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Mathias Magdowski

Auf Twitter wird gerade der KI-gestützte gefeiert, mit dem man (angeblich) in kurzer Zeit komplette Kurse inklusive eines Kursplans, Lernmaterialen, Fragen, Aktivitäten und weitere Resourcen erstellen kann.
Siehe z.B.:
twitter.com/DanFitzTweets/stat
oder
twitter.com/AmandaFoxSTEM/stat

Also habe ich das mal mit einem Beispiel aus (na was wohl) der Elektrotechnik ausprobiert.

Ein Thread: 1/x

TwitterDan Fitzpatrick on Twitter“You know that playing with ChatGPT blows your mind. BUT for teachers platforms like this 👇 will shake your world. In a few seconds, this platform produces full courses, with lesson plans, materials and resources (and more... coming soon). Here's @CopilotEdu”
07. Jan. 2023, 16:52·Öffentlich
7Mal geteilt·12Mal favorisiert
Öffentlich
Mathias Magdowski

Zunächst klickt man sich auf app.educationcopilot.com/ einen Account (im Moment wohl noch Beta) und geht auf den "Unit Planner".

Dort gibt einen "Unit Name" und das "Subject or Course" an, z.B.

"Fundamentals of Electrical Engineering for AI"

und

"Electrical Engineering".

2/x

Öffentlich
Mathias Magdowski

Dann fragt einen der noch nach einigen Details, also:

"This unit should cover:"

und

"Standards / Objectives:"

Ich habe da mal aus meiner Sicht relevante Dinge für die eingetragen.

- knowledge of basic terms like charge, current, voltage, resistance, capacitance, inductance, electric power and energy
- elements of circuit schematics
- series and parallel connection of resistors
- voltage divider and current divider
- basic electric circuits 3/x

This unit should cover: - knowledge of basic terms like charge, current, voltage, resistance, capacitance, inductance, electric power and energy - elements of circuit schematics - series and parallel connection of resistors - voltage divider and current divider - basic electric circuits Standards / Objectives: - calculate current, voltage and power in simple electric circuits - calculate the equivalent resistance of series and parallel connections of resistors - use the current divider rule and voltage divider rule for circuit calculation - calculate the resistance of a wire from the cross-section dimension, the length and the material parameters - integrate a time-dependent current function to calculate the accumulated charge as a function of time
Öffentlich
Mathias Magdowski

Schließlich kann man dem sagen, aus wie vielen Lerneinheiten der Kurs bestehen soll.

Ich habe mal 5 gewählt.

Mit einem Klick auf "Create Unit" kann man dann die Kursübersicht erzeugen. 4/x

Öffentlich
Mathias Magdowski

Nach einigen Sekunden generiert der dann folgende Übersicht:

Day 1
Introduction to Electrical Engineering

Day 2
Voltage and Current Calculations

Day 3
Resistance Calculations

Day 4
Charge Calculations

Day 5
Summary and Review

Modul 1 ist vermutlich immer eine Einführung, das letzte Modul vermutlich immer eine Zusammenfassung. Der restliche Inhalt wird auf die anderen Module aufgeteilt. Das ist bis dahin durchaus sinnvoll. 5/x

Day 1 Introduction to Electrical Engineering — Introduce the fundamentals of electrical engineering. — Explain basic terms like charge, current, voltage, resistance, capacitance, inductance, electric power and ener Day 2 Voltage and Current Calculations — Discuss how to calculate current, voltage and power in simple electric circuits. — Explain how to calculate the equivalent resistance of series and parallel connection Day 3 Resistance Calculations — Discuss how to calculate the resistance of a wire from the cross-section dimension, the length and the material parameters. — Introduce principles of Ohm's Law and how Day 4 Charge Calculations — Discuss how to integrate a time-dependent current function to calculate the accumulated charge as a function of time. — Introduce the concept of capacitance and its re Day 5 Summary and Review — Review and summarize the major points of the unit. — Discuss the elements of circuit schematics, series and parallel connection of resistors, current divider rule and
Öffentlich
Mathias Magdowski

Für jeden Tag bzw. jedes Modul kann man dann per Klick
- einen Lesson Overview
- Student Objectives
- Essential Questions
erzeugen. Das dauert dann wiederrum einige Sekunden. (6/x)

Öffentlich
Mathias Magdowski

Ich zeige hier mal die Ergebnisse für Modul Nr. 2
"Voltage and Current Calculations":

Die Ergebnisse sind ganz okay, wiederholen aber im Grunde nur meine Eingabe mit den Verben "Discuss", "Explain" und "Introduce".

