 2006 I attended the SANE 2006 conference. While there I took a lot of notes at various courses and panels. All my notes can be found below, as PDF documents.


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All my term papers for Didactics 2 (Vakproject Vakdidactiek 2)

2007-11-02 11:51:00

I assume that it's Hogeschool Utrecht's philosophy to start their students off with basic knowledge that can be applied in practice, followed by years of more advanced information. This methodology has irked quite a few of my classmates, but I really don't mind. I actually quite like it.

One of the more advanced courses (it's a second year's class) is Vakproject Vakdidactiek 2 (General & Maths didactics 2). This course is divided into two separate streams: one covering general didactics for the complete n00bs (like me) and one covering didactics in maths. The first stream is finalised with an exam, while the second stream requires the student to write a full dozen (12!!!) reports.

I have already written summaries on general didactics, which can be found on this page and on this page. The page you're currently browsing features -all- of my term papers for the maths didactics part.



Dossier opdracht 1

At the start of this second year's course we are asked what we believe makes a "good" maths teacher. We are asked to analyse our own strengths and weaknesses, so we can form goals for ourselves.

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



Dossier opdracht 2

This report is based on BIT-report 1. What's different is that dossier opdracht 2 also contains my description of the lessons I've drawn from the course material.

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



Dossier opdracht 3

We've already discussed direct instruction on earlier occasions (BIT-report 1). For this assignment, students are expected to design a class plan on the subject of the Pythagoras theorem.

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



Dossier opdracht 4

After working on dossier opdracht 3, students are asked to review each other's work in pairs. Report 4 contains the feedback that I've given one of my class mates.

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



Dossier opdracht 5

Term paper 8 requires that I spend some time teaching a class. Unfortunately I haven't been able to do that yet. Hence, there's no paper for you to review.



Dossier opdracht 6

This one's a huge one, weighing in at around thirty pages! We are asked to take an exam that's been handed out in class and turn it inside out. What's wrong with it? What's good about it? How would you grade the paper?

We are also given five tests as they were turned in by students. What did they do right? Where did they go wrong? Can you understand why they made certain mistakes?

This was a very interesting assignment, but IMHO it was just too fscking huge. I sank at least thirty hours into this report.

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



Dossier opdracht 7

Term paper 7 requires that I spend some time teaching a class. Unfortunately I haven't been able to do that yet. Hence, there's no paper for you to review.



Dossier opdracht 8

Term paper 8 requires that I spend some time teaching a class. Unfortunately I haven't been able to do that yet. Hence, there's no paper for you to review.



Dossier opdracht 9

This assignment focusses on the problems high school students may encounter when using the dutch language. Students are asked to read and analyse a few chapters on this matter.

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



Dossier opdracht 10

This assignment focusses on the problems high school students may encounter when using the dutch language. The object is to analyse an assignment that would've been used on an exam, to find its flaws and to rewrite it.

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



Dossier opdracht 11

This assignment focusses on cooperative learning, as pioneered by Dr. Spencer Kagan. It contains a summary of relevant chapters from our course books, as well as a BIT reading report.

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



Dossier opdracht 12

This assignment focusses on cooperative learning and takes a look at Wiki's as a learning tool.

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


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All my term papers for Statistics 1 (Statistiek - Vakdidactiek)

2007-11-02 10:30:00

The first year at Hogeschool Utrecht's study Tweedegraads docent wiskunde starts you off with a course in statistics. They could've picked any part of math to start out with, but it was this one :)

The course, Statistics 1, is divided into two classes: one dealing with the actual maths, the other dealing with the didactics involved with teaching statistics. The first class ends with an exam, while the second requires you to hand in a total of eight papers (called dossier opdrachten. This page serves as a portal to all eight of my reports.



Dossier opdracht 1

As their first assignment of the year, students are asked to investigate how statistics are taught in high school. We are asked to focus on the first three years of HS, thus limiting the scale of the job.

Each student picks one specific method and searches through all the books for those three years. Any mention of statistics should get a little footnote, while whole chapters on statistics deserve a thorough analysis. For my report I picked the Getal en ruimte method.

This document is available as a .PDF document and can be downloaded here. Be aware that the file is a whopping 10MB, due to the heavy use of images.



Dossier opdracht 2

In a similar light as the first paper, students are asked to investigate the final terms for statistics. The VMBO have a list with specific subjects from statistics that should be featured in the exams. We are asked to pick one assignment per subject from the method we used for the first paper.

This document is available as a .PDF document and can be downloaded here. Be aware that the file is a whopping 6MB, due to the heavy use of images.



Dossier opdracht 3

One of the many philosophies in teaching is direct instruction (directe instructie). One of the key principles of this philosophy is that one should keep student motivated. Motivated students are willing to accept education and will thus learn more efficiently. For more information on direct instruction, read BIT-report 1 on maths didactics.

In order to grasp students' attention it's good to start a class with a bang. We were asked to write three separate opening sessions (15 minutes each), which can be used in a class on statistics. One of these openings will be presented in class. For a report on these presentations, read my class notes for weeks 3 through 5.

My class openings use the following subjects:

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



Dossier opdracht 4

After giving the presentation mentioned with dossier opdracht 3, each student is given feedback by his classmates. Feedback is gathered through forms created by the student and through forms handed out by the teacher.

Dossier opdracht 4 gathers all the feedback into one report, for analysis. It's expected that I use this report as a guideline for future learning goals.

