Rene Grothmann

]]>Ich mache eine Präsentation für mein Seminarfach in der Schule und wollte Sie fragen ob Sie mir sagen könnten wie oft die Wörter „sind“, „die „und „zum“ in der Bibel vorkommen.

]]>I also find the matrix language cleaner and more flexible but that may just be me.

I have also used the recommended installation of Anaconda Python and extended it with the pyephem astronomy package and used the Python interface to sqlite3 for fast access to large amounts of data. EMT provides an easy to manage front end to all these features.

Just my 2c as they say.

Richard

]]>800 x 480 pixels. Both have their advantages and disadvantages.

In addition, it is as important to keep the i – Pad safe as

well as keep it look trendy. ]]>

I am not so much in the school business to know exactly how many teachers feature active learning in their classes. I would bet that most try to do just that. They pose problems, let the kids work, partly in groups, and at least try to activate the sleepier ones. Most of them seem to fail, however. One of the reasons might be that there is simply not enough time to start activation in 45 minutes, and too many lessons. From what I see in the University, the attitude they bring from school is not towards active participation.

Math at the University level has always included active learning in the form of problem sheets. Nowadays, we add tutoring to this to support the student. In the class, however, we still „teach“. I am yet unsure if we should change that or at least reduce the time the student is absorbing.

But I am convinced that we should stop writing blackboard after blackboard in front of a sleeping group of students with deactivated brains and active pencils. It does not make sense anymore in times of the Web. If students do not learn anything in their time of attendance it is a wasted time.

]]>http://www4.ncsu.edu/unity/lockers/users/f/felder/public/

This is the Professor Felder home page. Among other things, the main subject of many „Random Thoughts“ is devoted to teaching methods and learning styles. I also like the Professors sense of humor too.

]]>But I should have written the statement completely, as it would have been written in a math book: „For all a,b in the reals we have: a^2=b^2 implies a=b or a=-b“. „For all“ means for any real number you insert. „implies“ means that if the first thing is true for these numbers the second thing must be true too. Would that explanation help you?

Moreover: „+-a=+-b“ is something we should not write. What is the meaning of this? This is the reason why I prefer „a=b or a=-b“ in favor of „a=+-b“. It is logically clear and sound.

You are mentioning a difference between variables and numbers. These are terms of programming languages. Math is a bit like this, but not identical. It defines constants like pi, and sets variables to specific values like „let a=pi+3“, which makes „a“ a constant in the context. But a logical statement like „for all a,b …“ or „… implies …“ is something a programming language does not do.

I really should blog about logic. Math is also a social system with conventions. Students learn this from their teachers. So we should be careful what we say.

]]>Otherwise, wouldn’t this be true-

a^2 = b^2

then,

+- a = +- b rather than a=+-b ]]>