Captian Obvious sagt mir als Lehrperson aber natürlich, dass ich neue Themen einführen, erklären und diskutieren sollte.

Wenn ich von Didaktik gar keine Ahnung habe, ist das vielleicht hilfreich, sonst eher nicht, vor allem, weil das "Wie" ja erst mal offen bleibt. (7/x)

Lession Overview: — Discuss how to calculate current, voltage and power in simple electric circuits. — Explain how to calculate the equivalent resistance of series and parallel connections of resistors. — Introduce the current divider rule and voltage divider rule for circuit calculation.
Öffentlich
Mathias Magdowski

Die "Student Objectives" und "Essential Questions" gehen in die gleiche Richtung:

Die "Objectives" starten alle mit "Explain", "Calculate", Describe" und "Apply" und enden mit meinen Themenvorgaben.

Die "Questions" machen das Gleiche mit "How" und "What" am Anfang.

Okay, bisher hat die KI des also viel redundanten Blindtext nach meinen Vorgaben erzeugt, wirklich geholfen aber eher nicht. (8/x)

Student Objectives: 1. Explain the relationship between current, voltage, and power in simple electric circuits. 2. Describe the difference between series and parallel connections of resistors. 3. Calculate the current, voltage and power in simple electric circuits. 4. Calculate the equivalent resistance of series and parallel connections of resistors. 5. Apply the current divider rule and voltage divider rule for circuit calculation.
Essential Questions: 1. How is current related to voltage and power? 2. What is the formula for calculating equivalent resistance in a series resistor circuit? 3. What is the formula for calculating equivalent resistance in a parallel resistor circuit? 4. How is the current divider rule used to calculate current in a circuit? 5. How is the voltage divider rule used to calculate voltage in a circuit?
Öffentlich
Mathias Magdowski

Nun kann man per Klick auch einen
- Lesson Plan, ein
- Educational Handout & einen
- Context Builder
erstellen.

Das dauert dann auch mehrere Sekunden bis Minuten und erzeugt mehrseitige PDF-Dateien mit entsprechenden Kursmaterialien.

Was man für interaktive Lehrformate mit PDFs soll und warum z.B. nicht HTML, Markdown oder XML erzeugt wird, erschließt sich mir nicht wirklich. Meine "PDF-Wäscheleine" ist schon voll genug.

"AI Video Recommendations" werden in meinem Fall nicht angezeigt. (9/x)

Öffentlich
Mathias Magdowski

Okay, schauen wir mal auf den "Lesson Plan" für Tag 2.

Die Lernziele sind soweit okay, aber Caption Obvious lässt auch hier erneut freundlich grüßen, denn der Inhalt geht kaum über meine Vorgabe hinaus.

Nur die naheliegende Anwendung der Kompetenzen auf "real-world problems" hat die "KI" des ergänzt.

Zwischenfazit: bisher so lala (10/x)

Lesson Plan: Aim Students will learn how to calculate current, voltage, power and equivalent resistance of series and parallel connections in simple electric circuits, as well as how to use the current divider rule and voltage divider rule for circuit calculations. Objectives 1. Students will be able to calculate current, voltage, and power in simple electric circuits. 2. Students will be able to calculate the equivalent resistance of series and parallel connections of resistors. 3. Students will be able to use the current divider rule and voltage divider rule for circuit calculations. 4. Students will be able to apply these concepts to solve real-world problems.
Öffentlich
Mathias Magdowski

Anschließend schlägt mir der mögliche Lernmaterialien vor, die aber so auch auf jedes andere x-beliebige Thema passen würden.

