Hoe activeer en motiveer je niet-wiskunde studenten voor wiskunde?

Presentatie over: "Hoe activeer en motiveer je niet-wiskunde studenten voor wiskunde?"— Transcript van de presentatie:

1 Hoe activeer en motiveer je niet-wiskunde studenten voor wiskunde?
Innovatie eerstejaars wiskundeonderwijs TU Delft

2 Even voorstellen Naam: Annoesjka Cabo
Functie: Interfacultair Onderwijs Directeur Faculteit: EWI, TU Delft Wiskundige (UvA, CWI, TU Delft)

3 Programma vandaag WELK wiskundeonderwijs bedoelen we?
WAAROM innoveren we dat wiskundeonderwijs? HOE innoveren we dat wiskundeonderwijs? WAT zijn de resultaten? HOE nu verder?

4 Welk wiskundeonderwijs?
Interfacultair Onderwijs Civiele techniek Industrieel Ontwerpen Bouwkunde Technische Aardwetenschappen Werktuigbouwkunde en Maritieme Techniek Lucht- en Ruimtevaarttechniek Technische Natuurkunde MST Nanobiologie Klinische Technologie Technische Bestuurskunde Elektrotechniek Technische Informatica Basisvakken: Analyse 1 en 2 Lineaire algebra Kansrekening en statistiek

5 Waarom innoveren? Studenten motiveren Studenten activeren
Docenten activeren/motiveren

6 Hoe innoveren we? Prepare, Participate, Practice
Meer tijd voor oefenen tijdens college Context voorbeelden: maatwerk per opleiding! Learning analytics

7 Prepare Self study student Watch pre-lecture video
Make simple exercise Activate prior knowledge, acquire new knowledge

8 Participate Self study student Face-2-face
Introduce new concepts and context Understanding tested by interactive quiz with immediate feedback Watch pre-lecture video Make simple exercise Activate prior knowledge, acquire new knowledge Conceptual understanding of new concepts

9 Participate => Practice in class
Self study student Face-2-face Problem solving individually and in small groups in class Introduce new concepts and context Understanding tested by interactive quiz with immediate feedback Watch pre-lecture video Make simple exercise Activate prior knowledge, acquire new knowledge Conceptual understanding of new concepts Problem solving

10 Practice at home Self study student Face-2-face
Problem solving individually and in small groups in class Solve computer-aided exercises, exercises from book, interactive exercises Introduce new concepts and context Understanding tested by interactive quiz with immediate feedback Watch pre-lecture video Make simple exercise Activate prior knowledge, acquire new knowledge Conceptual understanding of new concepts Problem solving Processing new concepts, problem solving

11 Mathematical modelling
Real-world Problem Mathematical Model Formulate Test Solve Real-world Predictions Mathematical Conclusions Interpret

12 Hoe ziet dat er uit? Voorbeeld: Analyse 1 Werktuigbouwkunde, les 5 (separabele differentiaalvergelijkingen)

13 Calculus 1: lecture 5 Separable differential equations

14 Learning objectives After this lecture you will be able to:
recognize first-order separable differential equations; solve first-order separable differential equations and initial-value problems. Book Section 9.3 and pages

15 Programme FeedbackFruits exercises Solving separable DE’s FeedbackFruits exercises and other exercises Application: Mixing of gasoline Exercises and discussion

16 Separable or not separable?
A) Separable B) Not separable Answer A

17 Separable or not separable?
A) Separable B) Not separable Answer B

18 Solution method for separable DE’s
Separation of variables This can also be explained on the white-/blackboard. Please explain the two options for the separation (no differentials vs differentials). Please explain the change to y variable in the second step in the left integral. Taking the antiderivative Book Page

19 Solutions of a separable DE
This is called an implicit form of the solution. Constant C obtains a specific value if an initial condition is given for the DE. Antiderivatives If possible, solve for This can also be explained on the white-/blackboard. Please do an example after this explanation, for example dy/dx = xy, to show that the anti-derivative of 1/y equals ln|y| and how the C can change. Also focus on the fact that y=0 is also a(n equilibrium) solution. Explicit solution Book Page 600

20 Application: mixing of gasoline
In an oil refinery, a storage tank of gasoline is mixed with a special additive as preparation for winter weather. The storage tank contains 2000 L of gasoline that initially has 100 kg of additive dissolved in it.

21 Application: mixing of gasoline
45 L/min containing 2 kg additive per liter y(t) = amount of additive in the storage tank at time t (in kg) V = amount of liquid in the storage tank 100 kg additive in 2000 L gasoline at t = 0

22 Application: mixing of gasoline - model
Rate of change in Rate at which enters the tank Rate at which exits the tank =

23 A mixing problem - model
Rate of change in Rate at which enters the tank Rate at which exits the tank = Flow rate of liquid entering concentration additive in liquid entering Flow rate of liquid exiting concentration additive in liquid exiting = You can do this derivation also on the white-/blackboard.

24 Application: mixing of gasoline
40 L/min containing 2 g/L additive Initial-value problem from lecture 1: 100 g additive in 2000 L gasoline at t = 0 45 L/min containing 𝑦 𝑉 g/L additive Note that we changed the kilograms into grams as it is more likely so have 2 g/L than 2 kg/L.

25 Application: mixing of gasoline
Is this differential equation separable? Answer: no → In lecture 7 we will learn how to solve this initial-value problem

26 For next lecture: MyMathLab exercises (deadline: see Blackboard)
Study prelectures “Inverse Trigonometric Functions” and “Implicit Differentiation” In the next lecture you will learn to: use the inverse trigonometric functions; find the derivative of a function using implicit differentiation; find the derivative of the inverse trigonometric functions and recognize the result as these derivatives. Book section 1.5 and 3.5

27 Exercises 8th edition: Section 9.3 Exercises: 49, 45 7th edition:

28 See you next lecture! You can change this to a remark you prefer.

29 Wat vinden jullie ervan?
Stellingen: Deze aanpak helpt om het gestelde doel te bereiken Deze aanpak geeft alleen de docenten meer werk Deze aanpak lijkt een goed begin, maar heeft verbetering nodig Suggesties?

30 Hoe ging het (studenten)?
Online opgaven: heel nuttig Online opgaven: soms te makkelijk Quizzen: Activerend Quizzes: soms te lang

31 Hoe ging het (studenten)?
Context voorbeelden: motiverend Moeten actief zijn Mathematisch modelleren: moeilijk Kleine groepen: Fijn om in te werken

32 Hoe ging het (docenten <-> studenten)?
Voorbereiding Activeren van studenten Switchen tussen quiz, presentatie, bord, opgaven maken Wat doe je als de video’s weinig bekeken zijn?

33 Hoe ging het (docenten <-> docenten)?
Half way lunches Peer review Popcorn sessies Implementeren van verbeteringen

34 Andere projecten Boegbeeld project Wiskunde (wo): Deelbaar maken van online materiaal (in eerste instantie voor HBO schakelwiskunde) 4TU.AMI blended learning project: ontwikkeling HBO schakelprogramma wiskunde in online modules Pilot: honoursprogramma wiskunde vakken op HBO aanbieden

35 Informatie Pre-University Calculus MOOC math-explained.tudelft.nl: Alle video’s opgenomen voor de basisvakken wiskunde. Bel/mail

36 Discussie!