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

Even voorstellen Naam: Annoesjka Cabo Functie: Interfacultair Onderwijs Directeur Faculteit: EWI, TU Delft Wiskundige (UvA, CWI, TU Delft) a.j.cabo@tudelft.nl

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

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

Waarom innoveren? Studenten motiveren Studenten activeren Docenten activeren/motiveren

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

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

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

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

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

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

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

Calculus 1: lecture 5 Separable differential equations

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 608-609

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

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

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

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 599-600

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

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.

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

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

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.

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.

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

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

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

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

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?

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

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

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?

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

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

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

Discussie!