Als Vorgehensweise schlägt mir die KI vor, das Thema mit einer Diskussion und einem Brainstorming unter den Lernenden zu motivieren, dann die verschiedenen Begriffe und Konzepte einzuführen, sowie anhand von praktischen Probleme zu vertiefen und zu diskutieren. Soweit so banal. (11/x)

Possible Materials Needed 1. Textbook or educational handouts on electric circuits 2. Pictures of different circuit diagrams 3. Circuit Vocabulary Sheet 4. Electric Circuits Powerpoint Presentation 5. Short video on electric circuits Anticipatory Set 1. Begin the lesson by engaging the class in a discussion on electric circuits. Ask the class to brainstorm what components are needed to create a circuit and what happens when a circuit is connected. Discuss the concepts of current, voltage, and power and how they can be used to determine the amount of electricity flowing through a circuit. 2. Introduce the concept of equivalent resistance and how it can be used to calculate the total resistance of a circuit. Explain how different combinations of resistors can be used to create different equivalent resistances and how these resistances can be used to calculate the current and voltage in a circuit. 3. Lastly, introduce the current divider rule and voltage divider rule and how they can be used to calculate the current and voltage in a circuit when there are multiple resistors connected in series and parallel. Explain how these rules can be used to solve real-world problems.
Öffentlich
Mathias Magdowski

Als "Modellhafte Praxis" schlägt mir der dann vor, das Thema an einem Beispiel, an einem kleinen Laborversuch und anhand einer Diskussion weiter zu vertiefen.

Wie man dann nun konkret tut und was man dabei konkret beachten muss, um beim immerhin nicht ganz ungefährlichen Thema "Strom und Spannung" niemanden zu gefährden, bleibt leider komplett offen.

Hilft mir das als Neuling in der Lehre? Vielleicht.

Hilft mir das als erfahrende Lehrperson? Eher nicht. (12/x)

Modeled Practice 1. The teacher can provide an example of a simple electric circuit and explain how to calculate the current, voltage, and power in the circuit. The teacher can then ask the class to identify the different components in the circuit and how they interact with each other. 2. The teacher can provide a hands-on activity to help the students understand the concept of equivalent resistance. The teacher can provide each student with a set of resistors and ask them to create different circuits with different equivalent resistances. Ask the students to explain how they calculated the equivalent resistance and how it affects the current and voltage in the circuit. 3. The teacher can provide a discussion-based activity to help the students understand the current divider rule and voltage divider rule. The teacher can provide the class with a circuit diagram with multiple resistors and ask them to calculate the current and voltage in the circuit using the divider rules. Ask the students to explain how these rules can be used to solve real-world problems.
Öffentlich
Mathias Magdowski

Als geführten Praxisvorschlag schlägt mir der dann Gruppenarbeiten mit individualisierten Aufgaben (die ich mir aber wohl noch allein ausdenken muss) und anschließender Ergebnispräsentation oder die (didaktisch aus meiner Sicht auch eher unterklassige) Nutzung eines Arbeitsblatts vor. Zu diesem Arbeitsblatt kommen wir gleich noch.

Auch das sind wohl doch eher Basistricks aus dem didaktischen Werkzeugkasten. (13/x)

Guided Practice 1. Divide the class into small groups and have each group create a simple electric circuit with multiple resistors. Ask each group to calculate the current, voltage, and power in their circuit and explain how they arrived at the answer. Once the groups are finished, have them present their projects to the class and discuss the results. 2. Divide students into small groups and assign each group a different equivalent resistance (series or parallel connection). Ask each group to create a circuit with the assigned resistance and calculate the current and voltage in the circuit. Allow each group to present their results to the class and discuss how the different equivalent resistances affect the current and voltage in the circuit. 3. Provide students with a worksheet that asks them to calculate the current, voltage, and power in a given circuit. Ask them to use the current divider rule and voltage divider rule to calculate the current and voltage in a circuit with multiple resistors. Ask them to explain how these rules can be used to solve real-world problems.
Öffentlich
Mathias Magdowski

Als "eigenständige Übung" sollen die Lernenden einfach selbst ein paar Aufgaben rechnen, eine Geschichte zum Thema schreiben (die wird bestimmt super) oder eine PowerPoint-Präsentation vorbereiten, in der sie selbst das Thema vorstellen (laaaangweilig ;-)).

Ob die Geschichte und die Präsentation wirklich helfen, die Grundlagen der Elektrotechnik zu durchdringen, wage ich mal zu bezweifeln.