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



Dossier opdracht 5

In teaching statistics, schools often make a grab for software like MS Excel and VU Stat (or SPPS). For this report, students are asked to investigate the capabilities of these tools and to assess their usefulness in teaching statistics.

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



Dossier opdracht 6

For paper 5 we researched software that runs on the local computer, like Excel and VU Stat. With paper 6 we are asked to research online tools. One may not expect this, but there are a few websites out there that offer schools online learning suites.

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



Dossier opdracht 7

The students are asked to investigate GWAs. In this case, GWA stands for Geintegreerde Wiskunde Activiteit (Integrated Maths Activity). The idea behind GWAs are that they're supposed to help students discover the place math has in daily life.

GWA assignments pose the student a problem and give no hints as to the required theory. A student is expected to figure things out by himself. He'll need to discover which pieces of theory are required and how he should combine them.

Our investigation quickly glances over the how-and-why of GWAs. One of the most important conclusions of the report are five characteristics that a "good" GWA should have.

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



Dossier opdracht 8

As you may have read, dossier opdracht 8 gave me quite a bit of trouble.

The students are asked to create a GWA for students in their first, second or third year of high school. My report covers a GWA on electronic payments (electronisch betalen).

This document is available as a series of three .PDF documents. Part 1. Part 2. Part 3.


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A summary of "Lesgeven en zelfstandig leren"

2007-10-27 14:16:00

In my first year at Hogeschool Utrecht I will follow a few second year's courses, to speed up my studies. One of these second year courses is Project Vakdidactiek, which concerns the didactics behind teaching maths.

As part of this course we are also required to take a test labeled Algemene didactiek (general didactics). This test is based on materials we study in Vakdidactiek, but also on the book Lesgeven en zelfstandig leren, by Geerlings and Van Der Meer.

As part of my preparation for this exam I've composed a summary of the three relevant chapters.

My summary is compiled as a 30+ .PDF document. You can download my summary here.

We are also required to read parts of Leren op school, by C.F. van Parreren. As an aside we have also covered various learning styles as defined by American psychologist Kolb.

This summary is also available as a .PDF document. You can download my summary here.


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A summary of "Statistics 1"

2007-10-14 11:06:00

Statistics seems to be one of the least liked subjects among students taking maths as part of their curriculum. This seems to be the same in both high school and college. I'm not entirely sure why this is, but I've heard a lot of people call the subject matter vague and the rules fuzzy.

The HU must've thought it'd be good to start off with this tough subject, 'cause that's what they dropped on us for the first semester :) STAT1-VAK is one half of the Statistics course, the other half of the course focussing on didactics. STAT1-VAK is closed off with a test of three chapters on statistics, taken from the Moderne Wiskunde books.

This summary focuses on the following chapters from the Moderne Wiskunde books.

You can download the summary as a PDF document.


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A summary of maths didactics

2007-09-26 13:51:00

In my first year at Hogeschool Utrecht I will follow a few second year's courses, to speed up my studies. One of these second year courses is Project Vakdidactiek, which concerns the didactics behind teaching maths.

The final term for this project consists of a dozen reports and assignments, all of which should prove your comprehension of didactics. Materials used in this course include Effectief leren in de les by S. Ebbens e.a. and Wiskundeonderwijs in de basisvorming by APS Publishing.

A few of the assignments require us to make so-called BIT leesverslagen (reading reports). These reports include a summary of the relevant chapters, as well as a chapter covering reflection on the material. On this web page I'll publish the summary sections of these reports. I'll keep the other stuff to myself for now.

Currently, summaries for the following chapters are available.

BIT-report 1

This is part of dossieropdracht 2, which focuses on direct instruction (directe instructie).

You can download the summary as a PDF document.

BIT-report 2

This is part of dossieropdracht 11, which focuses on cooperative learning (samenwerkend leren).

You can download the summary as a PDF document.


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Tips from Stef Heinsman, our director

2007-08-31 11:40:00

On the 30th of August 2007, Stef Heinsman opened the new academic year at Instituut Archimedes. All freshmen for the tweedegraads docent course attended an introductory meeting, welcoming them to their new school.

Surprisingly, our director/rector Stef Heinsman had some interesting tidbits for the crowd. It wasn't the expected, useless ramble :)

The three most important lessons from his own past:

  1. Always attend lectures and sessions.
  2. Don't postpone your work.
  3. Be stubborn when you can afford it.

By attending lectures you build a solid relationship, both with your teachers and your fellow students. You will also remain emerged into the whole spirit of school and teaching, ensuring your continued enthusiasm.

By not postponing your work, Stef is convinced that you will build confidence in your own competences. By taking the same tests and projects as your fellow students, at the same time, you will realize that they're in the same boat. Things may be hard for you, but there are other people in the exact same situation.

At times you'll be convinced that your own approach to a certain situation is the best one. Don't feel forced to take the teacher's approach and verify your own opinions. Become autonomous, allowing you to do your own work when you need to.

Combining these three factors will help you with your motivation. It's what you're going to need when things get a little rough around the edges.

In conclusion, Stef also asks us to take care of our selves. Don't lose your health, don't burn out and make sure that things are fine at home. Because the people at home are your strongest foundations.

He also suggested that you should teach something that you enjoy. By doing that you'll not only convey knowledge, but also enthusiasm!


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SANE 2006 conference notes

2006-08-09 07:35:00

After months and months I've uploaded the notes that I took at the various lectures at SANE 2006. They might be usefull to -someone- out there. Who knows. Be aware though that portions of the notes are a mishmash of dutch and english :) The notes can be found as .PDFs in the menu on the left.


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