Einige Aufgaben zu rechnen ist da schon nützlicher. Aber welche genau? Und in welcher Reihenfolge? (14/x)

Independent Practice 1. Ask students to research a particular type of circuit and create a poster that includes information about the components, current, voltage, and power in the circuit. Students should also include a discussion of the current divider rule and voltage divider rule and how they can be used to solve real-world problems. 2. Ask students to write a story about a real-world problem that requires the use of the current divider rule and voltage divider rule to calculate the current and voltage in a circuit. 3. Ask students to create a PowerPoint presentation that explains how to calculate current, voltage, and power in a circuit. The presentation should include information on the current divider rule and voltage divider rule and how they can be used to solve real-world problems.
Öffentlich
Mathias Magdowski

Die "typischen Problemfelder" wiederholen dann einfach alle bisherigen Themen, klar die sind nicht einfach. 😉

Lösung: Einfach viele praktische Beispiele geben und die Lernenden selbst rechnen lassen, zu Fragen ermuntern und Diskussionen fördern. Caption Obvious ist wieder voll dabei.

Zum Abschluss:
- Lernende eine kurze Zusammenfassung schreiben lassen (Wer liest die?)
- Quiz machen (Mit welchen Fragen?)
- Feedback geben (Wie genau wird es konstruktiv?) (15/x)

Common Areas of Struggle When it comes to learning about electric circuits, the most common struggles are understanding the concepts of current, voltage, and power, as well as how to calculate the equivalent resistance of series and parallel connections of resistors. Students may also have difficulty understanding the current divider rule and voltage divider rule and how they can be used to solve real-world problems. Ensure that students are given plenty of opportunities to practice and discuss the concepts of electric circuits. Provide plenty of examples and visuals to help students better understand the concepts. Encourage students to ask questions and engage in discussions about the concepts. They should also be given plenty of time to practice solving real-world problems using the current divider rule and voltage divider rule. Closure At the end of the lesson, the teacher can ask the class to complete a writing prompt that asks them to consider a real-world problem that requires the use of the current divider rule and voltage divider rule to calculate the current and voltage in a circuit. The teacher can also assign a quiz to assess the students' understanding of the concepts discussed in the lesson. It is important to provide students with feedback on their work so that they can understand what areas they need to focus on and improve. Be sure to ask questions often related to the common areas of struggle.
Öffentlich
Mathias Magdowski

Okay, werfen wir noch einen Blick auf das vom erstellte Handout, in dem aus meiner Sicht die nötige Theorie zusammengefasst sein soll.

Der erste Abschnitt ist nicht grundlegend falsch, aber nahezu jeder x-beliebige Internetbetrag dazu ist besser, erst recht Lehrbücher und vor allem die Wikipedia.

Anstatt "Power" sollte dort inhaltlich auch eher Widerstand stehen, so dass der Verweis auf das Ohmsche Gesetz auch besser passt. (16/x)

Calculating Current, Voltage and Power in Simple Electric Circuits Handout Covers - Calculating current, voltage, and power in simple electric circuits - Calculating the equivalent resistance of series and parallel connections of resistors - Introducing the current divider rule and voltage divider rule for circuit calculation Calculating Current, Voltage, and Power in Simple Electric Circuits In order to understand how electricity works, it is important to learn how to calculate current, voltage, and power in simple electric circuits. Current, voltage, and power are the three fundamental parameters that determine the behavior of electric circuits. Current is measured in amperes (A) and is the rate of flow of electrons through a conductor. Voltage is measured in volts (V) and is the difference in electric potential between two points. Power is measured in watts (W) and is the rate at which energy is transferred or converted. To calculate current, voltage, or power in a simple electric circuit, we must first calculate the total resistance of the circuit, which can be done by calculating the equivalent resistance of series and parallel connections of resistors. Once the total resistance is known, current, voltage, and power can be calculated using Ohm's law.
Öffentlich
Mathias Magdowski

Weiter geht es mit den Formeln zur Reihenschaltung und Parallelschaltung von Widerständen. Diese sind formell richtig. sind aber natürlich suboptimal formatiert. Außerdem fehlt hier mal eine Skizze oder eine Visualisierung in Form eines Schaltbildes.

Erneut wäre nahezu jede andere Resource deutlich brauchbarer als das hier. (17/x)

Calculating the Equivalent Resistance of Series and Parallel Connections of Resistors When resistors are connected in series, the total resistance is the sum of all individual resistances. For example, if resistors R1, R2, and R3 are in series, the total resistance is R1 + R2 + R3. When resistors are connected in parallel, the total resistance is the reciprocal of the sum of the reciprocals of the individual resistances. For example, if resistors R1, R2, and R3 are in parallel, the total resistance is 1/ (1/R1 + 1/R2 + 1/R3). Once the total resistance is known, current, voltage, and power can be calculated using Ohm's law. Ohm's law states that the current in a circuit is equal to the voltage divided by the resistance (I = V/R).
Öffentlich
Mathias Magdowski

Inhaltlich falsch und damit wirklich "gefährlich" für Nicht-Expert*innen wird es dann bei der Stromteilerregel und Spannungsteilerregel.

Der Stromteiler ist korrekt erklärt, der Spannungsteiler nicht. Hier ist der Zusammenhang direkt proportional, nicht invers.

Der zweite Abschnitt ist sehr allgemein und damit auch eher weniger hilfreich.

Problem: Der Text vom klingt erst mal gut. Wenn man keine Ahnung hat, wird man das womöglich glauben. (18/x)

Calculating Current, Voltage and Power in Simple Electric Circuits Introducing the Current Divider Rule and Voltage Divider Rule for Circuit Calculation The current divider rule and voltage divider rule are useful tools for calculating current and voltage in complex circuits. The current divider rule states that the current flowing through each branch of a parallel circuit is inversely proportional to the resistance of the branch. The voltage divider rule states that the voltage across each branch of a circuit is inversely proportional to the resistance of the branch. These rules can be used to calculate the current and voltage in complex circuits with multiple resistors in series and parallel. For example, if a circuit has two resistors connected in parallel (R1 and R2), the current flowing through each resistor can be calculated using the current divider rule, and the voltage across each resistor can be calculated using the voltage divider rule.
Öffentlich
Mathias Magdowski

Die vom geschriebene Zusammenfassung ist ganz okay, ermöglicht aber auch nicht die Berechnung von allen einfachen Schaltbildern und weist nicht auf Grenzen hin, z.B. wenn eine Stern-Dreieck-Transformation notwendig ist.

Es gibt auch keine Literaturquellen oder Tipps zum weiteren Lesen.

Das Motto ist eher: Believe it or not. Don't question. I don't know it better either.

(19/x)

Conclusion In conclusion, understanding how to calculate current, voltage, and power in simple electric circuits is essential for understanding how electricity works. To calculate these values, it is necessary to first calculate the equivalent resistance of series and parallel connections of resistors. Once the total resistance is known, current, voltage, and power can be calculated using Ohm's law. Additionally, the current divider rule and voltage divider rule can be used to calculate current and voltage in complex circuits. Can you think of any applications of these calculations in the real world?
Öffentlich *
Mathias Magdowski

Außerdem generierte der noch eine Seite mit "Context", eine Art Glossar mit Definitionen, Erklärungen und Beispielen.

Diese sind nicht allzu falsch, aber auch nicht immer ganz klar und eindeutig (z.B. dass P = U * I das Ohmsche Gesetz sein soll, oder dass die Spannung und der Strom sich immer zu gleichen Teilen aufteilen).

Sehr störend ist der schlechte Formelsatz, die Overprints und dass statt einem Ω ein © angezeigt wird. UTF8 lässt grüßen. (20/x)

Context for: Vocabulary Terms Current Voltage Power Resistance Ohm's Law Series connection Parallel connection Current divider rule Voltage divider rule Circuit Current Definition: Current is the rate at which electrons flow through a conductor. It is measured in amperes (amps). 1. In a simple circuit with a battery, current flows from the positive terminal of the battery through the circuit to the negative terminal. This current can be measured with an ammeter. 2. In a circuit with a resistor, current will flow through the resistor and the amount of current will depend on the resistance of the resistor. The current can be calculated using Ohm's Law, which states that current (I) is equal to the voltage (V) divided by the resistance (R). Voltage Definition: Voltage is the potential difference between two points in an electric circuit. It is measured in volts (V). 1. In a simple circuit, the voltage is determined by the battery which is connected. The voltage is measured with a voltmeter. 2. In a circuit with a resistor, the voltage across the resistor will depend on the amount of current flowing through it. The voltage can be calculated using Ohm's Law, which states that voltage (V) is equal to the current (I) multiplied by the resistance (R).
Context for: Power Definition: Power is the rate at which energy is transferred in an electric circuit. It is measured in watts (W). 1. In a simple circuit, power is determined by the voltage and current. The power is calculated by multiplying the voltage and current together. 2. In a circuit with a resistor, the power is determined by the voltage and current flowing through it. The power can be calculated using Ohm's Law, which states that power (P) is equal to the voltage (V) multiplied by the current (I). Resistance Definition: Resistance is the opposition to the flow of current in an electric circuit. It is measured in ohms (©). 1. A resistor is a component which has a specific resistance, and it is used to control the amount of current flowing in a circuit. The resistance of the resistor can be calculated using Ohm's Law, which states that resistance (R) is equal to the voltage (V) divided by the current (I). 2. The resistance of a circuit is determined by the components which are connected in series and parallel. The equivalent resistance of a series connection is equal to the sum of the resistances of the individual components, while the equivalent resistance of a parallel connection is equal to the reciprocal of the sum of the reciprocals of the individual resistances. Ohm's Law Definition: Ohm's Law is a mathematical equation which states that voltage (V) is equal to current (I) multiplied by resistance (R).
Context for: Series connection Definition: A series connection is a type of circuit connection in which components are connect- ed in a line one after the other. 1. In a series connection, the current flowing through each component is the same as the current flowing through the entire circuit. For example, if the current flowing through a circuit is 1.2A and there are three components connected in series, then the current flowing through each component will be 1.2A. 2. The equivalent resistance of a series connection is equal to the sum of the resistances of the individual components. For example, if the three components have resistances of 10©, 12©and 15©,then the equivalent resistance of the series connection is 10© + 12© + 15© = 37©. Parallel connection Definition: A parallel connection is a type of circuit connection in which components are connected side-by-side. 1. In a parallel connection, the voltage across each component is the same as the voltage across the entire circuit. For example, if the voltage across a circuit is 12V and there are three components connected in parallel, then the voltage across each component will be 12V. 2. The equivalent resistance of a parallel connection is equal to the reciprocal of the sum of the reciprocals of the individual resistances. For example, if the three components have resistances of 10©, 12©and 15©,then the equivalent resistance of the parallel connection is 1/(1/10© + 1/12© + 1/15©) = 6©.
Context for: Voltage divider rule Definition: The voltage divider rule is a mathematical equation which states that the voltage across each component in a series connection is equal to the total voltage divided by the number of components. 1. The voltage divider rule can be used to calculate the voltage across each component in a series connection. For example, if the circuit has a total voltage of 12V and there are three components connected in series, then the voltage across each component will be 12V/3 = 4V. 2. The voltage divider rule can also be used to calculate the total voltage in a circuit. For example, if the circuit has three components with voltages of 4V, 6V and 7V, then the total voltage will be 4V + 6V + 7V = 17V. Circuit Definition: A circuit is an interconnected network of components through which electrical energy flows. 1. In a circuit, components can be connected in series or parallel to create different types of circuits. In a series connection, the components are connected in a line one after the other, while in a parallel connection, the components are connected side-by-side. 2. In a circuit, the current, voltage and power can be calculated using Ohm's Law and the current divider and voltage divider rules. These equations can be used to calculate the current, voltage and power in a circuit, as well as the equivalent resistance of series and parallel connections.
Öffentlich
Mathias Magdowski

Fazit: Ich kann die zum Teil euphorische und sehr positive Sichtweise nicht nachvollziehen.

Welcher Lehrperson soll das nützen? Weder als Einsteiger*in, Fortgeschrittene*r, noch Expert*in kann ich davon profitieren, weil ich es entweder nicht nachvollziehen kann oder besser weiß.

Auch als Lerner*in frage ich mich: Möchte ich so einen generisch KI-gebauten Kurs besuchen und durcharbeiten? Und wenn ja, warum genau jetzt? Warum nicht direkt explorativ oder konstruktivistisch lernen? (21/21)

Öffentlich (still)
MsBasement

@MMagdowski Ich habe ja nun wirklich überhaupt keine Ahnung von diesem Thema, aber mir schwebt gerade eine Art "Es war einmal das Leben"-Version für Elektrotechnik vor? Mit kleinen Strom-Dingens und irgendwas fliegt? 🫣😉 Fänd ich gut.

(Und fairerweise, wenn SuS das erstellen können, haben sie sehr viel verstanden.)

Aber danke für den thread, hatte von dem Programm noch gar nichts mitgekriegt und deine Darstellung ist interessant 🙂

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